Progress in Aerospace Sciences - Tsinghua University

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Progress in Aerospace Sciences

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Blade-end treatment to improve the performance of axial compressors: Anoverview

Xinqian Zhenga,⁎, Zhihui Lia,b

a Turbomachinery Laboratory, State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, Chinab School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

A B S T R A C T

This paper reviews the literature published over the past 30 years on the blade-end treatment in axialcompressors. The blade-end treatment reduces the endwall losses and extends the stable margin by modifyingthe blade shape near the endwall region with end-bend, end-dihedral and end-sweep flow control measures. Theend-bend improves the overall performance by aligning the blade inlet/outlet to the flow stream direction. Theend-dihedral reduces the blade force on the endwalls, while the end-sweep not only reduces the shock losses,but also controls the spanwise migration of the blade surface boundary layer. All these effects strongly influencethe compressor performance by modifying the blading loading distribution in the streamwise or spanwisedirections. However, the benefit of the endwall flow control comes with increased losses in the mainstream sothere is a trade-off between the improved endwall region flows and the degraded mid-span flows. Thus, how tocombine end-bend, end-dihedral and end-sweep to achieve the correct balance of loss distribution, appears tobe the key to a successful three-dimensional compressor design.

1. Introduction

The endwall boundary layers, secondary and tip leakage flowsseverely complicate the flow in multistage axial compressors and leadto flow losses and surge margin penalties. Approximately one-half ofthe total losses in the rear stages of a multistage compressor areassociated with the endwall boundary layers [1,2]. Thus, reducingendwall losses plays a significant role in modern compressor designs.

Many flow control measures have been proposed to improve thestage performance of axial compressors for aircraft engines.Wennerstrom [3] reviewed the flow control approaches used to achievevery high loadings in axial-flow compressors before the last decade ofthe twentieth century, for example, slotted airfoils, vortex generators,sweep of stators, etc. More recently Gümmer et al. [4] explored thebenefit of endwall boundary layer removal from critical regions ofhighly loaded axial compressor blade rows and found that theboundary layer removal reduced the local reversed flow, blockage,and losses in the near-casing region.

The blade ends of axial compressors are now normally designed toreduce the endwall losses. The designs can be divided into three groupswith end-bends, end-dihedrals and end-sweeps. Besides, the bladethickness distribution can be modified. However, due to its limitationof mechanical strength, there are few reports about this.

The end-bend technique has been shown to have an encouraging

impact on compressor performance by reducing local flow losses,improving end-wall flow matching and suppressing corner stall. End-bends are first described by Freeman [5]. After that, many companies[2,6,7] and researchers [8,10–13,21] have obtained remarkable effi-ciency gains and stable margin extensions by applying end-bends.

The modern blade-end flow control process inevitably needs tointroduce the effects of end-dihedral and end-sweep. The end-dihedraleffect can be explained by the lifting line mode [7,51] with a variety ofsuccessful applications of the end-dihedral effect [9,19,35]. Moreover,the basic effect of end-sweep is explained in Ref. [26]. End-sweeps caneffectively improve the performance of axial compressors [36–38].Benini and Biollo [32] showed that the use of swept blades effectivelyreduced shock losses and improved the aerodynamic behavior of thetransonic rotors. Comprehensive research of the blade sweep mechan-ism was also described in Refs. [41,43,44].

This review article presents the fundamental technical issuesrelated to blade-end treatments. Emphasis is placed on the summar-ized flow control mechanisms to explain the performance improve-ments. The relevant material is categorized into two parts, i.e.,experiments and numerical simulations. Then, the trends in theperformance gains by means of the blade-end treatment in the pastdecades are given. The prospects and challenges of blade-end flowcontrol measures are discussed at the end.

http://dx.doi.org/10.1016/j.paerosci.2016.09.001Received 14 April 2016; Accepted 13 September 2016

⁎ Corresponding author.

Progress in Aerospace Sciences xx (xxxx) xxxx–xxxx

0376-0421/ © 2016 Elsevier Ltd. All rights reserved.Available online xxxx

Please cite this article as: Zheng, X., Progress in Aerospace Sciences (2016), http://dx.doi.org/10.1016/j.paerosci.2016.09.001

http://www.sciencedirect.com/science/journal/03760421

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http://dx.doi.org/10.1016/j.paerosci.2016.09.001



2. End-bend

2.1. Definition

The classic definition of the end-bend is re-cambering of the blade-end, where the curvature of the camber is modified to adapt to theinlet/outlet flow. Twisting of the stagger angle along the spanwisedirection also can be regarded as an end-bend. One kind of re-cambering measure, by which the meanline angle distributions aremodified near the mid-section and trailing edge, is shown in Fig. 1. As aresult, the deviation angles and resulting aerodynamic losses werereduced. Next the end-bend will be reviewed as two parts, i.e. theexperimental studies and the numerical simulations followed by adiscussion of the control mechanism..

2.2. Experiments

The modern history of the blade-end flow control stems fromFreeman [5] who proposed re-cambering on both the hub and thecasing to achieve a reasonably constant incidence across the span andat the trailing edge to match the gas flow angles. Fig. 2 compares theeffectiveness of the end-bend and original designs, showing theimproved design point efficiency and broadened flow margin occurs.The end-bend design was successfully tested in the HP 9 single stage,high speed rig showing that end-bends yielded a 1% improvement inpeak efficiency [16]..

After the introduction of the end-bend technique, the end-bendswere widely tested to improve the peak efficiency [2,6,10,18] andstability margin [6,10,11,18]. The first generation Pratt & WhitneyControlled Diffusion Airfoil (CDA) blade elements were extended to theendwall flow region using an Integrated Core/Endwall Vortex designmodel, producing a new full span optimized second-generation CDAdesign [6]. The most influential change was to align the inlet metalangles to the gas angles, which led to delayed boundary layer separa-tion 15% further aft on the blade chord and a 25% reduction in endwalllosses. Studies showed that the reduced exit air angle resulted in a 28%reduction in total pressure losses. The reduction in the work requiredon the endwalls and the more efficient endwall sections also reducedthe aerodynamic loading on the endwalls, which improved the surgemargin. More stable state of the boundary layer and reduced sensitivityto stalling incidence on these endwall sections should delay the flowbreakdown that often occurs when the compressor is throttled up thespeedline. Finally, the geometry was adjusted to be more aft loaded. Asmentioned in this reference [6], the aft loading of the endwall sectionwith increasing the camber rate of the rear while reducing that of thefront part resulted in a further 14% reduction in loss, 5% movement aftof the separation point, and a 2.3° increase in section turning. Theimproved blade was tested at high speed on a full sized model of themiddle three stages of the PW2037 HPC and produced a 1.5% increasein the operating line efficiency and an 8% increase in the surge margin,

as shown in Fig. 3. A sample second-generation CDA stator stackedairfoil with these flow control techniques is shown in Fig. 4. Thus, re-cambering is a promising way to improve the performance of thecompressors...

Another successful application of an end-bent blade was used in thecompressors of the WP7 engine. Two stators of the three stage machinehad re-cambering over the rear 50% of the chord as shown in Fig. 5.The end-bend airfoil technique on the stator blades reduced the flowseparation and flow losses in the endwall boundary layer region.Experimental results indicated that the end-bend airfoil had littleeffect on the compressor air mass flow rate. The difference of the massflows between the original compressor and the modified one was 0.1–0.3 kg/s at lower speeds. This difference was even smaller at higherspeed. The reason is that the throat section area is slightly changedwith the application of the end-bend. The surge margin was greatlyimproved in the test compressor with both a uniform inlet flow anddistorted inlet flow. The machine had a dramatic efficiency improve-ment of 2.6–3.2%, with surge margin broadening of 4.9–5.2%. Theremight have been a re-matching effect in the efficiency gain..

In addition, increased stagger towards the wall was used as thesections were adjusted to match the stator leading edge incidenceangle. This reduced the section loading and secondary flow and bettermatched the flow onto the following rotors [17]. However, theeffectiveness of the end-bends near the clearance region was not as

Fig. 1. Comparison of the baseline and end-bend rotor meanline angles (Fig. 4 fromWisler [2]).

Nomenclature

ANN Artificial Neural NetworkCDA Controlled Diffusion AirfoilCEF Controlled Endwall FlowCFD computational fluid dynamics2D two dimensional3D three dimensionalDNS direct numerical simulationEAs Evolutionary AlgorithmsGas Genetic AlgorithmsLES large eddy simulationRANS Reynolds averaged Navier-Stokes

RSM Respond Surface MethodSWB backward-swept BladeSWF forward-swept bladeURANS unsteady Reynolds averaged Navier-Stokesρ densityp static pressurer radiusCu tangential absolute velocityCm meridional absolute velocityδ trajectory curvature angleFr radial blade forcem mass

X. Zheng, Z. Li Progress in Aerospace Sciences xx (xxxx) xxxx–xxxx

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obvious as that near the non-clearance region. Robinson et al. [11,12]presented results from tests of two stators, one conventional and onewith end-bends, operating at low speeds in the buried stage environ-ment of a 4-stage research compressor. The rotor and stator inlet andexit angles were changed in the third stage, which covered approxi-mately 30% of the span at both ends of the blades while the centralportions were not changed. The end-bends at the fixed casing end ofthe vane successfully delivered a fuller total pressure profile, alleviated

the suction surface corner stall, and improved the stall margin.However, the end-bend reduces the effectiveness near the free endsperhaps due to significant spanwise flows along the blade surfaces nearthe free ends. This paper did not quantify the overall performanceimprovements. The end-bends also reduced the flow capacity, as shownin the previous cases [10].

Tailored blades near the endwalls can also be regarded as one kindof end-bends [2]. General Electric (GE) has conducted a large amountof research on multistage compressor endwall flow phenomena. Testsof the GE baseline blading revealed high stator exit swirl angles nearboth endwalls and regions of separated flow near the hub. The airfoilsections near the rotor hub were then modified by un-cambering thetrailing edge region and over-cambering the leading edge region. Theelimination of the separated flow on the rotor hub gave a significant0.8% increase in the compressor efficiency at the design point. Themass flow rate and pressure rise were also increased substantiallybecause the reduction of the deviation angle attendant to the removal

Fig. 2. Performance comparison between straight and end-bend blades of the HP 9compressor (Fig. 37 from Freeman [5]).

Fig. 3. Improved operating line efficiency and surge margin with the end-bend design(Fig. 18 from Behlke [6]).

Fig. 4. Second-generation CDA stator profile (Fig. 15 from Behlke [6]).

Fig. 5. Stator designs with and without end-bend (Fig. 1 from Cai [10]).


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of the flow separation was larger than the anticipated value. Theresulting flow had no separated flow near the rotor hub section. Thedetailed performance characteristics are compared in Fig. 6..

Then, an alternative measure, namely unloaded the leading edgeand loaded the trailing edge near the tip clearance, was applied to rotorendwall regions. This is based on the mechanism that the tip clearanceflow entrains the suction surface boundary layer fluid, resulting in thinwakes near the tip. Thus, the rotor trailing edge region was able toexperience higher diffusion without separation. This gave a 0.3%improvement in the efficiency at the design point. Finally, due to thehigh swirl angles near both endwalls of the stators, the stagger wasincreased by 8–10° near both walls and reduced by around 2° at mid-height, which was called twist according to the definition above. This

retrofitted stator is shown in Fig. 7. The peak efficiency was increasedby 0.4%, implying a 10% reduction of the endwall losses. In addition,the pressure characteristics were improved from the peak efficiency tostall point by almost 5.4%. Moreover, Tubbs and Rea [18] demon-strated a 1% efficiency rise and 6% surge margin increase for the highpressure compressor in an IAE V2500 engine by adopting the end-bentCDA blades..

2.3. Numerical simulations

Some researchers have used numerical simulations to investigatethe effects of end-bends [13,19–21]. The effect of end-bent cantilev-ered stators with various stacking line choices in a 2-stage axialcompressor was studied numerically by Wang et al. [13] as following.The inlet blade angle was linearly increased from 0° to 10° from 85%span out to the casing while the exit blade angle was kept unchanged.Two blade stacking methods were applied to the end-bend stator vaneswith stacking on the leading edge and stacking on the center of gravity.The blade modification is shown in Fig. 8. They found that the peakisentropic efficiency of the retrofit compressor was 0.176% higher thanthat of the prototype compressor with edge stacking applied on theleading edge, while the center of gravity stacking reduced the efficiency.The limiting streamlines for the different stacking points are comparedin Fig. 9. The maximum flow rate and the stall margin were bothreduced by the center of gravity stacking. Better stage matchingbetween the rotor and the stator might compensate for the deterioratedstall margin which was due to the increased separation near the rotorhub. The leading edge stacking gave a positive curvature effect in theend-bend stator vanes while the center of gravity stacking gave anegative curving effect. Thus the stacking position significantly affectsthe performance and the re-cambering and the stacking positions bothneed to be carefully selected to improve the performance...

Some researchers have proposed end-bends in high through-flowfans, with a trailing edge de-camber to decrease the fan root (below20% span) flow turning [19]. Fig. 10 compares the two 3D fan blades.The end-bent fan improves the adiabatic efficiency near the designpoint by 1.33%. However, the mass flow rate and the total pressureratio in the fan both decreased as shown in Fig. 11. They furthershowed that the end-bend decreases the total pressure ratio at the fanroot because of the de-camber effect of the trailing edge which lowersthe diffusion. The end-bend was also applied to the booster stators withthe end-bent blades increasing the total pressure recovery coefficient atthe hub and tips of the stators, and the benefits from end-bent statorswere a 0.19% rise of the adiabatic efficiency near the design point. Theimproved stall margin is due to the reduced separation region near thestator endwalls. However, the total pressure ratio was reduced with theend-bent stators. The authors’ explanation is that the flow passage areaexpansion in stators with trailing edge de-camber is smaller than withstraight ones. Only the flow field details and the specific characteristicsof the two rows of stators were shown in the paper even though theend-bends were applied to four stators...

Some research has shown negative results when the stator camber

Fig. 6. Improved performance of the modified rotor relative to that of the baseline(Fig. 6 from Wisler [2]).

Fig. 7. Photograph of the twisted stator (Fig. 17 from Wisler [2]).

Fig. 8. End-bend stator vanes with different stacking lines (Figs. 2 and 3 from Wanget al. [13]).


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in the lower 50% of the blade was reduced to mitigate flow separation[20]. The total isentropic efficiency was reduced by 0.82%. It wasobserved that, although the hub separation was eliminated, there wasno significant improvement near the casing. This negative resultcontributes to the optional setting of the blade end flow control designas a comparative item. In fact, the end-bend design was not carefullyconsidered so the result was negative. Reference [21] studied the endwall boundary layer development pattern in a multistage axial com-pressor and found that it significantly impacted the stage matching. Inorder to improve the flow situation near the endwall region and to get

better overall performance, an endwall re-cambered design near thehub was applied to two rows of stators in a 5-stage axial compressor.Both the local performance and the stage matching were improved andthe total compressor peak efficiency was enhanced by 0.39% with thestable region and the total pressure rise remaining the same with theoriginal compressor.

2.4. Mechanism

Regions of 3D separation have been identified as an inherent flowfeature formed by the suction surface and the endwall of axialcompressors. These separated flows block the passage and limit thecompressor loading and pressure rise. The streamlines in the outer 3Dseparated region were shown in detail by Gbadebo et al. [22]. It wasfound that as the incidence onto the blade was increased, the numberof singular points increased and there exists a correlation for thenumber of singularities and the thickness of the separated region.Thus, it is reasonable to change the blade angle to give more turningand a larger pressure rise while keeping acceptable incidences. Just asCumpsty [23] mentioned, it is intuitively reasonable to align the inlet tothe blades so that the flow enters with only a small local incidence,especially for the high incidence in the endwall region. The localefficiency can be improved by eliminating the separation region,especially on the non-clearance side. In addition, the stall margin canbe improved which is always dominated by the local flow field in theendwall regions. There is also a trade-off between the reduced passagearea and the eliminated blockage near the endwalls, which stronglyaffect the flow capability of the compressor.

Besides, stage matching also has an important effect on theperformance of a multistage compressor. Re-cambering and twistsignificantly affect re-matching in the multistage compressor environ-ment and the stacking positions should be carefully chosen whenapplying them. However, the flow cannot be always allowed in thedirection where it is desirable. For instance, the relative flow directionis always perpendicular to the chord near the blade clearance region.End-bends have little influence on the tip clearance flow. Consequently,the variation in blade angle is limited out from the wall, especially nearthe clearance section.

3. End-dihedral

As Gallimore et al. [14] noted, the stacking line choice clearly

Fig. 9. Comparison of limiting streamlines on the suction surface and casing at thedesign condition (Fig. 5 from Wang et al. [13]).

Fig. 10. Conventional (black) and end-bent (red) fan shapes (Fig. 3 from Zhu et al.[19]). (For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)

Fig. 11. Performance characteristics for conventional and end-bent fans (Fig. 4 fromZhu et al. [19]).

Fig. 12. Definition of dihedral and sweep (Fig. 6 from Gallimore et al. [14]).


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introduces effects of dihedral and sweep when re-cambering is used.Therefore, re-cambering cannot be thought of as independent from thedihedral and sweep. In fact, the sweep and dihedral involved in theendwall shape modification have been applied in the open literature.

3.1. Definition

The detailed definition of the term end-dihedral is shown in Fig. 12.Movement normal to the airfoil section chord line will be termed asdihedral in this paper. Then, the dihedral angle is taken to be positive ifthe suction surface makes an obtuse angle with the end-wall and theangle is regarded as a negative one with an acute angle..

3.2. Experiments

Bowed blades that mean dihedral near both the hub and casingregions have been used in many experimental tests. Weingold et al. [7]investigated the bowed blade effect on the exit stator of a three-stageresearch compressor. The stator exit traverse data were experimentallycollected to compare with the prototype pressure distributions. Thedata indicated that the bowed stator efficiently reduced the totalpressure defect near the endwall regions. The bowed stator generatedradial forces on the flow field where reduced diffusion rates in thesuction surface corner and delayed formation of the corner separationoccurred. The overall dihedral effect on the compressor performancewas quantified with all three stages reassembled using the bowedstators mentioned above. The experimental testing has demonstratedthat the overall compressor efficiency was increased by 1% and the flowcapacity was increased on the operating line by 0.85%. However,application of the bowed stators in all three stator rows of this researchcompressor showed a small reduction of the stall margin due tomismatching with the adjoining rotors. Thus, one should be sensitiveto the re-matching issues when applying blade-end treatment in amultistage environment.

In order to systematically understand the influence of the dihedral,regular and independent changes of the dihedral angles, positions,directions, etc. should be applied, especially in linear compressorcascades. In Ref. [27], the authors reported that the dihedral effect isbeneficial when the angle between the endwall and the suction surfaceis obtuse. The test cases with different positive angles and dihedraldepths were experimentally compared, and the results for the wholeconfigurations are shown in Fig. 13. The largest dihedral angle anddepth gives the most losses while a dihedral angle of 15° with a depth of1/6 span gives the minimum value. The static pressure and diffusionfactor distributions in these experiment indicated that the dihedralimproved the losses through the unloading near the endwall region andoverloading near the mid-span. As a result, the corner stall wasalleviated and the secondary flow was decreased. However, the keyeffect was the inclination of the blade force. The explanation of bladeforce can also be found in Ref. [50]. However, Place and Cumpsty [51]explained the effects of dihedral by using the lifting line model. Theiraim was to describe the mechanism by means of the vortex dynamicsmodel in a novel way. The details are shown in Section 3.4. A similarendwall effect of the dihedral was given by Gümmer et al. [29]. Itshould be noted that dihedral has limited impact on the classicalsecondary flow pattern but reduces the extent of 3D endwall boundarylayer separation due to the unloading near the endwall regions..

Some researchers have included sweep, lean and re-cambering indesign philosophy for advanced three-dimensional designs. End-sweeps will be discussed in Section 3. Ref. [9] mentioned that, forthe multistage compressors, the predicted effect on the given endwallwas found to be as much a function of the geometric changes to theadjacent blades, as of the changes to the section in question. Thus, oneshould focus on the adjacent blades rather than only on the changedsection in the design of multistage turbomachinery. Finally, theadvanced blades were manufactured and tested. It was found that the

dihedral significantly reduced the loading over most of the chord whichreduced the losses associated with the leakage flow, as was also seen inother studies [7,27,29,50]. Zero lean at the leading edge and a positivelean at the trailing edge have also been considered. The measuredpolytropic efficiency of the datum and the 3D builds are compared inFig. 14. The peak efficiency of the modified design was 0.8% higherthan that of the datum compressor. There was an assumption thatlosses and stall margins were a function of the diffusion factor andsurge was triggered by the high endwall diffusion factors. The end-dihedral reduced the endwall diffusion. Thus, blades can be removedwithout increasing the maximum endwall diffusion factor, while notaffecting the stall margin..

After understanding the basic mechanism, comparative tests of thedatum build, modified compressor stages with changes in the tangen-tial stacking line of the stators (VRB1) and build with re-designedrotors and stators (VRB2) were conducted in Ref. [15]. VRB1 had a1.3% improvement in the peak efficiency with increased stall margin.VRB2 produced a further 0.9% increase in the peak efficiency, whileretaining a similar stall margin with the datum despite the reduction ofthe solidity in the design. The performance characteristics are com-pared in Fig. 15. The traverse results show that the design intent to theflow field had been achieved. It is also evidenced that the localperformance is efficiently improved by the modified blade shape nearthe endwalls. However, the stage matching issues should be carefullyconsidered in a multistage environment, when utilizing blade-endtreatments..


Due to the limitation of costs and observation in the experimentaltests, numerical simulations show their advantages in providingconvenient access to understanding the control mechanisms of end-dihedrals based on the detailed flow situations. Surface static pressuredistributions obtained from numerical simulations of positive andnegative dihedrals are shown in Fig. 16. The negative dihedral bladesshow an increase in the blade force and a reduction in the effectiveincidence near the endwall while the positive dihedral blades show theopposite trends. Overall, the positive dihedral reduces the hub cornerand tip clearance losses, resulting in a fuller boundary layer profile nearthe endwall region. The reduction of the loading near the endwalls alsoreduces the effects of the secondary flow due to the reduction of thecross-passage pressure gradient. The 3D blade shape with end-ends,end-dihedrals and end-sweeps are pictured in Fig. 17...

Multistage turbomachinery CFD analyses are vital to redesigningindustrial core compressors for improved performance. Stators includ-ing parabolic bows covering 25% of the span near the hub and 40%near the shroud in a 12-stage axial compressor gave a 0.2% increase in

Fig. 13. Overall loss comparison with the dihedral angle (Fig. 8 from Sasaki andBreugelmans [27]).


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the design point efficiency [35]. Then, the stator exit flow angles of therear stages were gradually increased with the simulations predicting1.6–2.7% in the design point efficiency. The influence of this dihedraleffect on the stator suction surface is illustrated in Fig. 18. The baselinedesign had pockets of reversed flow at both the hub and shroud asdenoted by the bold arrows, while these were eliminated by thedihedral design. The majority of the efficiency gain probably stemsfrom the re-matching between stages with the blade angles changed toimprove the stage matching. Fig. 19 shows the compressor perfor-mance for the original and redesigned compressors. The efficiency wasimproved, but there was little impact on the surge margin according toboth in-house correlations and numerical simulations...

Other successful applications of end-dihedrals have evidenced theireffectiveness near the fan endwalls. Positive bow of the end-bent

stators by restacking the sections of the vanes gave a 0.25% increasein the adiabatic efficiency of the fan [19]. The low energy flows near thehub and tip corners were removed by the main flows with the limitingstreamlines shown in Fig. 20 evidencing that the effect of bow oncontrolling the migration of the secondary flows and the flow separa-tions are distinct. In addition, the stall margin was increases by 8.1%near the design point as shown in Fig. 21. The bowed vanes more

Fig. 14. Measured polytropic efficiencies of the datum and 3D builds compared to thedesign intent (Fig. 13 from Woollatt et al. [9]).

Fig. 15. Measured characteristics for datum, VRB1 and VRB2 (Fig. 9 from Gallimoreet al. [15]).

Fig. 16. Surface static pressure distributions for datum and dihedral rotors (Fig. 8 fromGallimore et al. [14]).

Fig. 17. Front views of the suction surfaces of the 3D stage (Fig. 11 from Gallimore et al.[14]).

Fig. 18. Suction surface axial velocities for the original and bowed configurations (Fig. 7from Wellborn et al. [35]).


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effectively extended the stable range of the compressor than the re-cambered ones...

3.4. Mechanism

The overall effects of the dihedral have been described in manystudies [7,24–34]. The effect of the end-dihedral can be explained bythe inclination of the blade forces. The redial equilibrium equation is

ρpr

Cr

Cr

δ δ Cm

F1 ∂∂

= + cos − sin2

∂∂

+u m

m

mr

2 2 2

(1)

where ρ is the air flow density, r is the rotational radius, p means thestatic pressure, Cu and Cm are the particle tangential velocity and themeridional velocity respectively in absolute coordinates, δ is thetrajectory curvature angle and Fr means radial blade force. Thus, whena positive dihedral effect is introduced, the changed static pressuretends to move the low energy fluid away from the corner and reduce thecross flow accumulation, which reduces the endwall losses.

Another clearer explanation comes from the lifting line model asshown in Fig. 22. Since the modified stacking vortex line containsradial and tangential segments, a vortex pair occurs on the bladesurface which initially diverts the flow from the end-wall regiontowards the midspan region, then redirects the flow back to the end-wall. As a result, the meridional stream area in the suction surfacecorner is increased from upstream to the stacking line, which reducesthe peak Mach number. Meanwhile, the decreased stream area fromthe stacking line to the trailing line creates a favorable pressuregradient region which reduces the adverse pressure gradient.Moreover, changes in the blade loading caused by the modified velocityfield significantly affect the endwall loss generation..

For the tip clearance zone, the blade with a positive dihedralgenerates less tip clearance flow blockage and losses due to thedecreased blade loading near the endwall region and the resultingweaker interaction between the tip clearance leakage and the main-stream flow. The opposite trends are observed for the negativedihedral. The positive dihedral reduces the hub corner and tipclearance losses, but at the expense of increasing the losses near themid-height region [14]. The modification at the mid-span is usuallysmall so as to not penalize the stall range of the blade row as a whole asthis tends to be dominated by the endwalls reaching a limitingcondition. In addition, the reduction in loading near the endwallresults in a decreased cross-passage pressure gradient, which improvesthe secondary flow.

Fig. 19. Compressor performance for the original and final redesign configurations(Fig. 11 from Wellborn et al. [35]).

Fig. 20. Limiting streamlines on the suction surface of the stator near the design point(Fig. 33 from Zhu et al. [19]).

Fig. 21. Performance characteristic of total pressure ratio (Fig. 30 from Zhu et al. [19]).

Fig. 22. Sketch of the simplified lifting line model explaining aerodynamic effects ofend-dihedral stator.


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Overall, the dihedral provides access to rapid reduction of the bladeforce near the endwalls at the expense of an increased blade force at themidspan. The unloading effect can also be utilized to reduce thesecondary flow effects. A proper combination of the end-dihedral andthe end-bend is beneficial to the improvement of the peak efficiencyand the stall margin.

4. End-sweep

4.1. Definition

Fig. 12 shows that movements parallel to the aerofoil section chordline are termed sweep. The sweep angle is taken to be positive if theblade sections close to the end-wall are moved in the upstreamdirection. The angle is regarded as negative when moved in theopposite direction.

4.2. Experiments

A modified stator featuring forward symmetrical sweeps of theleading edge from the mid-span to the inner and outer annulus wallswas tested to better manage the end-wall flows [37,38]. The experimentindicated that the modified stator produced a flow field with morehigher-momentum fluid in the stator suction surface/corners.However, this was associated with a noticeable mid-span thickeningof the stator wake on the suction side, which is similar to the effect ofend-dihedrals. Fig. 23 shows that from 10% to 70% span from the hub,the losses on the baseline stator blade are appreciably less than on theswept stator blade. The swept leading edge results in more lower-momentum fluid being forced to the mid-span region of the blade.Furthermore, the leading-edge sweep is detrimental to the flow on thehub end when a running hub clearance is used. An accumulation oflower-momentum fluid scraped off from the rotating hub and a largerseparation region on the swept stator blade was shown to occur due tothe longer chord. The net effect of this secondary flow is to reduce thestator blade losses, especially for the shrouded hub case. The stall limitwas also improved by the swept vanes, possibly due to the eliminationof the stage stator hub leakage vortex by the swept stators. It should benoted that the swept stator has a longer blade chord, thus highersolidity than the baseline vane, which may also extend the stable range,but has always been neglected..

Fig. 24 shows a perspective view of the Controlled Endwall Flow(CEF) blade overlapping the baseline blade, in which the leading edgesweep and leading edge bend were applied while the same exit metal

angle with the original one was maintained. Experimental and numer-ical results confirmed that this flow control transported high momen-tum fluid in the main stream into the casing boundary layer. Thereforethe flow separation region moved downstream, consequently suppres-sing the secondary flow [36]. As a result, the maximum efficiency of theretrofit was 0.7% higher than the baseline rotor. The surge margin wasincreased by 0.4% when the stall condition was evaluated based on themaximum pressure rise coefficient. However, if the rotor stall inceptionwas based on the statistical nature of the pressure fluctuations on thecasing wall near the rotor leading edge, the increment of surge marginwas 6.4%. A comprehensive comparison of the sweep effects oncompressor performance was experimentally investigated in Ref.[27]. The cases with different sweep angles, depths, and directionswere tested and Fig. 25 shows oil-flow visualizations of the flow on aforward-swept blade (SWF) and a backward-swept blade (SWB). Thecorner stall at the suction surface endwall on the SWF is much smallerthan that on the SWB. Meanwhile, the minimum losses for each sweptconfiguration are shown in Fig. 26 which shows that, within the rangetested, the sweep angle has a linear effect on the loss variations andfurther efficiency improvements can be obtained if the sweep angle orthe sweep depth is increased more. After analyzing the detailed flowstructures, the authors mentioned that the beneficial effects of the SWFwere attributed to the delay of the onset of the corner stall and itsreduced pitchwise expansion from the suction surface. The basic flowmechanism behind the appearance is the vortex in the forward portionof the passage that has the opposite sense to the passage vortex. Thisinsight was also discussed by Place and Cumpsty by displaying thecirculation of the bound vorticity in Ref. [51]....


Some researchers have numerically modeled the impact of forwardsweep on the tip clearance flows in a transonic compressor with variousclearances [48]. The forward swept rotor improved efficiencies and stallmargins at all clearance levels analyzed as shown in Fig. 27. Theforward swept rotor showed a 6.8% higher throttle margin than theradial rotor with an extended flow range and larger peak pressure riseat the nominal clearance. These calculations showed the advantage ofthe forward sweep on the stable operating range and efficiency. Theblade-to-blade axial velocity contours in the gap with nominal clear-ance at peak efficiency are presented in Fig. 28. This contributes to theimproved loading capability of the blade tip due to the radial shift inthe flow toward the tip and subsequent reduced tip loading levels.Thus, the forward sweep had a shallower tip vortex trajectory, reducedtip leakage blockage and a smaller reversed flow region than theoriginal design. The results of sweep effects on the tip clearance floware similar to Ref. [36]. It can be concluded that end-sweep has a

Fig. 23. Constant span total-head losses for the baseline and swept stators (Fig. 13 fromTweedt et al. [38]).

Fig. 24. Perspective view of the baseline and CEF rotor blades (Fig. 2 from Inoue et al.[36]).


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stronger effect on improving the performance of clearance flows thanthe end-bend and end-dihedral...

As summarized by Woollatt et al. [9], for the non-clearance region,the sweep unloaded the forward part of the blade with more load in theaft section. For the clearance region where the losses are largely causedby the interaction between the clearance jet and the mainstream, thesweep reduces this interaction due to the reduced loading in the leadingedge region. Combined with the dihedral effect, the extent of negativeaxial velocity behind the separation line was reduced owing to thelower loading over most of the chord. The effect of sweep and dihedralon the blade surface pressure distribution is shown in Fig. 29. A similareffect can also be seen in Fig. 16 shown above. Hence sweep can be

used in conjunction with dihedral to improve the end-wall flows.However, the cruel reality exists that the beneficial effect of the end-wall flow control comes with increased loss in the mainstream. Finally,the peak efficiency of the advanced build was 0.8% higher than that ofthe baseline compressor through experimental validation. In addition,there is a correlation between the spanwise distributions of the 2Ddiffusion factor parameter and the predicted loss coefficient..

Fig. 30 also illustrates the reduction in the leading edge loading andthe movement of the peak suction point away from the leading edge.Moreover, the sweep also reduces the shock losses in a transoniccompressor and fan [26,72]. The shock loss is a strong function of theMach number component perpendicular to the shock front [49]. Thus,the sweep of the shock can be reduced for a given incident Machnumber which is the mechanism of the sweep effect on the shock loss..

Fig. 31 shows the relative Mach number inside the blade passagefor the peak efficiency point [32]. As is apparent, for the swept case, theshock has a more oblique pattern from the hub to the tip comparedwith the un-swept rotor. However, the pressure rise across the shockalso primarily depends on the normal Mach number component. If theshock strength decreases with the pressure rise, it means that the extrapressure rise should be gained by diffusion, which will generate extraboundary layer losses. This net effect really determines the final resultfrom the sweep. The sweep also significantly influences the stall pointof the fan [31]. If the blade is swept forwards, the stall point movescloser to the trailing edge. Stall then tends to occur when the shockreaches the leading edge at the tip, thus forward sweep makes thisoccur at smaller mass flow rates and higher pressure ratios than thatfor a conventional fan, leading to increased stall margin. It should benoted that the chord was extended near the endwalls for some cases,which also improves the system stability near stall..

4.4. Mechanism

A large number of researchers [39–47] have focused on the effect ofsweep on the compressor performance. Denton et al. [26] gave a novelway to look at the effects of sweep which is shown in Fig. 32. Thepressure gradient perpendicular to the end-wall is assumed to bealmost zero, since there can be no fluid acceleration perpendicular tothe wall. Hence, the blade loading near the lower wall will be reducednear the leading edge where the loading rapidly falls to zero with fluidmovement perpendicular away from the wall. Conversely, the loadingon the lower wall tends to increase near the trailing edge because thereshould be little pressure difference between that location and the more

Fig. 25. Oil flow visualization of the flow on the SWF and SWB blades at negativeincidence (Fig. 4 from Sasaki and Breugelmans [27]).

Fig. 26. Loss improvement in swept blades (Fig. 6 from Sasaki and Breugelmans [27]).

Fig. 27. Comparison of calculated rotor adiabatic efficiencies (Fig. 14 from Wadia et al.[48]).


10

highly loaded region above it. The same effect occurs near the upperwall..

Near the non-clearance region, the forward-swept blades create avortex in the forward portion of the passage, which has the oppositesense of rotation to that of the passage vortex. This vortex introduceshigh energy fluid into the suction surface/endwall corner and delaysthe onset of the corner stall. Thus, the forward-swept cases have muchbetter performance than the back-swept blades.

As for the clearance region, the improved loading capability withsweep is attributed to the radial shift in the flow towards the tip and thesubsequent reduction of the leakage flow, resulting in a shallower tipvortex trajectory, reduced tip blockage and a smaller reversed flowregion.

For transonic compressors and fans, swept blades reduce the shock

wave losses by changing the radial shock shape of the passage shocknear the casing by the endwall effect. In addition, the relative distancebetween the shock foot and the leading edge can be increased ordecreased by forward or backward sweep which significantly impactsthe stall margin.

Fig. 28. Comparison of blade-to-blade axial velocity contours at mid clearance at peak efficiency (Left: Radial blade; Right: Swept blade) (Fig. 10 from Wadia et al. [48]).

Fig. 29. Surface pressure plots at the casing with sweep and dihedral (Fig. 5 fromWoollatt et al. [9]).

Fig. 30. Effect of leading edge forward sweep on the surface pressure distributions of acompressor blade (Fig. 8 from Denton et al. [26]).

Fig. 31. Relative Mach number distributions near peak efficiency, meridional view(Fig. 13 from Benini et al. [32]).

Fig. 32. Sketch of the aerodynamic effects of end-sweeps.

Fig. 33. Peak efficiency gains due to blade-end flow control measures.


11

Consequently, sweep is an effective tool to control the spanwisemigration of the blade surface boundary layer and to reduce the shockwave losses. However, the improved end-wall condition is accompaniedby the loaded midspan, similar to the dihedral effect. The correctbalance of the spanwise loss distribution and the improved endwallconditions is of great significance to the overall performance.

5. Development trends

Peak efficiency gains caused by blade-bend treatment were collectedto summarize the tendency of blade-end treatment. Fig. 33 shows thepeak efficiency gains that have been published over the past almost 30years. During the early development stage, i.e. from 1980 to 2000, theblade-end treatments on average enhanced the peak efficiency by about1%, while these treatments produced 0.3–0.5% more recently..

The declining trend evidenced in the figure shows that the effects ofblade-end flow control are not as obvious as before. This might be dueto the wide use of three-dimensional CFD models in the original designprocess during which the complicated flow caused by the endwallboundary layer has been taken into account.

6. Discussion

Taylor and Miller [52] mentioned that three-dimensional designsshould consider the way in which the pressure gradient transverse tothe flow direction affects both separations and losses, although manydesign methods still basically rely on two-dimensional, sectional viewsof the blade aerodynamics. The mechanism for the end-bend is that theendwall flow is improved by changing the blade leading or trailing edgedirections. This is an efficient way to improve the efficiency and extendthe stable margin due to the unloaded endwall region with reducedseparation. For the multistage compressors, the end-bend should becarefully utilized with accounting for the stage matching issues.Furthermore, according to both numerical simulations and experi-ments, the tip leakage loss is not sensitive to the addition of end-bends.

The end-dihedral effectively unloads the endwall of the blade andreduces the separation region which improves the peak efficiency andthe stall margin, especially on the non-clearance side. However, asmentioned in many references, the performance gain is not obviousnear the free end region. In many cases, it is better to apply re-camberwith end-dihedral to get a better performance. There is a consensusthat the end-sweep reduces the leading edge loading and the tipclearance vortex flow losses. Furthermore, shock sweep can signifi-cantly reduce shock losses at high Mach numbers and the relativelocation of the shock foot to the leading edge can be modified by usingend-sweep. Thus, end-sweep has a significant influence on the com-pressor stall point.

Thus, re-cambering, twist, dihedral and sweep essentially affect theflow by the flow control of the blading loading in the streamwise andspanwise directions. In addition, there is a trade-off between theimproved endwall region and the deteriorated mid-span flow.Achieving the correct balance of the spanwise loss distribution appearsto be the key to successful three dimensional designs.

Although we can summarize that aligning the blade angle to theswirled flow direction, positive dihedral and forward sweep nearendwalls are beneficial to improve the endwall flow situation. But allof what we can learn from the experiments or numerical simulations isqualitative knowledge. How to quantitatively apply these measures toachieve better performance depends on the particular cases.

As mentioned in Ref. [14], aerofoil with forward sweep has a regionof negative dihedral close to the blade tip while the negatively sweptblade exhibits positive dihedral over most of the tip chord. Thus, theblade-end flow control effects are difficult to decouple. Besides, sweepcan be used in conjunction with dihedral to improve the endwall flow[9]. Thus, the re-cambering, twist, dihedral and sweep effects should becombined to reduce the overall losses.

The rapid development of the three dimensional CFD analyses haveenabled quantitative predictions of the effect of three-dimensionalityon the viscous flow. Although the accurate numerical simulations nearthe end-wall region are still challenging, the considerable research onlarge eddy simulations (LES) to model the larger eddies with thesmaller eddies represented by empirical expressions even directnumerical simulations (DNS) of the Navier-Stokes equations havemade it possible to tailor the blade shape with the aid of the flow fielddetails. In order to reduce the CPU time for unsteady simulations,Reduced Oder Modeling techniques should be developed further.

An alternative method is to find the “optimum” design with anadvanced multivariate optimization method, for instance, GeneticAlgorithms (GAs) [53–55], Evolutionary Algorithms (EAs) [56–59],Artificial Neural Network (ANN) [60–63]，Adjont Algorithms [64–67], Respond Surface Method (RSM) [68–71], etc. GAs and EAs havebeen successfully applied to aerodynamic design optimization pro-blems because of their ease of use, broad applicability, global perspec-tive and particular suitability for the multi-objective optimizationproblems encountered in aerospace designs. Lian et al. [58] gave acomprehensive review of the recent progress of EAs for aerodynamicapplications. In addition, the adjoint approach has been developed asan efficient method, especially for calculations subject to a largenumber of detailed geometric changes since the gradient in the adjointsystem can be determined by solving one set of state equations and oneset of adjoint equations, with the cost of solving the adjoint equationsat the same level as that of solving the corresponding flow equations.There are advantages and disadvantages for each method and they canbe combined to build hybridized algorithms. Currently, the majorchallenge with optimization methods is how to reduce the computationcost while improving the optimization accuracy at the same time.

A new way of viewing the relationship between CFD model andexperiments for 3D designs was given in Ref. [52], in which the core ofthe design method was to “de-risk”. The 3D stacking design space wassplit in half by the tolerance of different designs to uncertainty withhigh and low risk regions. In the “high risk” region, where failures aredue to open corner separations the flow exhibited extreme sensitivity tothe inlet conditions so inaccuracies in the CFD predictions have led tocorresponding error in flow details downstream. Thus, in this area, thedesigners have to be very brave and well informed to venture. However,in the “low risk” region, greater trust can be put in the CFD to predictthe correct trends in the underlying 3D mechanisms. This region offersa safer mode of operation for designers to choose. Although the CFDcan predict the flow details more accurately, there are still obviousuncertainties in the state of the art of CFD results. The advancedexperimental techniques are needed to further reduce these uncertain-ties and to provide better guidance in the design process.

7. Conclusions

The flow near the endwall region is very complicated and flowcontrol measures play a significant role in improving the overallperformance of axial compressors. This paper reviews the developmentof end-bend, end-dihedral and end-sweep designs. The followingconclusions can be draw from this study:

(1) During the early development stage, blade-end treatments can onaverage enhance the peak efficiency by about 1%. These treatmentsresulted in 0.3–0.5% efficient gains more recently. The decreasingtrend of blade-end flow control efficiency gain is mainly due to theuse of three-dimensional CFD in the original design process whichcan account for the complicated flow caused by the endwallboundary layers.

(2) The mechanism for the end-bend is to align the blade inlet/outletto the flow stream direction. Thus, it's an efficient way to improvethe peak efficiency and the stall margin. The end-bends alsoimprove the stage matching in multistage machines. However


12

there are the limitations that the whole pressure field whichcontrols the secondary flow barely changes regardless of how theblades are modified near the endwalls, especially in the clearanceregion of moderately large span blades.

(3) The end-dihedral provides access to introducing a rapid reductionin blade force near the endwalls at the expense of increasing theblade force at the mid-span. This reduces the cross-passagepressure gradient near the endwalls, which reduces the influenceof the secondary flow. The end-bend is always combined with end-dihedral to produce the needed blade force and proper incidence.

(4) The end-sweep not only reduces the shock losses, but also controlsthe spanwise migration of the blade surface boundary layer. End-sweep can also efficiently alleviate the tip clearance flow losses byunloading the leading edge. Furthermore, end-sweep also signifi-cantly influences the stall margin of the compressor by changingthe position of the foot of the shock relative to the leading edge, orby the changes of the local chord length.

(5) There is a trade-off between the improved endwall region and thedegraded mid-span flow. Although the effect of each measure isclear, it is hard to apply them quantitatively. How to achieve thebalance of the spanwise loss distributions is a further subject thatshould be focused on.

(6) The end-bend, end-dihedral and end-sweep all influence theperformance through the control of the blade loading in thestreamwise or spanwise direction. For example, positive dihedralincreases the leading edge loading while forward sweep reduces it.It would be better to combine these effects together to exploit eachother's strength. Thus, introducing combined end-bend, end-dihedral and end-sweep to achieve the balance of the spanwiseloss distribution, appears to be the key to successful three-dimensional designs.

(7) CFD will play more and more important role to develop blade-endtreatment technology in the future. The blade-end shape can beaccurately tailored based on high-fidelity endwall flow field detailswith the aid of improved CFD tools, such as URANS, LES or DNS,etc. The combined blade-end treatment can also be optimallyapplied based on advanced optimization algorithms, such as Multi-Objective/Multidisciplinary EAs, Adjoint Algorithms, etc. Therestill exist obvious uncertainties in the state of the art of numericalsimulations. Combined with CFD, further experiments should beconducted to reduce these uncertainties, finally providing moremeaningful guidance for the design process.

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grant no. 51176087).

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Progress in Aerospace Sciences - Tsinghua University

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