Experimental Investigations of Flow Through Conical

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Experimental investigations of flow through conical diffusers withand without wake type velocity distortions at inlet

N.V. Mahalakshmi a,*, G. Krithiga a, S. Sandhya a, J. Vikraman b, V. Ganesan c

a Department of Mechanical Engineering, College of Engineering Guindy, Anna University, Chennai 600 025, Tamil Nadu, Indiab Department of Manufacturing Engineering, College of Engineering Guindy, Anna University, Chennai 600 025, Tamil Nadu, India

c Department of Mechanical Engineering, Indian Institute of Technology, Madras, India

Received 19 September 2006; received in revised form 22 February 2007; accepted 26 February 2007

Abstract

Diffusers play a vital role in many fluid machines to convert kinetic energy into pressure energy. The field of application of diffusers isvery wide and diffusers are used in gas turbines, pumps, fans, wind tunnels, water tunnels and many other fluid flow systems. This paperdiscusses the results of flow through straight conical diffusers of half-cone angles 5 and 7 with steady uniform velocity of flow and waketype distorted flow at inlet. The wake type distortion at inlet was produced by a streamlined body and a bluff body. A low speed windtunnel was used for the experiments and the diffusers were fabricated from cast aluminium blocks. The mean velocity and the turbulenceparameters were measured using a constant temperature hot-wire anemometer. 2007 Elsevier Inc. All rights reserved.

Keywords: Diffusers; Bluff body; Streamlined body; Wakes; Reynolds stresses

1. Introduction

Diffusers play a vital role in many fluid machines to con-vert kinetic energy into pressure energy. The efficiency ofthis conversion process is important as it affects the overallperformance of the machine. The pressure recovery, whichis the measure of performance of diffusers, depends onmany geometrical and dynamical parameters. Some geo-metrical parameters that govern the performance of a dif-fuser are inlet length and size of the duct, area ratio of

the diffuser, angle of expansion, length of the diffuser,shape of the exit duct with free or submerged dischargeconditions, etc. The dynamical parameters are inlet velocityprofile, boundary layer parameters, Reynolds number,Mach number and so on. In the present work, two param-eters namely inlet velocity profile and the geometry of thediffuser were selected in order to study their effects on the

flow structure and performance of conical diffusers. Forthis purpose, three types of inlet conditions namely a flowwithout wake, flows with a shallow wake and with a deepwake were considered. In the first case only boundary layerdistortions were produced. The wake type distortions wereproduced by center bodies namely a streamlined body anda bluff body. Two straight conical diffusers of half-coneangles 5 and 7 were selected and investigated.

Considerable amount of experimental investigations hasbeen done on conical diffusers. Welsh [1] studied flow con-

trol in wide angled conical diffusers. He used star type flowcontrol device and concluded that the geometry of a starflow device necessary to improve the performance and flowstability in wide angled conical diffusers was sensitive to thediffuser inlet conditions. Shimizu et al. [2] studied the effectof different types of inlet velocity profiles on the perfor-mance of straight conical diffusers. Hoffman and Gonzalez[3] found that increasing the inlet turbulence intensityincreased pressure recovery of the diffuser. Okwuobi andAzad [4] reported that in a conical diffuser with a fully devel-oped flow at entry, the spectra profiles and characteristics

0894-1777/$ - see front matter 2007 Elsevier Inc. All rights reserved.

doi:10.1016/j.expthermflusci.2007.02.008

* Corresponding author. Tel.: +91 44 22203263; fax: +91 44 22351991.E-mail address: [email protected] (N.V. Mahalakshmi).

www.elsevier.com/locate/etfs

Experimental Thermal and Fluid Science 32 (2007) 133157
mailto:[email protected]:[email protected]


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were very similar to those reported for pipe flows and the

magnitude of energy convective diffusion due to kineticand pressure effects were comparable with that of energyproduction. Ubertini and Desideri [5] determined the flowdevelopment in terms of the mean and fluctuating compo-nents of the velocity and turbulence dissipating eddy lengthscales in annular exhaust diffuser. In another study [6], theyinvestigated the effect of struts on the pressure recovery ofindustrial gas turbine exhaust diffuser. They concluded thatpressure recovery in the diffuser with strut was 1020%lower than that of the diffuser without strut. Azad and Kas-sab [7] examined experimentally the turbulent flow in a con-ical diffuser with 8 total angle and found that the core

region in the final outlet region has higher turbulence activ-ity resulting from focusing of high ejecting fluid crossingover the axis.

Studies have been carried out in conical diffuser flowwith distortions. Dean and Senoo [8] investigated the influ-ence of temporal variations in the inlet velocity profile to avane less diffuser and concluded that the total pressure lossin the diffuser may be less for distorted inlet flow than forundistorted inlet flow. Rao [9] studied the effect of radialsplitters in wide angle conical diffuser with large area ratioand found that splitter opex provided with a circular discwhose area and location influence the maximum pressurerecovery. Senoo and Nishi [10] conducted experiments withvortex generator and found that vortex generators pre-vented the flow from separation in a conical diffuser upto a divergence angle of 16 and the pressure recovery coef-ficient was approximately equal to that of the conventionalbest conical diffuser. Bragg and Suk [11] used two predic-tion procedures namely a momentum separation theoryand a finite difference method to predict the velocity profilein a turbulent wake behind a single cylinder and a row ofarbitrarily spaced and sized cylinders in adverse pressuregradient conditions. Nakumura et al. [12] studied the effectof asymmetric uniform shear inlet flow on performance ofvarious conical diffusers and found that the performance

was decreased with an increased shear in the inlet flow

and the reduction rate was maximum for optimum diffuser

geometry for a uniform inlet flow without shear.A few computational studies have also been carried out

in diffusers in general. Baskharone [13] analyzed swirlingflow field in annular diffusers using finite-element method.His method was applicable to moderately separating flows,which are typically associated with off-design performanceof diffusers in gas turbines. Armfield and Fletcher [14] ana-lyzed the swirl effect in a conical diffuser using Reynoldsstress and ke models. Singh et al. [15] have carried outCFD studies using FLUENT code in annular diffusers withdifferent geometries but having same inlet cone angle. Theyreported that performance of annular diffuser having paral-

lel diverging hub and casing was improved on the introduc-tion of swirl. The optimum swirl angle was between 20and 30. They found that further increase in swirl degradedthe performance of diffusers.

The aim of this paper is to determine the flow andboundary layer development in conical diffusers withsteady uniform flow and wake type distorted flow at entryto the diffuser.

2. Experimental setup

A schematic representation of the test rig is shown inFig. 1. The experiments were carried out in a blower dri-ven, low speed wind tunnel. The wind tunnel consists ofa settling chamber with filters and a belt-mouthed nozzlegiving a low turbulence level (0.6% at 30 m/s) flow. Theflow at the exit of the nozzle could be changed by a suitablethrottle control. With the help of this, the mass flow ratecould be altered. Air was made to diffuse through the holesbefore it enters the settling chamber, so that flow fluctua-tion could be minimized to a large extent. A number of finemeshes were placed suitably in the settling chamber toreduce the turbulence level. The settling chamber is ofdimension 1 m 1 m 2 m. A contraction of 0.19 m lengthwith a contraction ration of 36:1 was designed according to

DIN standards and fitted at the exit of the settling cham-

Nomenclature

b wake half-widthCPR coefficient of pressure recoveryCf skin friction coefficient

k turbulent kinetic energyL axial length of the diffuserLES large eddy simulationM Mach numberRe Reynolds numberU streamwise component of mean velocityU0 local free stream velocityU average velocityUref velocity at the reference station (inlet station)

u, v velocity in x and y directionsuc velocity at the wake centre lineu, v, w velocity fluctuations in the x, y and z directions

u

0

, v

0

, w

0

RMS values of velocity fluctuations in the x, yand z directionsX distance measured from the inlet along the dif-

fuser axisY distance measured from the axis to the wall of

the diffuserx,y co-ordinate axesq density

134 N.V. Mahalakshmi et al. / Experimental Thermal and Fluid Science 32 (2007) 133157


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ber. The outer diameter of the nozzle is 57 mm (see Plate.1).

The conical diffusers that were used for the experimenthave a common inlet diameter and length of 57 mm and300 mm, respectively. Diffusers having half-cone angles of5 and 7 have been selected for investigations (Plate 2).The entry length, the pipe to hold the center bodies andthe diffuser are shown in Fig. 2. The diffuser is connectedto a pipe of 57 mm diameter and 83 mm length. This pipeis used to hold the centre bodies in position. The entry pipeis of diameter 57 mm and of length 500 mm. The diffuserexit is provided with exit pipe of length 200 mm. The diffus-ers and exit pipes were fabricated by casting out of alumin-ium blocks and then machined to the desired size in a lowspeed lathe. Thirteen measurement stations, including theinlet, designated as A, B, C, D, E, F, G, H, I, J, K, Land M are established along the axis of the diffusers by

suitable drilling of holes to insert probes. The distance of

these stations, X, measured from the inlet to the diffuseris given in Table 1 along with the lengths normalized withreference to the length, L (300 mm) of the diffuser. Thelocation of various measuring stations is represented inFig. 3.

Figs. 4a and b show the two types of the centre bodiesnamely a bluff body and a streamlined body used for pro-ducing wake type distortions in the velocity at inlet. These

centre bodies were machined from stainless steel rods and

Plate 1. Experimental setup.

Plate 2. Diffusers.

Fig. 1. Wind tunnel set up.

N.V. Mahalakshmi et al. / Experimental Thermal and Fluid Science 32 (2007) 133157 135


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welded with three small diameter struts 120 apart and thestruts were welded to a flange of 57 mm diameter to matchthe inlet diffuser and for the purpose of easy assembly bymeans of bolts and nuts (Plates 3 and 4).

The traversing system shown in Fig. 5 is a mechanicaltraversing and rotating device designed for use withDANTEC hot-wire anemometers. The primary functionsof the unit are to move around the probe and rotate itaround the probe axis. The flow parameters have beenmeasured using different instruments. Static pressure recov-ery coefficient (CPR) is defined as:

CPR Px Pi=qi;

where Px is the average static pressure at a station, Pi is theaverage static pressure at the diffuser inlet and qi is the dy-namic head.

The average static pressure (CPR) is found out by tra-versing the pressure probe across that station, at an inter-val of 2 mm. The static pressure measurements are maderelative to the atmospheric pressure exposing one of the

leads of the manometer to the atmosphere. Mean velocity,turbulent normal stresses and turbulent shear stresses aremeasured by two independent hot wire measurements.The hot-wire probe used is DISA 55P11 single wire probeof 5 lm diameter and 1.25 mm length, made of platinumcoated with tungsten. The probe is connected to a DISA56C17 constant temperature anemometer and the line dia-gram of the system used is shown in Fig. 6a. An overheatratio of 0.8 is taken for operation. The anemometer is lin-earised using a DISA 56N21 lineariser. Cross wires areused for the measurement of Reynolds stresses. The crosswire probes used are DISA X-probes of type 55P61 with awire length of 1.25 mm and a wire separation of 2 mm.The two wires are of nearly equal sensitivity and onlynew probes are used in the experiments. The two wiresof the X-probe are individually connected to two constanttemperature anemometers as illustrated in Fig. 6b. All theReynolds stresses are measured by placing the X-probe inboth the planes. The details of the measurement tech-niques are explained by Mahalakshmi [16].

Fig. 2. Diffuser assembly.

Table 1Various measuring stations

Station A B C D E F G H I J K L M

X/L 0 0.08 0.17 0.25 0.33 0.42 0.5 0.58 0.67 0.75 0.83 0.92 1.00

Fig. 3. Location of various measuring stations.



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Plate 3. Streamlined body.

Plate 4. Bluff body. Fig. 5. Traversing mechanism.

Fig. 4. Geometry of center bodies.



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2.1. Uncertainty analysis

The uncertainty in measurements is expressed in the fol-lowing way: Consider a variable Xi, which has a knownuncertainty dxi. The variable and its uncertainty areexpressed as

Xi Xi dxi say; odds20 : 1;

where Xi is the arithmetic mean of the measured values anddxi is evaluated based on standard deviation, the number ofsamples and the confidence level. In a single sample exper-iment, let the result R be a function of n independent vari-ables and it may be represented as

R RX1;X2;X3; . . . ;Xn:

The uncertainty in R if only one of the measurements, say,Xi has error:

dRXi dR

dXi dXi:

When several variables are involved in the function R, thecombined uncertainty is given by the root mean squaremethod (see [17])

Further, ifR Xa1Xb2X

c3; . . . ;X

mn

dR XN

i1

oR

oXi

dXi 2

" #1=2

; 1

dR

R a

dX1

X1

2 b

dX2

X2

2 m

dXn

Xn

2" #12: 2

The uncertainties in the present measurements are calcu-lated as follows:

(1) Mean velocity:The mean velocity is given by the expression

U

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2DPRT0g

Pa

s: 3

The uncertainty in mean velocity is calculated using Eq. (2)

dR

R

u

1

2

dDp

Dp

2

dPa

Pa

2

dTa

Ta

2" #12: 4

Typical values considered for various quantities are listedbelow:h = 6.16 mm H2O dh = 0.05 mm H2O

Ta = 33 C dTa = 0.05 C

Pa = 764.5 mmHg dPa = 0.127 mmHg

q = 1.165 kg/m3 dq = 0.0116 kg/m3

From Eq. (2)

dR

R

u

1

2

0:05

6:16

2

0:0116

1:165

2

0:05

33

2

0:127

764:5

2

" #12

0:00648 0:648%:

Hence, the uncertainty in the mean velocity measurementsU is 0.65%.

(2) Turbulence fluctuation u0:

u0

U

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieA eB

2

qEA EB

; 5

where EA and EB are the mean voltages from sensors A andB of the X-wire, eA and eB are the instantaneous values ofthe fluctuating voltages from sensors A and B. In the pres-ent measurements, EA % EB and let Ebe equal to either EAor EB. Then, the expression reduces to

u0

U


2

q2E

: 6

Following Eq. (2),

dR

R u0

1

2

d


2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieA eB

2q

0

B@

1

CA2

dE

E 2

2

64

3

75

12

: 7

Fig. 6. Hotwire system connections.



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Typical values in the present measurements are:

dE 0:05 V;

E 6:94 V;

d


2

q 0:012 V;


2

q 0:292 V;

Fig. 7. Velocity profile at various stations in 5 diffuser.

Fig. 8. Velocity profile at various stations in 7 diffuser.



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dR

R

u0

1

2

0:012

0:292

2

0:05

6:94

2" #12 0:0209:

That is, the uncertainty in the measurement of the turbu-lent fluctuation u0 is 2.09% with odds 20 to 1.

(3) Turbulent fluctuation v 0:

u0

U f1k


2q

EA EB; 8

where

f1k 1 k2

1 3k2 4k4

12

: 9

In the present measurements, EA % EB and let E be equalto either EA or EB. Then, the expression for v

0 reduces to

u0

U f1k


2

q2E

: 10

Following Eq. (2),

dR

R

v0

1

2

df1k

f1k

2

d


2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

eA eB2

q0B@

1CA

2

dE

E

2264375

12

:

11

Typical values in the present measurement (20:1 odds) are:

dE 0:05 V; E 6:94 V;

d ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieA eB2

q 0:01 V; ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieA eB2

q 0:23 V;df1k 0:008; f1k 1:083;

dR

R

v0

1

2

0:008

1:083

2

0:01

0:23

2

0:05

6:94

2" #12 0:0225:

Hence, the uncertainty in measurement of the turbulentfluctuation v 0 is 2.25% with odds 20 to 1.

(4) Turbulent fluctuation w 0:This is obtained by pacing the X-wire probe in the XZ

plane and by using the same expression as that for v 0.Hence the uncertainty in the measurement of the turbulentfluctuation w 0 is also 2.25% with odds 20 to 1.

3. Results and discussion

In order to study the influence of inlet conditions on theflow and turbulent parameters, three different types of flowat inlet have been experimentally investigated.

(i) The first one is a straight flow, which consists of onlyboundary layer type of distortions near the wall.

(ii) The second one is the flow with a streamlined centrebody with a wake type distortion at inlet in additionto the distortion due to wall boundary layer. In this

case, the wake produced by the streamlined body is

a shallow one. Here, at the rear stagnation point,the streamlines do not separate but merge with theflow near the axis.

(iii) The third one is the flow with wake generated by abluff body. In this case, there will be separation nearthe tail end of the body. The bluff body produces a

Fig. 9. Wake notation.

Fig. 10. Variation of wake half-width and relative wake depth in 5

diffuser with stream lined body.



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deep wake, i.e., the defect velocity is more than thatof a streamlined body wake.

These centre bodies were kept at 3 mm upstream of thediffuser inlet.

3.1. Mean velocity profiles

A study of mean velocity profiles at various downstreamsections of a diffuser is very important because it reveals theperformance and the effectiveness of the diffuser in convert-ing the kinetic energy into pressure energy. In this regionvery close to the wall of the diffusers, the mean velocity isaffected by the boundary layer development. In the centralcore region the presence of a wake produced by a centralbody in the upstream of the diffuser inlet will producevelocity deficit. If wake is not present, then the mean veloc-ity profile will be distorted only by the boundary layer.Figs. 7 and 8 show the measured mean velocity profilesat different axial stations of the diffuser having half-coneangles 5 and 7, respectively. The mean velocity and thecross stream distance across the station are normalizedwith the mass averaged velocity U and the radius of the dif-fuser Y(N), respectively, at a given station. The generaltrend of flow with the centre bodies is the effect of thesebodies in creating a wake in the immediate downstream

and the progressive decrease of wake velocity defect asthe flow traverses through the length of the diffuser.

Fig. 7 shows the radial distribution of axial velocity atvarious downstream stations [AL] in the case of 5 diffuserfor the three cases under consideration: flow without a cen-tre body, flow with a streamlined body and flow with a

bluff body at inlet. The normalized velocity distributionbrings out the effect of velocity distortion at the inlet. Itis seen that for the flow without any centre body at inlet,the flow distortion is only due to boundary layer develop-ment. It may be seen that initially (station A) the boundarylayer thickness which is about 20% (Y/Y(N) = 0.8) hasgrown to 55% (station L).

Two different situations arise for the flow with stream-lined body and bluff body at the inlet. In the case of stream-lined body, due to the presence of shallow wake, theboundary layer prevents wake decay and causes a wakegrowth. In the case of bluff body, the reverse happens asthe wake is deep. The flow is accelerated in the region

between the bluff body and the diffuser and hence the wakeslows down the growth of the boundary layer.

Further, a close look at the velocity profiles reveals thefollowing features. Compared to the flow without the cen-tre body, the centerline mean velocity is smaller at all crosssections for the flow with streamlined body and bluff body.At inlet (station A) in Fig. 7a the velocity profile for theflow with streamlined body has a shallow wake in the cen-


diffuser with bluff body.


diffuser with streamlined body.



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tral region and also the distortion due to boundary layernear the wall. However, the wake of streamlined bodydecays rapidly in the downstream and at the last stationthe memory of the wake has almost been lost. The wakeof bluff body is very deep at the inlet and owing to thepredominant blockage effect higher mean velocities are pre-

vailing in the region between the diffuser wall and the bluffbody. Due to this reason, the boundary layer at inlet isquite thin compared to the other two cases i.e. without cen-tre body and with streamlined body. The width of the wakeand the maximum defect velocity are more for the bluffbody than those for the streamlined body at inlet. In thiscase also the wake decay is reasonably rapid in the down-stream direction. The presence of the bluff body wake isseen even at the last station with a dip of velocity profilenear the axis.

The mean velocity profiles for the three cases of flow forthe 7 diffuser are given in Fig. 8. It is observed fromFig. 8a and b, that from the station G onwards the flow

without centre body has a maximum velocity at the axisshowing the fully developed boundary layer. At station J(area ratio: 3.88) the shape factor is found to be 3.91.Therefore from station J onwards, the flow tends tobecome elliptic. By the use of tuft probe at the exit of thediffuser it is found that the flow separation is incipient nearthe wall from the flutter of tuft. However, there is no cate-

gorical indication of flow separation and hence it may beargued that partially parabolic flow situation exists in the7 diffuser. In case of the streamlined body, even thoughthe wake is shallow at the inlet, it is clearly distinct evenat the last station. Further, from station G onwards thereis only a slight difference between the bluff body and the

streamlined body wakes in terms of defect velocities. Thesetrends are due to the effect of area ratio and the increasedadverse pressure gradient in the wake development.

3.2. Wake half-width and relative wake depth (RWD)

The wake geometry is characterized by the wake half-width, defined from the mean velocity distribution in thewake region. The wake half-width b corresponds to thelocation where the wake defect velocity w is equal to halfof the maximum defect velocity w0 which occurs at the cen-ter of the diffuser axis. The wake notation is shown in

Fig. 15. Variation of pressure recovery coefficient in 7 diffuser.

Fig. 14. Variation of pressure recovery coefficient in 5 diffuser.


diffuser with bluff body.



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Fig. 9. The relative wake depth (RWD) is the ratio of themaximum defect velocity w0 to the local free stream veloc-ity U0. The RWD gives an idea as to how far from the dif-fuser entry, the wake persists. The wake half-width is ameasure of the spreading of the wake with increase in dis-tance in the stream-wise direction. It also gives an idea of

the extent of the flow occupied by the wake.

Figs. 10 and 11 show the variation of wake half-widthand RWD for the streamlined body and bluff-body,respectively. In the case of the streamlined body, the wakehalf-width increases up to a distance of X/L = 0.17 andremains constant until X/L = 0.42 and decreases thereaf-ter till the last station. This is due to the spreading

of the wake, which is not rapid in the initial part of the

Fig. 16. Distribution of turbulence levels in 5 diffuser at X/L = 0.0: (a) without centre body Station A; (b) with streamlined body; (c) with bluff body.



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diffuser. The RWD decreases with increase in distance.This indicates that the wake has been decayed. A deepwake is seen in the case of bluff-body in 5diffuser as seenfrom Fig. 11a. The wake half-width increases in the firstpart of the diffuser and then decreases till the exit. TheRWD decreases with increase in distance as seen from

Fig. 10b. From Figs. 10 and 11, it can be seen that inboth the cases, the wake has decayed.

Figs. 12 and 13 show the decay of wakes in 7 diffuserfor the streamlined body and bluff body. With streamlinedbody, the RWD decreases up to X/L = 0.33 and thenincreases up to X/L = 0.5 and then decreases till the laststation. This indicates that the wake actually grows ratherthan decay under large pressure gradient. This behavior

has been reported by Hill et al. [18] and Stevens et al.[19]. They reported that the wake grows or decays depend-

Fig. 17. Distribution of turbulence levels in 5 diffuser at X/L = 0.17: (a) without centre body Station C; (b) with streamlined body; (c) with bluff body.



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ing on the relative values of the pressure and the shearforces. A considerably large pressure gradient is requiredfor RWD and wake depth to increase even though thewakes are thin.

It is seen from Fig. 12 that despite the high initialadverse pressure gradient due to high level of mixing, the

wake has decayed rapidly in the initial part of the diffuser.

The wake has grown from X/L = 0.33 to X/L = 0.5. This isdue to high pressure gradient. However, the wake hasdecayed towards the exit of the diffuser.

In case of bluff body, the RWD decreases till X/L = 0.08 and then remains constant between X/L = 0.08and X/L = 0.17 and then decreases rapidly. This is due

to the deep wake and the adverse pressure gradient, which

Fig. 18. Distribution of turbulence levels in 5 diffuser at X/L = 0.33: (a) without centre body Station E; (b) with streamlined body; (c) with bluff body.



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has arrested the wake decay. However, from X/L = 0.25to X/L = 0.5, the decay rate is slow and thereafter itdecreases rapidly. Therefore, it is concluded that in caseof 7 diffuser, the effect of the adverse pressure gradienton the wake is seen and there is an interaction betweenthe boundary layer (because of adverse pressure gradient)

and wake.

3.3. Coefficient of pressure recovery

The coefficient of pressure recovery in 5 and 7 diffuserswith three different inlet conditions is shown in Figs. 14 and15, respectively. It is observed from these figures that thereis a marginal increase in pressure recovery in the case of

flow with streamlined body when compared to flow with-

Fig. 19. Distribution of turbulence levels in 5 diffuser at X/L = 0.5: (a) without centre body Station G; (b) with streamlined body; (c) with bluff body.



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out centre body and flow with bluff body for the 5 diffuser.It shows that inlet velocity distortion has some effect onpressure recovery. However, when the flow tends towardspartially parabolic (i.e. in 7 diffuser) the effect is nullifieddue to higher adverse pressure gradient. This may be attrib-uted to the following: there is interaction between bound-

ary layer and the wake. Also the increase in pressure losscoefficient in the presence of wake is quite small, asreported by Stevens et al. [20]. Therefore, all the three cases

show almost same pressure recovery. It is to be noted thatthe coefficient of pressure recovery is higher at the exit inthe case of 7 diffuser compared to 5 diffuser. This is tobe expected because of higher area ratio.

3.4. Turbulence parameters in the diffusers

In general, the RMS values of fluctuating velocities,namely, u 0, v 0 and w 0 are normalized with the free stream

Fig. 20. Distribution of turbulence levels in 5 diffuser at X/L = 0.67: (a) without centre body Station I; (b) with streamlined body; (c) with bluff body.



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velocity Uref at the reference station A. In the turbulencelevel plots in the X-axis the distance (R(N) r) is normal-ized with R(N).

The distribution of u 0, v 0 and w 0 for the three types offlows is shown in Figs. 1629.

Figs. 16a22a show the distribution of u0, v0 and w 0 for

the flow in 5 diffuser without centre body. The maximumvalue of u0 in the boundary layer region varies from about

6% to 7.6%. The corresponding variations for v 0 and w 0 arefrom about 4.3% to 5.8% and from about 4.2% to 6%,respectively.

It is also seen from these figures that in general the rela-tion u0 > w0 > v 0 is valid in the boundary layer region. Thereason for this trend can be explained as follows: since the

boundary of the diffuser wall is at rest, the v fluctuationsvanish everywhere in the wall.

Fig. 21. Distribution of turbulence levels in 5 diffuser at X/L = 0.83: (a) without centre body Station K; (b) with streamlined body; (c) with bluff body.



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This condition is achieved by replacing the wall with anexactly identically fluctuating field of image vorticitybeneath the wall, which cancels the normal component ofvelocity at the location of the wall. But this image field ofvorticity does nothing to suppress the tangential velocityfluctuations. Therefore v 0 < u0 and w 0. This means that

whenever v fluctuations occur, they bring fluid particles

with high streamwise velocity nearer to the wall or lowerspeed fluid particles from the wall. This will cause u 0 tobe greater than w 0. Therefore, u0 > w0 > v 0 is valid in theboundary layer region. This observation is in conformitywith Willmarth [21].

It may also be noticed from the above figures that the

distributions of u0

, v0

and w0

in the boundary layer region

Fig. 22. Distribution of turbulence levels in 5 diffuser at X/L = 1.0: (a) without centre body Station M; (b) with streamlined body; (c) with bluff body.



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show a peak very close to the wall near the diffuser inlet,the peak gets shifted away from the wall with distance inthe stream wise direction clearly indicating the growth ofthe boundary layer. Similar trend is also reported in the lit-erature [4].

Figs. 16b22b show the distributions ofu 0, v 0 and w 0 for

5 with streamlined body. The general remarks made for thecase without centre body are also valid here. The maximumvalue ofu 0 in the boundary layer region at station A is about6.8%. The peak value in the boundary layer increases in the

stream wise direction and its value at station M is 7.2%. Thepeak of w 0 in the boundary layer decreases from 6.2% to5.6%. In this case also, the trend u0 > w 0 > v0 is found tobe valid in the boundary layer region. The peak values ofu 0, v0 and w 0 is also found to shift away from the wall inthe streamwise direction. The levels of turbulence intensities

in the wake region are higher than those in the boundarylayer region at station A, but the values of the intensitiesdecrease rapidly with increase in distance in the streamwisedirection. Generally, the relation u0 > w 0 > v0 is found to be

Fig. 23. Distribution of turbulence levels in 7 diffuser at X/L = 0.0: (a) without centre body Station A; (b) with streamlined body; (c) with bluff body.



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valid in the wake region also from station A to I. However,at stations K and M both the fluctuations are almost havingthe same value in the wake region.

The relative magnitudes of three normal stresses are par-ticularly noteworthy in the case of flow in 5 diffuser withbluff body. From Fig. 16c it is seen that in the portion of

the shear layer near the wall, w0

> u0

> v0

. This is differentfrom the situation observed in other two causes, whereu0 > w 0 > v0. With increase in distance in the stream wise

direction, however, the trend becomes u0 > w 0 > v0. Thesechanges in the degree of anisotropy of the turbulence arelikely to be due to the formation of vortices behind the bluffbody. The same trend has been observed in the 7 diffuserwith bluff body also.

In the wake region at station A, the level of fluctuations

ofu0

is greater than w0

. The level of fluctuation ofv0

has theleast value. The peak values of turbulence correspondto the point at which the mean velocity gradient has the

Fig. 24. Distribution of turbulence levels in 7 diffuser at X/L = 0.17: (a) without centre body Station C; (b) with streamlined body; (c) with bluff body.



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maximum value. From station C onwards the trend in thewake region is u0 > v 0 > w 0. In the boundary layer region,the presence of the wall makes the v fluctuation vanish atthe wall. This boundary condition is not applicable forthe wake, and therefore there is no such constraint forthe v fluctuation in the wake region. Since the v fluctuation

brings fluid particle possessing larger momentum from the

outer region to the centre of the wake, the u fluctuationexceeds the v fluctuation. In general the relation u0 > v0 > w 0

is valid in the wake region. The levels of fluctuationsincrease with increase in distance in the streamwise direc-tion. From Figs. 16c22c it is seen that the levels of fluctu-ations u 0, v 0 and w0 are almost constant across the diffuser

except the region close to the wall.

Fig. 25. Distribution of turbulence levels in 7 diffuser at X/L = 0.33: (a) without centre body Station E; (b) with streamlined body; (c) with bluff body.



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The distributions ofu0, v 0 and w 0 are shown for the threecases of flow for the 7 diffuser in Figs. 2329. From Figs.23a to 29a which is for flow without centre body it is seenthat the maximum value of u 0 is about 6.2% at station Aand increased to about 8% at the station I. At stations Kand M the levels of u 0 are constant except in the wall

region. The maximum value of v0

is about 4.6% at station

A and increased to 6.5% at station M which remains con-stant across the diffuser. The corresponding variation ofw 0 is from 2.8% to 6.5%. As in the previous cases, the peakvalue of fluctuation developed very close to the wall nearthe diffuser inlet shifts away from the wall on the stream-wise direction. But at the last two stations K and M, their

values remain constant across the diffuser. The relation

Fig. 26. Distribution of turbulence levels in 7 diffuser at X/L = 0.5: (a) without centre body Station G; (b) with streamlined body; (c) with bluff body.



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u0 > w 0 > v 0 is found to be generally valid in the boundarylayer region for this case also.

From Figs. 23b to 29b which are for streamlined body,it is seen that the relation u 0 > w 0 > v 0 is valid only in theboundary layer region from stations A to K. It is seenthat u0 is more than v 0 and w 0 in the last station M

(Fig. 29b). The values of v0

and w0

are equal at this sta-

tion. At station A in the wake regions u 0 and w 0 are nearlyequal. From station E onwards v 0 and w 0 are almostequal. In case of flow with bluff body (Figs. 23c29c) atinlet the relation w 0 > u 0 > v 0 is valid only in the boundaryregion as in the case of 5 diffuser with bluff body. In thewake region, the relation u0 > v 0 > w 0 is found to be gen-

erally valid.

Fig. 27. Distribution of turbulence levels in 7 diffuser at X/L = 0.67: (a) without centre body Station I; (b) with streamlined body; (c) with bluff body.



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4. Conclusion

In many applications where diffusers are used, especiallyin turbo-machines, the presence of center bodies ahead ofthe diffuser inlet produces wake-type central velocity dis-tortion along with the boundary layer type of distortion

near the walls. The presence of wake at the inlet causes astreamline curvature in the central core of the diffuser

and greatly affects its performance. From the present study,it can be concluded that for the 5 diffuser, there is a mar-ginal increase in pressure recovery with the presence of cen-ter bodies. However, for the 7 diffuser, in the case of thestreamline body, the wake has actually grown underadverse pressure gradient conditions since the wake is thin.

In the case of the bluff body, the wake decay rate is arresteddue to the interaction between boundary layer and wake.

Fig. 28. Distribution of turbulence levels in 7 diffuser at X/L = 0.83: (a) without centre body Station K; (b) with streamlined body; (c) with bluff body.



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Hence the pressure recovery is not affected when there iswake at the diffuser inlet.

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Fig. 29. Distribution of turbulence levels in 7 diffuser at X/L = 1.0: (a) without centre body Station M; (b) with streamlined body; (c) with bluff body.



25/25

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[21] W.W. Willmarth, Structure of turbulence in boundary layers, Adv.Appl. Mech. 15 (1975) 159.


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