Multilevel optimization of the splitter blade pro le in...

Scientia Iranica B (2017) 24(2), 707{714

Sharif University of TechnologyScientia Iranica

Transactions B: Mechanical Engineeringwww.scientiairanica.com

Multilevel optimization of the splitter blade pro�le inthe impeller of a centrifugal compressor

S.A. Moussavi Torshizi, A. Hajilouy Benisi� and M. Durali

School of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155/8639, Iran.

Received 31 October 2015; received in revised form 2 February 2016; accepted 2 May 2016

KEYWORDSCentrifugalcompressor;Optimization;Splitter blades;Blade pro�le;Incidence loss.

Abstract. In this research, multi-level optimization of the pro�le of the splitter bladesof a turbocharger compressor is performed using genetic algorithm in order to improve itsperformance. Successive corrections of the pro�le at hub, mid-span, and shroud of thesplitter blades, with the objective of decreasing the incidence losses at the leading edge andadjustment of the blade loading at the shroud, result in an impeller having improved splitterblades. The impeller ow �eld analysis shows that the optimization has been successful inreducing the ow leakage at the shroud region as well as the losses in the leading edge region.Although numerical simulations predict a decrease by 0.5% in pressure ratio at design point,a 2.2-point improvement in isentropic e�ciency is calculated. Based on the optimizationresults, a new impeller is designed, manufactured, and tested on a turbocharger test bed.Experimental results support the simulation predictions on the expected improvement inperformance.© 2017 Sharif University of Technology. All rights reserved.

1. Introduction

Flow visualization in the impeller of centrifugal com-pressors provided a good insight into what was reallyoccurring during the process. In the following, severalevidences are presented in the literature, showing thenon-conformity of the ow approaching the splitterblades, with the same pro�le as that of the mainblades. This implies that splitter blades must betreated di�erently, and that there is room for designmodi�cations and optimization.

To achieve an e�ective optimization, di�erentsources of losses must be considered. To this end,di�erent techniques have so far been implemented.Some papers have addressed this issue by performingcomplex experiments. For example, ow visualizationstudies were conducted by Fischer and Thoma [1] in apump. Other evidences were produced by the work of

*. Corresponding author. Tel.: +98 21 66165512E-mail address: [email protected] (A. Hajilouy Benisi)

Fowler [2] about the existence of strong non-uniform ow in the impeller of centrifugal compressors. The�rst explicit works discussing the jet-wake model in theimpeller date back to the work of Dean [3].

Beyond these, one of the most signi�cant piecesof information about the ow in unshrouded impellersis given in the work of Eckart [4,5] by the use of laseranemometry. Later, Krain [6] con�rmed these resultsby laser measurements on a more e�cient impeller.In these works, a wake was observed at the shroud-suction side corner of the blades. But it seems thatthis ow con�guration is not universal. The locationof the jet and wake is greatly dependent on impellershape and di�user performance. In these works, inaddition to the main stream, existence of secondary ows and deviation of the ow from the blade pro�leare observable. Cumpsty [7] states that it is quitecommon to �nd that the two passages divided by asplitter behave quite di�erently, a matter also shownby Senoo et al. [8].

CFD simulations have been widely used in the

708 S.A. Moussavi Torshizi et al./Scientia Iranica, Transactions B: Mechanical Engineering 24 (2017) 707{714

study of ow and optimization procedures of cen-trifugal compressors. The non-uniformity of owin impellers can be observed implicitly in all worksimplementing such methods [9-11].

These works con�rm that due to di�erent forcesexerted on the uid during the compression process,the ows at the two sides of splitter blades are notsimilar. It can be concluded that these two owsmust be treated di�erently. However, as pointed outin well known reference books discussing the design ofcentrifugal compressors [12,13] as well as what is reallypracticed in commercial products, splitter blades havethe same pro�le as main blades, except for having theleading part truncated to decrease inlet blockage.

Here we are trying to show that this con�gurationis not necessarily the best and better performance canbe achieved by accurate optimization of blades. Toinvestigate this, two methods can be considered. In the�rst method, splitter blades optimization is performedthrough variation of the location of the leading edge,without altering the blade pro�le. Details are discussedin [14]. In the second method presented in this work,more degrees of freedom are considered for the pro�leof the splitter blades with the permission to alter thedesign in three span layers. Since the compressor casinggeometry is considered as a constraint, the pro�le ofthe main blades is not changed and major dimensionsof the impeller are not a�ected.

2. Optimization scheme

To start the optimization process, geometry of theimpeller, especially blade pro�les, must be available.Here, angular de�nition of main blades, normalizedby meridional length, is used as the basic design forgenerating splitters. This is to �nd an optimized con-�guration near the existing pro�le by the perturbationmethod. This method will provide solutions with muchsimilarity to the pro�le of main blades, thus, easing themanufacturing process.

In general, three dimensional geometry of theblades is generated using blade pro�les in at leastthree span layers (hub, mid-span, and shroud). Tode�ne a pro�le, two methods can be implemented. Inthe �rst method, a �-M curve is used in which thepro�le is de�ned using blade slope versus meridionallocation. The second method uses the angular position(�) of points lying on the blades versus meridionallocation. Here, the second way is considered. Thus,the leading edge is always located at the origin. Foroptimization purpose, these continuous curves must bediscretized and represented by few parameters. Here,the pro�les are regenerated by 5 Bezier control points.This method needs a minimum number of data forcontour generation. Figure 1 shows the application ofthis method on hub pro�le of an impeller.

Figure 1. Angle de�nition of the main blades at hubspan.

Generally, the location of each control point isde�ned by a streamwise position (Mi) and an angularposition (�i). Considering �ve control points per layerand two inplane degrees of freedom for each pointresults in 30 optimization parameters, which imply aconsiderable amount of time to converge. Thus, thenumber of parameters must be minimized. To thisend, the �rst two points (to the left in Figure 1), whichare situated in the trimmed portion of splitter blade(vertical dash line), are �xed and others are allowed tomove vertically, thus, altering the angular distributionof blades.

In the optimization loop, the values of theseparameters are initially selected randomly in theirallowable range (limited by the feasibility of geometry)for the �rst generation, and then controlled by geneticalgorithm in succeeding generations. These parame-ters, combined by all others which are required to de�nethe impeller geometry, are logged into a text batch �le.This �le is then converted to a 3D CAD �le. The mainblades and impeller center body are recreated by splinecurves derived from the initial impeller, while splitterblades are generated using new locations of its controlpoints as calculated by Eq. (1).

�(M) =4Xi=0

�4i

�(1�M)4�iM i

�Mi�i

�: (1)

The resulting 3D geometry is meshed and prepared forCFD simulations. Finally, the compressor performanceis calculated from the CFD results and fed back intothe algorithm to close the optimization loop. All ofthese tasks are programmed to be executed sequentiallyuntil the convergence of objective function or otherprede�ned termination rules is achieved.

Having in mind the available computing hard-ware, 15 generations with 15 populations each areconsidered. To further ease the procedure, the opti-mization process in each span is considered indepen-dent. In other words, altering the pro�le in one spanwill not a�ect the ow in others. This assumption isusually made during the design process of impellers.

S.A. Moussavi Torshizi et al./Scientia Iranica, Transactions B: Mechanical Engineering 24 (2017) 707{714 709

Thus, 3 consecutive optimizations are performed onthe impeller at spans 0, 0.5, and 0.95. The objectivefunction is de�ned such that only the e�ciency atthe nominal working point (Eq. (2)) is maximized.Meanwhile, pressure ratio is not allowed to decreaseby more than 10% of its initial value. Compensatingthe pressure ratio has straightforward solutions such aschanging outer diameter or amount of backsweep andincreasing the speed.

' = 1� �: (2)

3. Flow simulation model

The computing tool in the optimization loop is a com-mercial CFD code, providing performance predictionof generated impellers. The ow domain is created andmeshed using a structured hexahedral grid. An O-gridscheme for leading edge and an H-grid for trailing edge(Figure 2) are used. In the optimization of impellergeometry, due to the number of required simulations,the volute is excluded from the model. Also, onlyone impeller passage (including inducer and di�user) isconsidered to further reduce the computational time.To capture ow details and have su�cient accuracyfor wall friction, a maximum y+ of 100 is considered.Thus, near-wall layers with 50 microns of thicknessare implemented. By performing a mesh independencyanalysis, it is observed that a minimum mesh densityof 450000 elements per passage is su�cient.

In simulations, the compressor inlet has a totalpressure of 1 bar and total temperature of 300�K. Theoutlet of the passage is set to have a speci�ed mass ow rate. Therefore, there is no need to assume astatic pressure distribution at outlet. This item willbe calculated during the solution. Also, the SSTmodel is implemented for the turbulence modeling.

Figure 2. Generated mesh for the impeller at hub span.

Convergence criteria are set to the reduction of theroot mean square of residuals for mass and momentumequations to less than 1.0E-5. Here, a virtual timestep equivalent to the inverse of rotating speed isconsidered. Although a steady state simulation isperformed, this parameter is needed to attain a fastand stable transition from initial conditions to �nalresults. Because of non-uniformity of ow at impelleroutlet, pressure ratio and e�ciency are calculated bymass ow averaging of these parameters:

PR =�ZZ

�V P0dA= _m�=P0;in; (3)

�tt = T0;in

�PR �1= � 1

�= (T0;out � T0;in) : (4)

4. Discussion and results

The optimization procedure is implemented on theimpeller of a sample centrifugal compressor of a com-mercial turbocharger. General speci�cations of theimpeller are given in Table 1.

The optimized impeller design is shown in Fig-ure 3. Detailed comparison of the impeller splitterblades reveals noticeable changes of leading edge sec-tion at hub span (Figure 4). Minor changes are also ob-servable at shroud. In addition, the pro�le has movedcircumferentially and, thus, is not located exactly atmid-distance between the two main blades (Figure 5).These relocations have deformed the leading edge of thesplitters, causing non-radial �laments. Concerns oversafety of the impeller in withstanding the centrifugalloading are checked with stress calculations by meansof structural FEM simulation.

From the performance point of view, the new im-peller has a maximum total to total isentropic e�ciencyof 87.23%, which shows 2.2 points of improvementover 85.02% of the existing impeller (both predicted byCFD calculations). At nominal working point, the new

Table 1. Speci�cations of the sample impeller

Parameter Value

N 6�1s 60 degree�2s 30 degreer1s 56 mmr1h 22 mmr2h 82 mmw2 5.5 mm

_mnom 287 g/sPRnom 2.17!nom 92000 rpm�nom 85.02%


Figure 3. Optimized impeller.

Figure 4. Comparison of splitter blade pro�le at hubspan.

Figure 5. Pro�le comparison at shroud span.

Figure 6. E�ciency predictions of the new and existingimpellers at 92000 rpm.

Figure 7. Streamline patterns at hub span for theexisting impeller (left) and the optimized one (right).

impeller presents a pressure ratio of 2.156 comparedto 2.168 of the existing impeller, which is a negligiblechange. Performance prediction of the new impellerand comparison with the original one at 92000 rpm isshown in Figure 6. These variations have also a�ectedthe choke margin. Simulations show that at nominalspeed, the maximum mass ow rate increases from381 g/s to 394 g/s, which is about 1.9% improvement.

To �nd the cause of the improvement, the ow�eld at di�erent spans is examined. Figure 7 shows ablade to blade view of the streamlines at hub span. Itcan be seen that in the improved impeller, the splitterblades are better adapted to ow direction comparedto the original blade, thus minimizing incidence losses.

The trailing edge portion has not moved. Sincethe blades have no direction change at the shroud, nonotable variations are observed at this span.

The static pressure distributions on the bladesurfaces at two spans are presented in Figures 8and 9. At the hub span, a meaningful change incurve impellers shapes, especially at the leading edgesection, is evident. As shown by the streamlines, dueto a negative angle of attack in the original impeller,loading lines cross each other. That is, the suction sidehas higher pressure than the pressure side, which isan undesirable situation. Due to corrections made tothe angle of attack, the pressure at the suction side ofthe blades has changed and, thus, curves are no more


Figure 8. Blade loading at hub of the improved (left) and the original (right) .

Figure 9. Blade loading at shroud of the improved (left) and the original (right) impellers.

intersecting and a normal loading curve is obtained.Loading of splitters at this span has changed up tothe trailing edge and a global decrease in blade load isobvious.

At the shroud, the new loading curve presents amuch smoother trend and the suction side static pres-sure strictly increases. Also, blade loading (pressuredi�erence across the blade) at shroud span (span 0.9)shows a small decrease. This directly a�ects the tipleakage and its subsequent vortex losses. Simulationsshow that the leakage mass ow rate has decreasedfrom 2.23 g/s to 1.97 g/s per blade, which presents11.6% improvement. These decreases in blade loadingare considered as the cause of the small impairmentin overall pressure ratio. In all �gures, loadings of themain blades have no notable change.

5. Experimental study

To validate the optimization result, the modi�ed im-peller is manufactured using Aluminum alloy 7075 T6.Stress calculations were performed using FEM analysis.The impeller body is meshed using tetrahedral ele-ments, adaptively re�ned in regions of high curvatureand stress concentration. Simulations are performedat 125000 rpm, maximum speed prescribed by themanufacturer. Considering 570 MPa as the ultimate

Figure 10. Stress contours of the modi�ed impeller at125 krpm.

strength of this alloy [15], a structural safety factor of1.53 is achieved at the weakest point; see Figure 10.

Finally, additional geometry details such as shafthole, �llets, seats, and tolerances are added to themodel to prepare it for manufacturing. The manufac-tured improved impeller is shown in Figure 11.

To test the new impeller, it is mounted on aturbine shaft; see Figure 12. The modi�ed compressoris mounted on the test bed at the Sharif Universityturbocharger lab. The compressor tests are performedat 50, 60, and 75 krpm with 5 operating points at


Figure 11. The manufactured impeller.

Figure 12. Modi�ed impeller mounted on turbochargershaft.

each speed several times with the new and existingimpeller. Mass ow rates of compressor and turbine areaccurately controlled with electro-pneumatic valves.Schematic of lab equipment is shown in Figure 13.Total pressure is sampled with Pitot tubes and mea-sured with pressure transducers at compressor inletand outlet. Total temperatures are measured by K-type thermocouples. A �ber optic sensor is used tomeasure the shaft speed. Compressor mass ow rate ismeasured with a bell mouth.

Some experimental results are shown in Figures 14

Figure 14. Experimental pressure ratio of the new andexisting compressors.

Figure 15. Experimental e�ciency of the new andexisting compressors.

and 15. The modi�ed impeller performs with highere�ciency and lower pressure ratio, as expected. Themaximum decrease in pressure ratio can be observedat 60 krpm by an amount of 3%. This deviationdecreases at higher speeds as well as lower mass owrates. The e�ciencies of the compressors are comparedin Figure 15. At low mass ow rates, compressorsbehave almost in the same manner. But, at higher mass ow rates, especially at higher speeds, advantage of

Figure 13. Schematic of turbocharger laboratory.


the new compressor is more pronounced. At 75 krpm,a maximum increase of 2.3 points in e�ciency isobserved. In general, with the modi�ed impeller,better performance of the compressor is notable at allspeeds and mass ow rates. Thus, the improvement isnot restricted to speci�c working conditions, which isessential for a turbocharger.

6. Conclusion

In this research, improvements on the impeller of aturbocharger compressor were performed by alteringthe design of the splitter blades. This was doneby rede�ning their pro�les by Bezier control pointsand �nding the best con�guration by implementingthree consecutive optimizations at hub, mid-span, andshroud sections. Structural analysis was performed onthe new geometry to assure integrity and structuralsafety of the modi�ed impeller. The impeller wasmanufactured and tested on a turbocharger test rig.Experiments con�rm an increase by 2.3 points ine�ciency at 75000 rpm. Precise examination of ow�elds from numerical simulations of the new impellerrevealed a decrease in incidence loss at the leading edgeof splitter blades, especially at hub span, compared tothe original impeller. Also, a decrease in leakage at theshroud region due to loading moderation is identi�edas the second cause of improvement. The results showthat impellers with a state of the art design have roomfor more modi�cations.

Acknowledgement

The authors gratefully acknowledge the �nancial sup-port of the research and technology o�ce and technicalassistance of the turbocharger laboratory sta� of SharifUniversity of Technology.

Nomenclature

A Area (m2)M Meridional position ()_m Mass ow rate (g/s)N Number of blades ()PR Pressure Ratio ()r Radius (mm)T Temperature (K)V Velocity (m/s)w Passage width (mm)� Blade angle (degree)� Isentropic e�ciency ()' Objective function ()

� Density (kg/m3)� Pro�le angle (degree)! Speed (rpm)

Subscripts

0 Stagnation conditions1 Compressor inlet2 Compressor outleth Hubs Shroud

References

1. Fisher, K. and Thoma, D. \Investigation of the owcondition in a centrifugal pump", Transaction ASMEHYD, 54(8), pp. 141-155 (1932).

2. Fowler, H.S. \The distribution and stability of ow inrotating channel", Trans ASME; J. of Engineering forPower, 90(3), pp. 229-235 (1968).

3. Dean, R.C. \On the unresolved uid dynamics of thecentrifugal compressor", Advanced Centrifugal Com-pressors, ASME, pp. 1-55 (1971).

4. Eckart, D. \Detailed ow investigation within a highspeed centrifugal compressor impeller", J. Fluids En-gineering, 98(3), pp. 390-399 (1976).

5. Eckart, D. \Flow �eld analysis of radial and backsweptcentrifugal compressor impeller. Part 1: Flow mea-surement using a laser velocimetre", 25th ASME GasTurbine Conference, 80-GT-33 (1980).

6. Krain, H. \Swirling impeller ow", ASME Gas TurbineConference, California, 87-GT-19 (1987).

7. Cumpsty, N.A, Compressor Aerodynamics, Longman(1999).

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14. Moussavi, S.A., Hajilouy, A. and Durali, M. \Op-timization of splitter leading edge location for per-formance improvement of centrifugal compressors",Submitted to Journal of Engineering for Gas Turbineand Power, ASME (2016).

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Biographies

Seyed Abolfazl Moussavi Torshizi received his BS(2002) and MS degrees (2006) in Mechanical Engineer-ing with a minor in Applied Design. He is currentlyPhD student at Sharif University in the �eld of Tur-bomachines. His studies are mainly focused on theaerodynamic and structural design and optimizationof centrifugal compressors. He has also been involvedin the design and implementation of MegaWatt classwind turbine blades, since 2009.

Ali Hajilouy-Benisi received his PhD degree fromMechanical Engineering Department of Imperial Col-lege at the University of London, in 1993. He was a

faculty member of the Institute of Water and Energyand since 1978 has been the faculty member of theSchool of Mechanical Engineering at Sharif Universityof Technology (SUT). He served as Director of theFluid Mechanics Lab (1993-1995), Founder and Direc-tor of the Turbocharger Lab (1993), TurbochargingLab (2000), and Gas Turbine Lab (2008), in theSchool of Mechanical Engineering of Sharif Universityof Technology. His research interests are experimentaland theoretical investigations of turbochargers, tur-bocharging, and gas turbines.

Mohammad Durali is a Professor in MechanicalEngineering Department at Sharif University of Tech-nology. He received a BSc degree in Mechanical Engi-neering from Sharif University, MS, and PhD degreesin the same �eld from Aero and Astro Departmentof MIT, in 1980. His research interests are designand automation, system dynamics, and propulsion.He is currently the Head of the Center for SystemDesign and Automation, and Creativity Lab. He hasdone numerous industrial design and manufacturingprojects.

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