Research ArticleExperimental and Numerical Investigation of Flow MeasurementMechanism andHydraulic Performance of Portable Pillar-ShapedFlumes in Rectangular Channels

Bin Sun Lei Yang Shun Zhu Quan Liu Chao Zhang and Jinping Zhang

School of Water Conservancy Engineering Zhengzhou University Zhengzhou 450001 China

Correspondence should be addressed to Chao Zhang chaozhangzzuoutlookcom

Received 30 June 2020 Revised 13 July 2020 Accepted 18 July 2020 Published 8 August 2020

Academic Editor Hong-jun Zhu

Copyright copy 2020 Bin Sun et al+is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Based on the principle of the critical flow and standard k-ε three-dimensional turbulence model experiments and simulationswere performed on a portable pillar-shaped flume with three contraction ratios under 12 working conditions By combining thenumerical simulations with the experiments the theoretical stage-discharge formula of the portable pillar-shaped flume wasdeveloped and the variations in the Froude number backwater height critical submergence head loss and velocity distributionwere examined +e simulation data obtained from the standard k-ε three-dimensional turbulence model are in good agreementwith the experimental results with amaximum error of 865+emaximum error in the difference between the theoretical stage-discharge formula and the measured value is 474 +e upstream Froude number is less than 05 and critical submergence isbetween 073 and 096 Compared to airfoil pillar-shaped flumes the portable pillar-shaped flume had a significantly smaller headloss and backwater height Finally the portable pillar-shaped flume can be used for flow measurement and has the advantages ofhigh measurement accuracy low backwater height and small head loss

1 Introduction

Rectangular channels as an indispensable infrastructure ineconomic development deal with the transportation ofwater resources irrigation water pollution control floodprevention storm drainage and other important functionsIt is widely used in the construction of water conservancyespecially in areas where the cultivated land resources arescarce or the efficiency of the cultivated land resources ishigh Flow measurement is an important basis for opti-mizing the allocation of water resources and monitoringwater quantity [1ndash3]

At present although there are various methods formeasuring the flow of open channels flow measurementbased on the concept of critical flow is the most widely usedtechnique and flumes with a local contraction of channel areuniversally applied as discharge measurement structuresespecially in scientific and hydrological research in irrigationsystems [4ndash6] Based on the principle of Venturi flume [7]

Parshall proposed a representative Parshall flume [8]Skogerboe et al [9ndash11] conducted experimental research onflowmeasurement under free and submerged conditions of aParshall flume In the field of fluid mechanics the cylinder isoften used to study vibration and energy collection [12ndash16]and it can also be used in the field of flow measurement +eturbulence characteristics of using the cylinder in thechannel to measure the flow are similar to the problem of theflow around the cylinder For example unlike a Parshallflume an improved venturi channel which had a contractionalong the channel axis rather than its side walls was proposedby Hager [17] central baffle flume was proposed by Kolavaniet al and Bijankhan and Ferro and the stage-discharge curveof the central baffle flume was studied experimentally[18 19] Each of the above studies has proposed a new type ofmeasuring flume and analyzed its hydraulic characteristicsHowever there are few studies on the optimization of theshape of the measuring flume according to the specifichydraulic characteristics Sun et al [20] performed the

HindawiShock and VibrationVolume 2020 Article ID 8815957 17 pageshttpsdoiorg10115520208815957

multiobjective optimization of an airfoil-shaped hydraulicstructure based on National Advisory Committee forAeronautics (NACA) thickness distribution and obtainedthe optimized airfoil profile control equation +ey alsocompared the solutions before and after optimization andshowed that the optimized airfoil-shaped flume had asmoother flow and a smaller head loss

Based on reviewing previous research studies it can beconcluded that reducing the head loss and increasing theovercurrent capacity as much as possible without decreasingthe measurement accuracy will be an important aspect offuture research Additionally most types of the measuringflumes cannot be applied to the channels already constructedand cannot be installed and removed conveniently +us inorder to solve these problems this paper presents a portablepillar-shaped flume based on the optimized airfoil equation[20] Currently most research in the field of fluids is basedon the combination of numerical simulation and modelexperiments [21ndash25] Numerical simulation has become animportant method for examining new water measuringfacilities especially in the study of open channel hydraulics[1 21 26ndash29] In order to further study the internal flow fielddistribution and to provide a theoretical basis for the op-timization and promotion of the portable pillar-shapedflume its hydraulic characteristics are analyzed by means ofcomputational fluid dynamics (CFD) using Fluent 192software which can accurately and conveniently computeand visualize the results

2 Materials and Methods

21 e Experimental Set-Up

211 Structure of the Portable Pillar-Shaped Flume In orderto solve the problem of the NACA airfoil-shaped flume ieits proneness to water blocking under low head conditionsthe NACA airfoil equation is moderately adjusted and finelyoptimized by utilizing parametric methods and the theory ofoptimization algorithm To this end a new airfoil equationwith better overcurrent characteristics is finally obtained+e airfoil profile of the portable pillar-shaped flume iscontrolled by this optimized equation [20]

y 10P 02737x

C

1113970

minus 04263x

C+ 11660

x

C1113874 1113875

21113890

minus 17570x

C1113874 1113875

3+ 07453

x

C1113874 1113875

41113891

(1)

where P is the maximum thickness of flume (m) C repre-sents its length (m) and x and y represent the coordinate ofthe equation on the X-axis and Y-axis

+e curve of optimized NACA airfoil equation is shownin Figure 1(a) the shapes of the NACA airfoil-shaped flumeand portable pillar-shaped flume are shown in Figure 1(b)Plan-view and profile-view sketches of the portable pillar-shaped flume are also illustrated in Figure 2 In this paperthree portable pillar-shaped flumes with different contrac-tion ratios were studied Moreover the parts of the hydrauliccharacteristics of the airfoil pillar-shaped flume controlled

by the NACA airfoil equation were studied in the same wayand compared with the portable pillar-shaped flume +econtraction ratio is defined as the ratio of the area of thethroat section to the total area of the channel section

ε Ac

A (2)

where ε is contraction ratio Ac is the area of the throatsection (m2) and A represents the total area of the channelsection (m2)

212 Experimental Setup +e portable pillar-shaped flumeused herein was installed in the Hydraulic Laboratory of theSchool of Water Conservancy Engineering of ZhengzhouUniversity Zhengzhou China +e experimental systemconsists of an upstream reservoir a downstream reservoir apump an electromagnetic flowmeter a water circulation pipea rectangular plexiglass channel a valve a portable pillar-shaped flume and a sluice gate Experiments were performedon a portable pillar-shaped flume with three contraction ratiosunder 12 working conditions (flow approximately rangingfrom 5 to 27Ls) and 36 sets of experimental data were finallyobtained An electromagnetic flowmeter is installed in thewater circulation pipe section to facilitate monitoring of theflow+e water level stylus is used tomeasure the water level ofthe channel flow with a measurement accuracy of 01mm+ecomprehensive roughness of the channel is 0011 +e totallength of the rectangular channel is 12m and the width of thechannel is 03m A sketch of the experimental setup of theportable pillar-shaped flume is depicted in Figure 3

+e model experiments on the hydraulic performance ofthe portable pillar-shaped flume were conducted using thischannel with three different contraction ratios +e detailedcharacteristics of the portable pillar-shaped flumes are listed inTable 1 Locations of the typical cross section of the flume forwater depth at the centerline of the channel are listed in Table 2

22 Deriving the eoretical Discharge Calculation Formula+e theoretical discharge calculation formula of the portablepillar-shaped flume can be derived by the critical flowequation and the dimensional analysis method Accordingto theΠ theorem of dimensional analysis after analyzing thehydraulic elements of the experimental process and thephenomenon of flow the physical quantities affecting theflow process of the portable pillar-shaped flume are deter-mined +e hydraulic characteristics of the portable pillar-shaped flume under free-flow conditions (Figure 2) can beexpressed by the following functional relationship

F Bc g ρ Kc H( 1113857 0 (3)

where F is a functional symbol Bc is the throat width (m) g

represents acceleration due to gravity (ms2) ρ indicates thedensity of fluid (kgm3) Kc is the critical water depth (m)and H stands for the depth of the upstream water (m)

+ere are five physical quantities in the above formulaand Bc g and ρ are selected as the basic physical quantities+e above equation can be described by two dimensionlessnumbers

2 Shock and Vibration

Y

XC

P = Ymax

Equation 1

(a)

Y

X

C

P = YmaxPprime = Ymax

NACA airfoil pillar-shaped flumePortable pillar-shaped flume

(b)

Figure 1 (a) +e curve of optimized NACA airfoil equation (b) the shapes of the NACA airfoil-shaped flume and portable pillar-shapedflume

C

QB

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bc2

Bc2

(a)

C

(b)

Figure 2 +e (a) plan-view and (b) profile-view of a portable pillar-shaped flume

Shock and Vibration 3

F Π1Π2( 1113857 0 (4)

where Π1 and Π2 are the dimensionless numbers expressedby

Π1 H

Bx1c gy1ρz1

(5)

Π2 KC

Bx2c gy2ρz2

(6)

where x1 y1z1 x2 y2 and z2 are determined according tothe principle of dimensional harmony

[H] Bc1113858 1113859x1[g]

y1[ρ]z1 (7)

Kc1113858 1113859 Bc1113858 1113859x2[g]

y2[ρ]z2 (8)

Length (L) time (T) and mass (M) are the basic di-mensions so equations (7) and (8) can be rewritten as follows

[L] [L]x1 LT

minus 21113960 1113961

y1ML

minus 31113960 1113961

z1 (9)

[L] [L]x2 LT

minus 21113960 1113961

y2ML

minus 31113960 1113961

z2 (10)

Since the exponents of the same dimension on both sidesof the equation are equal x1 y1 z1 x2 y2 and z2 can besolved as follows x1 1 y1 0 z1 0 x2 1 y2 0 andz2 0 +us equations (5) and (6) can be changed to

Π1 Kc

Bc

(11)

Π2 H

Bc

(12)

By substituting equations (11) and (12) into equation (4)the dimensionless number equation can be obtained

FKc

Bc

H

Bc

1113888 1113889 0 (13)

soKc

Bc

φH

Bc

1113888 1113889 (14)

where φ is a functional symbolTransforming equation (14) into an explicit form leads to

Kc

Bc

aH

Bc

1113888 1113889

n

(15)

where n is an undetermined number that can be obtained byexperimental data and a indicates a constant value dividedby the contraction ratio of the portable pillar-shaped flume

Upstream reservoir

Main channel

Valve

Pipe

Pump

RecirculatingSystem

Electromagnetic flow meter

Portable pillar-shaped flume

Downstreamreservior

Sluice gate

Figure 3 A sketch of the experimental setup

Table 1 Dimensions of the portable pillar-shaped flumes withdifferent contraction ratios

Channel width (cm) P (cm) C (cm) Bc (cm) ε30 90 50 12 0430 75 50 15 0530 60 50 18 06

Table 2 Locations of the typical cross-section of the flume forwater depth at the centerline of the channel

Section Distance from the inlet to the measuring points (m)1 25002 30003 31004 32005 32456 34007 35008 36009 370010 380011 390012 400013 500014 6000

4 Shock and Vibration

A critical flow is created in the portable pillar-shapedflume by installing an airfoil pillar across the flow If wesuppose that a critical flow is formed at the throat of theflume from the critical flow equation one may obtain

Q gA3

c

Bc

1113888 1113889

(13)

(16)

Ac BcKc (17)

where Q is the discharge rate (Ls)Kc can also be obtained from equations (16) and (17)

Kc Q(23)

g(13)B(23)c

(18)

Equation (18) is substituted into equation (15) as follows

Q(23)

g(13)B(53)c

aH

Bc

1113888 1113889

n

(19)

+e above equation can also be written as the explicitfunction of flow as follows

Q a(23)

g(12)

B25minus15nc H

15n (20)

23 Numerical Simulation

231 Governing Equations and Turbulence Model In thisstudy Fluent 192 was utilized to solve the computationalfluid dynamics simulations +e volume-of-fluid (VOF)method [30ndash33] and the standard k-ε three-dimensionalturbulence model [32] were chosen to simulate the flowdomain in the portable pillar-shaped flume +e motion ofNewtonian fluid flowing through the portable pillar-shapedflume is described by the continuity and NavierndashStokesequations ie respectively equations (21) and 22(andashc)

zρzt

+z(ρu)

zx+

z(ρv)

zy+

z(ρw)

zz 0 (21)

z(ρu)

zt+ div(ρuu) minus

zp

zx+ div(μgradu) + Fx

(22a)

z(ρv)

zt+ div(ρvu) minus

zp

zy+ div(μgradv) + Fy

(22b)

z(ρw)

zt+ div(ρwu) minus

zp

zz+ div(μgradw) + Fz

(22c)

where the concepts of divergence and gradient are intro-duced as div(a) (zaxzx) + (zayzy) + (zazzz) andgrad(b) (zbzx) + (zbzy) + (zbzz) u v and w representaverage flow velocity components in Cartesian coordinatesx y and z respectively (ms) Fx Fy and Fz stand for bodyforces (N) p is pressure (pa) t is time (s) and ρ represents thedensity of fluid (kgm3)

+e standard k-ε models include turbulent energyequation and turbulent dissipation equation +e equationsfor the turbulent kinetic energy and the dissipation rate ofthe standard k-ε model are defined as follows

ρdk

dt

z

zxi

μ +μt

σk

1113888 1113889zk

zxi

1113890 1113891 + Gk + Gb minus ρα (23)

ρdεdt

μ +μt

σε1113888 1113889

zεzxi

1113890 1113891 + C1εεk

Gk + C3εGb( 1113857 minus C2ερε2

k

(24)

where k is the turbulent kinetic energy (m2s2) α is turbulentenergy dissipation rate (kgmiddotm2s3) Gk is turbulent energycaused by average velocity gradient Gb is turbulent energycaused by buoyancy and μt is fluid turbulent viscosity (Nmiddotsm2) In this paper σk 139 σα 139 C1ε 142 C2ε 168and C3ε 009

232 Model Establishment ANSYS DesignModeler isemployed to create the portable pillar-shaped flume ge-ometry models with three different contraction ratios Inorder to make the flow pattern of the simulated channel assimilar as possible to the actual experimental results sim-ulate according to the geometry of the model experiments+e bottom center point of the upstream section of the flumeis selected as the coordinate origin the positive direction ofthe X-axis is the direction of the water flow the positivedirection of the Y-axis is the direction of the left bank of thechannel and the negative direction of the Z-axis is thedirection of gravity acceleration

233 Mesh Generation and Boundary ConditionsANSYS meshing is utilized to establish meshes for the flowdomain +e model uses hexahedron structured grids with aunit size of 002m Due to the drastic changes in the waterflow conditions near the portable pillar-shaped flume a localgrid encryption process is employed to simulate the waterflow conditions near the flume more accurately and the gridunit size is set at 001m

+e boundary conditions of the model are set accordingto the actual conditions of the experiment +e inlet is di-vided into a lower water inlet (inlet 1) and an upper air inlet(inlet 2)+e type of the water inlet is set at velocity inlet andthe air inlet is set at pressure inlet the outlet is set at pressureoutlet (pressure-outlet) and the wall boundary (wall) se-lected has no slip option According to the actual situation ofthe model experiment the roughness (roughness height) isset at 0000011m +e boundary conditions of the flumemodel are displayed in Figure 4

3 Results and Discussion

31 Verification of the Numerical Simulation Many re-searchers have verified that Fluent software can be utilizedfor the simulation of flow measuring flumes [34] In order tofurther validate the reliability of the simulation the nu-merical data are compared with the experimental results of

Shock and Vibration 5

water flow patterns and water depths along the water pathAccording to Figure 5 by comparing the measured andsimulated flow patterns the simulation data are almostconsistent with the experimental results of the water flowpattern

+e simulated and experimental results of the free watersurface line are also compared in Figure 6 It is obvious thatthe flow in the upstream section of the portable pillar-shapedflume is relatively smooth and the flow direction is relativelyparallel After entering the contraction section the watersurface slowly falls and it drops sharply near the down-stream section of the throat At the same time the watersurface fluctuates strongly +e results demonstrate that thesimulation data are consistent with the experimental resultswith a maximum and average error of 865 and 345respectively+erefore we can conclude that Fluent softwarecan reflect the hydraulic characteristics of the flumeaccurately

32 Discharge Calculation Formula and Its AccuracyEquation (24) is used to calculate the flow rate of the portablepillar-shaped flume To determine constants a and n in theequation one may take the logarithm of both sides ofequation (24) to derive

LnKc

Bc

1113888 1113889 Ln(a) + nLnH

Bc

1113888 1113889 (25)

+e 36 sets of experimental data ie KcBc and HBcmeasured in the portable pillar-shaped flumes with threecontraction ratios are plotted on double logarithmic coor-dinates as shown in Figure 7 All the test data show a verygood correlation regardless of the contraction ratio Ourresult is similar to those of Samani Magallanez BaiamonteFerro (SMBF) flume [35] and triangular central baffle flume[19]

Plotting of the experimental pairs of Ln(KcBc) andLn(HBc) in Figure 7 revealed that the stage-dischargecurves corresponding to different values lie on a single curveEquation (25) is fitted to the experimental data by using an aand n value of 07151 and 10377 respectively and the squareof the correlation coefficient (R2) is equal to 099895

Consequently the following stage-discharge relationship iscalibrated using all the available experimental data

Q 18939B09943c H

15566 (26)

In order to check the measuring accuracy of the flumethe measured upstream water depth is substituted intoequation (26) and the calculated data (Q1) are comparedwith the measured results (Q2) of the electromagneticflowmeter as presented in Table 3 +e maximum relativeerror in the flow measurement of the portable pillar-shapedflume is 474 and the relative error in the average currentmeasurement is 172 which proves that the measurementaccuracy of the portable pillar-shaped flume examinedherein can meet the actual requirements of water mea-surement and its flow calculation formula is simple ac-curate and convenient

33 e Froude Number and Submergence Limits +eFroude number is of great significance in analyzing thehydraulic characteristics of the flow of open channels It is acriterion for judging the flow pattern of open channels andcan be used as an important indicator of the water mea-surement performance of a flume Its calculation formula isexpressed in

Fr v

gh

1113969 (27)

where v is the average velocity of the channel section (ms) grepresents the acceleration of gravity (ms2) and h stands forthe average water depth of the section (m)

Herein various Froude numbers are figured out usingthe experiments based on three different contraction ratiosand 12 discharge rates Figure 8 illustrates the distribution ofthe Froude number in the portable pillar-shaped flume alongthe path when the contraction ratio is 05 and the flow rate is15 Ls From an energy point of view the Froude numberrepresents two times the square of the ratio of the averagekinetic energy to the average potential energy per unit massof liquid in the cross-section From the entrance of the flumeto the front of the diffusion section of the flume the watersurface shows a downward trend the average potential

Portable pillar-shaped flumeInlet 2

Outlet

Inlet 1

Wall05mMesh size

1cm times 1cm times 1cm

3mMesh size

2cm times 2cm times 2cm

85mMesh size

2cm times 2cm times 2cm

Figure 4 Model and boundary conditions of the portable pillar-shaped flume

6 Shock and Vibration

energy gradually decreases and the average kinetic energyincreases so the Froude number gradually rises However inthe second half of the trough exit the water surface has arising trend the average potential energy gradually in-creases and the average kinetic energy gradually drops sothe Froude number gradually falls

+e Froude number in front of the flume is one of theimportant factors affecting the flow measurement accuracyof the water flume An excessively large Froude number infront of the flume may cause large fluctuations in the watersurface in the upstream section of the flume affect theaccuracy of the water depth measurement and reduce theaccuracy of the current measurement Generally when theflow is measured in an open channel the Froude number in

front of the flume is less than 05 Froude numbers in Section1 with different contraction ratios and discharge rates areshown in Figure 9 It can be inferred from Figure 9 that allFroude numbers are less than 04 thereby meeting the re-quirements for measuring the flow of flume also the Froudenumber is proportional to the contraction ratio Moreoverat the same contraction ratio the Froude number risesslightly as the discharge rate increases

+e critical submergence is an important indicator ofmeasuring the performance of a flume and is defined as theratio of the downstream depth of the flume to the upstreamdepth of the flume

S hd

hu

(28)

where hu is the water depth in the upstream section of theflume (m) and hd is the water depth in the downstreamsection of the flume (m)

By sorting and analyzing the test data the relationshipbetween the critical submergence of the portable pillar-shaped flume and the discharge rate can be figured out as

Portable pillar-shaped flume

Flow direction

(a)

Watervolume fractionVolume rendering 1

0000 0250 0500 0750 1000

(b)

Figure 5 Comparison of the simulated and experimental flow patterns (a) profile of the measured flow pattern (b) profile of the simulatedflow pattern

024022020018016014012010008006004002000

Distance from flume section 2 (m)

Simulatedresults

Experimentalresults Q

907Ls1294Ls1705Ls2105Ls2506Ls

503Ls

ndash2 ndash1 0 1 2 3 4 5

Wat

er d

epth

(m)

Figure 6 Comparison of the simulated and experimental results offree water surface line

ε = 05ε = 06

ndash15

ndash10

ndash05

00

05

Ln (K

cBc)

ndash05 05ndash10 1000Ln (HBc)

Equation 25ε = 04

Figure 7 Relationship between Ln(KcBc) and Ln(HBc)

Shock and Vibration 7

tabulated in Table 4 It is clear that under the same flowconditions the critical submergence rises with an increase inthe contraction ratio Moreover according to Table 4 themaximum critical submergence can reach 096 and theaverage critical submergence is 085 +e maximum criticalsubmergence of a cylindrical flow measuring flume is 84which indicates that the critical submergence of the portablepillar-shaped flume is high under different flow conditionsand at different contraction ratios thus it has a large freeoutflow range

34 Head Loss +e measuring flumes are not allowed tohave a large head loss otherwise they lead to the excessivedecantation and silt deformation of the channel When theflow passes through the portable pillar-shaped flume thecross-section of the passing water shrinks changing theoverflow of the water from slow to rapid and then to slow asshown in Figure 10 +is results in a large head loss which ismuch greater than the head loss along the way+e head losscan be calculated in two ways one is the difference between

the total head losses of the first and last sections of the flumeknown as the head loss of the flume the other is the dif-ference between the total head losses of the upstream sectionof the flume and the section after the water jump known asthe head loss +is study found that the head loss of themeasuring flume is mainly caused by the water jump afterthe throat section and it is more meaningful to examine thehead loss between the upstream section and the downstreampostjump section therefore we choose the second method+e total head loss of the section is calculated by

HTotal z +c

p+

v2

2g (29)

where HTotal z c p v and g represent total head (m) theheight (m) of the free surface from the bottom of thechannel unit weight (Nm3) pressure (pa) velocity (ms)and acceleration (ms2) due to gravity respectively

+e head loss in this paper is defined as the difference inthe head loss of upstream Section 2 and that of downstreamSection 12 +e head loss is expressed by

hw Hu minus Hd (30)

where hw is head loss (m)Hu is the total head loss of Section2 (m) and Hd is total head loss of Section 12 (m)

To analyze the head loss of the portable pillar-shapedflume the development of cross-sectional velocity distri-butions and turbulent kinetic energy dissipation are simu-lated for various typical sections

Turbulent energy dissipation rate refers to the rate atwhich turbulent flow energy is continuously converted intomolecular kinetic energy by internal friction under theaction of molecular viscous forces Studying the turbulentenergy dissipation is of great significance to the flow mea-surement process and it provides a basis for the evaluationof and improvement in the measuring flume Figure 11depicts the development of cross-sectional turbulent ki-netic energy dissipation rate in six typical sections (as de-fined in Figure 2) of the portable pillar-shaped flume whenthe flow rate is 15 Ls Figure 11(a) shows that the flow of theupstream section of the portable pillar-shaped flume is veryslow the speed of water is less than 1ms the dissipation isconcentrated in the area near the wall and bottom and allthe energy dissipation rates are lower than 0004m2middotsminus3 Atthe inlet cross-section of the flume affected by the centralcolumn the water surface is high and the dissipation isconcentrated in the middle +e maximum turbulent kineticenergy dissipation rate is 002m2middotsminus3 as displayed inFigure 11(b) At the throat (Figure 11(c)) the cross-sectionof the water decreases the speed of the water increases andthe dissipation is concentrated in the area near the wall andbottom +e maximum turbulent energy dissipation rate is003m2middotsminus3 Figure 11(d) illustrates the turbulent kineticenergy dissipation in the outlet section of the flume wherethe section velocity reaches the maximum and the turbulentkinetic energy dissipation rate increases to 025m2middotsminus3Figure 11(e) shows the hydraulic jumping phenomenon inthe downstream section of the flume Turbulent kineticenergy dissipation is mainly concentrated on the surface of

Table 3 Comparison of the measured and calculated flow rates atdifferent contraction ratios

ε H (cm) Q1 (Ls) Q2 (Ls) |Error| ()

04

818 504 520 3321018 703 731 4071203 906 948 4741360 1114 1148 3061508 1294 1348 4161646 1517 1545 1881771 1708 1732 1361892 1897 1919 1162001 2101 2094 0352131 2306 2310 0182218 2514 2458 2222320 2703 2636 246

05

691 503 494 182865 704 701 0551018 907 903 0441153 1112 1096 1431275 1294 1282 1001398 1515 1479 2371519 1705 1683 1271625 1897 1869 1451718 2105 2039 3161841 2308 2270 1641931 2506 2445 2402018 2708 2619 330

06

622 502 498 085771 703 696 098910 907 900 0751032 1115 1095 1751152 1300 1300 0021248 1514 1472 2791361 1705 1685 1201471 1901 1902 0041557 2102 2077 1181656 2303 2287 0701744 2508 2478 1191837 2704 2687 062

8 Shock and Vibration

the water flow with a maximum rate of 021m2middotsminus3 +e flowof the postjump section tends to be stable and its distri-bution of the turbulent kinetic energy dissipation is similarto but higher than that of the upstream section Figure 11(f )shows that due to the hydraulic jump the total dissipationrate of the turbulent kinetic energy in the diffusion section isquite high and the dissipation is concentrated in the areanear the water surface where the hydraulic jump occurs

Furthermore airfoil pillar-shaped flumes [36] with threecontraction ratios were tested and simulated in the same

way and the head losses of the portable pillar-shaped flumeand airfoil pillar-shaped flume were compared as presentedin Figure 12 It can be seen that the head loss of the portablepillar-shaped flume is significantly lower than that of theairfoil pillar-shaped flume Similarly Figure 13 clearly showsthat the water head loss of the portable pillar-shaped flumeas a percentage of the total upstream water head loss issignificantly smaller than that of the airfoil pillar-shapedflume

We also found out that there is a good linear relationship(R2 097316) between the upstream water depth and headloss by sorting the test data (Figure 14) +e followingequation can be well fitted to the test data

hw 03637H minus 01282ε + 00539 (31)

where hw is head loss (m) H is the water depth in theupstream section of the flume (m) and ε is contraction ratio

Compared with the airfoil pillar-shaped flume the headloss of the portable pillar-shaped flume is smaller especiallyin the case of large contraction ratios

35 Upstream Backwater Height In the current work thebackwater height is defined as the value added to the originalchannel water depth after the installation of a flume and theoriginal channel water depth is measured through thechannel under the same flow conditions when the flume isnot installed

+e variations in the backwater height of the portablepillar-shaped flume and airfoil pillar-shaped flume versusthe discharge rate are delineated in Figure 15 +e pre-liminary analysis of the experimental data shows that thebackwater height of the portable pillar-shaped flume is in-versely proportional to the contraction ratio and directlyproportional to the discharge rate of the flume Figure 15clearly indicates that the backwater height of the portablepillar-shaped flume is smaller than that of the airfoil pillar-shaped flume which makes it more suitable for applicationin the constructed channels

36 Velocity Distribution Velocity distribution is an im-portant basis for studying the hydraulic characteristics of aflume Exploiting longitudinal time-averaged velocity dis-tribution for describing the flow of water along the flowdirection can reflect the regular pattern of the flow in theportable pillar-shaped flume

Figure 16 displays the simulated velocity distribution ofthe longitudinal flow of the water under free flow conditionsat a flow rate of 15 Ls and a contraction ratio of 05According to Figure 16(a) because the water flow in the

000 021 043 064 085 106 128 149 170 192 213

Fr

Figure 8 +e distribution of the Froude number in the portable pillar-shaped flume

5 10 15 20 25 30Q (Ls)

000

005

010

015

020

025

030

035

040

045

050

Fr

ε = 06

ε = 04ε = 05

Figure 9 +e Froude number at different contraction ratios anddischarge rates in Section 1

Table 4 Submergence limits at different contraction ratios anddischarge rates

ε Q (Ls) S ε Q (Ls) S ε Q (Ls) S

04

504 085

05

503 093

06

502 096703 088 704 088 703 093906 083 907 092 907 0941114 073 1112 088 1115 0861294 077 1294 087 1300 0871517 076 1515 086 1514 0901708 081 1705 085 1705 0901897 082 1897 083 1901 0912101 078 2105 086 2102 0842306 076 2308 084 2303 0862514 081 2506 083 2508 0872703 080 2708 080 2704 085

Shock and Vibration 9

Velocity (mmiddotsndash1)

000 035 070 105 141

Figure 10 +e streamline distribution in the portable pillar-shaped flume

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Turbulent kinetic energydissipation rate

Section 1

0000 0001 0002 0003 0004

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

Figure 11 Continued

10 Shock and Vibration

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

Y

XC

P = Ymax

Equation 1

(a)

Y

X

C

P = YmaxPprime = Ymax

NACA airfoil pillar-shaped flumePortable pillar-shaped flume

(b)

Figure 1 (a) +e curve of optimized NACA airfoil equation (b) the shapes of the NACA airfoil-shaped flume and portable pillar-shapedflume

C

QB

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Bc2

Bc2

(a)

C

(b)

Figure 2 +e (a) plan-view and (b) profile-view of a portable pillar-shaped flume

Shock and Vibration 3

F Π1Π2( 1113857 0 (4)

where Π1 and Π2 are the dimensionless numbers expressedby

Π1 H

Bx1c gy1ρz1

(5)

Π2 KC

Bx2c gy2ρz2

(6)

where x1 y1z1 x2 y2 and z2 are determined according tothe principle of dimensional harmony

[H] Bc1113858 1113859x1[g]

y1[ρ]z1 (7)

Kc1113858 1113859 Bc1113858 1113859x2[g]

y2[ρ]z2 (8)

Length (L) time (T) and mass (M) are the basic di-mensions so equations (7) and (8) can be rewritten as follows

[L] [L]x1 LT

minus 21113960 1113961

y1ML

minus 31113960 1113961

z1 (9)

[L] [L]x2 LT

minus 21113960 1113961

y2ML

minus 31113960 1113961

z2 (10)

Since the exponents of the same dimension on both sidesof the equation are equal x1 y1 z1 x2 y2 and z2 can besolved as follows x1 1 y1 0 z1 0 x2 1 y2 0 andz2 0 +us equations (5) and (6) can be changed to

Π1 Kc

Bc

(11)

Π2 H

Bc

(12)

By substituting equations (11) and (12) into equation (4)the dimensionless number equation can be obtained

FKc

Bc

H

Bc

1113888 1113889 0 (13)

soKc

Bc

φH

Bc

1113888 1113889 (14)

where φ is a functional symbolTransforming equation (14) into an explicit form leads to

Kc

Bc

aH

Bc

1113888 1113889

n

(15)

where n is an undetermined number that can be obtained byexperimental data and a indicates a constant value dividedby the contraction ratio of the portable pillar-shaped flume

Upstream reservoir

Main channel

Valve

Pipe

Pump

RecirculatingSystem

Electromagnetic flow meter

Portable pillar-shaped flume

Downstreamreservior

Sluice gate

Figure 3 A sketch of the experimental setup

Table 1 Dimensions of the portable pillar-shaped flumes withdifferent contraction ratios

Channel width (cm) P (cm) C (cm) Bc (cm) ε30 90 50 12 0430 75 50 15 0530 60 50 18 06

Table 2 Locations of the typical cross-section of the flume forwater depth at the centerline of the channel

Section Distance from the inlet to the measuring points (m)1 25002 30003 31004 32005 32456 34007 35008 36009 370010 380011 390012 400013 500014 6000

4 Shock and Vibration

A critical flow is created in the portable pillar-shapedflume by installing an airfoil pillar across the flow If wesuppose that a critical flow is formed at the throat of theflume from the critical flow equation one may obtain

Q gA3

c

Bc

1113888 1113889

(13)

(16)

Ac BcKc (17)

where Q is the discharge rate (Ls)Kc can also be obtained from equations (16) and (17)

Kc Q(23)

g(13)B(23)c

(18)

Equation (18) is substituted into equation (15) as follows

Q(23)

g(13)B(53)c

aH

Bc

1113888 1113889

n

(19)

+e above equation can also be written as the explicitfunction of flow as follows

Q a(23)

g(12)

B25minus15nc H

15n (20)

23 Numerical Simulation

231 Governing Equations and Turbulence Model In thisstudy Fluent 192 was utilized to solve the computationalfluid dynamics simulations +e volume-of-fluid (VOF)method [30ndash33] and the standard k-ε three-dimensionalturbulence model [32] were chosen to simulate the flowdomain in the portable pillar-shaped flume +e motion ofNewtonian fluid flowing through the portable pillar-shapedflume is described by the continuity and NavierndashStokesequations ie respectively equations (21) and 22(andashc)

zρzt

+z(ρu)

zx+

z(ρv)

zy+

z(ρw)

zz 0 (21)

z(ρu)

zt+ div(ρuu) minus

zp

zx+ div(μgradu) + Fx

(22a)

z(ρv)

zt+ div(ρvu) minus

zp

zy+ div(μgradv) + Fy

(22b)

z(ρw)

zt+ div(ρwu) minus

zp

zz+ div(μgradw) + Fz

(22c)

where the concepts of divergence and gradient are intro-duced as div(a) (zaxzx) + (zayzy) + (zazzz) andgrad(b) (zbzx) + (zbzy) + (zbzz) u v and w representaverage flow velocity components in Cartesian coordinatesx y and z respectively (ms) Fx Fy and Fz stand for bodyforces (N) p is pressure (pa) t is time (s) and ρ represents thedensity of fluid (kgm3)

+e standard k-ε models include turbulent energyequation and turbulent dissipation equation +e equationsfor the turbulent kinetic energy and the dissipation rate ofthe standard k-ε model are defined as follows

ρdk

dt

z

zxi

μ +μt

σk

1113888 1113889zk

zxi

1113890 1113891 + Gk + Gb minus ρα (23)

ρdεdt

μ +μt

σε1113888 1113889

zεzxi

1113890 1113891 + C1εεk

Gk + C3εGb( 1113857 minus C2ερε2

k

(24)

where k is the turbulent kinetic energy (m2s2) α is turbulentenergy dissipation rate (kgmiddotm2s3) Gk is turbulent energycaused by average velocity gradient Gb is turbulent energycaused by buoyancy and μt is fluid turbulent viscosity (Nmiddotsm2) In this paper σk 139 σα 139 C1ε 142 C2ε 168and C3ε 009

232 Model Establishment ANSYS DesignModeler isemployed to create the portable pillar-shaped flume ge-ometry models with three different contraction ratios Inorder to make the flow pattern of the simulated channel assimilar as possible to the actual experimental results sim-ulate according to the geometry of the model experiments+e bottom center point of the upstream section of the flumeis selected as the coordinate origin the positive direction ofthe X-axis is the direction of the water flow the positivedirection of the Y-axis is the direction of the left bank of thechannel and the negative direction of the Z-axis is thedirection of gravity acceleration

233 Mesh Generation and Boundary ConditionsANSYS meshing is utilized to establish meshes for the flowdomain +e model uses hexahedron structured grids with aunit size of 002m Due to the drastic changes in the waterflow conditions near the portable pillar-shaped flume a localgrid encryption process is employed to simulate the waterflow conditions near the flume more accurately and the gridunit size is set at 001m

+e boundary conditions of the model are set accordingto the actual conditions of the experiment +e inlet is di-vided into a lower water inlet (inlet 1) and an upper air inlet(inlet 2)+e type of the water inlet is set at velocity inlet andthe air inlet is set at pressure inlet the outlet is set at pressureoutlet (pressure-outlet) and the wall boundary (wall) se-lected has no slip option According to the actual situation ofthe model experiment the roughness (roughness height) isset at 0000011m +e boundary conditions of the flumemodel are displayed in Figure 4

3 Results and Discussion

31 Verification of the Numerical Simulation Many re-searchers have verified that Fluent software can be utilizedfor the simulation of flow measuring flumes [34] In order tofurther validate the reliability of the simulation the nu-merical data are compared with the experimental results of

Shock and Vibration 5

water flow patterns and water depths along the water pathAccording to Figure 5 by comparing the measured andsimulated flow patterns the simulation data are almostconsistent with the experimental results of the water flowpattern

+e simulated and experimental results of the free watersurface line are also compared in Figure 6 It is obvious thatthe flow in the upstream section of the portable pillar-shapedflume is relatively smooth and the flow direction is relativelyparallel After entering the contraction section the watersurface slowly falls and it drops sharply near the down-stream section of the throat At the same time the watersurface fluctuates strongly +e results demonstrate that thesimulation data are consistent with the experimental resultswith a maximum and average error of 865 and 345respectively+erefore we can conclude that Fluent softwarecan reflect the hydraulic characteristics of the flumeaccurately

32 Discharge Calculation Formula and Its AccuracyEquation (24) is used to calculate the flow rate of the portablepillar-shaped flume To determine constants a and n in theequation one may take the logarithm of both sides ofequation (24) to derive

LnKc

Bc

1113888 1113889 Ln(a) + nLnH

Bc

1113888 1113889 (25)

+e 36 sets of experimental data ie KcBc and HBcmeasured in the portable pillar-shaped flumes with threecontraction ratios are plotted on double logarithmic coor-dinates as shown in Figure 7 All the test data show a verygood correlation regardless of the contraction ratio Ourresult is similar to those of Samani Magallanez BaiamonteFerro (SMBF) flume [35] and triangular central baffle flume[19]

Plotting of the experimental pairs of Ln(KcBc) andLn(HBc) in Figure 7 revealed that the stage-dischargecurves corresponding to different values lie on a single curveEquation (25) is fitted to the experimental data by using an aand n value of 07151 and 10377 respectively and the squareof the correlation coefficient (R2) is equal to 099895

Consequently the following stage-discharge relationship iscalibrated using all the available experimental data

Q 18939B09943c H

15566 (26)

In order to check the measuring accuracy of the flumethe measured upstream water depth is substituted intoequation (26) and the calculated data (Q1) are comparedwith the measured results (Q2) of the electromagneticflowmeter as presented in Table 3 +e maximum relativeerror in the flow measurement of the portable pillar-shapedflume is 474 and the relative error in the average currentmeasurement is 172 which proves that the measurementaccuracy of the portable pillar-shaped flume examinedherein can meet the actual requirements of water mea-surement and its flow calculation formula is simple ac-curate and convenient

33 e Froude Number and Submergence Limits +eFroude number is of great significance in analyzing thehydraulic characteristics of the flow of open channels It is acriterion for judging the flow pattern of open channels andcan be used as an important indicator of the water mea-surement performance of a flume Its calculation formula isexpressed in

Fr v

gh

1113969 (27)

where v is the average velocity of the channel section (ms) grepresents the acceleration of gravity (ms2) and h stands forthe average water depth of the section (m)

Herein various Froude numbers are figured out usingthe experiments based on three different contraction ratiosand 12 discharge rates Figure 8 illustrates the distribution ofthe Froude number in the portable pillar-shaped flume alongthe path when the contraction ratio is 05 and the flow rate is15 Ls From an energy point of view the Froude numberrepresents two times the square of the ratio of the averagekinetic energy to the average potential energy per unit massof liquid in the cross-section From the entrance of the flumeto the front of the diffusion section of the flume the watersurface shows a downward trend the average potential

Portable pillar-shaped flumeInlet 2

Outlet

Inlet 1

Wall05mMesh size

1cm times 1cm times 1cm

3mMesh size

2cm times 2cm times 2cm

85mMesh size

2cm times 2cm times 2cm

Figure 4 Model and boundary conditions of the portable pillar-shaped flume

6 Shock and Vibration

energy gradually decreases and the average kinetic energyincreases so the Froude number gradually rises However inthe second half of the trough exit the water surface has arising trend the average potential energy gradually in-creases and the average kinetic energy gradually drops sothe Froude number gradually falls

+e Froude number in front of the flume is one of theimportant factors affecting the flow measurement accuracyof the water flume An excessively large Froude number infront of the flume may cause large fluctuations in the watersurface in the upstream section of the flume affect theaccuracy of the water depth measurement and reduce theaccuracy of the current measurement Generally when theflow is measured in an open channel the Froude number in

front of the flume is less than 05 Froude numbers in Section1 with different contraction ratios and discharge rates areshown in Figure 9 It can be inferred from Figure 9 that allFroude numbers are less than 04 thereby meeting the re-quirements for measuring the flow of flume also the Froudenumber is proportional to the contraction ratio Moreoverat the same contraction ratio the Froude number risesslightly as the discharge rate increases

+e critical submergence is an important indicator ofmeasuring the performance of a flume and is defined as theratio of the downstream depth of the flume to the upstreamdepth of the flume

S hd

hu

(28)

where hu is the water depth in the upstream section of theflume (m) and hd is the water depth in the downstreamsection of the flume (m)

By sorting and analyzing the test data the relationshipbetween the critical submergence of the portable pillar-shaped flume and the discharge rate can be figured out as

Portable pillar-shaped flume

Flow direction

(a)

Watervolume fractionVolume rendering 1

0000 0250 0500 0750 1000

(b)

Figure 5 Comparison of the simulated and experimental flow patterns (a) profile of the measured flow pattern (b) profile of the simulatedflow pattern

024022020018016014012010008006004002000

Distance from flume section 2 (m)

Simulatedresults

Experimentalresults Q

907Ls1294Ls1705Ls2105Ls2506Ls

503Ls

ndash2 ndash1 0 1 2 3 4 5

Wat

er d

epth

(m)

Figure 6 Comparison of the simulated and experimental results offree water surface line

ε = 05ε = 06

ndash15

ndash10

ndash05

00

05

Ln (K

cBc)

ndash05 05ndash10 1000Ln (HBc)

Equation 25ε = 04

Figure 7 Relationship between Ln(KcBc) and Ln(HBc)

Shock and Vibration 7

tabulated in Table 4 It is clear that under the same flowconditions the critical submergence rises with an increase inthe contraction ratio Moreover according to Table 4 themaximum critical submergence can reach 096 and theaverage critical submergence is 085 +e maximum criticalsubmergence of a cylindrical flow measuring flume is 84which indicates that the critical submergence of the portablepillar-shaped flume is high under different flow conditionsand at different contraction ratios thus it has a large freeoutflow range

34 Head Loss +e measuring flumes are not allowed tohave a large head loss otherwise they lead to the excessivedecantation and silt deformation of the channel When theflow passes through the portable pillar-shaped flume thecross-section of the passing water shrinks changing theoverflow of the water from slow to rapid and then to slow asshown in Figure 10 +is results in a large head loss which ismuch greater than the head loss along the way+e head losscan be calculated in two ways one is the difference between

the total head losses of the first and last sections of the flumeknown as the head loss of the flume the other is the dif-ference between the total head losses of the upstream sectionof the flume and the section after the water jump known asthe head loss +is study found that the head loss of themeasuring flume is mainly caused by the water jump afterthe throat section and it is more meaningful to examine thehead loss between the upstream section and the downstreampostjump section therefore we choose the second method+e total head loss of the section is calculated by

HTotal z +c

p+

v2

2g (29)

where HTotal z c p v and g represent total head (m) theheight (m) of the free surface from the bottom of thechannel unit weight (Nm3) pressure (pa) velocity (ms)and acceleration (ms2) due to gravity respectively

+e head loss in this paper is defined as the difference inthe head loss of upstream Section 2 and that of downstreamSection 12 +e head loss is expressed by

hw Hu minus Hd (30)

where hw is head loss (m)Hu is the total head loss of Section2 (m) and Hd is total head loss of Section 12 (m)

To analyze the head loss of the portable pillar-shapedflume the development of cross-sectional velocity distri-butions and turbulent kinetic energy dissipation are simu-lated for various typical sections

Turbulent energy dissipation rate refers to the rate atwhich turbulent flow energy is continuously converted intomolecular kinetic energy by internal friction under theaction of molecular viscous forces Studying the turbulentenergy dissipation is of great significance to the flow mea-surement process and it provides a basis for the evaluationof and improvement in the measuring flume Figure 11depicts the development of cross-sectional turbulent ki-netic energy dissipation rate in six typical sections (as de-fined in Figure 2) of the portable pillar-shaped flume whenthe flow rate is 15 Ls Figure 11(a) shows that the flow of theupstream section of the portable pillar-shaped flume is veryslow the speed of water is less than 1ms the dissipation isconcentrated in the area near the wall and bottom and allthe energy dissipation rates are lower than 0004m2middotsminus3 Atthe inlet cross-section of the flume affected by the centralcolumn the water surface is high and the dissipation isconcentrated in the middle +e maximum turbulent kineticenergy dissipation rate is 002m2middotsminus3 as displayed inFigure 11(b) At the throat (Figure 11(c)) the cross-sectionof the water decreases the speed of the water increases andthe dissipation is concentrated in the area near the wall andbottom +e maximum turbulent energy dissipation rate is003m2middotsminus3 Figure 11(d) illustrates the turbulent kineticenergy dissipation in the outlet section of the flume wherethe section velocity reaches the maximum and the turbulentkinetic energy dissipation rate increases to 025m2middotsminus3Figure 11(e) shows the hydraulic jumping phenomenon inthe downstream section of the flume Turbulent kineticenergy dissipation is mainly concentrated on the surface of

Table 3 Comparison of the measured and calculated flow rates atdifferent contraction ratios

ε H (cm) Q1 (Ls) Q2 (Ls) |Error| ()

04

818 504 520 3321018 703 731 4071203 906 948 4741360 1114 1148 3061508 1294 1348 4161646 1517 1545 1881771 1708 1732 1361892 1897 1919 1162001 2101 2094 0352131 2306 2310 0182218 2514 2458 2222320 2703 2636 246

05

691 503 494 182865 704 701 0551018 907 903 0441153 1112 1096 1431275 1294 1282 1001398 1515 1479 2371519 1705 1683 1271625 1897 1869 1451718 2105 2039 3161841 2308 2270 1641931 2506 2445 2402018 2708 2619 330

06

622 502 498 085771 703 696 098910 907 900 0751032 1115 1095 1751152 1300 1300 0021248 1514 1472 2791361 1705 1685 1201471 1901 1902 0041557 2102 2077 1181656 2303 2287 0701744 2508 2478 1191837 2704 2687 062

8 Shock and Vibration

the water flow with a maximum rate of 021m2middotsminus3 +e flowof the postjump section tends to be stable and its distri-bution of the turbulent kinetic energy dissipation is similarto but higher than that of the upstream section Figure 11(f )shows that due to the hydraulic jump the total dissipationrate of the turbulent kinetic energy in the diffusion section isquite high and the dissipation is concentrated in the areanear the water surface where the hydraulic jump occurs

Furthermore airfoil pillar-shaped flumes [36] with threecontraction ratios were tested and simulated in the same

way and the head losses of the portable pillar-shaped flumeand airfoil pillar-shaped flume were compared as presentedin Figure 12 It can be seen that the head loss of the portablepillar-shaped flume is significantly lower than that of theairfoil pillar-shaped flume Similarly Figure 13 clearly showsthat the water head loss of the portable pillar-shaped flumeas a percentage of the total upstream water head loss issignificantly smaller than that of the airfoil pillar-shapedflume

We also found out that there is a good linear relationship(R2 097316) between the upstream water depth and headloss by sorting the test data (Figure 14) +e followingequation can be well fitted to the test data

hw 03637H minus 01282ε + 00539 (31)

where hw is head loss (m) H is the water depth in theupstream section of the flume (m) and ε is contraction ratio

Compared with the airfoil pillar-shaped flume the headloss of the portable pillar-shaped flume is smaller especiallyin the case of large contraction ratios

35 Upstream Backwater Height In the current work thebackwater height is defined as the value added to the originalchannel water depth after the installation of a flume and theoriginal channel water depth is measured through thechannel under the same flow conditions when the flume isnot installed

+e variations in the backwater height of the portablepillar-shaped flume and airfoil pillar-shaped flume versusthe discharge rate are delineated in Figure 15 +e pre-liminary analysis of the experimental data shows that thebackwater height of the portable pillar-shaped flume is in-versely proportional to the contraction ratio and directlyproportional to the discharge rate of the flume Figure 15clearly indicates that the backwater height of the portablepillar-shaped flume is smaller than that of the airfoil pillar-shaped flume which makes it more suitable for applicationin the constructed channels

36 Velocity Distribution Velocity distribution is an im-portant basis for studying the hydraulic characteristics of aflume Exploiting longitudinal time-averaged velocity dis-tribution for describing the flow of water along the flowdirection can reflect the regular pattern of the flow in theportable pillar-shaped flume

Figure 16 displays the simulated velocity distribution ofthe longitudinal flow of the water under free flow conditionsat a flow rate of 15 Ls and a contraction ratio of 05According to Figure 16(a) because the water flow in the

000 021 043 064 085 106 128 149 170 192 213

Fr

Figure 8 +e distribution of the Froude number in the portable pillar-shaped flume

5 10 15 20 25 30Q (Ls)

000

005

010

015

020

025

030

035

040

045

050

Fr

ε = 06

ε = 04ε = 05

Figure 9 +e Froude number at different contraction ratios anddischarge rates in Section 1

Table 4 Submergence limits at different contraction ratios anddischarge rates

ε Q (Ls) S ε Q (Ls) S ε Q (Ls) S

04

504 085

05

503 093

06

502 096703 088 704 088 703 093906 083 907 092 907 0941114 073 1112 088 1115 0861294 077 1294 087 1300 0871517 076 1515 086 1514 0901708 081 1705 085 1705 0901897 082 1897 083 1901 0912101 078 2105 086 2102 0842306 076 2308 084 2303 0862514 081 2506 083 2508 0872703 080 2708 080 2704 085

Shock and Vibration 9

Velocity (mmiddotsndash1)

000 035 070 105 141

Figure 10 +e streamline distribution in the portable pillar-shaped flume

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Turbulent kinetic energydissipation rate

Section 1

0000 0001 0002 0003 0004

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

Figure 11 Continued

10 Shock and Vibration

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

F Π1Π2( 1113857 0 (4)

where Π1 and Π2 are the dimensionless numbers expressedby

Π1 H

Bx1c gy1ρz1

(5)

Π2 KC

Bx2c gy2ρz2

(6)

where x1 y1z1 x2 y2 and z2 are determined according tothe principle of dimensional harmony

[H] Bc1113858 1113859x1[g]

y1[ρ]z1 (7)

Kc1113858 1113859 Bc1113858 1113859x2[g]

y2[ρ]z2 (8)

Length (L) time (T) and mass (M) are the basic di-mensions so equations (7) and (8) can be rewritten as follows

[L] [L]x1 LT

minus 21113960 1113961

y1ML

minus 31113960 1113961

z1 (9)

[L] [L]x2 LT

minus 21113960 1113961

y2ML

minus 31113960 1113961

z2 (10)

Since the exponents of the same dimension on both sidesof the equation are equal x1 y1 z1 x2 y2 and z2 can besolved as follows x1 1 y1 0 z1 0 x2 1 y2 0 andz2 0 +us equations (5) and (6) can be changed to

Π1 Kc

Bc

(11)

Π2 H

Bc

(12)

By substituting equations (11) and (12) into equation (4)the dimensionless number equation can be obtained

FKc

Bc

H

Bc

1113888 1113889 0 (13)

soKc

Bc

φH

Bc

1113888 1113889 (14)

where φ is a functional symbolTransforming equation (14) into an explicit form leads to

Kc

Bc

aH

Bc

1113888 1113889

n

(15)

where n is an undetermined number that can be obtained byexperimental data and a indicates a constant value dividedby the contraction ratio of the portable pillar-shaped flume

Upstream reservoir

Main channel

Valve

Pipe

Pump

RecirculatingSystem

Electromagnetic flow meter

Portable pillar-shaped flume

Downstreamreservior

Sluice gate

Figure 3 A sketch of the experimental setup

Table 1 Dimensions of the portable pillar-shaped flumes withdifferent contraction ratios

Channel width (cm) P (cm) C (cm) Bc (cm) ε30 90 50 12 0430 75 50 15 0530 60 50 18 06

Table 2 Locations of the typical cross-section of the flume forwater depth at the centerline of the channel

Section Distance from the inlet to the measuring points (m)1 25002 30003 31004 32005 32456 34007 35008 36009 370010 380011 390012 400013 500014 6000

4 Shock and Vibration

A critical flow is created in the portable pillar-shapedflume by installing an airfoil pillar across the flow If wesuppose that a critical flow is formed at the throat of theflume from the critical flow equation one may obtain

Q gA3

c

Bc

1113888 1113889

(13)

(16)

Ac BcKc (17)

where Q is the discharge rate (Ls)Kc can also be obtained from equations (16) and (17)

Kc Q(23)

g(13)B(23)c

(18)

Equation (18) is substituted into equation (15) as follows

Q(23)

g(13)B(53)c

aH

Bc

1113888 1113889

n

(19)

+e above equation can also be written as the explicitfunction of flow as follows

Q a(23)

g(12)

B25minus15nc H

15n (20)

23 Numerical Simulation

231 Governing Equations and Turbulence Model In thisstudy Fluent 192 was utilized to solve the computationalfluid dynamics simulations +e volume-of-fluid (VOF)method [30ndash33] and the standard k-ε three-dimensionalturbulence model [32] were chosen to simulate the flowdomain in the portable pillar-shaped flume +e motion ofNewtonian fluid flowing through the portable pillar-shapedflume is described by the continuity and NavierndashStokesequations ie respectively equations (21) and 22(andashc)

zρzt

+z(ρu)

zx+

z(ρv)

zy+

z(ρw)

zz 0 (21)

z(ρu)

zt+ div(ρuu) minus

zp

zx+ div(μgradu) + Fx

(22a)

z(ρv)

zt+ div(ρvu) minus

zp

zy+ div(μgradv) + Fy

(22b)

z(ρw)

zt+ div(ρwu) minus

zp

zz+ div(μgradw) + Fz

(22c)

where the concepts of divergence and gradient are intro-duced as div(a) (zaxzx) + (zayzy) + (zazzz) andgrad(b) (zbzx) + (zbzy) + (zbzz) u v and w representaverage flow velocity components in Cartesian coordinatesx y and z respectively (ms) Fx Fy and Fz stand for bodyforces (N) p is pressure (pa) t is time (s) and ρ represents thedensity of fluid (kgm3)

+e standard k-ε models include turbulent energyequation and turbulent dissipation equation +e equationsfor the turbulent kinetic energy and the dissipation rate ofthe standard k-ε model are defined as follows

ρdk

dt

z

zxi

μ +μt

σk

1113888 1113889zk

zxi

1113890 1113891 + Gk + Gb minus ρα (23)

ρdεdt

μ +μt

σε1113888 1113889

zεzxi

1113890 1113891 + C1εεk

Gk + C3εGb( 1113857 minus C2ερε2

k

(24)

where k is the turbulent kinetic energy (m2s2) α is turbulentenergy dissipation rate (kgmiddotm2s3) Gk is turbulent energycaused by average velocity gradient Gb is turbulent energycaused by buoyancy and μt is fluid turbulent viscosity (Nmiddotsm2) In this paper σk 139 σα 139 C1ε 142 C2ε 168and C3ε 009

232 Model Establishment ANSYS DesignModeler isemployed to create the portable pillar-shaped flume ge-ometry models with three different contraction ratios Inorder to make the flow pattern of the simulated channel assimilar as possible to the actual experimental results sim-ulate according to the geometry of the model experiments+e bottom center point of the upstream section of the flumeis selected as the coordinate origin the positive direction ofthe X-axis is the direction of the water flow the positivedirection of the Y-axis is the direction of the left bank of thechannel and the negative direction of the Z-axis is thedirection of gravity acceleration

233 Mesh Generation and Boundary ConditionsANSYS meshing is utilized to establish meshes for the flowdomain +e model uses hexahedron structured grids with aunit size of 002m Due to the drastic changes in the waterflow conditions near the portable pillar-shaped flume a localgrid encryption process is employed to simulate the waterflow conditions near the flume more accurately and the gridunit size is set at 001m

+e boundary conditions of the model are set accordingto the actual conditions of the experiment +e inlet is di-vided into a lower water inlet (inlet 1) and an upper air inlet(inlet 2)+e type of the water inlet is set at velocity inlet andthe air inlet is set at pressure inlet the outlet is set at pressureoutlet (pressure-outlet) and the wall boundary (wall) se-lected has no slip option According to the actual situation ofthe model experiment the roughness (roughness height) isset at 0000011m +e boundary conditions of the flumemodel are displayed in Figure 4

3 Results and Discussion

31 Verification of the Numerical Simulation Many re-searchers have verified that Fluent software can be utilizedfor the simulation of flow measuring flumes [34] In order tofurther validate the reliability of the simulation the nu-merical data are compared with the experimental results of

Shock and Vibration 5

water flow patterns and water depths along the water pathAccording to Figure 5 by comparing the measured andsimulated flow patterns the simulation data are almostconsistent with the experimental results of the water flowpattern

+e simulated and experimental results of the free watersurface line are also compared in Figure 6 It is obvious thatthe flow in the upstream section of the portable pillar-shapedflume is relatively smooth and the flow direction is relativelyparallel After entering the contraction section the watersurface slowly falls and it drops sharply near the down-stream section of the throat At the same time the watersurface fluctuates strongly +e results demonstrate that thesimulation data are consistent with the experimental resultswith a maximum and average error of 865 and 345respectively+erefore we can conclude that Fluent softwarecan reflect the hydraulic characteristics of the flumeaccurately

32 Discharge Calculation Formula and Its AccuracyEquation (24) is used to calculate the flow rate of the portablepillar-shaped flume To determine constants a and n in theequation one may take the logarithm of both sides ofequation (24) to derive

LnKc

Bc

1113888 1113889 Ln(a) + nLnH

Bc

1113888 1113889 (25)

+e 36 sets of experimental data ie KcBc and HBcmeasured in the portable pillar-shaped flumes with threecontraction ratios are plotted on double logarithmic coor-dinates as shown in Figure 7 All the test data show a verygood correlation regardless of the contraction ratio Ourresult is similar to those of Samani Magallanez BaiamonteFerro (SMBF) flume [35] and triangular central baffle flume[19]

Plotting of the experimental pairs of Ln(KcBc) andLn(HBc) in Figure 7 revealed that the stage-dischargecurves corresponding to different values lie on a single curveEquation (25) is fitted to the experimental data by using an aand n value of 07151 and 10377 respectively and the squareof the correlation coefficient (R2) is equal to 099895

Consequently the following stage-discharge relationship iscalibrated using all the available experimental data

Q 18939B09943c H

15566 (26)

In order to check the measuring accuracy of the flumethe measured upstream water depth is substituted intoequation (26) and the calculated data (Q1) are comparedwith the measured results (Q2) of the electromagneticflowmeter as presented in Table 3 +e maximum relativeerror in the flow measurement of the portable pillar-shapedflume is 474 and the relative error in the average currentmeasurement is 172 which proves that the measurementaccuracy of the portable pillar-shaped flume examinedherein can meet the actual requirements of water mea-surement and its flow calculation formula is simple ac-curate and convenient

33 e Froude Number and Submergence Limits +eFroude number is of great significance in analyzing thehydraulic characteristics of the flow of open channels It is acriterion for judging the flow pattern of open channels andcan be used as an important indicator of the water mea-surement performance of a flume Its calculation formula isexpressed in

Fr v

gh

1113969 (27)

where v is the average velocity of the channel section (ms) grepresents the acceleration of gravity (ms2) and h stands forthe average water depth of the section (m)

Herein various Froude numbers are figured out usingthe experiments based on three different contraction ratiosand 12 discharge rates Figure 8 illustrates the distribution ofthe Froude number in the portable pillar-shaped flume alongthe path when the contraction ratio is 05 and the flow rate is15 Ls From an energy point of view the Froude numberrepresents two times the square of the ratio of the averagekinetic energy to the average potential energy per unit massof liquid in the cross-section From the entrance of the flumeto the front of the diffusion section of the flume the watersurface shows a downward trend the average potential

Portable pillar-shaped flumeInlet 2

Outlet

Inlet 1

Wall05mMesh size

1cm times 1cm times 1cm

3mMesh size

2cm times 2cm times 2cm

85mMesh size

2cm times 2cm times 2cm

Figure 4 Model and boundary conditions of the portable pillar-shaped flume

6 Shock and Vibration

energy gradually decreases and the average kinetic energyincreases so the Froude number gradually rises However inthe second half of the trough exit the water surface has arising trend the average potential energy gradually in-creases and the average kinetic energy gradually drops sothe Froude number gradually falls

+e Froude number in front of the flume is one of theimportant factors affecting the flow measurement accuracyof the water flume An excessively large Froude number infront of the flume may cause large fluctuations in the watersurface in the upstream section of the flume affect theaccuracy of the water depth measurement and reduce theaccuracy of the current measurement Generally when theflow is measured in an open channel the Froude number in

front of the flume is less than 05 Froude numbers in Section1 with different contraction ratios and discharge rates areshown in Figure 9 It can be inferred from Figure 9 that allFroude numbers are less than 04 thereby meeting the re-quirements for measuring the flow of flume also the Froudenumber is proportional to the contraction ratio Moreoverat the same contraction ratio the Froude number risesslightly as the discharge rate increases

+e critical submergence is an important indicator ofmeasuring the performance of a flume and is defined as theratio of the downstream depth of the flume to the upstreamdepth of the flume

S hd

hu

(28)

where hu is the water depth in the upstream section of theflume (m) and hd is the water depth in the downstreamsection of the flume (m)

By sorting and analyzing the test data the relationshipbetween the critical submergence of the portable pillar-shaped flume and the discharge rate can be figured out as

Portable pillar-shaped flume

Flow direction

(a)

Watervolume fractionVolume rendering 1

0000 0250 0500 0750 1000

(b)

Figure 5 Comparison of the simulated and experimental flow patterns (a) profile of the measured flow pattern (b) profile of the simulatedflow pattern

024022020018016014012010008006004002000

Distance from flume section 2 (m)

Simulatedresults

Experimentalresults Q

907Ls1294Ls1705Ls2105Ls2506Ls

503Ls

ndash2 ndash1 0 1 2 3 4 5

Wat

er d

epth

(m)

Figure 6 Comparison of the simulated and experimental results offree water surface line

ε = 05ε = 06

ndash15

ndash10

ndash05

00

05

Ln (K

cBc)

ndash05 05ndash10 1000Ln (HBc)

Equation 25ε = 04

Figure 7 Relationship between Ln(KcBc) and Ln(HBc)

Shock and Vibration 7

tabulated in Table 4 It is clear that under the same flowconditions the critical submergence rises with an increase inthe contraction ratio Moreover according to Table 4 themaximum critical submergence can reach 096 and theaverage critical submergence is 085 +e maximum criticalsubmergence of a cylindrical flow measuring flume is 84which indicates that the critical submergence of the portablepillar-shaped flume is high under different flow conditionsand at different contraction ratios thus it has a large freeoutflow range

34 Head Loss +e measuring flumes are not allowed tohave a large head loss otherwise they lead to the excessivedecantation and silt deformation of the channel When theflow passes through the portable pillar-shaped flume thecross-section of the passing water shrinks changing theoverflow of the water from slow to rapid and then to slow asshown in Figure 10 +is results in a large head loss which ismuch greater than the head loss along the way+e head losscan be calculated in two ways one is the difference between

the total head losses of the first and last sections of the flumeknown as the head loss of the flume the other is the dif-ference between the total head losses of the upstream sectionof the flume and the section after the water jump known asthe head loss +is study found that the head loss of themeasuring flume is mainly caused by the water jump afterthe throat section and it is more meaningful to examine thehead loss between the upstream section and the downstreampostjump section therefore we choose the second method+e total head loss of the section is calculated by

HTotal z +c

p+

v2

2g (29)

where HTotal z c p v and g represent total head (m) theheight (m) of the free surface from the bottom of thechannel unit weight (Nm3) pressure (pa) velocity (ms)and acceleration (ms2) due to gravity respectively

+e head loss in this paper is defined as the difference inthe head loss of upstream Section 2 and that of downstreamSection 12 +e head loss is expressed by

hw Hu minus Hd (30)

where hw is head loss (m)Hu is the total head loss of Section2 (m) and Hd is total head loss of Section 12 (m)

To analyze the head loss of the portable pillar-shapedflume the development of cross-sectional velocity distri-butions and turbulent kinetic energy dissipation are simu-lated for various typical sections

Turbulent energy dissipation rate refers to the rate atwhich turbulent flow energy is continuously converted intomolecular kinetic energy by internal friction under theaction of molecular viscous forces Studying the turbulentenergy dissipation is of great significance to the flow mea-surement process and it provides a basis for the evaluationof and improvement in the measuring flume Figure 11depicts the development of cross-sectional turbulent ki-netic energy dissipation rate in six typical sections (as de-fined in Figure 2) of the portable pillar-shaped flume whenthe flow rate is 15 Ls Figure 11(a) shows that the flow of theupstream section of the portable pillar-shaped flume is veryslow the speed of water is less than 1ms the dissipation isconcentrated in the area near the wall and bottom and allthe energy dissipation rates are lower than 0004m2middotsminus3 Atthe inlet cross-section of the flume affected by the centralcolumn the water surface is high and the dissipation isconcentrated in the middle +e maximum turbulent kineticenergy dissipation rate is 002m2middotsminus3 as displayed inFigure 11(b) At the throat (Figure 11(c)) the cross-sectionof the water decreases the speed of the water increases andthe dissipation is concentrated in the area near the wall andbottom +e maximum turbulent energy dissipation rate is003m2middotsminus3 Figure 11(d) illustrates the turbulent kineticenergy dissipation in the outlet section of the flume wherethe section velocity reaches the maximum and the turbulentkinetic energy dissipation rate increases to 025m2middotsminus3Figure 11(e) shows the hydraulic jumping phenomenon inthe downstream section of the flume Turbulent kineticenergy dissipation is mainly concentrated on the surface of

Table 3 Comparison of the measured and calculated flow rates atdifferent contraction ratios

ε H (cm) Q1 (Ls) Q2 (Ls) |Error| ()

04

818 504 520 3321018 703 731 4071203 906 948 4741360 1114 1148 3061508 1294 1348 4161646 1517 1545 1881771 1708 1732 1361892 1897 1919 1162001 2101 2094 0352131 2306 2310 0182218 2514 2458 2222320 2703 2636 246

05

691 503 494 182865 704 701 0551018 907 903 0441153 1112 1096 1431275 1294 1282 1001398 1515 1479 2371519 1705 1683 1271625 1897 1869 1451718 2105 2039 3161841 2308 2270 1641931 2506 2445 2402018 2708 2619 330

06

622 502 498 085771 703 696 098910 907 900 0751032 1115 1095 1751152 1300 1300 0021248 1514 1472 2791361 1705 1685 1201471 1901 1902 0041557 2102 2077 1181656 2303 2287 0701744 2508 2478 1191837 2704 2687 062

8 Shock and Vibration

the water flow with a maximum rate of 021m2middotsminus3 +e flowof the postjump section tends to be stable and its distri-bution of the turbulent kinetic energy dissipation is similarto but higher than that of the upstream section Figure 11(f )shows that due to the hydraulic jump the total dissipationrate of the turbulent kinetic energy in the diffusion section isquite high and the dissipation is concentrated in the areanear the water surface where the hydraulic jump occurs

Furthermore airfoil pillar-shaped flumes [36] with threecontraction ratios were tested and simulated in the same

way and the head losses of the portable pillar-shaped flumeand airfoil pillar-shaped flume were compared as presentedin Figure 12 It can be seen that the head loss of the portablepillar-shaped flume is significantly lower than that of theairfoil pillar-shaped flume Similarly Figure 13 clearly showsthat the water head loss of the portable pillar-shaped flumeas a percentage of the total upstream water head loss issignificantly smaller than that of the airfoil pillar-shapedflume

We also found out that there is a good linear relationship(R2 097316) between the upstream water depth and headloss by sorting the test data (Figure 14) +e followingequation can be well fitted to the test data

hw 03637H minus 01282ε + 00539 (31)

where hw is head loss (m) H is the water depth in theupstream section of the flume (m) and ε is contraction ratio

Compared with the airfoil pillar-shaped flume the headloss of the portable pillar-shaped flume is smaller especiallyin the case of large contraction ratios

35 Upstream Backwater Height In the current work thebackwater height is defined as the value added to the originalchannel water depth after the installation of a flume and theoriginal channel water depth is measured through thechannel under the same flow conditions when the flume isnot installed

+e variations in the backwater height of the portablepillar-shaped flume and airfoil pillar-shaped flume versusthe discharge rate are delineated in Figure 15 +e pre-liminary analysis of the experimental data shows that thebackwater height of the portable pillar-shaped flume is in-versely proportional to the contraction ratio and directlyproportional to the discharge rate of the flume Figure 15clearly indicates that the backwater height of the portablepillar-shaped flume is smaller than that of the airfoil pillar-shaped flume which makes it more suitable for applicationin the constructed channels

36 Velocity Distribution Velocity distribution is an im-portant basis for studying the hydraulic characteristics of aflume Exploiting longitudinal time-averaged velocity dis-tribution for describing the flow of water along the flowdirection can reflect the regular pattern of the flow in theportable pillar-shaped flume

Figure 16 displays the simulated velocity distribution ofthe longitudinal flow of the water under free flow conditionsat a flow rate of 15 Ls and a contraction ratio of 05According to Figure 16(a) because the water flow in the

000 021 043 064 085 106 128 149 170 192 213

Fr

Figure 8 +e distribution of the Froude number in the portable pillar-shaped flume

5 10 15 20 25 30Q (Ls)

000

005

010

015

020

025

030

035

040

045

050

Fr

ε = 06

ε = 04ε = 05

Figure 9 +e Froude number at different contraction ratios anddischarge rates in Section 1

Table 4 Submergence limits at different contraction ratios anddischarge rates

ε Q (Ls) S ε Q (Ls) S ε Q (Ls) S

04

504 085

05

503 093

06

502 096703 088 704 088 703 093906 083 907 092 907 0941114 073 1112 088 1115 0861294 077 1294 087 1300 0871517 076 1515 086 1514 0901708 081 1705 085 1705 0901897 082 1897 083 1901 0912101 078 2105 086 2102 0842306 076 2308 084 2303 0862514 081 2506 083 2508 0872703 080 2708 080 2704 085

Shock and Vibration 9

Velocity (mmiddotsndash1)

000 035 070 105 141

Figure 10 +e streamline distribution in the portable pillar-shaped flume

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Turbulent kinetic energydissipation rate

Section 1

0000 0001 0002 0003 0004

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

Figure 11 Continued

10 Shock and Vibration

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

A critical flow is created in the portable pillar-shapedflume by installing an airfoil pillar across the flow If wesuppose that a critical flow is formed at the throat of theflume from the critical flow equation one may obtain

Q gA3

c

Bc

1113888 1113889

(13)

(16)

Ac BcKc (17)

where Q is the discharge rate (Ls)Kc can also be obtained from equations (16) and (17)

Kc Q(23)

g(13)B(23)c

(18)

Equation (18) is substituted into equation (15) as follows

Q(23)

g(13)B(53)c

aH

Bc

1113888 1113889

n

(19)

+e above equation can also be written as the explicitfunction of flow as follows

Q a(23)

g(12)

B25minus15nc H

15n (20)

23 Numerical Simulation

231 Governing Equations and Turbulence Model In thisstudy Fluent 192 was utilized to solve the computationalfluid dynamics simulations +e volume-of-fluid (VOF)method [30ndash33] and the standard k-ε three-dimensionalturbulence model [32] were chosen to simulate the flowdomain in the portable pillar-shaped flume +e motion ofNewtonian fluid flowing through the portable pillar-shapedflume is described by the continuity and NavierndashStokesequations ie respectively equations (21) and 22(andashc)

zρzt

+z(ρu)

zx+

z(ρv)

zy+

z(ρw)

zz 0 (21)

z(ρu)

zt+ div(ρuu) minus

zp

zx+ div(μgradu) + Fx

(22a)

z(ρv)

zt+ div(ρvu) minus

zp

zy+ div(μgradv) + Fy

(22b)

z(ρw)

zt+ div(ρwu) minus

zp

zz+ div(μgradw) + Fz

(22c)

where the concepts of divergence and gradient are intro-duced as div(a) (zaxzx) + (zayzy) + (zazzz) andgrad(b) (zbzx) + (zbzy) + (zbzz) u v and w representaverage flow velocity components in Cartesian coordinatesx y and z respectively (ms) Fx Fy and Fz stand for bodyforces (N) p is pressure (pa) t is time (s) and ρ represents thedensity of fluid (kgm3)

+e standard k-ε models include turbulent energyequation and turbulent dissipation equation +e equationsfor the turbulent kinetic energy and the dissipation rate ofthe standard k-ε model are defined as follows

ρdk

dt

z

zxi

μ +μt

σk

1113888 1113889zk

zxi

1113890 1113891 + Gk + Gb minus ρα (23)

ρdεdt

μ +μt

σε1113888 1113889

zεzxi

1113890 1113891 + C1εεk

Gk + C3εGb( 1113857 minus C2ερε2

k

(24)

where k is the turbulent kinetic energy (m2s2) α is turbulentenergy dissipation rate (kgmiddotm2s3) Gk is turbulent energycaused by average velocity gradient Gb is turbulent energycaused by buoyancy and μt is fluid turbulent viscosity (Nmiddotsm2) In this paper σk 139 σα 139 C1ε 142 C2ε 168and C3ε 009

232 Model Establishment ANSYS DesignModeler isemployed to create the portable pillar-shaped flume ge-ometry models with three different contraction ratios Inorder to make the flow pattern of the simulated channel assimilar as possible to the actual experimental results sim-ulate according to the geometry of the model experiments+e bottom center point of the upstream section of the flumeis selected as the coordinate origin the positive direction ofthe X-axis is the direction of the water flow the positivedirection of the Y-axis is the direction of the left bank of thechannel and the negative direction of the Z-axis is thedirection of gravity acceleration

233 Mesh Generation and Boundary ConditionsANSYS meshing is utilized to establish meshes for the flowdomain +e model uses hexahedron structured grids with aunit size of 002m Due to the drastic changes in the waterflow conditions near the portable pillar-shaped flume a localgrid encryption process is employed to simulate the waterflow conditions near the flume more accurately and the gridunit size is set at 001m

+e boundary conditions of the model are set accordingto the actual conditions of the experiment +e inlet is di-vided into a lower water inlet (inlet 1) and an upper air inlet(inlet 2)+e type of the water inlet is set at velocity inlet andthe air inlet is set at pressure inlet the outlet is set at pressureoutlet (pressure-outlet) and the wall boundary (wall) se-lected has no slip option According to the actual situation ofthe model experiment the roughness (roughness height) isset at 0000011m +e boundary conditions of the flumemodel are displayed in Figure 4

3 Results and Discussion

31 Verification of the Numerical Simulation Many re-searchers have verified that Fluent software can be utilizedfor the simulation of flow measuring flumes [34] In order tofurther validate the reliability of the simulation the nu-merical data are compared with the experimental results of

Shock and Vibration 5

water flow patterns and water depths along the water pathAccording to Figure 5 by comparing the measured andsimulated flow patterns the simulation data are almostconsistent with the experimental results of the water flowpattern

+e simulated and experimental results of the free watersurface line are also compared in Figure 6 It is obvious thatthe flow in the upstream section of the portable pillar-shapedflume is relatively smooth and the flow direction is relativelyparallel After entering the contraction section the watersurface slowly falls and it drops sharply near the down-stream section of the throat At the same time the watersurface fluctuates strongly +e results demonstrate that thesimulation data are consistent with the experimental resultswith a maximum and average error of 865 and 345respectively+erefore we can conclude that Fluent softwarecan reflect the hydraulic characteristics of the flumeaccurately

32 Discharge Calculation Formula and Its AccuracyEquation (24) is used to calculate the flow rate of the portablepillar-shaped flume To determine constants a and n in theequation one may take the logarithm of both sides ofequation (24) to derive

LnKc

Bc

1113888 1113889 Ln(a) + nLnH

Bc

1113888 1113889 (25)

+e 36 sets of experimental data ie KcBc and HBcmeasured in the portable pillar-shaped flumes with threecontraction ratios are plotted on double logarithmic coor-dinates as shown in Figure 7 All the test data show a verygood correlation regardless of the contraction ratio Ourresult is similar to those of Samani Magallanez BaiamonteFerro (SMBF) flume [35] and triangular central baffle flume[19]

Plotting of the experimental pairs of Ln(KcBc) andLn(HBc) in Figure 7 revealed that the stage-dischargecurves corresponding to different values lie on a single curveEquation (25) is fitted to the experimental data by using an aand n value of 07151 and 10377 respectively and the squareof the correlation coefficient (R2) is equal to 099895

Consequently the following stage-discharge relationship iscalibrated using all the available experimental data

Q 18939B09943c H

15566 (26)

In order to check the measuring accuracy of the flumethe measured upstream water depth is substituted intoequation (26) and the calculated data (Q1) are comparedwith the measured results (Q2) of the electromagneticflowmeter as presented in Table 3 +e maximum relativeerror in the flow measurement of the portable pillar-shapedflume is 474 and the relative error in the average currentmeasurement is 172 which proves that the measurementaccuracy of the portable pillar-shaped flume examinedherein can meet the actual requirements of water mea-surement and its flow calculation formula is simple ac-curate and convenient

33 e Froude Number and Submergence Limits +eFroude number is of great significance in analyzing thehydraulic characteristics of the flow of open channels It is acriterion for judging the flow pattern of open channels andcan be used as an important indicator of the water mea-surement performance of a flume Its calculation formula isexpressed in

Fr v

gh

1113969 (27)

where v is the average velocity of the channel section (ms) grepresents the acceleration of gravity (ms2) and h stands forthe average water depth of the section (m)

Herein various Froude numbers are figured out usingthe experiments based on three different contraction ratiosand 12 discharge rates Figure 8 illustrates the distribution ofthe Froude number in the portable pillar-shaped flume alongthe path when the contraction ratio is 05 and the flow rate is15 Ls From an energy point of view the Froude numberrepresents two times the square of the ratio of the averagekinetic energy to the average potential energy per unit massof liquid in the cross-section From the entrance of the flumeto the front of the diffusion section of the flume the watersurface shows a downward trend the average potential

Portable pillar-shaped flumeInlet 2

Outlet

Inlet 1

Wall05mMesh size

1cm times 1cm times 1cm

3mMesh size

2cm times 2cm times 2cm

85mMesh size

2cm times 2cm times 2cm

Figure 4 Model and boundary conditions of the portable pillar-shaped flume

6 Shock and Vibration

energy gradually decreases and the average kinetic energyincreases so the Froude number gradually rises However inthe second half of the trough exit the water surface has arising trend the average potential energy gradually in-creases and the average kinetic energy gradually drops sothe Froude number gradually falls

+e Froude number in front of the flume is one of theimportant factors affecting the flow measurement accuracyof the water flume An excessively large Froude number infront of the flume may cause large fluctuations in the watersurface in the upstream section of the flume affect theaccuracy of the water depth measurement and reduce theaccuracy of the current measurement Generally when theflow is measured in an open channel the Froude number in

front of the flume is less than 05 Froude numbers in Section1 with different contraction ratios and discharge rates areshown in Figure 9 It can be inferred from Figure 9 that allFroude numbers are less than 04 thereby meeting the re-quirements for measuring the flow of flume also the Froudenumber is proportional to the contraction ratio Moreoverat the same contraction ratio the Froude number risesslightly as the discharge rate increases

+e critical submergence is an important indicator ofmeasuring the performance of a flume and is defined as theratio of the downstream depth of the flume to the upstreamdepth of the flume

S hd

hu

(28)

where hu is the water depth in the upstream section of theflume (m) and hd is the water depth in the downstreamsection of the flume (m)

By sorting and analyzing the test data the relationshipbetween the critical submergence of the portable pillar-shaped flume and the discharge rate can be figured out as

Portable pillar-shaped flume

Flow direction

(a)

Watervolume fractionVolume rendering 1

0000 0250 0500 0750 1000

(b)

Figure 5 Comparison of the simulated and experimental flow patterns (a) profile of the measured flow pattern (b) profile of the simulatedflow pattern

024022020018016014012010008006004002000

Distance from flume section 2 (m)

Simulatedresults

Experimentalresults Q

907Ls1294Ls1705Ls2105Ls2506Ls

503Ls

ndash2 ndash1 0 1 2 3 4 5

Wat

er d

epth

(m)

Figure 6 Comparison of the simulated and experimental results offree water surface line

ε = 05ε = 06

ndash15

ndash10

ndash05

00

05

Ln (K

cBc)

ndash05 05ndash10 1000Ln (HBc)

Equation 25ε = 04

Figure 7 Relationship between Ln(KcBc) and Ln(HBc)

Shock and Vibration 7

tabulated in Table 4 It is clear that under the same flowconditions the critical submergence rises with an increase inthe contraction ratio Moreover according to Table 4 themaximum critical submergence can reach 096 and theaverage critical submergence is 085 +e maximum criticalsubmergence of a cylindrical flow measuring flume is 84which indicates that the critical submergence of the portablepillar-shaped flume is high under different flow conditionsand at different contraction ratios thus it has a large freeoutflow range

34 Head Loss +e measuring flumes are not allowed tohave a large head loss otherwise they lead to the excessivedecantation and silt deformation of the channel When theflow passes through the portable pillar-shaped flume thecross-section of the passing water shrinks changing theoverflow of the water from slow to rapid and then to slow asshown in Figure 10 +is results in a large head loss which ismuch greater than the head loss along the way+e head losscan be calculated in two ways one is the difference between

the total head losses of the first and last sections of the flumeknown as the head loss of the flume the other is the dif-ference between the total head losses of the upstream sectionof the flume and the section after the water jump known asthe head loss +is study found that the head loss of themeasuring flume is mainly caused by the water jump afterthe throat section and it is more meaningful to examine thehead loss between the upstream section and the downstreampostjump section therefore we choose the second method+e total head loss of the section is calculated by

HTotal z +c

p+

v2

2g (29)

where HTotal z c p v and g represent total head (m) theheight (m) of the free surface from the bottom of thechannel unit weight (Nm3) pressure (pa) velocity (ms)and acceleration (ms2) due to gravity respectively

+e head loss in this paper is defined as the difference inthe head loss of upstream Section 2 and that of downstreamSection 12 +e head loss is expressed by

hw Hu minus Hd (30)

where hw is head loss (m)Hu is the total head loss of Section2 (m) and Hd is total head loss of Section 12 (m)

To analyze the head loss of the portable pillar-shapedflume the development of cross-sectional velocity distri-butions and turbulent kinetic energy dissipation are simu-lated for various typical sections

Turbulent energy dissipation rate refers to the rate atwhich turbulent flow energy is continuously converted intomolecular kinetic energy by internal friction under theaction of molecular viscous forces Studying the turbulentenergy dissipation is of great significance to the flow mea-surement process and it provides a basis for the evaluationof and improvement in the measuring flume Figure 11depicts the development of cross-sectional turbulent ki-netic energy dissipation rate in six typical sections (as de-fined in Figure 2) of the portable pillar-shaped flume whenthe flow rate is 15 Ls Figure 11(a) shows that the flow of theupstream section of the portable pillar-shaped flume is veryslow the speed of water is less than 1ms the dissipation isconcentrated in the area near the wall and bottom and allthe energy dissipation rates are lower than 0004m2middotsminus3 Atthe inlet cross-section of the flume affected by the centralcolumn the water surface is high and the dissipation isconcentrated in the middle +e maximum turbulent kineticenergy dissipation rate is 002m2middotsminus3 as displayed inFigure 11(b) At the throat (Figure 11(c)) the cross-sectionof the water decreases the speed of the water increases andthe dissipation is concentrated in the area near the wall andbottom +e maximum turbulent energy dissipation rate is003m2middotsminus3 Figure 11(d) illustrates the turbulent kineticenergy dissipation in the outlet section of the flume wherethe section velocity reaches the maximum and the turbulentkinetic energy dissipation rate increases to 025m2middotsminus3Figure 11(e) shows the hydraulic jumping phenomenon inthe downstream section of the flume Turbulent kineticenergy dissipation is mainly concentrated on the surface of

Table 3 Comparison of the measured and calculated flow rates atdifferent contraction ratios

ε H (cm) Q1 (Ls) Q2 (Ls) |Error| ()

04

818 504 520 3321018 703 731 4071203 906 948 4741360 1114 1148 3061508 1294 1348 4161646 1517 1545 1881771 1708 1732 1361892 1897 1919 1162001 2101 2094 0352131 2306 2310 0182218 2514 2458 2222320 2703 2636 246

05

691 503 494 182865 704 701 0551018 907 903 0441153 1112 1096 1431275 1294 1282 1001398 1515 1479 2371519 1705 1683 1271625 1897 1869 1451718 2105 2039 3161841 2308 2270 1641931 2506 2445 2402018 2708 2619 330

06

622 502 498 085771 703 696 098910 907 900 0751032 1115 1095 1751152 1300 1300 0021248 1514 1472 2791361 1705 1685 1201471 1901 1902 0041557 2102 2077 1181656 2303 2287 0701744 2508 2478 1191837 2704 2687 062

8 Shock and Vibration

the water flow with a maximum rate of 021m2middotsminus3 +e flowof the postjump section tends to be stable and its distri-bution of the turbulent kinetic energy dissipation is similarto but higher than that of the upstream section Figure 11(f )shows that due to the hydraulic jump the total dissipationrate of the turbulent kinetic energy in the diffusion section isquite high and the dissipation is concentrated in the areanear the water surface where the hydraulic jump occurs

Furthermore airfoil pillar-shaped flumes [36] with threecontraction ratios were tested and simulated in the same

way and the head losses of the portable pillar-shaped flumeand airfoil pillar-shaped flume were compared as presentedin Figure 12 It can be seen that the head loss of the portablepillar-shaped flume is significantly lower than that of theairfoil pillar-shaped flume Similarly Figure 13 clearly showsthat the water head loss of the portable pillar-shaped flumeas a percentage of the total upstream water head loss issignificantly smaller than that of the airfoil pillar-shapedflume

We also found out that there is a good linear relationship(R2 097316) between the upstream water depth and headloss by sorting the test data (Figure 14) +e followingequation can be well fitted to the test data

hw 03637H minus 01282ε + 00539 (31)

where hw is head loss (m) H is the water depth in theupstream section of the flume (m) and ε is contraction ratio

Compared with the airfoil pillar-shaped flume the headloss of the portable pillar-shaped flume is smaller especiallyin the case of large contraction ratios

35 Upstream Backwater Height In the current work thebackwater height is defined as the value added to the originalchannel water depth after the installation of a flume and theoriginal channel water depth is measured through thechannel under the same flow conditions when the flume isnot installed

+e variations in the backwater height of the portablepillar-shaped flume and airfoil pillar-shaped flume versusthe discharge rate are delineated in Figure 15 +e pre-liminary analysis of the experimental data shows that thebackwater height of the portable pillar-shaped flume is in-versely proportional to the contraction ratio and directlyproportional to the discharge rate of the flume Figure 15clearly indicates that the backwater height of the portablepillar-shaped flume is smaller than that of the airfoil pillar-shaped flume which makes it more suitable for applicationin the constructed channels

36 Velocity Distribution Velocity distribution is an im-portant basis for studying the hydraulic characteristics of aflume Exploiting longitudinal time-averaged velocity dis-tribution for describing the flow of water along the flowdirection can reflect the regular pattern of the flow in theportable pillar-shaped flume

Figure 16 displays the simulated velocity distribution ofthe longitudinal flow of the water under free flow conditionsat a flow rate of 15 Ls and a contraction ratio of 05According to Figure 16(a) because the water flow in the

000 021 043 064 085 106 128 149 170 192 213

Fr

Figure 8 +e distribution of the Froude number in the portable pillar-shaped flume

5 10 15 20 25 30Q (Ls)

000

005

010

015

020

025

030

035

040

045

050

Fr

ε = 06

ε = 04ε = 05

Figure 9 +e Froude number at different contraction ratios anddischarge rates in Section 1

Table 4 Submergence limits at different contraction ratios anddischarge rates

ε Q (Ls) S ε Q (Ls) S ε Q (Ls) S

04

504 085

05

503 093

06

502 096703 088 704 088 703 093906 083 907 092 907 0941114 073 1112 088 1115 0861294 077 1294 087 1300 0871517 076 1515 086 1514 0901708 081 1705 085 1705 0901897 082 1897 083 1901 0912101 078 2105 086 2102 0842306 076 2308 084 2303 0862514 081 2506 083 2508 0872703 080 2708 080 2704 085

Shock and Vibration 9

Velocity (mmiddotsndash1)

000 035 070 105 141

Figure 10 +e streamline distribution in the portable pillar-shaped flume

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Turbulent kinetic energydissipation rate

Section 1

0000 0001 0002 0003 0004

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

Figure 11 Continued

10 Shock and Vibration

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

water flow patterns and water depths along the water pathAccording to Figure 5 by comparing the measured andsimulated flow patterns the simulation data are almostconsistent with the experimental results of the water flowpattern

+e simulated and experimental results of the free watersurface line are also compared in Figure 6 It is obvious thatthe flow in the upstream section of the portable pillar-shapedflume is relatively smooth and the flow direction is relativelyparallel After entering the contraction section the watersurface slowly falls and it drops sharply near the down-stream section of the throat At the same time the watersurface fluctuates strongly +e results demonstrate that thesimulation data are consistent with the experimental resultswith a maximum and average error of 865 and 345respectively+erefore we can conclude that Fluent softwarecan reflect the hydraulic characteristics of the flumeaccurately

32 Discharge Calculation Formula and Its AccuracyEquation (24) is used to calculate the flow rate of the portablepillar-shaped flume To determine constants a and n in theequation one may take the logarithm of both sides ofequation (24) to derive

LnKc

Bc

1113888 1113889 Ln(a) + nLnH

Bc

1113888 1113889 (25)

+e 36 sets of experimental data ie KcBc and HBcmeasured in the portable pillar-shaped flumes with threecontraction ratios are plotted on double logarithmic coor-dinates as shown in Figure 7 All the test data show a verygood correlation regardless of the contraction ratio Ourresult is similar to those of Samani Magallanez BaiamonteFerro (SMBF) flume [35] and triangular central baffle flume[19]

Plotting of the experimental pairs of Ln(KcBc) andLn(HBc) in Figure 7 revealed that the stage-dischargecurves corresponding to different values lie on a single curveEquation (25) is fitted to the experimental data by using an aand n value of 07151 and 10377 respectively and the squareof the correlation coefficient (R2) is equal to 099895

Consequently the following stage-discharge relationship iscalibrated using all the available experimental data

Q 18939B09943c H

15566 (26)

In order to check the measuring accuracy of the flumethe measured upstream water depth is substituted intoequation (26) and the calculated data (Q1) are comparedwith the measured results (Q2) of the electromagneticflowmeter as presented in Table 3 +e maximum relativeerror in the flow measurement of the portable pillar-shapedflume is 474 and the relative error in the average currentmeasurement is 172 which proves that the measurementaccuracy of the portable pillar-shaped flume examinedherein can meet the actual requirements of water mea-surement and its flow calculation formula is simple ac-curate and convenient

33 e Froude Number and Submergence Limits +eFroude number is of great significance in analyzing thehydraulic characteristics of the flow of open channels It is acriterion for judging the flow pattern of open channels andcan be used as an important indicator of the water mea-surement performance of a flume Its calculation formula isexpressed in

Fr v

gh

1113969 (27)

where v is the average velocity of the channel section (ms) grepresents the acceleration of gravity (ms2) and h stands forthe average water depth of the section (m)

Herein various Froude numbers are figured out usingthe experiments based on three different contraction ratiosand 12 discharge rates Figure 8 illustrates the distribution ofthe Froude number in the portable pillar-shaped flume alongthe path when the contraction ratio is 05 and the flow rate is15 Ls From an energy point of view the Froude numberrepresents two times the square of the ratio of the averagekinetic energy to the average potential energy per unit massof liquid in the cross-section From the entrance of the flumeto the front of the diffusion section of the flume the watersurface shows a downward trend the average potential

Portable pillar-shaped flumeInlet 2

Outlet

Inlet 1

Wall05mMesh size

1cm times 1cm times 1cm

3mMesh size

2cm times 2cm times 2cm

85mMesh size

2cm times 2cm times 2cm

Figure 4 Model and boundary conditions of the portable pillar-shaped flume

6 Shock and Vibration

energy gradually decreases and the average kinetic energyincreases so the Froude number gradually rises However inthe second half of the trough exit the water surface has arising trend the average potential energy gradually in-creases and the average kinetic energy gradually drops sothe Froude number gradually falls

+e Froude number in front of the flume is one of theimportant factors affecting the flow measurement accuracyof the water flume An excessively large Froude number infront of the flume may cause large fluctuations in the watersurface in the upstream section of the flume affect theaccuracy of the water depth measurement and reduce theaccuracy of the current measurement Generally when theflow is measured in an open channel the Froude number in

front of the flume is less than 05 Froude numbers in Section1 with different contraction ratios and discharge rates areshown in Figure 9 It can be inferred from Figure 9 that allFroude numbers are less than 04 thereby meeting the re-quirements for measuring the flow of flume also the Froudenumber is proportional to the contraction ratio Moreoverat the same contraction ratio the Froude number risesslightly as the discharge rate increases

+e critical submergence is an important indicator ofmeasuring the performance of a flume and is defined as theratio of the downstream depth of the flume to the upstreamdepth of the flume

S hd

hu

(28)

where hu is the water depth in the upstream section of theflume (m) and hd is the water depth in the downstreamsection of the flume (m)

By sorting and analyzing the test data the relationshipbetween the critical submergence of the portable pillar-shaped flume and the discharge rate can be figured out as

Portable pillar-shaped flume

Flow direction

(a)

Watervolume fractionVolume rendering 1

0000 0250 0500 0750 1000

(b)

Figure 5 Comparison of the simulated and experimental flow patterns (a) profile of the measured flow pattern (b) profile of the simulatedflow pattern

024022020018016014012010008006004002000

Distance from flume section 2 (m)

Simulatedresults

Experimentalresults Q

907Ls1294Ls1705Ls2105Ls2506Ls

503Ls

ndash2 ndash1 0 1 2 3 4 5

Wat

er d

epth

(m)

Figure 6 Comparison of the simulated and experimental results offree water surface line

ε = 05ε = 06

ndash15

ndash10

ndash05

00

05

Ln (K

cBc)

ndash05 05ndash10 1000Ln (HBc)

Equation 25ε = 04

Figure 7 Relationship between Ln(KcBc) and Ln(HBc)

Shock and Vibration 7

tabulated in Table 4 It is clear that under the same flowconditions the critical submergence rises with an increase inthe contraction ratio Moreover according to Table 4 themaximum critical submergence can reach 096 and theaverage critical submergence is 085 +e maximum criticalsubmergence of a cylindrical flow measuring flume is 84which indicates that the critical submergence of the portablepillar-shaped flume is high under different flow conditionsand at different contraction ratios thus it has a large freeoutflow range

34 Head Loss +e measuring flumes are not allowed tohave a large head loss otherwise they lead to the excessivedecantation and silt deformation of the channel When theflow passes through the portable pillar-shaped flume thecross-section of the passing water shrinks changing theoverflow of the water from slow to rapid and then to slow asshown in Figure 10 +is results in a large head loss which ismuch greater than the head loss along the way+e head losscan be calculated in two ways one is the difference between

the total head losses of the first and last sections of the flumeknown as the head loss of the flume the other is the dif-ference between the total head losses of the upstream sectionof the flume and the section after the water jump known asthe head loss +is study found that the head loss of themeasuring flume is mainly caused by the water jump afterthe throat section and it is more meaningful to examine thehead loss between the upstream section and the downstreampostjump section therefore we choose the second method+e total head loss of the section is calculated by

HTotal z +c

p+

v2

2g (29)

where HTotal z c p v and g represent total head (m) theheight (m) of the free surface from the bottom of thechannel unit weight (Nm3) pressure (pa) velocity (ms)and acceleration (ms2) due to gravity respectively

+e head loss in this paper is defined as the difference inthe head loss of upstream Section 2 and that of downstreamSection 12 +e head loss is expressed by

hw Hu minus Hd (30)

where hw is head loss (m)Hu is the total head loss of Section2 (m) and Hd is total head loss of Section 12 (m)

To analyze the head loss of the portable pillar-shapedflume the development of cross-sectional velocity distri-butions and turbulent kinetic energy dissipation are simu-lated for various typical sections

Turbulent energy dissipation rate refers to the rate atwhich turbulent flow energy is continuously converted intomolecular kinetic energy by internal friction under theaction of molecular viscous forces Studying the turbulentenergy dissipation is of great significance to the flow mea-surement process and it provides a basis for the evaluationof and improvement in the measuring flume Figure 11depicts the development of cross-sectional turbulent ki-netic energy dissipation rate in six typical sections (as de-fined in Figure 2) of the portable pillar-shaped flume whenthe flow rate is 15 Ls Figure 11(a) shows that the flow of theupstream section of the portable pillar-shaped flume is veryslow the speed of water is less than 1ms the dissipation isconcentrated in the area near the wall and bottom and allthe energy dissipation rates are lower than 0004m2middotsminus3 Atthe inlet cross-section of the flume affected by the centralcolumn the water surface is high and the dissipation isconcentrated in the middle +e maximum turbulent kineticenergy dissipation rate is 002m2middotsminus3 as displayed inFigure 11(b) At the throat (Figure 11(c)) the cross-sectionof the water decreases the speed of the water increases andthe dissipation is concentrated in the area near the wall andbottom +e maximum turbulent energy dissipation rate is003m2middotsminus3 Figure 11(d) illustrates the turbulent kineticenergy dissipation in the outlet section of the flume wherethe section velocity reaches the maximum and the turbulentkinetic energy dissipation rate increases to 025m2middotsminus3Figure 11(e) shows the hydraulic jumping phenomenon inthe downstream section of the flume Turbulent kineticenergy dissipation is mainly concentrated on the surface of

Table 3 Comparison of the measured and calculated flow rates atdifferent contraction ratios

ε H (cm) Q1 (Ls) Q2 (Ls) |Error| ()

04

818 504 520 3321018 703 731 4071203 906 948 4741360 1114 1148 3061508 1294 1348 4161646 1517 1545 1881771 1708 1732 1361892 1897 1919 1162001 2101 2094 0352131 2306 2310 0182218 2514 2458 2222320 2703 2636 246

05

691 503 494 182865 704 701 0551018 907 903 0441153 1112 1096 1431275 1294 1282 1001398 1515 1479 2371519 1705 1683 1271625 1897 1869 1451718 2105 2039 3161841 2308 2270 1641931 2506 2445 2402018 2708 2619 330

06

622 502 498 085771 703 696 098910 907 900 0751032 1115 1095 1751152 1300 1300 0021248 1514 1472 2791361 1705 1685 1201471 1901 1902 0041557 2102 2077 1181656 2303 2287 0701744 2508 2478 1191837 2704 2687 062

8 Shock and Vibration

the water flow with a maximum rate of 021m2middotsminus3 +e flowof the postjump section tends to be stable and its distri-bution of the turbulent kinetic energy dissipation is similarto but higher than that of the upstream section Figure 11(f )shows that due to the hydraulic jump the total dissipationrate of the turbulent kinetic energy in the diffusion section isquite high and the dissipation is concentrated in the areanear the water surface where the hydraulic jump occurs

Furthermore airfoil pillar-shaped flumes [36] with threecontraction ratios were tested and simulated in the same

way and the head losses of the portable pillar-shaped flumeand airfoil pillar-shaped flume were compared as presentedin Figure 12 It can be seen that the head loss of the portablepillar-shaped flume is significantly lower than that of theairfoil pillar-shaped flume Similarly Figure 13 clearly showsthat the water head loss of the portable pillar-shaped flumeas a percentage of the total upstream water head loss issignificantly smaller than that of the airfoil pillar-shapedflume

We also found out that there is a good linear relationship(R2 097316) between the upstream water depth and headloss by sorting the test data (Figure 14) +e followingequation can be well fitted to the test data

hw 03637H minus 01282ε + 00539 (31)

where hw is head loss (m) H is the water depth in theupstream section of the flume (m) and ε is contraction ratio

Compared with the airfoil pillar-shaped flume the headloss of the portable pillar-shaped flume is smaller especiallyin the case of large contraction ratios

35 Upstream Backwater Height In the current work thebackwater height is defined as the value added to the originalchannel water depth after the installation of a flume and theoriginal channel water depth is measured through thechannel under the same flow conditions when the flume isnot installed

+e variations in the backwater height of the portablepillar-shaped flume and airfoil pillar-shaped flume versusthe discharge rate are delineated in Figure 15 +e pre-liminary analysis of the experimental data shows that thebackwater height of the portable pillar-shaped flume is in-versely proportional to the contraction ratio and directlyproportional to the discharge rate of the flume Figure 15clearly indicates that the backwater height of the portablepillar-shaped flume is smaller than that of the airfoil pillar-shaped flume which makes it more suitable for applicationin the constructed channels

36 Velocity Distribution Velocity distribution is an im-portant basis for studying the hydraulic characteristics of aflume Exploiting longitudinal time-averaged velocity dis-tribution for describing the flow of water along the flowdirection can reflect the regular pattern of the flow in theportable pillar-shaped flume

Figure 16 displays the simulated velocity distribution ofthe longitudinal flow of the water under free flow conditionsat a flow rate of 15 Ls and a contraction ratio of 05According to Figure 16(a) because the water flow in the

000 021 043 064 085 106 128 149 170 192 213

Fr

Figure 8 +e distribution of the Froude number in the portable pillar-shaped flume

5 10 15 20 25 30Q (Ls)

000

005

010

015

020

025

030

035

040

045

050

Fr

ε = 06

ε = 04ε = 05

Figure 9 +e Froude number at different contraction ratios anddischarge rates in Section 1

Table 4 Submergence limits at different contraction ratios anddischarge rates

ε Q (Ls) S ε Q (Ls) S ε Q (Ls) S

04

504 085

05

503 093

06

502 096703 088 704 088 703 093906 083 907 092 907 0941114 073 1112 088 1115 0861294 077 1294 087 1300 0871517 076 1515 086 1514 0901708 081 1705 085 1705 0901897 082 1897 083 1901 0912101 078 2105 086 2102 0842306 076 2308 084 2303 0862514 081 2506 083 2508 0872703 080 2708 080 2704 085

Shock and Vibration 9

Velocity (mmiddotsndash1)

000 035 070 105 141

Figure 10 +e streamline distribution in the portable pillar-shaped flume

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Turbulent kinetic energydissipation rate

Section 1

0000 0001 0002 0003 0004

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

Figure 11 Continued

10 Shock and Vibration

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

energy gradually decreases and the average kinetic energyincreases so the Froude number gradually rises However inthe second half of the trough exit the water surface has arising trend the average potential energy gradually in-creases and the average kinetic energy gradually drops sothe Froude number gradually falls

+e Froude number in front of the flume is one of theimportant factors affecting the flow measurement accuracyof the water flume An excessively large Froude number infront of the flume may cause large fluctuations in the watersurface in the upstream section of the flume affect theaccuracy of the water depth measurement and reduce theaccuracy of the current measurement Generally when theflow is measured in an open channel the Froude number in

front of the flume is less than 05 Froude numbers in Section1 with different contraction ratios and discharge rates areshown in Figure 9 It can be inferred from Figure 9 that allFroude numbers are less than 04 thereby meeting the re-quirements for measuring the flow of flume also the Froudenumber is proportional to the contraction ratio Moreoverat the same contraction ratio the Froude number risesslightly as the discharge rate increases

+e critical submergence is an important indicator ofmeasuring the performance of a flume and is defined as theratio of the downstream depth of the flume to the upstreamdepth of the flume

S hd

hu

(28)

where hu is the water depth in the upstream section of theflume (m) and hd is the water depth in the downstreamsection of the flume (m)

By sorting and analyzing the test data the relationshipbetween the critical submergence of the portable pillar-shaped flume and the discharge rate can be figured out as

Portable pillar-shaped flume

Flow direction

(a)

Watervolume fractionVolume rendering 1

0000 0250 0500 0750 1000

(b)

Figure 5 Comparison of the simulated and experimental flow patterns (a) profile of the measured flow pattern (b) profile of the simulatedflow pattern

024022020018016014012010008006004002000

Distance from flume section 2 (m)

Simulatedresults

Experimentalresults Q

907Ls1294Ls1705Ls2105Ls2506Ls

503Ls

ndash2 ndash1 0 1 2 3 4 5

Wat

er d

epth

(m)

Figure 6 Comparison of the simulated and experimental results offree water surface line

ε = 05ε = 06

ndash15

ndash10

ndash05

00

05

Ln (K

cBc)

ndash05 05ndash10 1000Ln (HBc)

Equation 25ε = 04

Figure 7 Relationship between Ln(KcBc) and Ln(HBc)

Shock and Vibration 7

tabulated in Table 4 It is clear that under the same flowconditions the critical submergence rises with an increase inthe contraction ratio Moreover according to Table 4 themaximum critical submergence can reach 096 and theaverage critical submergence is 085 +e maximum criticalsubmergence of a cylindrical flow measuring flume is 84which indicates that the critical submergence of the portablepillar-shaped flume is high under different flow conditionsand at different contraction ratios thus it has a large freeoutflow range

34 Head Loss +e measuring flumes are not allowed tohave a large head loss otherwise they lead to the excessivedecantation and silt deformation of the channel When theflow passes through the portable pillar-shaped flume thecross-section of the passing water shrinks changing theoverflow of the water from slow to rapid and then to slow asshown in Figure 10 +is results in a large head loss which ismuch greater than the head loss along the way+e head losscan be calculated in two ways one is the difference between

the total head losses of the first and last sections of the flumeknown as the head loss of the flume the other is the dif-ference between the total head losses of the upstream sectionof the flume and the section after the water jump known asthe head loss +is study found that the head loss of themeasuring flume is mainly caused by the water jump afterthe throat section and it is more meaningful to examine thehead loss between the upstream section and the downstreampostjump section therefore we choose the second method+e total head loss of the section is calculated by

HTotal z +c

p+

v2

2g (29)

where HTotal z c p v and g represent total head (m) theheight (m) of the free surface from the bottom of thechannel unit weight (Nm3) pressure (pa) velocity (ms)and acceleration (ms2) due to gravity respectively

+e head loss in this paper is defined as the difference inthe head loss of upstream Section 2 and that of downstreamSection 12 +e head loss is expressed by

hw Hu minus Hd (30)

where hw is head loss (m)Hu is the total head loss of Section2 (m) and Hd is total head loss of Section 12 (m)

To analyze the head loss of the portable pillar-shapedflume the development of cross-sectional velocity distri-butions and turbulent kinetic energy dissipation are simu-lated for various typical sections

Turbulent energy dissipation rate refers to the rate atwhich turbulent flow energy is continuously converted intomolecular kinetic energy by internal friction under theaction of molecular viscous forces Studying the turbulentenergy dissipation is of great significance to the flow mea-surement process and it provides a basis for the evaluationof and improvement in the measuring flume Figure 11depicts the development of cross-sectional turbulent ki-netic energy dissipation rate in six typical sections (as de-fined in Figure 2) of the portable pillar-shaped flume whenthe flow rate is 15 Ls Figure 11(a) shows that the flow of theupstream section of the portable pillar-shaped flume is veryslow the speed of water is less than 1ms the dissipation isconcentrated in the area near the wall and bottom and allthe energy dissipation rates are lower than 0004m2middotsminus3 Atthe inlet cross-section of the flume affected by the centralcolumn the water surface is high and the dissipation isconcentrated in the middle +e maximum turbulent kineticenergy dissipation rate is 002m2middotsminus3 as displayed inFigure 11(b) At the throat (Figure 11(c)) the cross-sectionof the water decreases the speed of the water increases andthe dissipation is concentrated in the area near the wall andbottom +e maximum turbulent energy dissipation rate is003m2middotsminus3 Figure 11(d) illustrates the turbulent kineticenergy dissipation in the outlet section of the flume wherethe section velocity reaches the maximum and the turbulentkinetic energy dissipation rate increases to 025m2middotsminus3Figure 11(e) shows the hydraulic jumping phenomenon inthe downstream section of the flume Turbulent kineticenergy dissipation is mainly concentrated on the surface of

Table 3 Comparison of the measured and calculated flow rates atdifferent contraction ratios

ε H (cm) Q1 (Ls) Q2 (Ls) |Error| ()

04

818 504 520 3321018 703 731 4071203 906 948 4741360 1114 1148 3061508 1294 1348 4161646 1517 1545 1881771 1708 1732 1361892 1897 1919 1162001 2101 2094 0352131 2306 2310 0182218 2514 2458 2222320 2703 2636 246

05

691 503 494 182865 704 701 0551018 907 903 0441153 1112 1096 1431275 1294 1282 1001398 1515 1479 2371519 1705 1683 1271625 1897 1869 1451718 2105 2039 3161841 2308 2270 1641931 2506 2445 2402018 2708 2619 330

06

622 502 498 085771 703 696 098910 907 900 0751032 1115 1095 1751152 1300 1300 0021248 1514 1472 2791361 1705 1685 1201471 1901 1902 0041557 2102 2077 1181656 2303 2287 0701744 2508 2478 1191837 2704 2687 062

8 Shock and Vibration

the water flow with a maximum rate of 021m2middotsminus3 +e flowof the postjump section tends to be stable and its distri-bution of the turbulent kinetic energy dissipation is similarto but higher than that of the upstream section Figure 11(f )shows that due to the hydraulic jump the total dissipationrate of the turbulent kinetic energy in the diffusion section isquite high and the dissipation is concentrated in the areanear the water surface where the hydraulic jump occurs

Furthermore airfoil pillar-shaped flumes [36] with threecontraction ratios were tested and simulated in the same

way and the head losses of the portable pillar-shaped flumeand airfoil pillar-shaped flume were compared as presentedin Figure 12 It can be seen that the head loss of the portablepillar-shaped flume is significantly lower than that of theairfoil pillar-shaped flume Similarly Figure 13 clearly showsthat the water head loss of the portable pillar-shaped flumeas a percentage of the total upstream water head loss issignificantly smaller than that of the airfoil pillar-shapedflume

We also found out that there is a good linear relationship(R2 097316) between the upstream water depth and headloss by sorting the test data (Figure 14) +e followingequation can be well fitted to the test data

hw 03637H minus 01282ε + 00539 (31)

where hw is head loss (m) H is the water depth in theupstream section of the flume (m) and ε is contraction ratio

Compared with the airfoil pillar-shaped flume the headloss of the portable pillar-shaped flume is smaller especiallyin the case of large contraction ratios

35 Upstream Backwater Height In the current work thebackwater height is defined as the value added to the originalchannel water depth after the installation of a flume and theoriginal channel water depth is measured through thechannel under the same flow conditions when the flume isnot installed

+e variations in the backwater height of the portablepillar-shaped flume and airfoil pillar-shaped flume versusthe discharge rate are delineated in Figure 15 +e pre-liminary analysis of the experimental data shows that thebackwater height of the portable pillar-shaped flume is in-versely proportional to the contraction ratio and directlyproportional to the discharge rate of the flume Figure 15clearly indicates that the backwater height of the portablepillar-shaped flume is smaller than that of the airfoil pillar-shaped flume which makes it more suitable for applicationin the constructed channels

36 Velocity Distribution Velocity distribution is an im-portant basis for studying the hydraulic characteristics of aflume Exploiting longitudinal time-averaged velocity dis-tribution for describing the flow of water along the flowdirection can reflect the regular pattern of the flow in theportable pillar-shaped flume

Figure 16 displays the simulated velocity distribution ofthe longitudinal flow of the water under free flow conditionsat a flow rate of 15 Ls and a contraction ratio of 05According to Figure 16(a) because the water flow in the

000 021 043 064 085 106 128 149 170 192 213

Fr

Figure 8 +e distribution of the Froude number in the portable pillar-shaped flume

5 10 15 20 25 30Q (Ls)

000

005

010

015

020

025

030

035

040

045

050

Fr

ε = 06

ε = 04ε = 05

Figure 9 +e Froude number at different contraction ratios anddischarge rates in Section 1

Table 4 Submergence limits at different contraction ratios anddischarge rates

ε Q (Ls) S ε Q (Ls) S ε Q (Ls) S

04

504 085

05

503 093

06

502 096703 088 704 088 703 093906 083 907 092 907 0941114 073 1112 088 1115 0861294 077 1294 087 1300 0871517 076 1515 086 1514 0901708 081 1705 085 1705 0901897 082 1897 083 1901 0912101 078 2105 086 2102 0842306 076 2308 084 2303 0862514 081 2506 083 2508 0872703 080 2708 080 2704 085

Shock and Vibration 9

Velocity (mmiddotsndash1)

000 035 070 105 141

Figure 10 +e streamline distribution in the portable pillar-shaped flume

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Turbulent kinetic energydissipation rate

Section 1

0000 0001 0002 0003 0004

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

Figure 11 Continued

10 Shock and Vibration

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

tabulated in Table 4 It is clear that under the same flowconditions the critical submergence rises with an increase inthe contraction ratio Moreover according to Table 4 themaximum critical submergence can reach 096 and theaverage critical submergence is 085 +e maximum criticalsubmergence of a cylindrical flow measuring flume is 84which indicates that the critical submergence of the portablepillar-shaped flume is high under different flow conditionsand at different contraction ratios thus it has a large freeoutflow range

34 Head Loss +e measuring flumes are not allowed tohave a large head loss otherwise they lead to the excessivedecantation and silt deformation of the channel When theflow passes through the portable pillar-shaped flume thecross-section of the passing water shrinks changing theoverflow of the water from slow to rapid and then to slow asshown in Figure 10 +is results in a large head loss which ismuch greater than the head loss along the way+e head losscan be calculated in two ways one is the difference between

the total head losses of the first and last sections of the flumeknown as the head loss of the flume the other is the dif-ference between the total head losses of the upstream sectionof the flume and the section after the water jump known asthe head loss +is study found that the head loss of themeasuring flume is mainly caused by the water jump afterthe throat section and it is more meaningful to examine thehead loss between the upstream section and the downstreampostjump section therefore we choose the second method+e total head loss of the section is calculated by

HTotal z +c

p+

v2

2g (29)

where HTotal z c p v and g represent total head (m) theheight (m) of the free surface from the bottom of thechannel unit weight (Nm3) pressure (pa) velocity (ms)and acceleration (ms2) due to gravity respectively

+e head loss in this paper is defined as the difference inthe head loss of upstream Section 2 and that of downstreamSection 12 +e head loss is expressed by

hw Hu minus Hd (30)

where hw is head loss (m)Hu is the total head loss of Section2 (m) and Hd is total head loss of Section 12 (m)

To analyze the head loss of the portable pillar-shapedflume the development of cross-sectional velocity distri-butions and turbulent kinetic energy dissipation are simu-lated for various typical sections

Turbulent energy dissipation rate refers to the rate atwhich turbulent flow energy is continuously converted intomolecular kinetic energy by internal friction under theaction of molecular viscous forces Studying the turbulentenergy dissipation is of great significance to the flow mea-surement process and it provides a basis for the evaluationof and improvement in the measuring flume Figure 11depicts the development of cross-sectional turbulent ki-netic energy dissipation rate in six typical sections (as de-fined in Figure 2) of the portable pillar-shaped flume whenthe flow rate is 15 Ls Figure 11(a) shows that the flow of theupstream section of the portable pillar-shaped flume is veryslow the speed of water is less than 1ms the dissipation isconcentrated in the area near the wall and bottom and allthe energy dissipation rates are lower than 0004m2middotsminus3 Atthe inlet cross-section of the flume affected by the centralcolumn the water surface is high and the dissipation isconcentrated in the middle +e maximum turbulent kineticenergy dissipation rate is 002m2middotsminus3 as displayed inFigure 11(b) At the throat (Figure 11(c)) the cross-sectionof the water decreases the speed of the water increases andthe dissipation is concentrated in the area near the wall andbottom +e maximum turbulent energy dissipation rate is003m2middotsminus3 Figure 11(d) illustrates the turbulent kineticenergy dissipation in the outlet section of the flume wherethe section velocity reaches the maximum and the turbulentkinetic energy dissipation rate increases to 025m2middotsminus3Figure 11(e) shows the hydraulic jumping phenomenon inthe downstream section of the flume Turbulent kineticenergy dissipation is mainly concentrated on the surface of

Table 3 Comparison of the measured and calculated flow rates atdifferent contraction ratios

ε H (cm) Q1 (Ls) Q2 (Ls) |Error| ()

04

818 504 520 3321018 703 731 4071203 906 948 4741360 1114 1148 3061508 1294 1348 4161646 1517 1545 1881771 1708 1732 1361892 1897 1919 1162001 2101 2094 0352131 2306 2310 0182218 2514 2458 2222320 2703 2636 246

05

691 503 494 182865 704 701 0551018 907 903 0441153 1112 1096 1431275 1294 1282 1001398 1515 1479 2371519 1705 1683 1271625 1897 1869 1451718 2105 2039 3161841 2308 2270 1641931 2506 2445 2402018 2708 2619 330

06

622 502 498 085771 703 696 098910 907 900 0751032 1115 1095 1751152 1300 1300 0021248 1514 1472 2791361 1705 1685 1201471 1901 1902 0041557 2102 2077 1181656 2303 2287 0701744 2508 2478 1191837 2704 2687 062

8 Shock and Vibration

the water flow with a maximum rate of 021m2middotsminus3 +e flowof the postjump section tends to be stable and its distri-bution of the turbulent kinetic energy dissipation is similarto but higher than that of the upstream section Figure 11(f )shows that due to the hydraulic jump the total dissipationrate of the turbulent kinetic energy in the diffusion section isquite high and the dissipation is concentrated in the areanear the water surface where the hydraulic jump occurs

Furthermore airfoil pillar-shaped flumes [36] with threecontraction ratios were tested and simulated in the same

way and the head losses of the portable pillar-shaped flumeand airfoil pillar-shaped flume were compared as presentedin Figure 12 It can be seen that the head loss of the portablepillar-shaped flume is significantly lower than that of theairfoil pillar-shaped flume Similarly Figure 13 clearly showsthat the water head loss of the portable pillar-shaped flumeas a percentage of the total upstream water head loss issignificantly smaller than that of the airfoil pillar-shapedflume

We also found out that there is a good linear relationship(R2 097316) between the upstream water depth and headloss by sorting the test data (Figure 14) +e followingequation can be well fitted to the test data

hw 03637H minus 01282ε + 00539 (31)

where hw is head loss (m) H is the water depth in theupstream section of the flume (m) and ε is contraction ratio

Compared with the airfoil pillar-shaped flume the headloss of the portable pillar-shaped flume is smaller especiallyin the case of large contraction ratios

35 Upstream Backwater Height In the current work thebackwater height is defined as the value added to the originalchannel water depth after the installation of a flume and theoriginal channel water depth is measured through thechannel under the same flow conditions when the flume isnot installed

+e variations in the backwater height of the portablepillar-shaped flume and airfoil pillar-shaped flume versusthe discharge rate are delineated in Figure 15 +e pre-liminary analysis of the experimental data shows that thebackwater height of the portable pillar-shaped flume is in-versely proportional to the contraction ratio and directlyproportional to the discharge rate of the flume Figure 15clearly indicates that the backwater height of the portablepillar-shaped flume is smaller than that of the airfoil pillar-shaped flume which makes it more suitable for applicationin the constructed channels

36 Velocity Distribution Velocity distribution is an im-portant basis for studying the hydraulic characteristics of aflume Exploiting longitudinal time-averaged velocity dis-tribution for describing the flow of water along the flowdirection can reflect the regular pattern of the flow in theportable pillar-shaped flume

Figure 16 displays the simulated velocity distribution ofthe longitudinal flow of the water under free flow conditionsat a flow rate of 15 Ls and a contraction ratio of 05According to Figure 16(a) because the water flow in the

000 021 043 064 085 106 128 149 170 192 213

Fr

Figure 8 +e distribution of the Froude number in the portable pillar-shaped flume

5 10 15 20 25 30Q (Ls)

000

005

010

015

020

025

030

035

040

045

050

Fr

ε = 06

ε = 04ε = 05

Figure 9 +e Froude number at different contraction ratios anddischarge rates in Section 1

Table 4 Submergence limits at different contraction ratios anddischarge rates

ε Q (Ls) S ε Q (Ls) S ε Q (Ls) S

04

504 085

05

503 093

06

502 096703 088 704 088 703 093906 083 907 092 907 0941114 073 1112 088 1115 0861294 077 1294 087 1300 0871517 076 1515 086 1514 0901708 081 1705 085 1705 0901897 082 1897 083 1901 0912101 078 2105 086 2102 0842306 076 2308 084 2303 0862514 081 2506 083 2508 0872703 080 2708 080 2704 085

Shock and Vibration 9

Velocity (mmiddotsndash1)

000 035 070 105 141

Figure 10 +e streamline distribution in the portable pillar-shaped flume

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Turbulent kinetic energydissipation rate

Section 1

0000 0001 0002 0003 0004

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

Figure 11 Continued

10 Shock and Vibration

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

the water flow with a maximum rate of 021m2middotsminus3 +e flowof the postjump section tends to be stable and its distri-bution of the turbulent kinetic energy dissipation is similarto but higher than that of the upstream section Figure 11(f )shows that due to the hydraulic jump the total dissipationrate of the turbulent kinetic energy in the diffusion section isquite high and the dissipation is concentrated in the areanear the water surface where the hydraulic jump occurs

Furthermore airfoil pillar-shaped flumes [36] with threecontraction ratios were tested and simulated in the same

way and the head losses of the portable pillar-shaped flumeand airfoil pillar-shaped flume were compared as presentedin Figure 12 It can be seen that the head loss of the portablepillar-shaped flume is significantly lower than that of theairfoil pillar-shaped flume Similarly Figure 13 clearly showsthat the water head loss of the portable pillar-shaped flumeas a percentage of the total upstream water head loss issignificantly smaller than that of the airfoil pillar-shapedflume

We also found out that there is a good linear relationship(R2 097316) between the upstream water depth and headloss by sorting the test data (Figure 14) +e followingequation can be well fitted to the test data

hw 03637H minus 01282ε + 00539 (31)

where hw is head loss (m) H is the water depth in theupstream section of the flume (m) and ε is contraction ratio

Compared with the airfoil pillar-shaped flume the headloss of the portable pillar-shaped flume is smaller especiallyin the case of large contraction ratios

35 Upstream Backwater Height In the current work thebackwater height is defined as the value added to the originalchannel water depth after the installation of a flume and theoriginal channel water depth is measured through thechannel under the same flow conditions when the flume isnot installed

+e variations in the backwater height of the portablepillar-shaped flume and airfoil pillar-shaped flume versusthe discharge rate are delineated in Figure 15 +e pre-liminary analysis of the experimental data shows that thebackwater height of the portable pillar-shaped flume is in-versely proportional to the contraction ratio and directlyproportional to the discharge rate of the flume Figure 15clearly indicates that the backwater height of the portablepillar-shaped flume is smaller than that of the airfoil pillar-shaped flume which makes it more suitable for applicationin the constructed channels

36 Velocity Distribution Velocity distribution is an im-portant basis for studying the hydraulic characteristics of aflume Exploiting longitudinal time-averaged velocity dis-tribution for describing the flow of water along the flowdirection can reflect the regular pattern of the flow in theportable pillar-shaped flume

Figure 16 displays the simulated velocity distribution ofthe longitudinal flow of the water under free flow conditionsat a flow rate of 15 Ls and a contraction ratio of 05According to Figure 16(a) because the water flow in the

000 021 043 064 085 106 128 149 170 192 213

Fr

Figure 8 +e distribution of the Froude number in the portable pillar-shaped flume

5 10 15 20 25 30Q (Ls)

000

005

010

015

020

025

030

035

040

045

050

Fr

ε = 06

ε = 04ε = 05

Figure 9 +e Froude number at different contraction ratios anddischarge rates in Section 1

Table 4 Submergence limits at different contraction ratios anddischarge rates

ε Q (Ls) S ε Q (Ls) S ε Q (Ls) S

04

504 085

05

503 093

06

502 096703 088 704 088 703 093906 083 907 092 907 0941114 073 1112 088 1115 0861294 077 1294 087 1300 0871517 076 1515 086 1514 0901708 081 1705 085 1705 0901897 082 1897 083 1901 0912101 078 2105 086 2102 0842306 076 2308 084 2303 0862514 081 2506 083 2508 0872703 080 2708 080 2704 085

Shock and Vibration 9

Velocity (mmiddotsndash1)

000 035 070 105 141

Figure 10 +e streamline distribution in the portable pillar-shaped flume

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Turbulent kinetic energydissipation rate

Section 1

0000 0001 0002 0003 0004

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

Figure 11 Continued

10 Shock and Vibration

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

Velocity (mmiddotsndash1)

000 035 070 105 141

Figure 10 +e streamline distribution in the portable pillar-shaped flume

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Turbulent kinetic energydissipation rate

Section 1

0000 0001 0002 0003 0004

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

Figure 11 Continued

10 Shock and Vibration

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

Turbulent kinetic energydissipation rate

0000 0005 0010 0015 0020

Section 2

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(b)

Turbulent kinetic energydissipation rate

Section 5

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0007 0015 0022 0030

(c)

Figure 11 Continued

Shock and Vibration 11

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

Turbulent kinetic energydissipation rate

Section 7

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

0000 0063 0125 0188 0250

(d)

Turbulent kinetic energydissipation rate

0000 0052 0105 0158 0210

Section 12

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(e)

Figure 11 Continued

12 Shock and Vibration

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

upstream section of the flume is gentle the flow in the frontof the portable pillar-shaped flume is relatively slow and thevelocity distribution is relatively uniform Furthermore the

time-averaged flow velocity of the water is larger in themiddle of the section than on the side wall and the max-imum time-averaged flow velocity is achieved near the water

Turbulent kinetic energydissipation rate

0000 0007 0015 0022 0030

Section 14

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 11 Development of cross-sectional turbulent kinetic energy dissipation rate (unit m2middotsminus3)

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Hea

d lo

ss (c

m)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 12 Relationship between the head loss and flow rate atdifferent contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

05 10 15

Q (Ls)20 25 30

Hea

d lo

ss p

erce

ntag

e (

)

5

10

15

20

25

30

35

40

45

50

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 13 Relationship between the percentage of head loss andflow rate at different contraction ratios

Shock and Vibration 13

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

surface Figure 16(b) clearly illustrates the velocity distri-bution of the water flow in the first section (Section 2) of theflume and the velocity of the intermediate water flow is closeto zero Affected by the central pillar the water flow velocitygradually increases from the central pillar to both sidesreaching the maximum value between the central pillar andthe side wall when entering the contraction section of theportable pillar-shaped flume As shown in Figure 16(c) theflow velocity distribution gradually becomes uneven due tothe gradual decrease of the overcurrent section the gradualincrease in the speed of water and the deflection of thestreamline due to the inertia effect Figure 16(d)

demonstrates that the water depth in the outlet section ofthe flume drops and the flow velocity further rises Also themaximum flow velocity is achieved near the water surfaceFigure 16(e) also depicts the flow velocity distribution in thedownstream section of the flume Under the influence of theportable pillar-shaped flume the flow direction of the waterflowing out of the flume is deflected which causes the waterflowing through the flume to diffuse converge and form awater jump After the water jump the flow velocity becomesuniform and the maximum velocity is obtained in themiddle and lower parts of the flow as displayed inFigure 16(f )

Equation 31 Experimental results

000

005 010 015H (m)

020 025

h w (m

)002

004

006

008

010

012

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 14 Relationship between the head loss (hw) and the upstream water depth (H) at different contraction ratios

Protable pillar-shaped flume Airfoil pillar-shaped flume

00 5 10 15

Q (Ls)20 25 30

Back

wat

er h

eigh

t (cm

)

123456789

101112

ε = 04ε = 05ε = 06

ε = 04ε = 05ε = 06

Figure 15 +e variation of the backwater height of the portable pillar-shaped flume versus discharge rate

14 Shock and Vibration

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Velocity

Section 1

000 005 009 014 019 028023 037033 042

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(a)

000 005 010 015 020 025 035030 040 045

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 2

(b)

Velocity000 011 022 034 045 056 079067 090 101

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 5

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(c)

000 015 030 045 060 075 105090 120 135

035

03

025

02

015

01

005

0

Dep

th (m

)

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity

Y (m)

Section 7

(d)

Figure 16 Continued

Shock and Vibration 15

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

4 Conclusions

For the purpose of reducing head loss and backwater heightof discharge measurement this study reports on a portablepillar-shaped flume Based on Fluent 192 software thestandard k-ε turbulence model is used to carry out a three-dimensional numerical simulation of the portable pillar-shaped flume and the simulation data are verified usingexperimental results +e obtained results show that thesimulation data are consistent with the experimental resultsalso the maximum relative error in water depth is 865+eFroude number at the inlet of the portable pillar-shaped flumeis less than 05 which meets the requirements for dischargemeasurement +e relative error in the maximum flowmeasurement of the portable pillar-shaped flume is 474and the relative error in the average flow measurement is172+e portable pillar-shaped flume has a small backwaterheight and its critical submergence degree is large in fact thecritical submergence is between 073 and 096 which suits theportable pillar-shaped flume to existing channels Further-more with a certain degree of measurement accuracy thehead loss of the portable pillar-shaped flume is smaller thanthat of the airfoil pillar-shaped flume and present higher flowcapacity In addition the portable pillar-shaped flume with asimple structure and a small size is convenient to carry andinstall On the whole it is concluded that the portable pillar-shaped flume has the advantages of easy installation simplestructure high accuracy high critical submergence degreesmall head loss small backwater height and suitability forapplication in constructed channels

Data Availability

+e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e authors gratefully acknowledge the support provided bythe National Natural Science Foundation of China (no51909242)

References

[1] A S Ramamurthy and R Tadayon ldquoNumerical simulation offlows in cut-throat flumesrdquo Journal of Irrigation and DrainageEngineering vol 134 no 6 pp 857ndash860 2008

[2] W Dabrowski and U Polak ldquoImprovements in flow ratemeasurements by flumesrdquo Journal of Hydraulic Engineeringvol 138 no 8 pp 757ndash763 2012

[3] C I +ornton B A Smith S R Abt and M D RobesonldquoSupercritical flow measurement using a small Parshallflumerdquo Journal of Irrigation and Drainage Engineeringvol 135 no 5 pp 683ndash692 2009

[4] W Boiten ldquoFlow measurement structuresrdquo Flow Measure-ment and Instrumentation vol 13 no 5-6 pp 203ndash207 2002

035

03

025

02

015

01

005

0

Dep

th (m

)

Y (m)

Section 12

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

Velocity000 010 020 030 040 050 070060 080 090

(e)

035

03

025

02

015

01

005

0

Dep

th (m

)000 006 013 019 026 032 045039 052 058

Velocity

Y (m)

Section 14

ndash02 ndash015 ndash01 ndash005 0 005 01 015 02

(f )

Figure 16 Development of the cross-sectional velocity distributions of the longitudinal flow of the water at a flow rate of 15 Ls and acontraction ratio of 05 (unit mmiddotsminus1)

16 Shock and Vibration

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17

[5] Z Samani ldquo+ree simple flumes for flow measurement inopen channelsrdquo Journal of Irrigation and Drainage Engi-neering vol 143 no 6 2017

[6] A R Vatankhah and A Mahdavi ldquoSimplified procedure fordesign of long-throated flumes and weirsrdquo FlowMeasurementand Instrumentation pp 79ndash84 2012

[7] V Conee Venturi Flume US Government Printing OfficeWashington DC USA 1917

[8] R L J C Parshall e Improved Venturi flume Springer-Verlag Berlin Heidelberg Germany 1928

[9] G V Skogerboe M L Hyatt and J D England Design andCalibration of Submerged Open Channel Flow MeasurementStructures Part 2-Parshall Flumes Utah State UniversityLogan Utah 1967

[10] G V Skogerboe M L Hyatt and K O EgglestonDesign andCalibration of Submerged Open Channel Flow MeasurementStructures Part 1-Submerged Flow Utah State UniversityLogan Utah 1967

[11] G V Skogerboe M L Hyatt and J D England MeasuringWater with Parshall Flumes Utah State University LoganUtah 1966

[12] H Zhu G Li and J Wang ldquoFlow-induced vibration of acircular cylinder with splitter plates placed upstream anddownstream individually and simultaneouslyrdquo Applied OceanResearch vol 97 Article ID 102084 2020 pages

[13] J Wang S Zhou Z Zhang and D Yurchenko ldquoHigh-per-formance piezoelectric wind energy harvester with Y-shapedattachmentsrdquo Energy Conversion and Management vol 181pp 645ndash652 2019

[14] J Wang L Tang L Zhao and Z Zhang ldquoEfficiency inves-tigation on energy harvesting from airflows in HVAC systembased on galloping of isosceles triangle sectioned bluff bod-iesrdquo Energy vol 172 pp 1066ndash1078 2019

[15] G Hu J Wang Z Su G Li H Peng and C S KwokldquoPerformance evaluation of twin piezoelectric wind energyharvesters under mutual interferencerdquo Applied Physics Let-ters vol 115 no 7 2019

[16] J Wang L Tang L Zhao G Hu R Song and K XuldquoEquivalent circuit representation of a vortex-induced vi-bration-based energy harvester using a semi-empirical lum-ped parameter approachrdquo International Journal of EnergyResearch vol 44 no 6 pp 4516ndash4528 2020

[17] W H Hager ldquoModified venturi channelrdquo Journal of Irriga-tion and Drainage Engineering vol 111 no 1 pp 19ndash35 1985

[18] F L Kolavani M Bijankhan and C Di Stefano ldquoExperi-mental study of central baffle flumerdquo Journal of Irrigation andDrainage Engineering vol 145 no 3 Article ID 0401900214 pages 2019

[19] M Bijankhan and V Ferro ldquoExperimental study on triangularcentral baffle flumerdquo FlowMeasurement and Instrumentationvol 70 Article ID 101641 7 pages 2019

[20] B Sun H Lv and C Song ldquoMulti-objective optimization ofairfoil-shaped hydraulic structure based on hicks-henneshaped function and MIGArdquo Journal of Sichuan Universityvol 45 no 04 pp 13ndash20 2013 (in Chinese)

[21] H Hu J Huang Z Qian W Huai and G Yu ldquoHydraulicanalysis of parabolic flume for flow measurementrdquo FlowMeasurement and Instrumentation vol 37 pp 54ndash64 2014

[22] H Zhu J Yao YMa H Zhao and Y Tang ldquoSimultaneous CFDevaluation of VIV suppression using smaller control cylindersrdquoJournal of Fluids and Structures vol 57 pp 66ndash80 2015

[23] H Zhu and J Yao ldquoNumerical evaluation of passive control ofVIV by small control rodsrdquo Applied Ocean Research vol 51pp 93ndash116 2015

[24] H Zhu W Liu and T Zhou ldquoDirect numerical simulation ofthe wake adjustment and hydrodynamic characteristics of acircular cylinder symmetrically attached with fin-shapedstripsrdquo Ocean Engineering vol 195 Article ID 106756 2020pages

[25] K Yang J Wang and D Yurchenko ldquoA double-beam piezo-magneto-elastic wind energy harvester for improving thegalloping-based energy harvestingrdquo Applied Physics Lettersvol 115 no 19 2019

[26] Y Xiao W Wang X Hu and Y Zhou ldquoExperimental andnumerical research on portable short-throat flume in thefieldrdquo Flow Measurement and Instrumentation vol 47pp 54ndash61 2016

[27] X Li L Jin and B A Engel ldquoInfluence of the structure ofcylindrical mobile flumes on hydraulic performance char-acteristics in U-shaped channelsrdquo Flow Measurement andInstrumentation vol 72 2020

[28] N R B Olsen and H M Kjellesvig ldquo+ree-dimensionalnumerical flowmodelling for estimation of spillway capacityrdquoJournal of Hydraulic Research vol 36 no 5 pp 775ndash7841998

[29] G E Ferrari M Politano and L Weber ldquoNumerical sim-ulation of free surface flows on a fish bypassrdquo Computers ampFluids vol 38 no 5 pp 997ndash1002 2009

[30] F Xiao and A Ikebata ldquoAn efficient method for capturing freeboundaries in multi-fluid simulationsrdquo International Journalfor Numerical Methods in Fluids vol 42 no 2 pp 187ndash2102003

[31] CW Hirt and B D Nichols ldquoVolume of fluid (VOF) methodfor the dynamics of free boundariesrdquo Journal of Computa-tional Physics vol 39 no 1 pp 201ndash225 1981

[32] L Jiang M Diao and H Sun ldquoNumerical modeling of flowover a rectangular broad-crested weir with a sloped upstreamfacerdquo Water vol 10 no 11 2018

[33] A N Ziaei N S R Nikou A Beyhaghi F Attarzadeh andS R Khodashenas ldquoFlow simulation over a triangular lab-yrinth side weir in a rectangular channelrdquo Progress inComputational Fluid Dynamics An International Journalvol 19 no 1 pp 22ndash34 2019

[34] H Saadatnejadgharahassanlou R I Zeynali andA Gharehbaghildquo+ree dimensional flow simulation over a sharp-crestedV-Notch weirrdquo Flow Measurement and Instrumentation vol 712020

[35] F G Carollo C Di Stefano and V Ferro ldquoNew stage-dis-charge equation for the SMBF flumerdquo Journal of Irrigationand Drainage Engineering vol 142 no 5 2016

[36] H Liu R Zhao and J Huang ldquoExperimental Research onAirfoil Pillar-shaped Measuring-flumerdquo China Rural Waterand Hydropower vol 06 pp 170ndash172 2014 (in Chinese)

Shock and Vibration 17