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Hidetaka Okui1

Mitsubishi Heavy Industries, LTD,

2-2-1 Shinhama Arai-Cho Takasago,

Hyogo, 676-8686 Japan

e-mail: [email protected]

Tom Verstraetee-mail: [email protected]

R. A. Van den Braembusschee-mail: [email protected]

Zuheyr Alsalihie-mail: [email protected]

Turbomachinery and Propulsion Department,

von Karman Institute for Fluid Dynamics,

Waterloose steenweg 72,

1640 Sint-Genesius-Rode, Belgium

Three-Dimensional Design andOptimization of a TransonicRotor in Axial Flow CompressorsThis paper presents a 3-D optimization of a moderately loaded transonic compressorrotor by means of a multiobjective optimization system. The latter makes use of a differ-ential evolutionary algorithm in combination with an Artificial Neural Network and a 3DNavier-Stokes solver. Operating it on a cluster of 30 processors enabled the evaluation ofthe off-design performance and the exploration of a large design space composed of thecamber line and spanwise distribution of sweep and chord length. Objectives were anincrease of efficiency at unchanged stall margin by controlling the shock waves and off-design performance curve. First designs of single blade rows allowed a better under-standing of the impact of the different design parameters. Forward sweep with unchangedcamber improved the peak efficiency by only 0.3% with the same stall margin. Backwardsweep with an optimized S shaped camber line improved the efficiency by 0.6% atunchanged stall margin. It is explained how the camber line control can introduce thesame effect as forward sweep and compensate the expected negative effects of backwardsweep. The best results (0.7% increase in efficiency and unchanged stall margin) havebeen obtained by a stage optimization that allows also a spanwise redistribution of therotor flow and an increase of loading by extra flow turning. The latter compensates the

loading shift induced by the backward sweep in order to reduce the inlet Mach number atthe downstream stator hub.[DOI: 10.1115/1.4006668]

1 Introduction

The recent trend to increase the capacity of modern heavy dutygas turbine compressors requires high performance transonicrotors with increasing tip Mach numbers. It is well known that thehighly three-dimensional flow in those rotors interacts with aradially swept shock wave [1,2]. New sophisticated designapproaches based on 3-D CFD and rig tests are therefore neededto maximize their performance.

Blade sweep is known to be an effective technique to redistrib-ute the radial loading [3,4] and has been widely used to controlthe shock wave in transonic fans and rotors. Backward sweepwas initially investigated by Hah and Wennerstrom [2]. Theydeveloped a three-dimensional shock structure model and built anaft-swept blade, rotor6, to strengthen the sweep effect. This rotorshowed a significant improvement of the peak efficiency [5,6] buta large decrease of the stall margin.

After several investigations, Wadia et al. [7] concluded that thepenalty on the stall margin was caused by the local increase ofloading at the tip section resulting in a stronger bow shock and anaccumulation of the low momentum fluid at that section. In addi-tion, no overall efficiency gain was achieved with the aft-sweptblade in spite of the better performance of the inboard section.Forward sweep on the contrary, demonstrated a significant

improvement in stall margin and a slightly higher peak efficiency.Shock waves tend to be normal to the casing wall and in combi-

nation with the forward sweep become oblique in the blade toblade surface. This reduces the losses and stabilizes the flow inthe tip region. The result of the numerical investigations of Xuand Denton [8] and Blaha et al. [9] supported this conclusionabout the advantage of forward sweep, but less successful resultshave also been reported [10].

Ji [11] reviewed the previous studies in 2005, and concludedthat sweep is a degree of freedom (DOF) that controls the span-wise matching of the blade to blade flows. It is therefore incom-plete to discuss the performance and stability according to thetype of sweep only. The impact of sweep depends also on the orig-inal loading distribution, which is affected by other design param-eters. Several researchers indicated that the thickness distribution[6], camber distribution [12] and solidity [13] have an equally

large influence on the performance of transonic rotors as sweepand that they all need to be optimized simultaneously.

Another aspect of sweep is that it often disturbs the matchingwith the following stage due to a radial redistribution of the load-ing and mass flow [7,9].

Inverse methods seem to be suited for the design of transonicfans and rotors. The loading or pressure distribution can be explic-itly specified and the geometry, which satisfies the given designintend almost exactly, is quickly found [14]. However, the methodexperiences some practical difficulties in establishing criteria foran optimal loading distribution and in imposing the mechanicalconstraints.

Watanabe and Zangeneh [15] used an inverse method to designa swept transonic fan aiming to compensate the change in specificwork and pressure ratio caused by the given forward sweep. They

reasonably recovered the speed line and achieved an efficiencyimprovement of 0.5% by specifying a very smooth loading distri-bution at the tip section. The method, however, did not includethe tip clearance flow and the sweep was not optimized for thegiven loading distribution but explicitly specified.

In this study, an efficient optimizing design system developed atthe von Karman Institute [16,17] has been applied to a moderatelyloaded transonic rotor for heavy-duty gas turbine compressors. Amultiobjective optimization for the design and off-design opera-tion was carried out, in which the sweep, chord length and the cam-ber distributions are controlled. By tailoring these parameterssimultaneously, the loading distribution could be optimized so thatboth the stability and the performance were improved. A constantspeed line calculation evaluated the off-design performance.

1Corresponding author.Contributed by the International Gas Turbine Institute (IGTI) Division of ASME

for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December18, 2011; final manuscript received January 30, 2012; published online March 25,2013. Editor: David Wisler.

Journal of Turbomachinery MAY 2013, Vol. 135 / 031009-1CopyrightVC 2013 by ASME

wnloaded From: http://turbomachinery.asmedigitalcollection.asme.org/ on 04/04/2013 Terms of Use: http://asme.org/terms

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Three studies have been carried out. The sweep and the chordlength were optimized in the first one. The camber distributionwas added as an additional variable in the second one. The pur-pose of these first cases was to validate the design method and toclarify the effect of the camber line control. Finally, a stage opti-mization was made to evaluate the possible impact of previousdesign parameters on the stage performance.

2 Baseline Blade Geometry

The specifications of the original blade are summarized inTable1. The baseline blade, specially designed for this study, is atypical front stage transonic rotor for heavy duty gas turbines. No

lean or sweep was introduced yet. The controlled diffusion airfoil(CDA) design concept was used to define the multiple circulararcs (MCA) blade sections at five representative positions (10, 30,50, 70, and 90% span). The other sections were obtained by inter-polation in the radial direction. The shock wave was appropriatelycontrolled at the tip section so that it attached to the leading edgeat the design point. As a result, the adiabatic efficiency of thisbaseline rotor, predicted by CFD, was already high. To achieve afurther efficiency gain by optimization was therefore a quite chal-lenging task.

3 Optimization Method

Figure1shows the algorithm of the optimization system usedfor the present study. One of its advantages is the use of a meta-model, based on an artificial neural network (ANN) as an interpo-lation tool by which the performance corresponding to the givendesign parameters are predicted. It reduces the large computa-tional cost of evaluating the blade performance by 3D-CFD and;consequently, enables an increase of the number of DOF for theoptimization. These advantages have been demonstrated by manycomplicated 3D industrial design problems [1821].

The algorithm consists of two steps. The first one is an approxi-mated loop with ANN predictions based on the information storedin the database. The differential evolutionary (DE) algorithmselects promising designs that are then verified in an accurate loopby means of a full 3D Navier-Stokes solver. The results of theseevaluations are added to the database which allows improvementsto the accuracy of the next ANN predictions. This cycle isrepeated until the CFD confirms that the optimization is based onaccurate ANN predictions. A more detailed description of the

optimization method is given in Refs. [16] and [17]. The follow-ing subsections summarize some components and theirapplication.

3.1 Navier-Stokes Evaluation. The performance of newblades is evaluated by means of the Reynolds averaged full 3DNavier-Stokes solver TRAF3D, which has been validated with theexperimental data of Rotor67 [22]. The convection term is discre-tized by a central differential scheme and stabilized by Jamesonsartificial dissipation. Turbulence closure is by the Baldwin-Lomaxmodel. The boundary layer on the blade surface is assumed to befully turbulent from the leading edge. The accuracy was verifiedby comparing predictions of several similar geometries with MHI

in-house data. In addition, all of the efficiency gains and the stallmargin achieved in each optimization study have been confirmedby the ANSYS CFX solver with SST turbulence model.

The stall limit was defined as the point where the flow fieldbecomes numerically unstable. A threshold of the residual was

defined in advance, based on several numerical tests. In order toverify the choking, stall margin and peak efficiency, calculationswere done at seven points on a constant speed line using 30CPUs of the VKI parallel computing system.

Figure 2shows the computational mesh used for the analysis.The structured H-type mesh has 220 53 53 points in, respec-tively, the stream, pitch and spanwise directions. In order to avoidthe grid dependency on the shock wave, more than 100 grid lineswere clustered in the front passage area where the bow shock isexpected. The minimum grid spacing from the wall was adjustedto y< 5 in accordance with the requirements of the BaldwinLomax turbulence model. The downstream grid is parallel to theexpected exit flow angle to avoid artificial dissipation of the wake.The dependency of the performance on these mesh parameterswas carefully evaluated in advance by the verification tests.

The spanwise distributions of the absolute total pressure andtemperature, swirl and pitch angle were specified as inlet bound-ary conditions. The average static pressure was imposed at theexit and the spanwise variation is obtained from radial equilib-rium. A constant speed line is obtained by modifying the backpressure, leaving the inlet conditions unchanged.

Table 1 Specification of the baseline blade design

Pressure ratio 1.35 Specific flow 180.6 kg/s/m2

Number of blades 22Corrected speed 3600 rpmTip relative Mach number 1.20 Mid Diffusion Factor 0.34 Tip clearance 0.3 % height

Fig. 1 Optimization algorithm

Fig. 2 Computational mesh

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3.2 Geometry Definition. New blades are derived from non-

dimensional 2D profiles defined at the five previously specifiedrepresentative positions. They differ by the thickness and camber-line distributions. In the present study, the thickness distributionhas been maintained at its original value to eliminate the effect onthroat area [23] and to avoid mechanical problems. Figure 3shows the parameterization of the camber line. It is defined by thelocal slope angle whose change directly relates to the local load-ing. The current definition requires only the four variables listedon Fig.3. The two additional control points are displaced togetherwith the leading, trailing edge and the central points. They intendto keep the curvature in the front and rear parts unchanged inorder to avoid undesirable local accelerations or decelerations.

The advantages of this second order expression of the camberline are its relative simplicity, smoothness and the capacity to rep-resent relatively complicated camber lines. The trailing edge

metal angle was kept constant in the single row optimizations, toconserve the stage matching. It was a variable in the stage optimi-zation, because the matching was then implicitly guaranteed bythe stage performance.

The spanwise variation of chord length and stacking line is par-ameterized by B-Spline curves to create smooth and reasonabledistributions (Fig.4). They are linked to each other by the samespanwise positions to reduce the number of variables. Sweep isdefined by six parameters. S1, S2, A1 and A2 can be positive ornegative corresponding to forward or backward sweep. The chordlength is specified by four parameters as a fraction of the localchord length of the original blade.

It was verified that this parameterization could accurately repro-duce the baseline airfoil.

3.3 Problem Definition. The optimization requires the trans-formation of the given engineering problem into a mathematical oneby defining objective and constraint functions [17]. A multiobjectiveoptimization aiming for higher performance and stability was carriedout by minimizing the following objective functions.

Obj1 1:0 Peak Efficiency (1)

Obj2 0:3 Throttle Margin (2)

where the throttle margin is defined as a function of the exitcorrected mass flow at stall and design operating point( mout_design/mout_stall 1). The latter is a design target and thus,explicitly specified.

The optimization is governed by following constraints.

Cons1 min chokjbaseline min chokjdesign 0 (3)

where min is the inlet corrected mass flow. Equation(3)requiresthat the choking mass flow is larger than or equal to the baselineone.

Cons2 mout design mout stall

mout choke mout design

0

(4)

guarantees that a new speed line includes the design throttle point.These definitions allow a shift of the speed line due to a small

change of the mass flow induced by the swept stacking, whichaccelerates the optimization.

After the convergence, the optimization provides a so-calledPareto-front [17]. The best result is the one that respects thestall margin (Obj2

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4 Results and Discussion

4.1 The First Optimization. The first optimization allowsonly a spanwise variation of sweep and chord length. The opti-mized geometry, specified on Fig. 5, shows a combination of astrong forward sweep and varying chord length. The latter isreduced by 5% at 80% span but is almost back to its original valueat the tip.

The resulting performance curve (Fig.6) has lower Obj1 valuesand respects the design requirements specified by the constraintfunctions. The new pressure rise curve conserves the originalcharacteristics except for a small decrease near stall point(Fig.6(a)). Figure6(b) confirms the efficiency gain attributed toforward sweep by previous researchers [7,8]. One observes a sub-stantial improvement (0.3%) of the peak efficiency and a small ef-ficiency drop near stall point. The latter explains the smalldecrease of the pressure ratio near stall point.

The design point flow pattern of the new blade is comparedwith the one of the baseline blade on Figs. 710. These figuresalso include the results of the backward swept blade, which is theoutcome of a second optimization and explained in the followingsubsection. The same color scales are used for each group offigures, so that one can directly compare the strength of the shock

wave, the level of the Mach number and the magnitude of thelosses.

Figure7 is the meridional view of the static pressure contourson the blade suction surface. Since the shock wave has to beperpendicular to the outer wall, he does not follow the leadingedge above the 80% span of the optimized blade (Fig.7(b)). Thestrong forward swept blade cuts the bow shock into a very weakcompression shock on the suction side and a weaker passageshock.

This is also visible on the static pressure contours in the bladeto blade surface (Fig.8). The surface of reference is indicated bythe red line on the small meridional contours in the right lowercorners. At 95%Ht one observes again a passage shock incombination with a weak shock type deceleration impinging onthe suction side at 25% chord length. The smaller acceleration onthe suction side results in a lower Mach number approaching theleading edge. The static pressure recovery in the passage area isby a multiple shock system consisting of a weak oblique shockattached to the leading edge, followed by the passage normalshock. This multiple shock pattern reduces the local shock lossand the interaction loss with the suction side boundary layer. Theflow at 70% span is almost identical to the one of the baselineblade (Fig.8(e)).

Fig. 5 (a) Resultant geometry of the first optimization: spanwise variation of sweep. (b) Resultant geometry of the firstoptimization: spanwise variation of chord length.

Fig. 6 (a) Compressor map: speed line. (b) Compressor map: efficiency.



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The lower pressure difference between the suction and pressureside indicates a lower tip loading. The effect on the tip leakagevortex is illustrated by the entropy contours at 99% height(Fig.9). The high entropy region, marked by yellow and red, indi-cates the tip vortex. It shows that the leakage vortex is weakened

and turned in the downstream direction. The vortex no longerimpinges on the adjacent blade as it does on the baseline blade. Inthe latter the low momentum fluid perturbs the pressure side flowand leaks again to the suction side of the adjacent blade. Thisdouble leakage [24,25] contributes also to the thicker wake ofthe baseline blade.

The spanwise distribution of the inlet axial velocity and adia-batic efficiency are presented in Fig.10. It shows that the axial ve-locity increases at the tip section and decreases below 50% span.The velocity increase at the tip section reduces the incidence. As aresult, the shock wave moves into the passage as previouslyexplained and the loading at the tip section is reduced. On thecontrary, the decreased velocity below mid section increases theincidence and flow turning and thus, the loading in that region.

This spanwise loading redistribution is typical of forward swepttransonic blades. It persists when increasing the pressure ratio,and causes a larger separation in the hub to mid region, which isresponsible for the small efficiency drop near stall point (Fig.6).

The reduced shock strength and the smaller leakage flow discussed

in previous paragraphs, result in a considerable gain in adiabatic effi-ciency in the tip region with only a slight decrease in the hub region.These mechanisms are in agreement with previous observations [7,8]and therefore verify the validity of present optimization system.

4.2 The Second Optimization. The second optimizationallows a modification of the camber line in addition to sweep andchord length. Figure11shows that the optimized geometry has a rel-atively strong backward sweep and a slightly barreling chord(Fig.7(c)). The later helps to reduce the mid-span loading and weak-ens the local shock (Fig. 8(c)). The chord length in the outwardregion is now increased by 3% of its original value while in the for-ward swept blade it was reduced with a minimum at 80% span. The

Fig. 9 Comparison of entropy contours at 99% height section

Fig. 10 (a) Spanwise distribution of inlet axial velocity. (b) Spanwise distribution of efficiency at rotor exit.



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comparison of both results indicates that the camber line control hasa significant influence on the optimum stacking line.

Figure 12(a) shows a comparison of the new camber line at90% height with the original one. It is noted that the optimizedblade has an S-shaped camber line with negative camber in thefront chord area and the peak camber position moved 18%upstream. This position roughly corresponds to the throat, whichis just upstream of the location where the passage shock usuallyoccurs. Figure12(b) shows the spanwise distribution of the shiftin peak camber position between the baseline and the optimizedblade. One observes a gradual change from the 18% forward shift(neg. abscissa) at the blade tip, to a small backward shift (pos.abscissa) below 50% span. Its effect on the performance of thenew blade is discussed later.

The corresponding performance map is compared to the previous

one in Fig.13. It includes also the results of the first optimization forcomparison. The shape of the original speed line, which is importantfor the stage matching [12], is better conserved. The 0.6% increase inpeak efficiency is larger than in the first optimization and sustainedover the entire operation range in spite of the strong backward sweep.

Contrarily to the previous case, this blade is tip critical for stabilitybecause of the backward sweep. The conservation of the original stallmargin must therefore be attributed to the camber line control. Thisresult shows that the optimum stacking distribution depends on theloading distribution and that the optimizer can find it to achieve thebest combination of performance and stability.

The tip Mach number distributions at the design operationpoint are shown on Fig. 14 with the blade center of gravitysuperimposed. They illustrate the impact of the camber-line on

stability. Figure14(a) shows a comparison between the baselineblade and the second optimized one. The leading edge positionof each blade is indicated by an arrow. It shows that the bowshock of the optimized blade is attached at the leading edge andthat the passage shock is more oblique and incidents on the suc-tion side at the same position as the baseline blade. Figure 14(b)shows the comparison between the baseline blade and one withthe optimized backward sweep and chord length, but with theoriginal camber line distribution. One observes that, in the lattercase, the bow shock is completely detached and normal to thesuction side. This normal shock moves further upstream withincreasing back pressure and stall occurs sooner due to too highpositive incidence. This explains the reduction in operatingrange often observed with back swept blades. The backwardswept blade with the original camber distribution does not show

any performance improvement. This is different from whatoccurs with the optimized camber where, at increasing backpres-sure, the oblique passage shock first increases strength byincreasing the shock angle, before it detaches from the leadingedge. Therefore, it is obvious that the camber-line control stabil-izes the blade by compensating for the forward shift of loadingby backward sweep.

The experimental result of Low and Wadia [6] showed a similarchange of shock position and stall margin by a spanwise shift ofthe maximum thickness location. In present study, a similarchange in suction side shape is obtained by modifying the camber-line (Fig.12(b)). This has a stronger influence on the shock posi-tion without the negative effect on efficiency due to the increaseof the wedge angle.

Fig. 11 (a) Resultant geometry of the second optimization: spanwise variation of sweep. (b)Resultant geometry of the second optimization: spanwise variation of chord length.

Fig. 12 (a) Chordwise camber line distribution (90%Ht). (b) Difference of peak camber location.

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In addition, the S-shaped tip section has smaller flow accelera-

tion upstream of the bow shock (Fig. 8(c)). This reduces the lead-ing edge relative Mach number and results in a weaker shock. Itrequires a larger subsonic diffusion in the downstream part but thecorresponding diffusion losses are normally lower than the equiv-alent shock losses. Consequently, the losses at the tip section ofthe second optimized blade are also reduced in spite of the back-ward sweep (Fig.10). As one can see from the pressure differencein the Fig. 8(c), the optimized S-shaped camberline reduces theloading in the front part. It displaces the leakage flow to down-stream (Fig.9(c)) which has favorable impact on both the stabilityand performance.

It is noted that the S-shaped blade has a reacceleration down-stream of passage shock (Fig. 8(c)), resulting from the smallerthroat section than the original cambered blades. A local decreaseof the throat section is usually acceptable if it can be compensatedby an increase at the other spanwise positions. In present optimi-

zation the overall choking mass flow is automatically guaranteedby the constrain (Eq.(3)).

In addition to the improvement of the tip region flow, the shockfront is inclined at mid span due to the backward sweep and theextended chord locally reduces the peak Mach number. As aresult, the passage shock is significantly weakened and has partlydisappeared in the mid span region (Fig.8(f)).

The optimized blade therefore, profits from the positive effect

of the backward sweep without the disadvantages and the effi-ciency gain is achieved over almost the entire span (Fig.10).

4.3 The Stage Optimization. Before carrying out the lastoptimization, stage calculations have been made with the rotorgeometries obtained by the previous optimizations. The perform-ance maps are shown on Fig. 15 together with the full stage opti-mization results, explained later.

The two optimized rotors still demonstrate certain advantagesover the baseline stage and the trend of the pressure rise curvesand the stall margins are roughly consistent with the rotor onlyresults. However the efficiency gain achieved with the Opt. 2 rotor(back swept blade) is now 30% lower than its rotor only value.

Table2 summarizes the performance changes at the rotor peakefficiency point. It shows that the single row efficiency gain of theOpt. 2 (backward swept rotor) is still the highest but that the stageefficiency is badly hurt by the increased stator losses. The radialshift of mass flow at the rotor peak efficiency point due to thebackward sweep is considerably larger than the one with forwardsweep (Fig. 10). As a result, a rotor-stator mismatching occursand the efficiency gain is reduced.

Figure16 shows the design point absolute Mach number distri-bution at the stator inlet and exit. It is found that the backward

Fig. 14 (a) Superimposed tip Mach number contours (baseline versus backward sweep withoptimized camber). (b) Superimposed tip Mach number contours (baseline versus backwardsweep with baseline camber).




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swept blade has the highest inlet Mach number in the hub region.The latter results from the increased loading in that region by theswept stacking. The higher inlet Mach number causes the highertotal pressure loss on the stator suction side, which is responsiblefor the smaller gain in stage efficiency.

In order to avoid such a matching problem, the rotor geometryhas been optimized again, considering the full stage performanceand allowing for a variation of the rotor exit metal angle. Thesteady multirow calculations have been made with the mixingplane technique at the rotor-stator interface. Details of the newly

optimized blade are not shown because, apart from a change ofthe rotor exit metal angle, the resulting geometry is almost identi-cal to the S-shaped backward swept blade (Fig.11). However, thestage efficiency showed a large (0.7%) improvement against thebaseline blade while maintaining the stall margin (Fig.15).

Figure17 shows the difference between the exit flow angle ofthe optimized and the baseline blade. Positive values indicatemore turning; hence a decrease of the exit flow angle. One

observes that the exit flow angle is decreased over the entire span.This does not mean an increase of stator loading or mass flow atthe design point because the operating point is defined by the cor-rected mass flow at the stage exit (see the design throttle line inFig.15(a)). This implies that, without a significant change in thestator losses, the corrected mass flow and thus also the averagedMach number at the stator inlet are approximately conserved evenwhen the speed line is significantly shifted.

However, the optimized change of rotor exit angle modifies thespanwise loading distribution. The variation of the outlet flowangle for a constant increase of enthalpy rise along the span issuperposed on Fig. 17 for comparison. The difference betweenthese curves characterizes the spanwise redistribution of the load-ing with the rotor exit flow angle. It is found that the optimized


Table 2 Performance at the rotor peak efficiency point (differ-ence against the baseline blade case)

Opt.1 Opt.2

DRotor Efficiency 1 0.37%. 0.52%DStage Efficiency 0.37% 0.18%DStator Loss 0.01% 0.19%

Fig. 16 Stator inlet and outlet Mach number (comparison of

single row optimization geometries)

Fig. 17 Difference of rotor exit flow angle



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blade decreases the work at the hub relative to the one at the midspan and tip. Although the total pressure globally increases, itlocally decreases at the hub and hence also the Mach number. Inaddition, the increased work in the mid region pulls more flowinto the center of the blade, which further reduces the axial veloc-ity in hub region.

This is confirmed on Fig.18showing that the stage optimizedblade indeed has a lower inlet Mach number at the hub; hencedecreases the stator total pressure loss and improves the stage effi-

ciency (Fig.15). It can therefore, be concluded that the stage opti-mization controlled the rotor exit flow angle to compensate thenegative effect of the backward swept blade on the stagematching.

In addition, since the pressure recovery in the tip area isachieved by the combination of a shock wave followed by a sub-sonic diffusion, the reduction of the exit metal angle increases therear camber and the extra subsonic diffusion further weakens theleading edge shock.

This is confirmed by the blade to blade static pressure contoursat the tip of the stage optimized blade, compared in Fig. 19 withthe ones obtained by the single row optimized S-shaped blade (instage operation). It appears that the bow shock became even moreoblique.

5 Conclusions

It has been shown that a three-dimensional optimization methodis a powerful tool to find out what changes of the camber line,chord length and stacking distributions will result in performanceimprovements and to understand the mechanisms that govern thecomplex flow pattern in transonic compressors.

The following conclusions about those mechanisms could bedrawn:

(1) The best results in terms of rotor efficiency and stall marginhave been obtained with a strong backward swept stackingline in combination with an S-shaped camber line and abarreling chord length. The 0.6% improvement in the rotorpeak efficiency with unchanged stall margin results from adecrease of losses over the outer part of the blade span.

(2) The well-known negative effects of backward sweep on sta-bility and efficiency at the tip section can be compensatedby an optimum control of the chord wise blade loading.

A S-shaped camber line reduces the suction side Machnumber, makes the shock at the tip oblique in the blade toblade surface and shifts the loading towards the aft part.This reduces the shock and tip leakage losses and enhancesthe stability.

A forward shift of the spanwise peak camber positionnear the tip section introduces a forward sweep like effectwhich makes the shock at the tip attached at the leading

edge.(3) The strong backward sweep in combination with the barrel-

ing chord length reduces the loading in the mid span regionand weakens the leading edge shock.

(4) The stage with the backward swept blade, obtained by therotor only optimization, did not result into an equivalentimprovement of the stage efficiency because of theincreased stator losses due to an off design operation result-ing from a strong radial shift of mass flow induced by thebackward sweep.

(5) The latter can be avoided by a full stage optimization allow-ing also a change of rotor exit flow angle. The correspond-ing modification of the spanwise loading reduces the statorloss and results in a gain of stage efficiency that exceeds theone for the rotor only at unchanged stall margin.

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sonic Compressor Rotors,J. Aircr.,17, pp. 2837.[2] Hah, C., and Wennerstrom, A. J., 1991, Three-Dimensional Flow Fields inside

a Transonic Compressor with Swept Blades, ASME J. Turbomach., 113, pp.241251.

[3] Yamaguchi, N., Tominaga, T., and Hattori, S., 1991, Secondary-Loss Reduc-tion by Forward-Skewing of Axial Compressor Rotor Blading, InternationalGas Turbine Congress in Yokohama.

[4] Sasaki, T., and Breugelmans, F., 1997, Comparison of Sweep and DihedralEffects on Compressor Cascade Performance, ASME Paper No. 97-GT-2.

[5] Law, C. H., and Wadia, A. R., 1993, Low Aspect Ratio Transonic Rotors:Part 1: Baseline Design and Performance, ASME J. Turbomach., 115, pp.218225.

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Haselhoff, S., 2000, Numerical Investigation of the Flow in an Aft-SweptTransonic Compressor Rotor, ASME Paper No. 2000-GT-0490.

[10] Beneini, E., and Biollo, R., 2006, On the Aerodynamics of Swept and LeanedTransonic Compressor Rotors, ASME Paper No. GT2006-90547.

[11] Ji, L., Chen, J., and Lin, F., 2005, Review and Understanding on Sweep inAxial Compressor Design, ASME Paper No. GT2005-68473.

[12] Medd, A. J., Dang, T. Q., and Larosiliere, L. M., 2003, 3D Inverse DesignLoading Strategy for Transonic Axial Compressor Blading, ASME Paper No.GT2003-38501.

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Fig. 18 Stator inlet and outlet Mach number (comparison ofsingle row and stage optimization geometries)

Fig. 19 Static pressure contours at 90% height


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