Numerical and experimental investigation of the cavitating ...isromac-isimet.univ-lille1.fr/upload_dir/finalpaper/288.revised... · ball valves to CP2 are closed to prevent a bypass

Numerical and experimental investigation of the cavitatingflow in a low specific speed centrifugal pump andassessment of the influence of surface roughness onhead predictionPhillip Limbach1*, Tim Müller1, Martin Blume1, Romuald Skoda1

SYM

POSI

A

ON ROTATING MACHIN

ERY

ISROMAC 2016

InternationalSymposium on

TransportPhenomena and

Dynamics ofRotating Machinery

Hawaii, Honolulu

April 10-15, 2016

AbstractIn order to assess the numerical model for the prediction of the pump performance of a low specificspeed centrifugal pump in cavitating flow conditions a numerical 3D analysis with a state-of-the-art CFDmethod and cavitation model by Zwart et al. [1] is performed for both, design and off-design conditionswith varying surface roughness. Measured head and suction head data of in-house experiments withtwo different volute roughness levels are used to validate the unsteady simulation results. Regardingsingle-phase flow, significant differences to the measured head are observed assuming hydraulicallysmooth walls in the numerical model, in particular for over load. By employing a surface roughnessmodel the simulation results show a decrease of the head at higher flow rates according to themeasurements. Further deviations between simulation and measured data at over load are attributed toflow separation at the tongue of the volute, which is inaccurately resolved by the wall function approach.For cavitating flow conditions the influence of the surface roughness on the 3% suction head is minor.The trend of the measured N PSH3% curve is qualitatively reproduced by the simulation. A steep rise ofthe N PSH3% curve towards over load is attributed to cavitation at the volute tongue.

1Chair of Hydraulic Fluid Machinery, Ruhr-Universität Bochum, Germany*Corresponding author: [email protected]

INTRODUCTION

Centrifugal pumps are increasingly required to operate inan extended range of flow rates, which deviate significantlyfrom the design point, leading to unsteady flow instabilities,performance losses and cavitation. Cavitation may lead tounstable pump operation, noise, head drop and even materialerosion. Despite the fact that the operation disturbance due tocavitation is well known, it is often not taken into account incommon engineering CFD simulations because of the com-plexity of the cavitation physics, e.g. unsteadiness, bubbledynamics, evaporation and condensation or air release.

Models for the simulation of cavitating flows are princi-pally divided into interface-tracking, Volume of Fluid (VoF),discrete-bubble as well as two-phase flow models [2]. Infact, no cavitation model resolves the physics of all abovementioned phenomena. For engineering simulations of cen-trifugal pumps, incompressible, implicit flow solvers withVoF-methods and a transport equation for the void fraction areusually employed due to their moderate computational effortand good solver stability. Mass transfer between the phasesis calculated by a source/sink term based on a simplified bub-ble dynamics equation, such as the Rayleigh equation (e.g.[1, 3]). In order to compensate the physical simplifications ofthe Rayleigh equation empirical parameters are implementedin the source/sink terms, which may need to be calibrated

to the particular flow situation. This model class has beenapplied for the simulation of cavitating flow in centrifugalpumps of high or intermediate specific speed in order to eval-uate the characteristics of head drop and net positive suctionhead (N PSH), and the measured N PSH3% curve has beenreproduced with reasonable accuracy by the simulations (e.g.[4, 5, 6]). However, the accuracy of the prediction of suctionperformance is case-dependent according to Nohmi [7], inparticular for low specific speed pumps.

Simulation results of low specific speed centrifugal pumpscommonly deviate from measured performance data consider-ably, even for single-phase flow conditions [8, 9, 10, 11, 12].Due to narrow flow channels the relative surface roughnessincreases with decreasing nominal pump size. As a result, theperformance of the pump is influenced significantly by the sur-face finish [13]. Varley [14], Tamm et al. [15] and Gülich [16]varied the roughness of various impeller components of dif-ferent centrifugal pumps and registered only a slight increaseof the head with increasing roughness in their experiments.Tamm et al. [15] and Gülich [16] identified the roughnessof the volute to have a major influence on the head, whichdecreases significantly with a roughened volute. Juckelandtet al. [11] figured out that the neglect of surface roughness inthe numerical model causes significant differences betweensimulation results and measured data of low specific speed

Numerical and experimental investigation of the cavitating flow in a low specific speed centrifugal pump and assessment of theinfluence of surface roughness on head prediction — 2/9

1. Tank2. Closed ball valves3. Piezoresistive pressure transducer (on the suction side)4. Piezoresistive pressure transducer (on the pressure side)5. Magnetic inductive flow meter6. Throttle7. Connection to the vacuum pump8. Vacuum pumpCP1 Centrifugal pump 1 (nq = 12 min−1)CP2 Centrifugal pump 2 (not used here)

Figure 1. Closed circuit centrifugal pump test rig.

centrifugal pumps. In addition, Juckelandt and Wurm [12]used a low specific speed centrifugal pump with polishedsurfaces and reveal that flow separation at the tongue of thevolute is inaccurately predicted by the wall function approach,hence, a high resolution of the boundary layer is necessary fora reliable prediction of the flow field and pump performance.

The present paper focuses on the assessment of the nu-merical model for the prediction of the head drop due tocavitation in a low specific speed centrifugal pump. In-houseexperiments are carried out in order to validate the simulationresults. The commercial 3D CFD code ANSYS CFX 15.0is employed. For single-phase flow, the influence of severalgeometry and model simplifications as well as of the grid reso-lution on the pump performance is analysed. For single-phaseas well as cavitating flow, the surface roughness is varied inthe simulation as well as experiment.

1. METHODOLOGY

1.1 Experimental set-upExperiments are performed at the closed circuit centrifugalpump test rig of the Chair of Hydraulic Fluid Machineryat Ruhr-Universität Bochum. The test rig is equipped withpiezoresistive pressure transducers to measure the static pres-sure up- and downstream of the pump as well as a magneticinductive flow meter and a throttle to adapt the volume flow.A stroboscope is used to verify a constant rotational speed.In order to reduce the impact of flow inhomogeneity up- anddownstream of the pump the undisturbed suction and pres-sure pipes extend 32D and 47D, respectively, D being thepipe diameter. Utilising a vacuum pump in the tank of thetest rig, the absolute system pressure is variable between 1and 0.05 bar. A simplified N PSH3% measurement procedureis applied. Starting with an atmospheric tank pressure andwater saturated with air at atmospheric pressure, the systempressure is decreased continuously at constant flow rate from

1 bar to 0.05 bar within about 10 minutes. Measured data arerecorded every ∆t = 0.5 s until the N PSH3% is determined at3% head drop. This procedure is repeated five times per flowrate and the standard deviation of the N PSH3% is determinedand depicted as error bars in figure 6. In comparison to exem-plary stationary measurements at a multitude of distinct tankpressure levels, i.e. the common N PSH3% measurement pro-cedure, a maximum deviation regarding the N PSH3% of 10%is observed at over load, which is considered to be acceptablein the present study. The test rig is shown in figure 1. Theball valves to CP2 are closed to prevent a bypass flow in theexperiments.

Table 1. Pump performance data.

Nominal rotational speed 1450 min−1

Nominal flow rate 15 m3/hNominal head 15.5 mNominal power consumption 1.5 kWSpecific speed 12 min−1

Flange nominal diameter onthe suction side

DN 50

Flange nominal diameter onthe pressure side

DN 32

A single-stage low specific speed (nq = 12 min−1) cen-trifugal pump (CP1 in figure 1) with a seven blade closedimpeller and spiral volute is investigated. The nominal ro-tational speed and nominal flow rate at the best efficiencypoint equal n = 1450 min−1 and Qopt = 15 m3/h, respec-tively. Since in low specific speed centrifugal pumps thevolute has a major influence on the pressure losses [15, 16],two different surface qualities are investigated for the volute.On the one hand the untreated cast iron surface is kept, onthe other hand the roughness is decreased by cathodic dip


painting. For the investigations of both volute samples, a ca-thodic dip painted impeller is used. Since the thickness of thecoating is in the order of ~100 µm and can be neglected to theflow channel width, the total volume flow is practically not re-duced and unevenness created from possibly inhomogeneousdistribution of the paint is small. The roughness values aredetermined by surface profile measurements with a contactprofilometer. The mean roughness, Rz , and arithmetical meanroughness, Ra , of uncoated surfaces amount to approximatelyRz = (39 ± 5) µm and Ra = (8 ± 1) µm, respectively. Thisuncoated volute surface case is referred to as EXP_R39/8 inthe following. Rz = (13 ± 3) µm and Ra = (3 ± 1) µm are ob-tained for coated surfaces which is referred to as EXP_R13/3in the following. Geometry and performance data of the pumpare summarised in table 1.

1.2 Cavitation modelThe ANSYS CFX 15.0 implementation of the cavitationmodel of Zwart et al. [1] is utilised and briefly summarisedin the following. Assuming the two-phase flow as a homo-geneous mixture of incompressible phases, the governingequations of the two-phase flow are based on the continuityequation for each phase and conservation equations for mo-mentum of the mixture, cf. equation 1 and 2. Thermal effectsare neglected, thus the energy equation is not solved. Thisis equivalent with the assumption of an isothermal flow. Theturbulent eddy viscosity of the mixture, µtm , appears in theReynolds averaged Navier-Stokes equations.

∂(αk ρk )∂t

+∂(αk ρkui )

∂xi= Sk (1)

∂(ρmui )∂t

+∂(ρmu jui )

∂x j=

−∂p∂xi

+∂

∂x j

[(µm + µtm )

(∂ui∂x j

+∂u j

∂xi

)] (2)

The volume fraction αk of both phases (k = l,v) is subjectto the constraint αl + αv = 1. The mass fraction equation 1 isreformulated as a volume fraction equation. The governingequation set consists of the mixture continuity equation, mix-ture momentum equations, the vapour volume fraction equa-tion as well as transport equations of the turbulence model.A mass source term in the vapour volume fraction equationaccounts for the mass exchange between the phases, liquidwater and vapour (Svap = −Scond) and is calculated on thebasis of the Rayleigh equation (equation 3), which relatesthe temporal change of the bubble radius to the differencebetween ambient static pressure and vapour pressure [17].

dRdt

=

√23

pv − pρl

(3)

Inserting the Rayleigh equation in the rate of change equa-tion of mass of a single bubble and specifying NB = αv/

43πR3

bubbles per unit volume, the total interphase mass transfer rateper unit volume is formulated in equation 4 for vaporisation(p < pv) and condensation (p > pv). Empirical coefficients,Fvap , Fcond , RB and αnuc , are employed to compensate thesimplifications in the Rayleigh equation and to account fordifferent time scales of vaporisation and condensation.

Svap,cond =

Fvap

3αnuc (1−αv )ρvRB

√23pv−pρl

if p < pv

Fcond3αv ρvRB

√23p−pv

ρlif p > pv

(4)

Due to the assumption of constant temperature (T =

298.15 K), the density of the liquid, ρl , and vapour, ρv , aswell as the vapour pressure, pv , are assumed to be constant(cf. table 3). The empirical coefficients, Fvap , Fcond , RB andαnuc , are specified as recommended by Zwart et al. [1].

1.3 Numerical set-upThe geometry model contains the seven blade impeller, volutecasing, side gaps as well as the suction and pressure pipes,which are extended (>4D) in axial direction to reduce theeffect of the boundary conditions on the internal flow. Thecomputational domain and the grid of the impeller are shownin figure 2. Preliminary single-phase flow simulations haveshown that the influence of geometry details, i.e. the radiibetween the blades and hub/shroud, ribs in the suction pipe,axial thrust balance holes as well as tolerances of the radialclearance of the gap between impeller shroud and casingon the predicted head is minor (∆H < 1%). Hence, thesegeometry details are neglected in the numerical model.

A block structured grid is generated with three differ-ent resolutions containing approximately 1,850,000 (CWF),16,330,000 (FWF) and 16,510,000 nodes (FLRe). The gridsof the impeller, side gaps and suction pipe are generated withan in-house turbomachinery grid generator. The volute as wellas the pressure pipe grids are generated with the commercialprogram ICEM CFD. Regarding the grid FWF, the length ofthe cell edges of CWF is at least halved in each direction. Forthe generation of the grid FLRe, additional cells are added inthe boundary layer region of the volute of FWF in order toresolve the boundary layer flow down to a non-dimensionalwall distance y+ ∼ 1. For the approximation of the Reynoldsstresses the shear stress transport (SST) turbulence model [18]is used in combination with an automatic wall function. Thewall treatment, i.e. the integration to the wall (low-Reynoldsnumber model) or the matching of a logarithmic velocity pro-file (wall function), is blended automatically depending on theresolution of the grid near the wall [19, 20]. The wall adjacentresolution of the grids CWF and FWF is optimised for the useof wall functions, whereas the grid FLRe is constructed fora low-Reynolds number approach in the volute. The wall y+

distribution is summarised in table 2.According to Lechner and Menter [21], the surface rough-

ness, which is described by an equivalent sand grain roughnessof an average roughness height, is modelled by placing thewall nodes at 50% of the sand grain roughness height in com-bination with a modification of the automatic wall function,


Figure 2. Computational domain and grid of the impeller (CWF).

which is shifted downwards depending on the dimensionlesssand grain roughness height. The viscous sublayer is lostquickly with increasing dimensionless sand grain roughnessheight, hence, the blending function activates the viscous sub-layer formulation only for small values of the dimensionlesssand grain roughness height [21]. The relative error of thewall shear stress of an incompressible plane Couette flowincreases with increasing grid resolution up to ∼10% [21].

Table 2. Average wall y+ for different grids and domains.

Suctionpipe

Pressurepipe

Impeller Sidegaps

Volute

CWF 60 100 60 100 80FWF 30 50 30 50 40FLRe 30 50 30 50 1

The equivalent sand grain roughness can be assessed onthe basis of the measured arithmetic mean roughness Ra byusing an equivalence coefficient, ceq (ks = 6Ra/ceq) [13]. Awide range of equivalence coefficients that connect the arith-metical mean roughness and equivalent sand grain roughnessis used in the literature (e.g. [15, 16, 13]). In order to circum-vent this ambiguity, in the present investigation the equivalentsand grain roughness height is varied until the simulation re-sults with the grid CWF match the measured data EXP_R39/8at nominal load. An equivalent sand grain roughness heightof ks = 140 µm is obtained, which corresponds to a rathersmall conversion coefficient and a high value of the equiva-lent sand grain roughness compared to the result of measuredmean roughness, Rz ∼ 39 µm, and arithmetic mean roughnessRa ∼ 8 µm. Since Tamm et al. [15] and Gülich [16] haveshown that the impeller roughness has a minor effect on thehead, a fact which has been confirmed in preliminary simu-

lations in the present study, the entire computational model(impeller, side gaps and volute) is equipped either with a hy-draulically smooth (SMOOTH) or a rough wall (ks140). Thesuccessive case names of the simulation runs are composedof the grid resolution and the surface treatment.

A constant velocity is specified at the inlet of the suctionpipe (turbulence intensity 5%) and a uniform static pressureis defined at the outlet of the pressure pipe. Unsteady single-phase and cavitating flow simulations are performed for fiveand three flow rates, respectively. A time step size corre-sponding to an impeller rotation of 1◦ is used. Second orderdiscretisation in space and time as well as double precisionfloating point number accuracy is applied. Further details ofthe numerical set-up are listed in table 3. The performancequantities of the pump, which are described in section 2.1,are evaluated by means of sufficiently long time-averaging, atleast over the complete final revolution. The approximate out-let pressure conditions for the determination of the ∼3% headdrop and N PSH3% are available from steady state simulations,which have been performed in a previous study [10]. Due tothe fact that a head drop of 3% is not matched precisely in thesimulations, intermediate N PSH3% values are determined bymeans of linear interpolation.

2. RESULTS

2.1 Evaluation of performance quantitiesThe head is computed according to equation 5. Regarding thesimulation results, the total pressure is mass-averaged at theevaluation surfaces ES1 and ES2 (cf. figure 2) considering aconstant geodetic height difference of the evaluation surfacesof 0.24 m. In the experiments, the total pressure is determinedby measuring the static pressure (pressure transducers), dy-namic pressure (flow meter and pipe diameter) and the height


Table 3. Summary of the numerical setup.

Single-phase flow Cavitating flow

Fluid properties Water (ρl = 998 kg/m3) Water (ρl = 998 kg/m3),vapour (ρv = 0.023 08 kg/m3, pv = 3170 Pa)

Turbulence model Shear stress transport (SST) Shear stress transport (SST)Operation points (0.3, 0.5, 0.7, 1.0, 1.3, 1.5) Qopt (0.7, 1.0, 1.3) Qopt

Inlet boundary Normal velocity Normal velocity, αl = 1Outlet boundary Static pressure Static pressure, αl = 1Wall boundary Adiabatic, smooth (no slip) and

rough (ks = 140 µm)Adiabatic, smooth (no slip) andrough (ks = 140 µm)

Cavitation model parameters RB = 1 × 10−6 m, rnuc = 5 × 10−4,Fvap = 50, Fcond = 0.01

Convergence criteria Rmax < 1 × 10−4, imbalances < 1 % Rmax < 1 × 10−4, imbalances < 1 %

difference of the pressure transducers.

H =pt,ES2 − pt,ES1

ρg(5)

The net positive suction head (N PSH) is evaluated interms of the required N PSH of the pump (N PSH R) whichcan be considered as a measure for the margin against vapori-sation of the fluid in the pump.

N PSH =pt,ES1 − pv

ρg(6)

N PSH3% is evaluated at a 3% head drop.

2.2 Single-phase flowIn a previous study [10] the measured head is significantlyoverestimated by the simulation results with a computationalgrid that approximately corresponds to the resolution em-ployed in the grid CWF of the present study. The result ofLimbach et al. [10] is essentially reproduced in the presentstudy with hydraulically smooth walls and the grid CWF, cf.case SIM_CWF_SMOOTH in figure 3. Comparing the re-sults of SIM_CWF_SMOOTH and SIM_FLRe_SMOOTH, asdepicted in figure 3, no significant dependence of the gridresolution on the head can be observed for flow rates upto the nominal operating point (Qopt = 15 m3/h). How-ever, the resolution of the boundary layer of the volute inthe SIM_FLRe_SMOOTH case leads to a noticeable decreaseof head in over load operation. Regarding over load, the exam-ination of the velocity profiles shows a high angle of incidenceat the volute tongue, which varies periodically because of themovement of the blades relative to the volute tongue. As aresult, flow separation occurs, which cannot be resolved bythe wall function. Using the grid FWF (cf. section 1.3) no sig-nificant discrepancies to SIM_CWF_SMOOTH are observed(not shown here). Thus, the accurate resolution of the separa-tion at the volute tongue is not a feature of the overall numberof nodes but of the accurate resolution of the boundary layer(y+ ∼ 1) with a low-Reynolds number wall approach. The

low accuracy of the wall function due to its inability to predictflow separation in a low specific speed pump volute has beenalready pointed out by Juckelandt and Wurm [12] and is thusconfirmed in the present study.

Q [m³/h]

H[m

]

0 5 10 15 20 255

10

15

20

EXP_R39/8

SIM_CWF_SMOOTH

SIM_FLRe_SMOOTH

Figure 3. Head characteristics dependent on the gridresolution (hydraulical smooth surfaces in the simulation).

In order to exclude the assumption of Reynolds stressisotropy in the eddy viscosity turbulence model as a furthersource of prediction uncertainty, a test on the grid CWF withthe ANSYS CFX 15.0 implementation of the BSL Reynoldsstress model, which accounts for the turbulence anisotropy,has been performed for over load and does not lead to signifi-cant changes of the head (∆H < 1%). Hence, the assumptionof isotropic turbulence due to the scalar eddy viscosity ofthe SST turbulence model seems to be acceptable for theprediction of the head.

The influence of surface roughness on the head is illus-trated in figure 4 and discussed in the following. Experimentswith varying roughness of the surfaces show a trend of de-creasing head with increasing surface roughness. Roughen-ing of the surface leads to an increase of the friction lossesand hence to a reduction of head at a fixed flow rate at overload. Since friction losses also depend on the Reynolds num-ber, the head loss is more distinctive with increasing flowrate. The experimental data clearly figure this out. Simula-tion results accounting for surface roughness are presentedfor the grid CWF with an equivalent sand grain roughness


height of ks = 140 µm (cf. section 1.3) and compared tothe EXP_R39/8 measurement. Following from the adaptionprocedure of ks , the simulated head is per definition equalto the measured head at nominal flow rate Qopt = 15 m3/hand yields essentially a low difference to the measured headover the entire flow rate spectrum. The remaining differencebetween simulation and experiment is much less distinctivethan the significant overestimation of the over load head bythe hydraulically smooth surface simulation. However, aslight remaining under- and overestimation of the experimentEXP_R39/8 is discernible in part and over load, respectively.It is obvious that the inclusion of the roughness in the simula-tion model essentially compensates the overestimation of thehead at over load that has been predicted by the hydraulicallysmooth model. However, a main source of head overestima-tion at over load remains, i.e. inaccurate representation of theseparation due to the wall function. Therefore, the particularsand grain roughness height of ks = 140 µm is to be consid-ered as an empirical correction factor of the simulation results.This conclusion is supported by the fact that ks = 140 µm israther high compared to the measured values of Rz ∼ 39 µmand Ra ∼ 8 µm.

X

X

X

XX

X

XX

XXXX

Q [m³/h]

H[m

]

0 5 10 15 20 255

10

15

20

EXP_R13/3EXP_R39/8SIM_CWF_SMOOTHSIM_CWF_k

s140

X

Figure 4. Head characteristics dependent on the surfaceroughness.

It can be concluded that the usage of wall functions andthe neglect of surface roughness are two main sources of un-certainty in the prediction of the head in low specific speedpumps and restrict the accuracy of the numerical simulation.Essentially the same conclusions have been drawn by Juck-elandt et al. [11] and Juckeland and Wurm [12] and are con-firmed by the present study. Thus, a low-Reynolds numberwall approach has to be employed in the volute in order toresolve the separation. Furthermore, wall roughness has tobe taken into account in the simulation model. The validityof a simultaneous application of the low- Reynolds numberapproach in combination with the roughness model [21] hasto be clarified yet, since the wall adjacent cell distance ofthe FLRe grid is lower than the applied roughness height ofks = 140 µm. An alternative may be the direct resolutionof the wall roughness geometry by a low-Reynolds numberapproach and a correspondingly fine grid. However, this pro-cedure is out of the scope of the present study. Therefore, inthe present study, we content ourselves with the knowledge

that an inaccurate resolution of separation at the volute tongueleads to a head overprediction at over load and proceed withthe wall function approach for cavitating flow.

2.3 Cavitating flowExperiments and simulations for cavitating flow conditions areperformed in order to analyse the effect of surface roughnesson the N PSH . Figure 5 presents the evolution of the measuredhead depending on the N PSH for four flow rates exemplarilyfor the case EXP_R13/3.

NPSH [m]H

[m]

0 2 4 6 80

5

10

15

20

0.7 Qopt

=10.5 m3/h

Qopt

=15 m3/h

1.3 Qopt

=19.5 m3/h

1.4 Qopt

=21 m3/h

Figure 5. Measured head dependent on the net positivesuction head for case EXP_R13/3.

A sharp head drop is observed in part and nominal load,whereas the head decreases more smoothly in over load. Theshape of the head drop curves from steady state simulations[10] is in qualitative agreement with the experiments. TheN PSH3% curve is depicted in figure 6. The standard deviationof the measurements is presented if the error bar exceeds thesymbol size.

X XX

XX

X

X

X

X

X

X

X

Q [m³/h]

NP

SH

3%

[m]

5 10 15 20 250

2

4

6

8

EXP_R13/3EXP_R39/8SIM_CWF_SMOOTHSIM_CWF_k

s140

X

Figure 6. N PSH3% characteristics dependent on the surfaceroughness.

While the single-phase flow experiments reveal that thesurface roughness has a considerable influence on the head(cf. figure 4), for the measured N PSH3% the influence ofthe roughness on the N PSH3% is minor (note also the scaledifference of the ordinate in figure 4 and 6). An explanationof the minor impact of the volute roughness on the N PSH3%curve is that the evaluation of the N PSH3% value (equation6) is based on the total pressure on the suction side only.


Figure 7. Snapshot of the location of the cavitation zones illustrated by iso-surfaces of the vapour volume fraction, αv = 0.1:View through the side gap of the suction side and the shroud for a) 0.7 Qopt and b) 1.0 Qopt ; c) view on the volute tonguethrough the wall of the volute for 1.3 Qopt .

Therefore, the pressure losses on the pressure side and par-ticularly in the volute due to roughness have a minor effecton the N PSH3%. Also the N PSH3% curve evaluated fromthe simulation results does essentially not deviate betweenhydraulically smooth and rough walls. A slight underestima-tion of the measured N PSH3% values in part and nominalload is observed. The steep increase towards over load is alsodistinctive in the simulation results, but occurs at a lower flowrate than in the experiment and results in an overestimation ofthe measured N PSH3% values by the simulation at over load.

For a more detailed analysis of the cavitating flow thesimulation results are analysed concerning the location of thecavitation zones in figure 7. The cavitation zones appear es-sentially stationary, and this fact is discussed further below.While the cavitation zones are mainly located at the suctionside of the blades leading edge in part load, they move to-wards the pressure side with increasing flow rate (nominalload) due to a decreasing angle of incidence relative to theleading edge. At nominal load cavitation occurs on both, suc-tion and pressure side. For part load conditions the impellerflow channels are uniformly filled, whereas the shape of thecavitation zones changes in circumferential direction from oneflow channel to the other for nominal load depending on theposition of the impeller relative to the volute tongue. At highflow rates (1.3 Qopt ) cavitation is observed at the tongue ofthe volute prior to cavitation at the blades, cf. figure 7c. As aconsequence, according to the simulation results, the steep in-crease of N PSH3% towards over load (cf. figure 6) is affectedby the presence of vapour regions within the volute whichis in agreement with the remarks of Gülich [13]. The steeprise of N PSH3% in the simulation occurs at lower flow ratesthan in the measurement. However, the qualitative appearanceof the N PSH3% curve, in particular the presence of a steeprise towards over load, is obvious in both, experiment andsimulation results. In the present study only sheet cavitationis observed in the simulation results at the blades as well as

at the volute tongue, while also unsteady cloud cavitation isexpected in the cavitation and Reynolds number regime inlow specific speed centrifugal pumps. While in the case ofcloud cavitation the unsteady nature of periodically detachingvapour clouds from a hydrofoil originates from the formationof a reentrant jet, the unsteady behaviour of cavitation at thevolute tongue is also enforced from the changing flow angledue to the blade movement relative to the volute tongue [22].Experiments of Bachert et al. [22] reveal the occurence ofperiodic cloud cavitation at the volute tongue of a centrifugalpump (nq = 26 min−1), which is a very erosive type of cavita-tion as reported by Dular et al. [23]. However, periodic cloudcavitation is not captured by the present simulation model.

Summarising, the N PSH3% deviation between experi-ment and simulation and particularly the rise of the N PSH3%at too low flow rates in the simulation are supposed to origi-nate from the following error sources:

• Although the neglect of axial thrust balance holes has es-sentially no effect for single-phase flow head evaluation,it may have a significant influence for the N PSH3%evaluation: flow rate through the impeller increases dueto leakage flow leading to a larger flow angle at theblade leading edge, whereas the volume flow throughthe volute does not change.

• Standard values for the cavitation model parameters,Fvap and Fcond , have been utilised (cf. section 1.2).These parameters may have to be optimised for theparticular flow situation in low specific speed pumps.This assumption is supported by the fact that cavitationzones appear essentially steady, while also unsteadycloud cavitation is expected.

• In addition to the parameter optimisation, a local reduc-tion of the mixture eddy viscosity may lead to unsteadyseparation of the cavitation zones as shown by CoutierDelgosha et al. [24]. Although Zwart et al. [1] followed


this approach in their investigations, the mixture eddyviscosity is not modified by default in the ANSYS CFX15.0 implementation of the SST turbulence model.

• It has been observed for single-phase flow that the gridresolution has a major influence to predict flow separa-tion and pressure losses at the volute tongue. A coarsegrid with wall function is used that cannot resolve theseparation. The usage of a coarse grid is assumed to bea further reason for the absence of cloud cavitation inthe simulation results.

3. CONCLUSIONS

3D CFD simulations as well as in-house experiments of alow specific speed centrifugal pump with varying surfaceroughness for single-phase and cavitating flow conditionsare performed. Measured single-phase data show a trendof decreasing head with increasing surface roughness of thevolute towards over load. For a reliable prediction of the headin the entire operation range of the pump the over load flowseparation at the volute tongue should be captured by a low-Reynolds number wall approach and a correspondingly finenear-wall grid as well as by the simultaneous consideration ofthe surface roughness of the volute.

Concerning pump operation in cavitating flow the influ-ence of surface roughness on N PSH3% is minor in the experi-ments as well as in the simulation results. Although the mea-sured N PSH3% characteristics are slightly underestimated inpart and nominal load and overestimated in over load, a dis-tinctive and steep slope of the N PSH3% curve is observed inboth, the experiments and simulations for over load. Simula-tion results for this operation range confirm that the location ofthe cavitation zones switches from the impeller blade leadingedges to the volute tongue.

The simultaneous application of low-Reynolds numberwall treatment and roughness model, an extension of the gridstudy from single-phase flow to cavitating flow, the consid-eration of geometry details as axial thrust balance holes, theoptimisation of the cavitation model parameters for the par-ticular flow situation in low specific speed pumps as wellas a modification of the mixture eddy viscosity followingCoutier-Delgosha et al. [24] are suggested for future numeri-cal research.

ACKNOWLEDGMENTS

The authors wish to gratefully acknowledge the financial sup-port by the Verband Deutscher Maschinen- und Anlagenbaue.V. (VDMA), “Allianz Industrie Forschung” (AiF) as well asthe Kompetenzzentrum Hydraulische Strömungsmaschinen(KHS) of the Ruhr-Universität Bochum.

NOMENCLATURE

Roman symbolsceq Equivalence coefficient [−]D Diameter [m]F Empirical parameter [−]

g Acceleration due to gravity [m s−2]ks Sand grain roughness height [m]NB Number of bubbles per unit volume [−]N PSH Net positive suction head [m]n Rotational speed [min−1]nq Specific speed [min−1]p Static pressure [Pa]pt Total pressure [Pa]Q Flow rate [m3 s−1]R Radius [m]Ra Arithmetical mean roughness [m]Rz Mean roughness [m]S Surface tension [N m−1]S Mass generation rate [kg m−3 s−1]t Time [s]T Temperature [K]u Velocity [m s−1]x Cartesian space coordinate [m]y+ Non dimensional wall distance [−]

Greek Charactersα Volume fraction [−]∆ Delta operator [−]µ Dynamic viscosity [kg m−1 s−1]ν Kinematic viscosity [m2 s−1]ρ Density [kg m−3]

Subscripts3% Variable is related to a head drop of 3%B Bubblecond CondensationES1,2 Evaluation surface 1, 2i, j Coordinate indexk Phasel Liquidm Mixturenuc Nucleation siteopt Best efficiency pointt Turbulentv Vapourvap Vaporisation

Abbreviations and denominations3D Three dimensionalBSL BaselineCFD Computational fluid dynamicsCP1,2 Centrifugal pumpCWF coarse grid, wallfunctionES Evaluation surfaceEXP_R39/8 Experiments with an untreated voluteEXP_R13/3 Experiments with a coated voluteFLRe fine grid, low-Reynolds number ap-

proach in the voluteFWF fine grid, wall functionNPSH Net positive suction head


NPSHR Net positive suction head requiredSIM_CWF_SMOOTH Simulation results with grid CWF

and hydraulically smooth wallsSIM_FLRe_SMOOTH Simulation results with grid FLRe

and hydraulically smooth wallsSIM_CWF_ks140 Simulation results with grid CWF

and rough wallsSST Shear stress transportVoF Volume of Fluid

REFERENCES[1] P. J. Zwart, A. G. Gerber, and T. Belamri. A two-phase

flow model for predicting cavitation dynamics. In Pro-ceedings of ICMF 2004 International Conference on Mul-tiphase Flow, Yokohama, Japan, 2004.

[2] A. H. Koop. Numerical simulation of unsteady three-dimensional sheet cavitation. PhD thesis, University ofTwente, Enschede, Netherland, 2008.

[3] G. H. Schnerr and J. Sauer. Physical and numerical mod-eling of unsteady cavitation dynamics. In Proceedings of4th International Conference on Multiphase Flow, NewOrleans, USA, 2001.

[4] M. Frobenius, R. Schilling, J. Friedrichs, and G. Kosyna.Numerical and experimental investigations of the cavitat-ing flow in a centrifugal pump impeller. In Proceedingsof ASME Fluid Engineering Division Summer Meeting,Montreal, Quebec, Canada, pages 361–368, 2003.

[5] M. Frobenius, R. Schilling, R. Bachert, B. Stoffel, andG. Ludwig. Three-dimensional unsteady cavitation ef-fects on a single hydrofoil and in a radial pump - mea-surements and numerical simulations. In Proceedings of5th International Symposium on Cavitation (CAV2003),Osaka, Japan, 2012.

[6] D. Iiu, H. Iiu, Y. Wang, S. Zhuang, J. Wang, and D. Hui.Numerical simulation and analysis of cavitating flow ina centrifugal pump. In Proceedings of 8th InternationalSymposium on Cavitation (CAV 2012), Singapore, 2012.

[7] M. Nohmi. A review: A basic research on total predictionsystem for cavitation phenomena. In Proceedings of8th International Symposium on Cavitation (CAV 2012),Singapore, 2003.

[8] Y. Wang and W. J. Wang. Applicability of eddy viscos-ity turbulence models in low specific speed centrifugalpump. IOP Conference Series: Earth and EnvironmentalScience, 15, 2012.

[9] H. Benigni, H. Jaberg, H. Yeung, T. Salisbury, O. Berry,and T. Collins. Numerical simulation of low specificspeed american petroleum institute pumps in part-loadoperation and comparison with test rig results. Journalof Fluids Engineering, 134, 2012.

[10] P. Limbach, M. Kimoto, C. Deimel, and R. Skoda. Numer-ical 3d simulation of the cavitating flow in a centrifugal

pump with low specific speed and evaluation of the suc-tion head. In Proceedings of ASME Turbo Expo 2014,Düsseldorf, Germany, 2014.

[11] K. Juckelandt, S. Bleeck, and F. H. Wurm. Analysis oflosses in centrifugal pumps with low specific speed withsmooth and rough walls. In Proceedings of 11th EuropeanConference on Turbomachinery, Madrid, Spain, 2015.

[12] K. Juckelandt and F. H. Wurm. Applicability of wall-function approach in simulations of turbomachines. InProceedings of ASME Turbo Expo 2015, Montreal,Canada, 2015.

[13] J. F. Gülich. Centrifugal Pumps. Springer, 2010.[14] F. A. Varley. Effects of impeller design and surface rough-

ness on the performance of centrifugal pumps. Proceed-ings of the Institution of Mechanical Engineers, 175:955–969, 1961.

[15] A. Tamm, L. Eikmeier, and B. Stoffel. The influencesof surface roughness on head, power input and efficiencyof centrifugal pumps. In Proceedings of XXI IAHR Sym-posium on Hydraulic Machinery and Systems, Lausanne,Swiss, 2002.

[16] J. F. Gülich. Effect of reynolds number and surface rough-ness on the efficiency of centrifugal pumps. Journal forFluids Engineering, 125:670–679, 2003.

[17] L. Rayleigh. On the pressure development in a liquidduring the collapse of a spherical cavity. Phil. Mag.,34:94–98, 1917.

[18] F. R. Menter. Two-equation eddy-viscosity turbulencemodels for engineering applications. AIAA Journal,32:1598–1605, 1994.

[19] ANSYS INC. CFX 15.0 Documentation. 2014.[20] H. Grotjans and F. R. Menter. Wall functions for general

application cfd codes. ECCOMAS 1998, 1:1112–1117,1998.

[21] R. Lechner and F. R. Menter. Development of a roughwall boundary condition for ω-based turbulence models.In Technical Report ANSYS / TR-04-04, 2004.

[22] R. Bachert, B. Stoffel, and M. Dular. Unsteady cavitationat the tongue of the volute of a centrifugal pump. Journalfor Fluids Engineering, 132, 2010.

[23] M. Dular, R. Bachert, B. Stoffel, and B. Širok. Relation-ship between cavitation structures and cavitation damage.Wear, 257:1176–1184, 2004.

[24] O. Coutier-Delgosha, R. Fortes-Patella, and J. L. Reboud.Evaluation of the turbulence model influence on the nu-merical simulations of unsteady cavitation. Journal forFluids Engineering, 125:38–45, 2003.

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