numerical investigation of low solidity vaned diffuser ......pressure centrifugal compressor - part...

JongSik OhSenior Aerodynamic Design Engineer

e-mail: [email protected]

Charles W. BuckleyEngineering Manager


Giri L. AgrawalPresident


R&D Dynamics Corporation,

49 West Dudley Road,

Bloomfield, CT 06002

Numerical Investigationof Low Solidity Vaned DiffuserPerformance in a High-PressureCentrifugal Compressor—Part III:Tandem VanesAs Part III, following the authors’ previous studies, the aerodynamic performance of twodifferent tandem LSDs (low solidity diffusers), Tandem (A) and (B), in a high-pressurecentrifugal compressor was numerically investigated over flow rates from impeller choketo minimal flows available in computation. Tandem (A) was of conventional design wherethe first row came directly from the authors’ previous studies (Part I Oh and Agrawal,2007, “Numerical Investigation of Low Solidity Vaned Diffuser Performance in a High-Pressure Centrifugal Compressor - Part I : Influence of Vane Solidity,” ASME Paper No.GT2007-27260, and Part II: Oh et al., 2008, “Numerical Investigation of Low SolidityVaned Diffuser Performance in a High-Pressure Centrifugal Compressor - Part II : Influ-ence of Vane Stagger,” ASME Paper No. GT2008-50178) selected as the highest effi-ciency vane at design flow, and the second row was designed to be added consideringflow conditions at the exit of the first row vane. Tandem (B) followed a creative patent-pending concept where the number of the first row vanes was doubled with much smallervane chord keeping a low solidity. A position parameter of RCP (relative circumferentialposition) was introduced to see the effect of the relative location of the second row vane.Using an in-house Navier-Stokes solver with finite volume time marching methods, over-all performance was predicted to be compared with each other. Detailed investigation onthe behavior of the static pressure recovery and the total pressure loss coefficient in bothdiffuser designs helps determine why Tandem (A) design is better and the case ofRCP¼ 0.3 gives the best performance. [DOI: 10.1115/1.4006300]

Introduction

As the LSD in centrifugal or mixed-flow compressors hasbecome popular, especially in industrial applications, the aerody-namic designer has to determine important design parameters,such as the solidity, the vane profile, the vane stagger, and the ra-dial position of the vane. Many experimental and computationalresearch studies have been conducted on this area, but not manyparametric studies have been tried in a systematic way which arereally needed for designers. The high cost of experimental studieswould be one reason for the lack of such a parametric research,but the CFD (computational fluid dynamics) approach providesreasonably accurate predictions in a cost-effective way as long asit is limited to finding out the trend of overall compressor aerody-namic performance. The authors have studied numerically theinfluence of those design parameters for a single row LSD with anidentical centrifugal impeller through studies in series [1,2]. Thepresent study, as Part III, is about the design parameters for a tan-dem LSD.

The tandem vane is another option in the LSD design toincrease the static pressure recovery more than a single row caseby adding the second row of vanes. Pampreen [3] made a compar-ison between three-row vanes and a single channel-wedge dif-fuser, and argued that the tandem vane was superior in testperformance. A wider operating range and higher efficiency wasfound for the tandem LSD than for the channel diffuser. Senoo [4]

tested a tandem LSD with a blower impeller and found only asmall gain in performance over a single row LSD, as summarizedby Osborne and Sorokes [5]. Because the inlet flow condition ofthe second row vane is not the same as that of a single row case, adifferent set of vane profiles and vane staggers should be selectedto diffuse with minimum losses. A critical design parameter forthe performance of the tandem vane is the relative circumferentialposition (RCP) of the second row vanes (See Fig. 1) because testresults have shown that there is a definite preference for position-ing the second row relative to the first. Very limited systematicdesign information is available for tandem LSDs in publishedreferences. Japikse [6] quotes unpublished test data by Pampreenthat lower loss was achieved when the suction surface of the

Fig. 1 Definition of RCP

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publi-cation in the JOURNAL OF TURBOMACHINERY. Manuscript received July 13, 2011; finalmanuscript received July 26, 2011; published online September 4, 2012. Editor:David Wisler.

Journal of Turbomachinery NOVEMBER 2012, Vol. 134 / 061025-1Copyright VC 2012 by ASME

Downloaded 28 Jan 2013 to 132.244.95.6. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

second row leading-edge was close to the pressure surfacetrailing-edge of the first row (when RCP is close to 1.0). Seleznevand Galerkin [7] obtained the best aerodynamic loading with thesecond row placed 10% from either side of the trailing-edge of the

first row, that is RCP¼ 0.1 or 0.9, from analytical results. Maxi-mum efficiency was found when RCP¼ 0.1, and the next best effi-ciency at RCP¼ 0.9, which differs from the above statement.Bandukwalla [8] proposed an interesting design concept of thetandem LSD where a high number of vanes, between 19 and 22,was assigned to the first row, with a split tandem vane for the sec-ond row. The first row had to have a much smaller chord to keepthe solidity less than 1.0, and the vane number of the second rowwas decreased to half the number of the first row. The conceptintended to provide the combined advantages of the low solidityand high solidity diffuser because it was believed that, for goodefficiency, the diffuser vane number should be 10% to 50% morethan the impeller blade number.

Among many design parameters to select in the tandem LSD,the authors need to know what range of RCP gives high perform-ance. Furthermore, to find out the feasibility of Bandukwalla’sconcept [8], another design version (Tandem (B)) was added tothe conventional original design (Tandem (A)), as shown inFig. 2. As RCP was varied from 0.0 to 0.9 for six cases, overallcompressor performance was numerically investigated for bothdesign versions of Tandem (A) and (B) at design speed of rotationfrom impeller choke to minimal flows available in computation.

Centrifugal Compressor

The centrifugal compressor in this study is, as shown in Figs. 2and 3, from a marine use turbocharger for medium-class shipengines whose design pressure ratio (total-to-static) is 4.0 anddesign isentropic efficiency (total-to-static) is 80%. The design airmass flow rate is 3.0 kg/s at design speed of 34,000 rpm. The

Fig. 2 Front view of Tandem (A) and (B) when RCP 5 0.5

Fig. 3 Centrifugal compressor geometry in meridional view

061025-2 / Vol. 134, NOVEMBER 2012 Transactions of the ASME


unshrouded open impeller has 18 full blades, and is 45-deg back-swept. Tandem (A) is of a conventional original design where thefirst row comes directly from the authors’ previous studies (Part Iand Part II), selected as the highest efficiency vane at design flow,and the second row is designed to be added considering flow con-ditions at the exit of the first row vane. Tandem (B), as mentionedbefore, follows the creative concept of Bandukwalla [8] where thenumber of the first row vanes is doubled with much smaller vanechord keeping a low solidity. Detailed information of both tandemvanes is shown Table 1. The second row of Tandem (A) has rela-tively lower solidity because the fixed location of the volute inletlimits radial space required for the second row in the present case.In other words, if the volute inlet location is flexible, moreimproved performance may be possible. Because the stagger inTable 1 is an angle obtained using a straight line in the radialplane, the first rows of Tandem (A) and (B) have different stag-gers despite the same design angle of attack. The selected LSDvane profiles are NACA65-(4A10)06 for the first row, andNACA65-(12A10)10 for the second row, as one of the most popu-lar airfoil combinations, which are transformed onto a radialplane. Original thickness distributions of both vanes were how-ever intentionally increased to provide a way of cost-effective fab-rication. A vaneless space downstream of the impeller is gentlycontracted to give a pinch for improving flow stability. A muchstronger contraction is intentionally provided at CFD exit bound-ary, only for calculation purposes, which is usually required toapproach lower flows by partly eliminating reverse flows.

Numerical Method

Compressible flow in a whole domain from CFD inlet boundaryto CFD exit boundary, shown in Fig. 3, was analyzed using anin-house code, CNSTURBO [9,10], that employs the finite vol-ume method with 4-step Runge-Kutta time integration schemeand the 2nd/4th-order artificial dissipation damping. It has beenextended to cover a cut-off trailing-edge of blades and a realisticrectangular tip clearance region using multi-block grid capability,and to add the k-omega equation model, used in the present studyas a turbulence closure. Due to its original features of time march-ing methods, upstream boundary total pressure and temperatureare given with flow directions, and static pressure is imposed asthe exit boundary condition to obtain a converged mass flow rateas part of solution. In grid generation, normally about 206,000nodes and about 390,000 nodes were used to build the impellerand tandem LSD domains, respectively, using the H-type struc-tured grids, as shown in Fig. 4. A grid sensitivity study had beenmade in Part I [1] where doubling the sizes of the computationalgrids had produced a difference in performance within 1.6%range, and of course much more computation time and memoryrequirement. The current grid sizes are therefore recognized to bereasonable and efficient because the authors are only interested ina steady state solution for overall compressor performance tobuild a supporting design guide. Both impeller and diffuserdomains were combined to produce a single domain with the so-called stage interaction (or mixing plane) scheme applied whereall computed flow properties were circumferentially averaged,while the spanwise variation was still preserved, for a steady state

solution in a simple way at the rotational/stationary interfacelocated at halfway distance. A 5% of span was consistently treatedas running tip clearance from impeller inlet to exit. By varyingstatic pressures at the exit boundary, computational flow pointswere shifted from choke toward stall. In the present study, thelowest mass flow point for each configuration does not mean atrue stall/surge location, because any reverse flows occurring forlower flow rates in the numerical computation become an obstacleto solution convergence. It has to be understood that each lowestflow in the present study is a minimum flow with an acceptabletolerance of solution convergence. Steady numerical solution atany flow less than each lowest flow was not converged success-fully. The convergence criteria used in this study is that the solu-tion was regarded as converged when the normalized residual, ameasure of local imbalance of each conservative control volume,fell below 1.0� 10�5. In data reduction, all performance parame-ters were evaluated using mass-averaged pressure, temperatureand velocities at any plane sections.

Results and Discussion

Figures 5 and 6 show the total-to-static pressure ratio and isen-tropic efficiency distributions, respectively, when RCP variesfrom 0.0 to 0.9 for both Tandem (A) and (B) cases. The pressureratio was calculated from the impeller upstream up to the locationof the volute inlet. Irrespective of RCP, Tandem (A) providesmore elevated pressure rise and efficiency than Tandem (B). InTandem (A), the case of RCP¼ 0.3 shows the highest pressurerise with a wide operating range. As RCP moves from 0.3 to 0.9crossing over 0.0 (that is, as the second row vane moves to thecounter-clock wise direction from RCP¼ 0.3 in Fig. 1), the per-formance drops accordingly. However, the case of RCP¼ 0.7 hasthe lowest pressure rise despite the widest range of operation, andinterestingly it is inferior to the case of RCP¼ 0.5. In Tandem(B), the operation range is severely restricted in the case ofRCP¼ 0.1. The cases of RCP¼ 0.7 or 0.9 provide the best overallperformance unlike those in Tandem (A).

Figure 7 was produced at design flow in both Tandem (A) and(B) to make a comparison among the pressure ratio, the isentropicefficiency and the numerical operation range. The numerical oper-ating range is defined as the ratio of mass flow rate changebetween maximum and minimum flow rates to maximum flowrate. In Tandem (A), considering all three performance

Fig. 4 Computational grids for whole domain when RCP 5 0.5

Table 1 Diffuser vane information

Tandem (A) Tandem (B)

1st-row 2nd-row 1st-row 2nd-row

Number of vanes 11 11 22 11Solidity 0.71 0.591 0.613 0.72Stagger (deg) 19.58 28.44 24.75 25.36routlet/rinlet 1.2 1.2 1.08 1.2rvolute inlet/routlet 1.08 1.2

Journal of Turbomachinery NOVEMBER 2012, Vol. 134 / 061025-3


parameters, the case of RCP¼ 0.3 shows the best performance,and the next best performance is found at the case of RCP¼ 0.9.The cases of RCP¼ 0.1 and 0.0 show as good pressure rise and ef-ficiency at design flow as that of RCP¼ 0.9, but has poor operat-ing ranges. The largest range of operation is found at the case ofRCP¼ 0.7, but the case shows the worst performance at designflow. In Tandem (B), all the cases provide lower design perform-ance than Tandem (A) as mentioned earlier. It is interesting tonote that the case of RCP¼ 0.0 shows a good operating range de-spite its lower pressure rise and efficiency.

To see more details at each row of both tandem LSDs, Figs. 8and 9 show the distributions of static pressure recovery factor(CP) in the first and the second row, respectively. Figures 10 and11 are the distributions of total pressure loss coefficient (LC) inthe first and the second row, respectively. The total pressure losscoefficient is defined as a ratio of total pressure drop to upstreamdynamic pressure, and the static pressure recovery factor isdefined as a ratio of static pressure rise to upstream dynamicpressure.

All cases in Tandem (B) show much lower static pressure re-covery in the first row because of smaller vane chord (Fig. 8), and

they are high in total pressure loss coefficient in the second row(Fig. 11), which drives Tandem (B) away from acceptable per-formance. In static pressure recovery in the second row (Fig. 9)and total pressure loss coefficient in the first row (Fig. 10), no re-markable difference is found between Tandem (A) and (B).

Fig. 6 Compressor isentropic efficiency characteristic

Fig. 8 Static pressure recovery characteristic in the first row

Fig. 5 Compressor pressure ratio characteristic

Fig. 7 Compressor performance at design flow



In Tandem (A), the case of RCP¼ 0.9 shows the highest staticpressure recovery in the first row, while the case of RCP¼ 0.1 hasthe highest in the second row. Some limited references have statedthat either case would be considered optimal in aerodynamic per-formance, and recommended in design.

As shown in Figs. 8 and 9, however, either case of RCP¼ 0.1or 0.9 fails to provide reasonably high pressure recovery in bothfirst and second rows, on account of the absence of uniform load-ings at each vane row. Moreover, the case of RCP¼ 0.1 shows thehighest total pressure loss in the first row, according to Fig. 10.When RCP¼ 0.7 or 0.9, in other words, when the second rowleading-edge is approaching the pressure surface of the first row,the static pressure recovery is rising in the first row, but fallingdown in the second row. The case of RCP¼ 0.3, which providesthe best overall performance already found in Figs. 5 and 6, hasthe lowest total pressure loss in the first row, and has good levelsof static pressure recovery around 0.6 in both rows.

Static pressure contours at mid-span at design flow rate areshown in Figs. 12(a) and 12(b), respectively for Tandem (A)and (B), where the static pressure contour values are normalizedby compressor upstream total pressure. At first sight, Tandem(B) fails to provide as much static pressure recovery, comparedto Tandem (A), because of the much smaller chord of the firstrow vane of low solidity. The worst non-uniform distribution ofblade loadings in Tandem (B) is found at RCP¼ 0.1 which con-tributes to the restriction of the machine operation range, asalready seen in Figs. 5 and 6. As RCP increases, the blade load-ings become more uniform, and the case of RCP¼ 0.7 or 0.9 inTandem (B) provides the best loading distribution around thevanes.

In Tandem (A), it is clear that the presence of the leading-edgeof the second row vane generates a local jump in static pressuredistributions due to the formation of stagnation flow. As RCPincreases from 0.0 to 0.1, the static pressure jump expands to therear portion on the suction surface of the first row vane, resultingin a sudden rise of static pressure on the suction surface of the firstrow vane and a sudden drop on the suction surface of the second.At RCP¼ 0.3, however, the non-uniform blade loading is muchweakened because the second row vane is located far awayenough to damp the static pressure jump. However, fromRCP¼ 0.5 to 0.7, the second row vane destroys again the staticpressure rise on the pressure surface of the first row vane, becauseof accelerating flow in the reduced passage. Especially whenRCP¼ 0.5, even though the second row vane is positioned exactlyhalfway to the first row channel, its presence accelerates the flowaround the pressure surface of the first row vane resulting in poorstatic pressure recovery of the first row. When RCP¼ 0.9, how-ever, the flow acceleration is much weakened by a small gapbetween the two vanes resulting in the best static pressure recov-ery of the first row, but the static pressure recovery of the secondrow drops.

The authors were also interested in performance comparisonof LSDs with channel-wedge diffusers which are well known asone of high efficiency diffusers. For the same impeller, twodifferent channel-wedge diffusers were designed for the perform-ance comparison, and the results were summarized in the Appen-dix. The highest efficiency was confirmed with the channel-wedge diffuser, but the present Tandem (A) was found moreattractive for both design issues of the efficiency and the operat-ing range.

Fig. 10 Total pressure loss characteristic in the first row

Fig. 11 Total pressure loss characteristic in the second rowFig. 9 Static pressure recovery characteristic in the second row



Conclusions

As Part III, the aerodynamic performance of two different tandemLSDs in a high-pressure centrifugal compressor was numericallyinvestigated. When the relative location of the second row vane wasvaried using a position parameter of RCP from 0.0 to 0.9 in Tandem(A) and (B), the followings are drawn as concluding remarks.

(a) Irrespective of RCP, Tandem (A) provides more elevatedpressure rise and efficiency than Tandem (B), because Tan-dem (B) has much lower static pressure recovery in the firstrow due to smaller vane chord, and higher total pressureloss coefficient in the second row.

(b) Considering all three design parameters of pressure ratio,efficiency and operating range in Tandem (A), the case ofRCP¼ 0.3 shows the best performance, and the next ac-ceptable performance is found in the case of RCP¼ 0.9.

(c) The case of RCP¼ 0.9 in Tandem (A) fails to provide rea-sonably high pressure recovery in the second row, onaccount of the absence of uniform blade loadings.

(d) The case of RCP¼ 0.1 in Tandem (A) shows a reasonablelevel of pressure recovery in both vane rows, comparable tothe case of RCP¼ 0.3, but has a limited operating range.

NomenclatureSolidity ¼ (vane chord)/(tangential pitch)

LC ¼ total pressure loss coefficient (¼ a ratio of totalpressure drop to upstream dynamic pressure)

CP ¼ static pressure recovery factor (¼ a ratio of staticpressure rise to upstream dynamic pressure)

23 ¼ between the impeller exit and the first-row diffuservane inlet

34 ¼ between the first-row diffuser vane inlet and exit45 ¼ between the second-row diffuser vane inlet and exit56 ¼ between the second-row diffuser vane exit and the

volute inlet(See Fig. 3)

Appendix: Comparison With Channel-Wedge Diffuser

Through a series of studies from Part I to Part III, a parametricinvestigation on some important design variables in the LSD foran identical high-pressure centrifugal impeller has been success-fully completed using CFD work. Another interest that attractedthe authors was about performance gap from channel-wedge dif-fusers which are well known for higher efficiency. At first, anoptimal channel was designed for the given geometry which isnamed “Channel-wedge Optimal,” as shown in Table 2 but vanesare choked at far less than design flow rate despite higher per-formance. In order to open throat area more, the second channelwas designed with fewer vanes and changes of stagger which isnamed as “Channel-wedge,” and has some choke margin at designflow rate. Both channel-wedge diffusers were calculated with the

Fig. 12 Static pressure contours at midspan at design flow



same impeller using the same CFD code from deep choke to thesmallest flow that the calculation allows at design speed by speci-fying an exit boundary static pressure. See Fig. 13.

The distributions of pressure ratio and isentropic efficiency ofboth channel-wedge diffusers are shown in Figs. 14 and 15, wherethose of other different types of diffusers are reproduced to becompared together. The other different types are directly from theauthors’ studies of Part I to III including a purely vaneless dif-fuser. The “LSD Single Row” design has a solidity of 0.71 with astagger of 19.58 deg which showed the best acceptable perform-ance in the parametric analysis from Part I and II. The “LSDTandem” design is the Tandem (A) with RCP¼ 0.3 in Part IIIwhich showed the best performance in the tandem LSD paramet-ric analysis. Even though the vane throat is choked at far earlier

than the design flow rate in Channel-wedge Optimal, the designshowed the highest pressure ratio of 4.31 and the highest isentropicefficiency of 81% due to the optimal combination of design param-eters. However, for the application of the current centrifugal com-pressor design duty, the optimal has to be abandoned to move toChannel-wedge design to secure a reasonable choke margin atdesign flow rate. At design flow rate, it showed the highest effi-ciency of 81%, which was the same as that of Channel-wedge Opti-mal, and the pressure ratio of 4.15. In terms of the operating range,Channel-wedge Optimal may look inferior to Channel-wedge, butagain the smallest flow on the map does not mean a true stall/surgeflow, which would be one of restrictions that any CFD study has.

An interesting result is that nearly the same level of the pressurerise distribution was found in LSD Tandem in spite of a slightdrop of maximum efficiency to 80% which value is still highly ac-ceptable. Furthermore, it was found to provide wider range ofoperation than Channel-wedge, as shown Fig. 16 (where the rangeof operation is defined as the ratio of mass flow rate change

Table 2 Design Parameters of channel-wedge diffuser vanes

Version L/w3th AS AR34 2h 2u a3b NV

Channel-wedge Optimal 14.8 1.10 2.86 7.45 3.14 16.2 34Channel-wedge 11.0 0.84 2.68 8.81 3.60 18.0 29

Note: See Fig. 13 for design parameter definitions.

Fig. 13 Static pressure contours at design flow in channelwedge diffuser vanes

Fig. 14 Pressure ratio characteristics of different diffusertypes

Fig. 15 Efficiency characteristics of different diffuser types

Fig. 16 Performance comparison at design flow for differentdiffuser types



between maximum and minimum flow rates to maximum flowrate, depending on the solution convergence when exit static pres-sure is specified as a boundary condition.) The next lower per-formance was found in the LSD Single Row which comes betweenthe vaneless diffuser and LSD Tandem or Channel-wedge. It isworthy to note that the maximum isentropic total-to-static effi-ciency of a single-row LSD in a high-pressure (around 4.0 oftotal-to-static stage pressure ratio) centrifugal compressor like thepresent machine is around 78% at most. Of course, when the vo-lute is added, an additional recovery of static pressure in the vo-lute will raise the total-to-static efficiency.

In conclusion, the tandem LSD diffuser is recognized as one ofattractive options in the selection of vaned diffusers for bothdesign issues of the efficiency and the operating range.

References[1] Oh, J. S., and Agrawal, G. L., 2007, “Numerical Investigation of Low Solidity

Vaned Diffuser Performance in a High-Pressure Centrifugal Compressor—PartI: Influence of Vane Solidity,” ASME Paper No. GT2007-27260.

[2] Oh, J. S., Buckley, Ch.W., and Agrawal, G. L., 2008, “Numerical Investigationof Low Solidity Vaned Diffuser Performance in a High-Pressure CentrifugalCompressor—Part II: Influence of Vane Stagger,” ASME Paper No. GT2008-50178.

[3] Pampreen, R. C., 1972, “The use of Cascade Technology in Centrifugal Com-pressor Vaned Diffuser Design,” Trans. ASME J. Eng. Power, 94, pp.187–192.

[4] Senoo, Y., Hayami, H., and Ueki, H., 1983, “Low-Solidity Tandem-CascadeDiffusers for Wide Flow Range Centrifugal Blowers,” ASME Paper No.83-GT-3.

[5] Osborne, C., and Sorokes, J. M., 1988, “The Application of Low Solidity Dif-fusers in Centrifugal Compressors,” Flows in Non-Rotating TurbomachineryComponents, ASME FED, 69.

[6] Japikse, D., 1996, Centrifugal Compressor Design and Performance, ConceptsETI, White River Junction, VT.

[7] Seleznev, K. P., and Galerkin, I. B., 1982, Centrifugal Compressors, L:Mashi-nostroenie, Leningrad Division, Moscow, Russia.

[8] Bandukwalla, P., 1988, “Diffuser Having Split Tandem Low Solidity Vanes,”US Patent No. 4824325.

[9] Oh, J. S., and Ro, S. H., 2001, “Analysis of 8 Centrifugal Compressor ImpellersUsing Two Different CFD Methods—Part I: Code Validation,” ASME PaperNo. 2001-GT-326.

[10] Oh, J. S., 1998, “Numerical Investigation of Internal Flow Field for ModifiedEckardt Backswept Impeller,” ASME Paper No. 98-GT-296.



http://dx.doi.org/10.1115/1.3445671

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numerical investigation of low solidity vaned diffuser ......pressure centrifugal compressor - part...

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