Indian Journal of Engineering & Materials SciencesVol. 5, February 1998, pp.15-21

Optimum inlet swirl for annular diffuser performance using CFD

Ratan Mohan", S N Singh" & D P Agrawal"

"Department of Applied Mechanics, bDepartment of Mechanical Engineering,

Indian Institute of Technology, Hauz Khas, New Delhi 110016, India

Received 14 October 1996; accepted 19 June 1997

A computational study has been made to determine the best performance for a set of annulardiffusers with and without swirling inlet flow. Three straight walled annular diffusers each of area ratio3.0 and equivalent half-cone angles of 12.5°, 15° and 17.5° have been taken. 6-8 levels of swirl havebeen imparted to inlet flow in each of the diffusers. A 2-D axisymmetric flow code has been modified toinclude the swirl component and used for the calculations. For each diffuser, the results show animprovement in pressure recovery up to a particular swirl level and a fall thereafter. The extent ofimprovement has been found to be maximum for the 17.5° equivalent half cone angle diffuser. Theabsolute values for the pressure recoveries are, however, highest in the 12.5° case, as is to be expected.The study illustrates the usefulness of the computational approach in finding the optimal diffuserperformance in an economical way.

Annular diffusers are found in turbomachinesystems where the flow occurs around a centralshaft. Typically it may be present after thecompressor to reduce the flow velocities to thecombustor, or at the exhaust of the turbine toreduce back-pressure. As with other type ofdiffusers, the annular diffuser serves to reduceflow velocities and build up static pressure.Sometimes, as when the diffuser exit flow is toenter the compressor, flow uniformity also isimportant. Depending upon the objective, i.e., adesired pressure recovery, velocity reduction orflow uniformity, the diffuser parameters: shape,area ratio, length, inlet flow conditions, etc. maybe varied to achieve the same. A frequentconstraint here, however, is the length (size) of thediffuser. But shorter length increases thepossibility of flow separation, affecting diffuserperformance adversely.

One of the measures known to control flowseparation and improve diffuser performance is theimposition of swirl on inlet flow. Swirl at diffuserinlet imposes radial pressure gradients which forcethe flow outwards and suppress separation on theouter wall. In other applications, an important usefor swirl is in gas turbine combustors to create thecentral recirculation zone for flame stabilizationand better fuel conversion. Relatively morenumber of studies on swirling flow in

turbomachine/gas turbine systems are, m fact,related to this latter application.

Effect of swirl on flow in annular diffusers hasbeen investigated experimentally by severalresearchers. Coladipietro et al,' and Shaalan et al. 2

studied the effect of swirl but on a single diffuser.Lohmann et al. 3 studied 8 annular diffusers withinlet swirl between 0-48°. They systematicallyexamined the effect of parameters such as length,area ratio, cant angles on performance, exitvelocity profile distortion and flow separation.Kumar and Kumar4 experimentally studied 5annular diffusers with inlet swirl upto 25° andfound an overall increase in static pressurerecovery. Morsi and Clayton5

,6 presentedexperimental and numerical study of turbulentflow in annular ducts with a view to examine thepredictions against experimental data. Singh et al. 7

have investigated wide-angled annular diffusersand again found inlet swirl to increase pressurerecovery and suppress separation.

A second approach to flowfield andperformance determination is the numericalmethod. Though started much earlier, it is only inthe last decade or so that rapid developments incomputational hardware have given great impetusto the development of the computationalapproaches. Presently several CFD (computationalfluid dynamics) codes capable of handling

16 INDIAN J. ENG. MATER. scr., FEBRUARY 1998

complex flow geometries: PHOENICS, STAR,CONCERT, and TASCflo, are availablecommercially. While it cannot be said that they area substitute for experiments, in many cases resultsstatisfactory for engineering purposes may beobtained from them. In such cases the code, i.e.,the numerical method, is a valuable tool in designactivity enabling a significant reduction in the needfor experiments.

In the present study, a 2-D plane/axisymmetriccode developed earlier has been extended toinclude the swirl component. The code has beenvalidated for non-swirling flows and reported

1· 202324 In h f' u flear ier ' '. t e case 0 swir mg ows,experimental and numerical studies in literatureappear to be more in relation to combustor flows,swirling flow in sudden expansion and dumpcombustorsS

-I2 Results from the present

formulation are first validated against those fromone of the above studies8

• Subsequently,predictions are made for 3 straight walled annulardiffusers of area ratio 3.0 and equivalent half-coneangles of 12.5°, 15° and 17.5°, without and withswirl. The numerical formulation, the details of thegeometries and flow conditions, and the analysis ofresults are presented here.

Numerical FormulationThe numerical method employed for the

calculations is based on the finite volumeapproach. Earlier numerical work6

,13-l5 on swirlingflow has mostly employed the cylindrical polar co-ordinate system (z,r,cjl). Habib and Whitelawl6 intheir work on conical diffusers used the curvilinearorthogonal co-ordinates in the meridian plane inplace of (z,r). However, the general non-orthogonal system has since become more popularas it affords better grid control and boundaryfitting for curvilinear geometries. A description ofthe 2-D finite volume method using non-orthogonal co-ordinates, along with the relevantequations is available in earlier studies 17.20.

For the present work, the appropriate co-ordinate system is (~,l1,cjl); ~,11 being the generalnon-orthogonal co-ordinates in the meridian (2-D)plane. It may be noted that although in this planethe transport equations are cast in terms of thegeneral directions ~, 11, for solution thedecomposition of the velocity vector v is chosen tobe in the Cartesian components u and v (refs.18,19). The required transformations now cause

the equations to become more complicated withcross derivative terms, but ill behaved curvatureterms along with consequent convergence

bl 'd dl8,l9 I' . flpro ems are avOl e . n axisymmetric ows,additional terms appear in the v-equation. Theseare -2J..lv// and, if vcjl=I- 0, -pv//r.On the otherhand, because $-direction symmetry, all the 8( )/8$terms in the cjl-mornentum equation vanish and itreduces to

... (1)

where Vi is the velocity component in the i-direction, aij is the shear stress and g (= /(x'; rnXr{ci) is the determinant of the metric tensorcomponents, v¢ (or v¢) is the more familiar w-(swirl)- velocity component. Since w does notfigure in the continuity equation and the flowfieldcalculating equations are still the U-, v- and p-equations, the w-velocity component can be treatedas a scalar and the above equation transformed tothe scalar transport equation of 2-D formulationwith Cartesian u, v components.

The basic solution algorithm remains same as inthe 2~D non-swirling case except that now thescalar w-equation also is to be solved. The standardk-s turbulence model is used. Although thestandard form of the model is not strictly valid inrepresenting the turbulence physics in swirlingflows, its use has been found to be successful inpredicting flowfield and recirculating zones well2l.The effect of the gradients of w on turbulencegeneration is included in the source term of theturbulent kinetic energy equation. Boundaryconditions are assigned as the given inlet values atWest-boundary (inlet), no-slip at the walls (North-and South-boundaries) and zero-flux condition atthe East-boundary (outlet).

Boundary fitted non-orthogonal grids were usedfor the calculations. A typical grid (46x 18) is I

shown in Fig. 1. Two other grids, 62x32 and82x42 were used. The results presented later arefrom the 62x32 grid as it was found to yield

MOHAN et al.: OPTIMUM INLET SWIRL FOR ANNULAR DIFFUSER 17

7.75 3.80 9.575 15.118~.__~ . ._._. ~__.__L _

(s) Diffuser dimensions (in em)

(b) Typ;cal Grid

Fig. I-Annular diffuser geometry

satisfactory values with no significantimprovement from the 82x42 grid. Upwinddifferencing scheme was used in the calculations.

dimensions. To obtain the three different diffusersof equivalent half cone angles 12.5°, 15° and17.5°, essencially the length, L, of the diffuser isvaried as 22.3, 18.46 and 15.69 em respectively. Itmay be mentioned here that, in principle,combination of the various geometrical parameterscan give rise to infinite diffuser geometries. Thethree diffusers are just a small selection, meantonly for assessing the effectiveness of thecomputational approach in finding the bestgeometry and inlet condition. The axial velocityprofile in the computations is again taken as flat,with an average value of 25 mls. For Wo at inlet, theshape of the experimental velocity profiles ofMorsi and Clayton" were taken as a guide. Thoughthese appear free vortex like, the actual variation isapproximately more linear than the -:' variation. Wo

were hence 'set as Wo=Uo tane at the outer walland made to increase linearly to 1.6 times thatvalue at the inner wall. Exactly at the walls Wo willof course be zero, but since the computational nodewill always be a little away from the wail, thevalues from the above defined profile will bereasonable.

Results and Discussion

Results of the present calculations for thesudden expansion geometry matched very well

Flow Geometries and Inlet Conditions with those of Rhode et al. In the no swirl case, theThe first geometry used in the calculations is the reattachment length xRID was computed to be 2.03,

axisymmetric sudden expansion of Rhode et al.8 i.e., xR/h = 8.1, almost the same as by Rhode et al.The objective was to compare the swirling-flow Then in Fig. 2, the axial velocity profiles at threeresults of the present calculations with those axial locations are compared for (i) $ = 0° and (ii)obtained by Rhode et al. In this geometry, flow in $ = 45°. Chaturvedi's" measured values are alsoa smaller (inlet) pipe of 15 em diameter exits into a shown on the figure for the $ = 0° case. As can belarger pipe of 30 em diameter. The dimensions seen the comparison is very good. Fig. 2c showsgive a step height of 7.5 ern, i.e., hiD = 0.25. the w-velocity profiles at 3 axial locations. OnceRhode et al. made the calculations for inlet Re = again the agreement is seen to be excellent.1.26x 105 based on the inlet pipe diameter. This Having thus verified the modified code to givecorresponds to an inlet average axial velocity of proper results for swirling flows, attention was12.95 mls. Further in their work, the inlet velocity turned to annular diffuser calculations. Theprofile was assumed to be flat for both the axial objective now being to find out the improvementsvelocity, uo' and the tangential (swirl) velocity, WOo in pressure recoveries for the three diffusers forAccordingly Uav = uo' Wo was taken directly as Wo = given swirl levels and hence determine theuotan$, where $ is the swirl angle. The optimum swirl value for best diffuser performance.specifications are thus precise and complete for First the general flowfield picture for the 17.5°calculation purposes. case is depicted in Fig. 3, by means of the velocity

The second geometry, straight walled annular vector plot, pressure contours and the streamlinediffuser, is the subject of this study. It is shown plot. Figs 3a-3c show the no swirl case and Figsschematically in Fig. 1 along with th~., _ -.;--. f show the 32° swirl results. (This particular&" ~.\.'f'"' -'C;'"

{&~r~,:~~:'.~-c.~i~~~,~~ .ll~ l _ •... '\ ,~\,

18

0.4

0.3riD

INDIAN J. ENG. MATER. SCI., FEBRUARY 1998

xID = 0.3 xID = 1.0 xlD = 1.57

~\... :~.

0.2 . \.

0.1 ..... 1.

OLL~~~~LL~~~~~LL~~~~~~~~~~~~LLLL~~~~LLLL~-0.5 o 0.5 1.0 ~0.5 o 0.5

u/ua

1.0 -0.5 o 05 1.0 1.5

0.5r-~------------------'-----~-------------'-------''------------'

0.4

0.3rID

xID = 0.3

",... ;. ~.

xID = 1.0

1.0 -0.5

xID = 1.57

1.0 1.5

xID = 0.32

o 0.5u/ua

o 0.5

0.5r---~----~----.-----.---~--~------~---'---------------------'

rID

0.4

xlD = 1.08 xlD = 1.68

OLL~~~~LL~~~~~LL~~~~~LLLL~~~~~LL~~~~~LL~~-0.5 0 0.5 1.0 -0.5 0 0.5 1.0 -0.5 0 0.5 1.0 1.5

w/uaFig. 2---Comparison of axial and swirl velocity profiles

(--) Rhode et al.; (e) Chaturvedi; (-) calculated

0.3

0.2

0.1

value of <I> was found to grve the mmimum in the streamwise direction, starting from about 0separation in this diffuser). In the no swirl case, the at the inlet to about 230 N/m2 in the downstreamvector plot and the streamlines show a fairly large straight section. However, recovery after section 2separation zone on the outer (casing) wall near the IS not much. In the case with inlet swirl, theexit (Fig. 1). This results in the fall of pressure separation zone at exit is reduced considerably,recovery. The pressure contours show a steady rise ,though not eliminated altogether. From the

MOHAN et al.: OPTIMUM INLET SWIRL FOR ANNULAR DIFFUSER 19

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 3-Velocity vectors, pressure contours andstreamlines in 17.5° diffuser (a-c) no swirl; (d-f) 32° swirl

pressure contours it is seen, expectedly, that now asignificant gradient exists in the radial directiontoo.Near inlet it is as high as 300 N/m2 because ofthe high centrifugal forces there but reduces toabout 60 N/m2 at section 2 because of decay inswirl. In the streamwise direction, the pressurebuild-up is approximately from 150 to 640 N/m2

between inlet to section 2. Hence significantincrease in pressure recovery results.

Fig. 4 shows a sample plot of the exit velocityprofiles (at section 2) for the 15° diffuser, for

various swirl levels. Initially, in the no swirl case,the profile is skewed towards the hub, as is mostlyobserved in annular diffusers. Effect of inlet swirlis seen to lift the velocity maximum from the hubside and ultimately push it towards the casing wall.However, high swirl levels -are needed (approx. >.20°) in order to cause a significant shift in thevelocity maximum. This is because only with highinlet swirl, sufficient swirl (centrifugal force) isstill available at section 2 to drive the flowoutwards.

20 INDIAN J. ENG. MATER. sci., FEBRUARY 1998

0.8

0.6

0.4

0.2

OLu~~~~~~~LUJJ~~~LW

-0.25 o 0.25 0.50 0.75 1.00 1.25

Fig. 4--Exit velocity profiles (at section 2) for variousdegrees of inlet swirl

For the calculation of pressure recovery, thefollowing formula is used.

f (P2 / p)dm2 - f (PI / p)dmlC = drill = pujdAjPI.

f-utld~2 ... (2)

The use of this formula is more appropriatebecause here Uti is used in normalisation. Uti is themagnitude of the total velocity vector at section 1and therefore includes the contribution of w to thedynamic energy. It may be noted that as w changesfor each case, Uti will also change. This impliesthat we have a variable normalization factor.However, the effect on Cp is very small becausePI> P2 also adjust accordingly to Uti. For aparticular test case with 17.5° diffuser, the axialvelocity in no swirl case was increased from 25 to32 mls to make it equal to Uti in a swirling case(about 30°). But Cp was found to change only from52.13 to 52.53 %. We can thus regard the Cp

values to be representative of the diffuserefficiency, even if the inlet dynamic energy is notthe same in every case.

The complete calculated Cp sets are shown as Cp

versus Ij> plots in Fig. 5. The results are alongexpected lines, as reported in earlier experimentalworks on the annular diffusers, i.e., swirl helps toimprove pressure recovery up to a point butthereafter has a detrimental effect. Quantitatively,

08·

r~07 ~

~0.6

Cp

0.5 • 125

.---.

\•

• 150

• 175

0.4 LL--'---'-'-.L...L..LJLL.L....L-L..L-L--'---'-'-~-'-L-L---'---'---'

o 20 30 40 5010

ql (deg)

Fig. 5-Pressure recovery versus swirl angle for the threediffusers

the pressure recovery values for no swirl in thediffusers are 0.68, 0.613 and 0.52 for the 12.5°, 15°and the 17.5° cases respectively. With swirlpresent, the maximum Cp values become 0.72, 0.69and 0.66 (for Ij> = 25°, 28° and 32°) for the samethree cases. The maximum increase inperformance (about 25 %) is for the shortestdiffuser (17.5°). This is because the diffuser has alarger separation zone to begin with in the no swirlsituation and therefore has the most scope forimprovement. But the overall losses are highestand so the best Cp value is still lower than that inthe other two diffusers. Also from the curves it isevident that the sensitivity of the 17.5° diffuser isgreater, i.e., if the Ij> value deviates from theoptimum (32°), the performance falls sharply.

ConclusionsThis study focuses on the capability of a 2-D

axisymmetric code (modified to include swirl) ingiving useful results for annular diffuserperformance. Three annular diffusers of equivalenthalf-cone angles 12.5°, 15° and 17.5° were takenand flowfield and pressure recoveries calculatedfor various swirl levels given at inlet. It is seen thatthe computed results can give good preliminaryinsight into the nature and extent of improvementin diffuser performance, at much less cost thanexperimentation. Specific conclusions are:

(i) Inlet swirl up to a particular level improvespressure recoveries but thereafter has a detrimental

MOHAN et af.: OPTIMUM INLET SWIRL FOR ANNULAR DIFFUSER 21

effect. Cp vs <\> curves go through a maximum forall three diffusers. Maximum pressure recoveriesobtained are 72, 69 and 66 % for the 12.5°, 15° and17.5° cases respectively.

(ii) The extent of improvement is most in the17.5° diffuser. From a no swirl value of 52 %, itincreases to 66 % for 32° swirl.

(iii) Although the extent of improvement is mostin the 17.5° diffuser, it is also the most sensitive tovariations in <\>. If <\> deviates from operating at theoptimal value, performance falls sharply.

AcknowledgementThe authors wish to acknowledge the financial

support given by Propulsion Panel, AeronauticalResearch & Development Board, Bangalore, in oneof the earlier projects on 2-D code development.

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