performance evaluation of an air-conditioning compressor part ii: volute...

International ,Iournal of Rotating Machinet3,

1999, Vol. 5, No. 4, pp. 241 250

Reprints available directly from the publisherPhotocopying permitted by license only

1999 OPA (Overseas Publishers Association) N.V.Published by license under

the Gordon and Breach Science

Publishers imprint.Printed in Malaysia.

Performance Evaluation of an Air-ConditioningCompressor Part II: Volute Flow Predictions*

YU-TAI LEE and THOMAS W. BEIN

David Taylor Model Basin, 9500 MacArthur Blvd., West Bethesda, MD 20817-5700, USA

(Received 12 May 1998," In finalform 10 July 1998)

A numerical method that solves the Reynolds-averaged Navier-Stokes equations is used tostudy an inefficient component of a shipboard air-conditioning HCFC-124 compressorsystem. This high-loss component of the centrifugal compressor was identified as the volutethrough a series of measurements given in Part of the paper. The predictions were madeusing three grid topologies. The first grid closes the connection between the cutwater and thedischarge diffuser. The other two grids connect the cutwater area with the discharge diffuser.Experiments were performed to simulate both the cutwater conditions used in the predictions.Surface pressures along the outer wall and near the inlet of the volute were surveyed forcomparisons with the predictions. Good agreements between the predicted results and themeasurements validate the calculations. Total pressure distributions and flow stream tracesfrom the prediction results support the loss distribution through the volute. A modified voluteconfiguration is examined numerically for further loss comparison.

Keywords." Air-conditioning compressor, Volute, Cutwater (tongue), Diffuser,Reynolds-averaged Navier-Stokes equations

INTRODUCTION

U.S. Navy shipboard centrifugal chilled water air-conditioning systems currently utilize refrigerantCFC-114. In response to the world communitydecision to eliminate the use of CFC refrigerants,the U.S. Navy has begun a program to convert theair conditioning plants to an environmentallyacceptable refrigerant. HCFC-124 was identifiedas a potential candidate to replace the CFC-114.

A generic centrifugal compressor unit, as shownin Fig. 1, was designed based on the properties ofthe HCFC-124. The compressor consists of tworows of inlet guide vanes, an impeller, a vanelessdiffuser, an elbow, and a volute and its dischargediffuser. The isentropic efficiency of the new

compressor was measured to be 10% lower thanthe design prediction. A detailed measurement ofthe systems component performance, as shown inBein and Lee (1998), indicated that the volute

This paper was originally presented at ISROMAC-7.Corresponding author. Tel." 301 227 1328. Fax: 301 227 5707. E-mail: [email protected].

241

242 Y.T. ILEE AND T.W. BEIN

FIGURE Generic compressor unit for shipboard air-condi-tioning system.

contains the largest area of loss in the compressor.Thus, a computational analysis was made to investi-gate the loss in the volute.

Limited studies (Iversen et al., 1960; Stiefel, 1972;Brownell and Flack, 1985; Van Den Braembusscheand Hande, 1990; Elholm et al., 1992; Ayder et al.,1993; Ayder and Van Den Braembussche, 1991;1994) were performed for the volute flow and itsinteraction with other rotating and non-rotatingcomponents of centrifugal compressors. Most ofthese works concentrated on the experimentalstudies. A recent study by Ayder and Van DenBraembussche (1994) used an Euler solver toexamine the volute flow. They implemented a lossmodel in the code to account for the friction losses.The current numerical model solves Reynolds-averaged Navier-Stokes equations. In the follow-ing sections, the experimental facility used to recordthe volute flow characteristics and the measured

quantities are first introduced. A brief review of thecurrent numerical method follows. For the numer-ical results, three different gridding approaches areexamined and the predicted pressure distributionsare compared with the experimental data. The flowregion with a high loss is identified from totalpressure distributions. A modified volute config-uration is studied based on the present numericalmodel to evaluate the effect of flow recirculationdownstream of the cutwater region.

EXPERIMENTAL SETUP

l.n order to provide detailed information for under-standing the compressor performance shown inFig. 1, an experimental setup using the CentrifugalCompressor Development Facility at the AnnapolisLaboratory of the David Taylor Model Basin wasestablished. There are two rows ofinlet guide vanes.The shrouded impeller has 13 main blades and 13splitter blades with a 30 backswept. At the designpoint, the impeller rotates at 17,983 rpm with a tipspeed of 630 fps (192 m/s). The impeller exit radiusis 4.02in (102.11mm). The radius ratio of thevaneless diffuser exit to the impeller exit is 1.52.The inlet width of the vaneless diffuser is 0.35 in(8.89 mm) and the exit width is 0.1425 in (3.62 mm).The flow coefficient is 0.0654 and the head coef-ficient is 1.2324. The specific speed is 0.0903 (whichis calculated using rpm, cfs, and enthalpy differ-ence). A total of 40 static pressure taps wereinstalled along the front plate and the back plateof the compressor in the vaneless diffuser and thevolute sections. They are distributed along thecomplete volute flow passage with a concentrationof pressure taps at the cutwater. In addition, fivetotal pressure probes were installed to measurevelocities at the exit of the vaneless diffuser, insidethe volute immediately downstream of the cut-

water, in the middle of the volute, and at the exit ofthe discharge diffuser. Three dynamic pressuretransducers were installed in the vaneless diffuserand one in the volute to measure the dynamicpressure response. The estimated error for the static

AIR-CONDITIONED COMPRESSOR: PART II 243

pressure measurements is 2%. The details of themeasurement setup are shown in Bein and Lee(1998a,b).

For evaluating the effect of the flow through thevolute, the measurements were carried out in two

steps. A flush mounted movable cutwater plug wasinstalled near the cutwater. This plug, when pushedout from outside of the back plate, was designed toblock the fluid flowing back to the cutwater fromthe discharge diffuser. The experimental conditionwas adjusted to the compressor design condition.

Three sets of pressure data were taken from eachpressure probe. The steady static pressures, referredto as the data of the open cutwater, were obtainedby averaging these three data sets. Under the same

conditions, a second set of measurements was

performed for the closed cutwater. The secondseries is referred to as the data of the closedcutwater. The measured isentropic efficiency ofthe closed cutwater condition drops 0.5% whencompared with the open cutwater condition asshown in Bein and Lee (1998a,b).

FIGURE 2 Volute configuration and coordinate system.

C 0.09. The source term in Eq. (1) is

COMPUTATIONAL METHOD

Governing equations, including the continuity,momentum and energy equations, for compressibleflows are solved with a two-equation k-c turbulencemodel for the volute flow. The coordinate fordepicting the volute geometry is shown in Fig. 2.The governing equations in curvilinear coordinatesare written as:

J Ot(pq) -i DUiq -+- #effGii-i -+- Sq

where q 1, ux, uy, uz, h, k, c] and p, J, Ui, G(j repre-sent fluid density, the Jacobian of the coordinatetransformation, transformed velocities, and diffu-sion metrics, respectively. The effective viscosity

#eff represents a sum of the laminar viscosity # andthe turbulent eddy viscosity #t then re-scaled by a

turbulence Prandtl number or Schmidt number Crq.The turbulent eddy viscosity #t--pC#k2/c and

0

--Pxi -+- V[#eff(b{J)xi] (#effVb{J)xiDp+ (2)Sq Dtp(P c)

_p(c/k)[(C1 + C3(Pr/c))Pr C2c]_

and Pr stands for the turbulence kinetic energyproduction rate. The constants for the c-equationare C1 1.15, C2 1.90 and C3 0.25.

Finite-difference approximations are used todiscretize the transport equations on non-staggeredgrid mesh systems. A second-order upwind schemeis used to model the convective terms and second-order central difference schemes are used for theviscous and source terms of Eqs. (1) and (2). Forturbulence quantities, the convection process ismodeled by a first-order upwind scheme. A pressurebased predictor/corrector solution procedure shownin Chen (1989) is employed to achieve velocity-pressure coupling. The discretized systems are

solved by an implicit Euler time-marching scheme.

244 Y.T. LEE AND T.W. BEIN

The numerical solutions were considered convergedwhen the residuals of each discretized equationdrop five orders of magnitude.

PREDICTION FOR CLOSED CUTWATER

For the flow past the vaneless diffuser and theelbow, both calculations and the experimental dataindicated that flow past the vaneless diffuser iscompletely mixed out before reaching the 90-degreeelbow. Thus, the inflow condition for the presentcalculations to the volute after the elbow wasassumed to be uniform initially along the merid-ional direction. The swirl component of the inletvelocity was taken from the measured value. As thetime-marching scheme proceeded the total massflow through the volute inlet was maintained at thedesign condition. It is worth noting that theuniform-flow assumption was used in the conven-tional volute design theory described by Traupel(1977) and by Eckert and Schnell (1980). Themeasured static pressure at exit plane of thedischarge diffuser was used as the exit boundarycondition. In order to account for the real gasproperties (HCFC-124) the computation was

performed using the perfect gas law with an

isentropic exponent for the real gas.An O-grid topology, shown in Fig. 3, at each

volute cross section was first used to study the flowpattern. The grid contains 151 meridional nodesand 75 x 25 nodes at each cross plane. This gridsystem has a singular line at the center of the volutecross section. This singular line prevents thegeneralization of the grid transition in the cutwaterregion for connecting with the discharge diffuser.The predicted pressure distributions at the volute

inlet and at the wall of mid-radius are comparedin Fig. 4 with the measured distributions for theclosed cutwater case. The labeled "EXP (INLET)"pressure is the measured pressure at the vanelessdiffuser exit. The cutwater region starts at 0=22.5 where the measured minimum pressureoccurs. The computational grid starts at 0 25Since the cutwater was not connected, the pressurerecovery at smaller volute angles was not predicted.The predictions agree well with the measurementsat the inlet and the wall locations. Both theprediction and the measurement, however, showdifferences between the inlet and the wall pressures.Figure 5 shows a calculated pressure contour plotover a typical cross section (e.g. 0 145) along the

65 -0"

/" ,...,60

"55 ,/T GLOSED OUTwATEH7,’

50J; at EXP (WALL)[.,’

45 i-4r_ 1 EXP (INLET)

40 F PRED (INLET)

35 - PRED (WALL)

/

3’o , oo 3 oo 4 ooTANGENTIAL ANGLE (DEG)

FIGURE 3 The O-grid structure for the closed cutwatervolute.

FIGURE 4 Comparison of static pressure for the closed cut-water volute.


FIGURE 5 Predicted static pressure contours at 0= 145O-grid for closed cutwater. (See Color Plate at the back ofthis issue.)

FIGURE 6 The H-grid one-block topology for using opencutwater volute.

volute pass. The pressure distribution is uniformlydistributed on the left side of the figure, i.e. largerradius wall. There is a pressure gradient between theinlet and the bottom wall as it is shown in Fig. 4. Inaddition, the results indicated that the sharp suctionpressure near the cutwater was not produced by thereturning flow from the discharge diffuser throughthe cutwater. This result also confirms the smallmeasured difference in efficiency between the closedand open cutwater cases.

PREDICTION FOR OPEN CUTWATER

In order to connect the cutwater with the dischargediffuser, the O-grid topology was changed to an H-grid. In Fig. 6, the H-grid is a one block structuredgrid and has 162 nodes in the meridional direction,8 x 14 nodes on each cross plane ofthe volute pass.

Since the inlet portion of the grid is relatively finerthan the other parts, the gridlines are very skew nearthe inlet. The overall grid distribution is coarsebecause of the restriction of the grid skewness.Similar boundary conditions were applied exceptan interface boundary was used at the connectingplane of the cutwater between the volute and thedischarge diffuser. The predicted inlet and wallpressures shown in Fig. 7 show that the variation

7o

65

60

rr 55

a.. 50

45

4O

OPEN CUTWATER1-BLOCK H-GRID

EXP (INLET)

EXP (WALL)

PRED (INLET)

PRED (WALL)

0 100 200 300 400 500TANGENTIAL ANGLE (DEG)

FIGURE 7 Comparison of static pressure for open cutwatervolute using one-block grid.

in pressure across each cross section is small.Although the predicted low pressure near thecutwater agrees well with the open-cutwatermeasurement, the calculated results overpredictthe measured pressures in the other volute sections.A two-block grid structure was generated to

reduce the grid skewness of the one-block ap-proach. Figure 8 shows the 2-block grid structure.The first block contains the inlet portion and


FIGURE 8 The H-grid two-block topology for open cut-water volute.

7O

65

60

,5,5

45

40

35

3O

| OPEN CUTWATER

__t z 2-BLOCK H-GRID

-I1 C) EXP (INLET)

PRED (INLET)

PRED (WALL)

0 oo 200 300 400TANGENTIAL ANGLE (DEG)

500

FIGURE 9 Comparison of static pressures for open cut-water volute using two-block grid.

consists of l9 x 21 47 nodes and the secondblock has 201 x 35 47 nodes. The grid nodesat each cross-section are more than quadrupled.The predicted pressure is compared with the mea-surement in Fig. 9. The agreement between thecalculation and the measurement is better than theone-block approach due to the grid resolution andgrid distribution. Figure 10 shows the predicted

FIGURE 10 Predicted static pressure contours at 0= 145using two-block grid for open cutwater. (See Color Plate Il atthe back of this issue.)

pressure contours for the open cutwater conditionat the same section as Fig. 5 shows. The generalfeature is similar between Figs. 5 and 10 except theoverall pressure levels. Due to the opening of thecutwater, the inlet pressure and its gradient betweenthe inlet and the wall are lower than the closedcutwater case. Both cases from the experiment andthe calculation, however, show that the lowpressure occurs near the cutwater.

Figure 11 shows a combined plot for the openand the closed cutwater conditions from bothmeasurements and predictions. Unfilled symbolsused in Fig. 11 are for the open cutwater and filledsymbols are for the closed cutwater. It is shownclearly from calculations and measurements thatthe inlet pressure is consistently lower for the opencase than for the closed case. The wall pressure,however, remains similar. The measured datashows that the pressure for the open cutwatercondition is about 2-4% lower than that for theclosed cutwater condition at the inlet and thedifference is less than 2% at the wall. Althoughboth the measurement and the prediction showlower peak pressures for the open cutwater case atthe design condition, the peak low pressure near thecutwater is independent of whether the cutwater is


open or closed. This matches with the efficiencymeasured results between the two conditions.

Figure 12 shows the predicted total pressurecontours at six cross-sections. The total pressurecontours shown indicate that a large loss occurs

7O

65

60

5,5

40

35

300

’] EXP (CLSD, INLET)

PRED (CLSD, WALL)

i! EXP (INLET)

_!i"--t’,

EXP (WALL)

/ /" PRED (INLET)

I ,- PRED (WALL)

.100 200 300 400 500

TANGENTIAL ANGLE

FIGURE 11 Composite plot of Figs. 4 and 9.

downstream ofthe cutwater and at the opposite sideof the inlet on the plane of the volute sections

(02 35.5 and 02 53.5). The flow of this mixingarea (between 0 30 and 0 60) originates fromthe inflow at the cutwater as shown in Fig. 12. Thisflow mixing and the recirculation cause the lossand low pressure which is independent of thecutwater conditions for the returning flow fromthe discharge diffuser.

A MODIFIED SHAPE INTHE MIXING AREA

Since the flow recirculation region occupied thebottom portion of the cross section downstream ofthe cutwater, a modified volute shape from 0 27to 0= 125 was examined. Figure 13 shows thedifference between the original and the modifiedshapes at 0 56. Transition of the cross-sectionalshape was smoothly changed. Figure 14 shows thedifference in calculated pressures along the volutewall. The peak suction pressure at the cutwaterincreases slightly, but the pressure recovery throughthe rest of the volute increases. The volute exit

inletinlet 0= 22.5 o 3.

inletII e: 535

inlet inlet

II o: 197.3 II 0 372.6 Discharaenearthe TongueDiffuser

FIGURE 12 Comparison of static pressures for open cutwater volute using two-block grid.


(a) (b)

FIGURE 13 Predicted total pressure contours at 0= 56 for (a) original (b) modified volute cross sections. (See Color Plate IIIat the back of this issue.)

80

75

70

65

40

35

30

-[ /4 2 BLK H-GRID

-f’ OPEN TONGUE

lI, /X. EXP (WALL)

-:

0 100 200 300 400 500TANGENTIAL ANGLE (DEG)

FIGURE 14 Comparison of predicted wall static pressurefor original and modified volute cross sections.

3

l: JI R!GINN-_2.9 MODIFIED

O 2.1t

2.7

2.6

2.5

2.3

Z 2,,1,,,I,,1,,,I,

0 50 1 1 2 2 3 3 0THETA()

FIGURE 15 Distributions of mass averaged total pressurealong volute pass for original and modified volute crosssections.

pressure, however, was not changed due toprescribing the same exit pressure during thecalculation. Figure 1.5 shows the mass-averagedtotal pressure on each cross section along the volutepass for both the original and the modified cross

sections. The modified shape produces slightlylarger loss at the cutwater. The loss that occurs inthe other part of the volute decreases, although itremains the same at the exit due to the prescribedboundary condition.


CONCLUSIONS NOMENCLATURE

A numerical method that solves the Reynolds-averaged Navier-Stokes equations was used tostudy the volute flow of a shipboard air condi-tioning compressor system. The predictions were

made using three grid topologies. The first gridcloses the connection of the cutwatef region withthe discharge diffuser. The other two grids connectthe cutwater area with the discharge diffuser.Experiments were performed to simulate both thecutwater conditions used in the predictions. Goodagreements between the predicted results and themeasurements validate the calculations. The com-

parison between the prediction results and mea-surements indicates that (i) the low pressure andthe large loss at the cutwater are not related to thevolute returning flow through the cutwater andare related to the inlet flow at the cutwater fromthe vaneless diffuser and the cutwater’s specificgeometry; (ii) the loss occurs downstream of thecutwater due to flow mixing and recirculation and is

improved by reshaping the cross section; (iii) whenthe cutwater is closed, the pressure gradient thatexisted between the inlet and the wall is larger thanthe open cutwater case, and so is the secondary loss;(iv) the conventional cutwater design at the opera-ting condition has an adverse contribution in pres-sure recovery due to the low-pressure peak producedat the cutwater.

Acknowledgments

This work was supported by the Chief of NavalOperstions under the Shipboard Energy Conserva-tion Program. The program monitors are Mr. H.Hodgkins ofOPNAV N420C and Mr. W. Stoffel ofNSWC Code 8590. Partial computational resourcewas given by the DoD Major Shared ResourceCenter of the Naval Oceanographic Office atStennis Space Center, Mississippi. Special thanksare due to Mr. M. Tse of the Vector ResearchDivision of the A&T Engineering Technologies forhis preparation of several figures shown in this

paper.

C1,2,3,#G/hJk

PPrPtqSq

UiX, y, z

#t0

PO-q

turbulence model constants

1/J OCi/Oxk O.j/OxenthalphyJacobian, 0(c, rl, )/O(x, y, z)turbulent kinetic energystatic pressureproduction rate of ktotal pressurevector of dependent variables in Eq. (1)source termstime/-component velocity

u./JO/ox,Cartesian coordinatesturbulent dissipationdiffusion terms in energy equationlaminar viscosityeffective viscosity (# + #t)/aqturbulent eddy viscosityvolute tangential anglefluid densityturbulent Prandtl or Schmidt numbertransformed coordinates, i.e. , r/,

References

Ayder, E. and Van Den Braembussche, R.A. (1991) Experi-mental study of the swirling flow in the internal volute of acentrifugal compressor, ASME Paper No. 91-GT-7.

Ayder, E., Van Den Braembussche, R.A. and Brasz, J.J. (1993)Experimental and theoretical analysis of the flow in a centri-fugal compressor volute, ASME Journal oj’ Turbomachinery,115, 582-589.

Ayder, E. and Van Den Braembussche, R.A. (1994) Numericalanalysis of the three-dimensional swirling flow in centrifugalcompressor volutes, ASME Journal of Turbomachinery, 116,462-468.

Bein, T.W. and Lee, Y.T. (1998a) Performance evaluation of 125ton HCFC-124 centrifugal compressor, Carderock Division,Naval Surface Warfare Center, Report CARDIVNSWC-TR-82-98/08.

Bein, T.W. and Lee, Y.T. (1998b) Performance evaluation ofan air-conditioning compressor. Part I: Measurement anddesign modeling, ISROMAC-7, Proc. the 7th InternationalSymposium on Transport Phenomena and Dynamics of Rotat-ing Machinery, Vol. C, pp. 1624-1633.

Brownell, R.B. and Flack, R.D. (1985) Flow characteristics inthe volute and tongue region of a centrifugal pump, ASMEPaper No. 85-GT-82.


Chen, Y.S. (1989) Compressible and incompressible flowcomputations with a pressure based method, AIAA 89-0286,27th Aerospace Science Meeting.

Eckert, B. and Schnell, E. (1980) Axial und Radialkompressoren,2nd ed., Springer-Verlag.

Elholm, T., Ayder, E. and Van Den Braembussche, R.A. (1992)Experimental study of the swirling flow in the volute of acentrifugal pump, ASME Journal of Turbomachinery, 114,366-372.

Iversen, N., Rolling, R. and Carlson, J. (1960) Volute pressuredistribution, radial force on the impeller, and volute mising

losses of a radial flow centrifugal pump, ASME Journal ofTurbomachinery, 82(2), 120-126.

Stiefel, W.L. (1972) Experiences in the development of radialcompressors, Lecture Notes for Advanced Radial CompressorCourse held at von Karman Institute, Brussels.

Traupel, W. (1977) Thermische Turbomaschinen, 3 ed., Springer-Verlag.

Van Den Braembussche, R.A. and Hande, B.M. (1990) Experi-mental and theoretical study of the swirling flow in centrifugalcompressor volutes, ASME Journal of Turbomachinery, 112,38-43.

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