Influence of coupled boundary layer suction and bowed blade on flow field and performance of a diffusion cascade

Cao Zhiyuan,Liu Bo,Zhang Ting,Yang Xiqiong,Chen Pingping

aCollege of Engineering,Peking University,Beijing 100871,China

bSchool of Power and Energy,Northwestern Polytechnical University,Xi’an 710072,China

cAECC Xi’an Aero-engine Controls Co.,LTD,Xi’an 710077,China

Influence of coupled boundary layer suction and bowed blade on flow field and performance of a diffusion cascade

Cao Zhiyuana,*,Liu Bob,Zhang Tingc,Yang Xiqiongb,Chen Pingpingb

aCollege of Engineering,Peking University,Beijing 100871,China

bSchool of Power and Energy,Northwestern Polytechnical University,Xi’an 710072,China

cAECC Xi’an Aero-engine Controls Co.,LTD,Xi’an 710077,China

Axial compressor;Boundary layer suction;Bowed blade;Corner separation;Coupled method;Passage vortex

Based on the investigation of mid-span local boundary layer suction and positive bowed cascade,a coupled local tailored boundary layer suction and positive bowed blade method is developed to improve the performance of a highly loaded diffusion cascade with less suction slot.The effectiveness of the coupled method under different inlet boundary layers is also investigated.Results show that mid-span local boundary layer suction can effectively remove trailing edge separation,but deteriorate the flow fields near the endwall.The positive bowed cascade is beneficial for reducing open corner separation,but is detrimental to mid-span flow fields.The coupled method can further improve the performance and flow field of the cascade.The mid-span trailing edge separation and open corner separation are eliminated.Compared with linear cascade with suction,the coupled method reduces overall loss of the cascade by 31.4%at most.The mid-span loss of the cascade decreases as the suction coefficient increases,but increases as bow angle increases.The endwall loss increases as the suction coefficient increases.By contrast,the endwall loss decreases signif icantly as the bow angle increases.The endwall loss of coupled controlled cascade is higher than that of bowed cascade with the same bow angle because of the spanwise inverse ‘C”shaped static pressure distribution.Under different inlet boundary layer conditions,the coupled method can also improve the cascade effectively.

1.Introduction

Boundary layer suction,or aspiration,was first introduced by Kerrebrock et al.in 1997 with the purpose of increasing aerodynamic loading and avoiding severe flow separation of axial flow compressors in the meanwhile.1–3

A transonic aspirated compressor stage and an aspirated fan stage are designed and experimentally investigated to validate the application of boundary layer suction in axial flow compressor.4,5The transonic aspirated compressor stage has a design tip speed of 457 m/s,and it achieved a maximum pressure ratio of 1.58 and efficiency of 90%under the design conditions.The design tip speed of the fan stage is 229 m/s,and it achieved a total pressure ratio of more than 3.0 at the design rotation speed in the experiment.Gbadebo et al.first investigated the nature of three-dimensional(3D)separations in axial compressors.6,7Then,with the application of boundary layer suction,he eliminated the typical compressor stator hub corner 3D separation.8Chen et al.9performed active control of corner separation in a linear cascade by boundary layer suction,and investigated the influence of the location of the endwall suction slot.Wang,Chen,Song et al.10–13also investigated the application of boundary layer suction in compressors.In their investigations on the control of corner separation,the optimum slot is the endwall slot,which is sufficiently long to remove the limiting streamline.However,the suction slot on the blade surface cannot effectively eliminate the corner separation.

In a highly loaded compressor,the suction surface boundary layer suction and endwall suction are combined to eliminate trailing edge separation and corner separation.5However,suction slots on the suction surface and endwall lead to the complexity of the suction system.Investigation on the possibility to control the corner separation and trailing edge separation by a single suction slot is rarely seen in published literatures.

In the 1960s,Deich et al.adopted 3D blade to reduce the loss of turbines.14In the 1980s,Wang Zhongqi et al.reported that it was the spanwise redistribution of static pressure that reduced the loss of cascade.15Breugelmans16and Shang et al.17investigated the leaned and bowed cascade in a wind tunnel.The results showed that the corner separation was eliminated by bowed blade,but the loss of mid-span increased as low momentum fluid migrated to the region.The increment of mid-span loss may exceed the decrement of endwall loss.Thus,the overall loss of cascade may be more than that of the linear cascade.Bogod18investigated five different bowed stators in a multi-stage compressor.In his investigation,positive bowed stators could increase stage efficiency by 1.0%–1.5%,whereas negative bowed stators could increase stage efficiency by 2.0%–3.0%at most.Positive bowed stator overloads the mid-span and improves the near endwall flow field.Fischer et al.19investigated the influence of strongly bowed stator on the performance of a four-stage axial flow compressor.The efficiency and total pressure ratio between design and blocking conditions decreased as the increased surface area increased the fraction loss.The ef ficiency and total pressure ratio between maximum total pressure ratio and stall conditions increased as the corner separation was eliminated.

As the bowed blade can effectively improve the endwall flow field and control the corner separation,bowed cascade is appropriate for coupling with mid-span boundary layer suction to control the trailing edge separation and corner separation.In this study,a highly loaded compressor cascade,which has both corner separation and trailing edge separation,is investigated.First,mid-span local boundary layer suction and bowed blade are adopted in the cascade separately,and four different bow angles are investigated.Then,coupled mid-span local boundary layer suction and bowed blade is adopted to further improve the performance of the cascade.Moreover,the length effect of the suction slot is also investigated.Corner separation and trailing edge separation are effectively controlled by the coupling method with a single suction slot.

2.Diffusion cascade description and experimental procedure

A highly loaded compressor linear cascade is investigated in the study.The details of the cascade are given in Table 1.Design inlet Mach number is 0.6,and design incidence angle is 0.5°.Airfoil of the cascade is shown in Fig.1.The baseline linear cascade was experimentally investigated in a high subsonic cascade wind tunnel at inlet Mach number of 0.6,incidence angle of 0.5°and 5.0°,and Reynolds number(Re)of 8.02×105under the design conditions based on the chord.Fig.2 shows the test region of the linear cascade wind tunnel.This study assessed blade surface static pressure coefficient(Cp)of baseline linear cascade.Blade surface static pressure was measured from static pressure holes,located at the midspan of the suction surface and pressure surface.

3.Computational method and validations

3.1.Computational method

The 3D numerical simulation is performed on a single cascade passage with the assumption of periodicity.The structure grid is created by AUTOGRID in NUMECA FINE/TURBO.The‘O-type” mesh is created around the blade to achieve a high quality.The total grid number of the baseline linear cascade is approximately 1,030,000.The mesh on the blade surface and endwall is shown in Fig.3.The ‘H-type” mesh is created for the suction slot by IGG of NUMECA FINE/TURBO.The simulation code employed is FINE/TURBO.The Spalart-Allmaras turbulence model is utilized in the simulations.Inlet total pressure,inlet total temperature,inlet flow angle,and outlet static pressure are presented at the boundary according to the experimental data.The investigation is conducted at an incidence angle of 0.5°.In the experiment,the endwall boundary layer is removed by boundary layer suction at one chord upstream the inlet of the cascade,and thus the simulations in most of the study are conducted with clean inlet conditions.With the purpose of validating the effectiveness of coupled method under different inlet endwall boundary layer characteristics,two different inlet endwall boundary layers are defined and investigated in Section 4.5.

Table 1 Main geometric parameters of cascade.

3.2.Validations

Fig.4 comparesCpof the experimental and numerical results at the mid-span of the baseline linear cascade at the inlet Mach number of 0.6 and incidence angles(i)of 0.5°and 5.0°.In the figure,PS is pressure surface,and SS is suction surface.Cpis the ratio of the local static pressure to the inlet total pressure.The numerical results show excellent agreement with the experimental results.From approximately 60%axial chord position to the trailing edge,where the camber angle is larger than that of the front segment of the blade,theCpon the suction surface increases abruptly.At the trailing edge,a weak separation is evident.

Since there is no experimental data of surface visualization for the investigated cascade,and rarely any published experimental data for highly loaded compressor cascade is found,the experimental results of NACA 65 cascade from DLR20are utilized in this study to validate the capability of the numerical code on capturing the separation structure and nearwall flow filed.The cascade features approximate diffusion factor and similar corner separation with the cascade investigated in this study.Thus,it is appropriate for validation.Fig.5 compares the suction surface flow field of the experimental and numerical results.The numerical results show excellent agreement with the experimental results.

4.Results and discussion

4.1.Boundary layer suction in linear cascade

The position and suction coefficient of the suction slot have an important effect on the suction effectiveness.In order to select appropriate slot position and suction coefficient for further investigation,four different suction slot schemes for the linear cascade are designed and investigated.The positions of the four suction slot schemes are at 53.9%(Slot-A),67.5%(Slot-B),76.6%(Slot-C)and 87.7%(Slot-D)axial chords;they are 1 mm in width and distribute from 20%to 80%spans.Fig.6 illustrates the configurations of the four suction schemes.

The comparison for the mid-span loss coefficient of the four suction schemes is shown in Fig.7.The mid-span loss is de fined as the mass flow averaged loss coef ficient of 60%mass flow in the mid-span.It is indicated that the mid-span loss of the four suction schemes all reduces as the suction coef ficient increases.Slot-Cexhibits the lowest mid-span loss.However,as the mid-span loss of Slot-Bis just slightly higher than that of Slot-C,and the blade thickness near Slot-Bis greater than that near Slot-C,the slot position of Slot-Bis adopted in the subsequent investigation for better blade strength.

The mid-span loss coef ficient of Slot-Band Slot-Calmost does not change as the suction coefficient approaches 1.92%.Therefore,in order to compare the flow fields and the performance of different suction schemes at the same suction coeff icient,the suction coefficient of 1.92%is adopted for the following analysis.

Fig.8 compares limiting streamlines/static pressure contours on the suction surface of the baseline linear cascade and linear cascade with suction.The suction coefficient is 1.92%.After boundary layer suction,the trailing edge separation line(TSL)vanishes completely.With suction,the corner separation line(CSL)does not joint with the TSL,but ends at a focus point(F)near the trailing edge.Moreover,static pressure at the trailing edge of the mid-span increases signif icantly,which indicates that the diffusion ability of the cascade increases.

However,the corner separation enlarges significantly after mid-span boundary layer suction.Saddle point&focus point(S&F)structure in the suction surface corner indicates that the cascade exhibits an open corner separation.The streamlines in the suction corner are reversed by the streamwise gradient.After mid-span boundary layer suction,the reverse flow region in the suction surface corner increases.Moreover,theS&Fpoints move closer to the endwall.

Fig.9 shows the pitchwise mass flow averaged loss coeff icient at the outlet of cascade.After mid-span boundary layer suction,the loss coefficient at the mid-span decreases signif icantly as the suction coefficient increases.However,the loss coefficient of 0–28%spans increases remarkably because of the increase in corner separation.

Fig.10 compares the loss coefficient(Cp*)contours at different axial sections and 3D corner streamlines of the baseline linear cascade and the linear cascade with suction.The high loss coefficient region mainly distributes in the suction corner.The 3D streamlines show severe reverse flow in the corner and further prove that the cascade exhibits an open corner separation.The corner separation region enlarges after mid-span boundary layer suction because of the spanwise inverse ‘C’shaped static pressure distribution after mid-span suction prevents the migration of low energy fluid towards the mid-span.More low energy fluid concentrates to the suction surface/endwall corner.The spanwise static pressure distribution is shown together with other schemes.

4.2.Application of bowed blade in diffusion cascade

The spanwise inverse ‘C’shaped static pressure distribution enlargesthe cornerseparation,and the bowed blade redistributes the spanwise static pressure.So the bowed blade is combined with the mid-span boundary layer suction to improve the corner flow filed of the cascade.The stacking curve of the bowed blade is defined as an arc that goes through the endpoints of the baseline stacking line(straight line).The stacking curve is shown in Fig.11.The bow angle is defined as the angle between bowed stacking curve and baseline stacking line.Four bowed cascades are investigated in this study.The bow angles are 10°,20°,30°and 40°.Fig.12 shows the surface mesh of 40°bowed cascade.

The bowed cascade is investigated first before being combined with boundary layer suction.Fig.13 shows the suction surface limiting streamlines and static pressure contours of the bowed cascade.Compared with the baseline linear cascade,the S&F points in the suction corner of the 10°bowed cascade move towards the mid-span,and the limiting streamlines migrate to the mid-span.As bow angle increases,the open corner separation is replaced by closed corner separation.Meanwhile,static pressure near the endwall increases with the bow angle.However,the mid-span trailing edge separation line of the bowed cascade moves upstream,and mid-span static pressure decreases,indicating that the flow field in the mid-span is deteriorated.

The ‘C’shaped distribution of the bowed cascade is benef icial for improving the endwall flow field.Therefore,the midspan boundary layer suction combined with the bowed cascade is a promising method to improve the flow field of the cascade,which includes both the flow field of mid-span and that near the endwall.Then,combined mid-span local boundary layer suction and bowed blade is applied in the cascade.The position,width and length as well as suction coefficients of the suction slot are the same as those of the linear cascade with suction.

4.3.Application of coupled local boundary layer suction and bowed bade in diffusion cascade

In bowed cascades,if the absolute length is equal to the suction slot in the linear cascade,the projected length will be shorter;if the projected length is equal to the suction slot of the linear cascade,its absolute length will be longer.The selection of absolute length or the projected length will influence the performance of the cascade.In order to investigate the influence of the selection,the disparity of absolute length and projected length and the overall loss coefficients of the bowed cascades with different slots are compared in Figs.14 and 15.

It is indicated in Fig.14 that the disparity of absolute length and projected length is rather small;at 20°bow angle,which is the optimal bow angle shown in the following part of this sec-tion,the disparity is 0.7%of the absolute length.Fig.15 provides the comparison of overall loss coefficient for the same absolute length and projected length of suction slot at 20°bow angle.It shows that the two loss curves almost overlap with each other.Thus the selection of the slot length does not affect the bowed cascade much at the optimal bow angle.The same projected length is selected in the paper for the following investigation.

Fig.16 compares the suction surface limiting streamlines and static pressure contours of the bowed cascade at the suction coefficient of 1.92%.After mid-span boundary layer suction,mid-span separations of the four bowed cascades are removed.The trailing edge shows a significant increase in static pressure.The mid-span flow field is similar to the linear cascade after suction.

Compared with the linear cascade with suction,the corner separation of the bowed cascade shows remarkable variations.The S&F structure of the 10°bowed cascade is farther from the endwall,which indicates the increase of spanwise static pressure gradient.The low energy fluid has more driving force to migrate towards the mid-span.TheS&Fstructure vanishes as the bow angle increases to more than 10°,which indicates that the open corner separation is replaced by the closed corner separation.

Streamlines in the corner separation region still flow in reverse under the streamwise pressure gradient.Compared with the bowed cascade without boundary layer suction in Fig.13,the reversed flow trend increases because of the increase in mid-span static pressure after boundary layer suction.As bow angle increases,the streamline curvature of the corner separation region also increases.

Taylor and Miller21de fined the corner shape factor as the angle between forward facing flow vector(V1)and reversed flow vector(V2),as shown in Fig.17.The corner shape factor varies between 0 and π.The endwall loss increases with the corner shape factor.In Fig.16,the shape factor decreases as the bow angle increases,which indicates that endwall loss reduces.However,compared with the bowed cascade without boundary layer suction,the corner shape factor increases after boundary layer suction,which indicates that the near endwall flow field is deteriorated.Variations similar to that of the linear cascade after boundary layer suction are observed.

Fig.18 shows the endwall limiting streamlines and static pressure contours of the bowed cascade with suction coef ficient of 1.92%.Endwall static pressure increases steadily as the bow angle increases.On the endwall,the most important flow structure is the horseshoe vortex system which originates from the leading edge saddle point.The suction leg of the horseshoe vortex(HS) flows around the leading edge of the blade and then crosses the suction surface at the driving force of the pressure gradient.The pressure leg of the horseshoe vortex(HP) flows towards the suction surface of the adjacent blade at the driving force of the static pressure gradient and crosses the rear part of the suction surface.As bow angle increases,the intersection position of the HS and HP with suction surface moves upstream,which indicates the increase of endwall static pressure gradient.

Variations of HS and HP can be further explained by the static pressure distribution near the endwall,which is shown in Fig.19(a).Endwall static pressure of the bowed cascade is higher than that of the baseline linear cascade and linear cascade with suction,and static pressure increases with bow angle.Near the leading edge of suction surface,the static pressure of the baseline linear cascade decreases after the leading edge peak.As the bow angle increases to more than 20°,static pressure no longer decreases near the leading edge.Therefore,the local static pressure gradient near the leading edge of the bowed cascade is higher than baseline linear cascade,which leads to the earlier intersection of HS with suction surface.

HP flows towards the suction surface under the transverse gradient and streamwise static pressure gradient of the endwall.Endwall streamwise overall static pressure gradient from inlet to outlet increases with the bow angle.Therefore,the intersection position of HP with the suction surface moves upstream.Meanwhile,corner separation is reduced.For linear cascade,static pressure near the trailing edge of the suction surface remains the same,which indicates a corner stall.As bow angle increases,the static pressure also increases steadily from the leading edge to the trailing edge,and the corner stall is reduced.

Fig.19(b)shows the mid-span static pressure coefficient distribution.Static pressure at the front section of the pressure surface decreases slightly.From 5%axial chord to the suction slot of the suction surface, static pressure decreases significantly after boundary layer suction;static pressure decreases as bow angle increases.Near the suction slot,static pressure shows a sudden change.Then,static pressure increases steadily to the trailing edge.Boundary layer separation of the mid-span is removed completely.

Fig.20 shows the spanwise static pressure distribution for the trailing edge of the suction surface.The baseline linear cascade,linear cascade with suction and bowed cascades with and without suction are all shown in the figure.The suction coeff icient is 1.92%.Mid-span static pressure of the linear cascade increases significantly after mid-span suction,whereas the static pressure near the endwall decreases slightly.Therefore,a spanwise inverse ‘C’shaped static pressure is established.The low energy fluid near the endwall concentrates to the suction surface/endwall corner,and can hardly migrate to the mid-span.

Bowed cascade without suction increases the static pressure near the endwall.However,the static pressure in the mid-span decreases.Thus,a spanwise ‘C’shaped static pressure is established.The ‘C’shaped distribution of static pressure is benef icial for the migration of low energy fluid towards the midspan.Therefore,endwall loss decreases,but mid-span loss increases.

After mid-span boundary layer suction on the bowed cascades,mid-span static pressure increases remarkably.Static pressure near the endwall increases as well,but the increment is much smaller than that of the mid-span.An inverse ‘C’shaped static pressure distribution forms for each bowed cascade with boundary layer suction.The inverse ‘C’shaped static pressure distribution leads to the increase in endwall loss after mid-span boundary layer suction.However,the static pressure gradient is much smaller than the linear cascade with suction.Thus,the increment of endwall loss is smaller than the linear cascade with suction.

Fig.21 shows the loss coefficient contours at different axial sections and 3D corner streamlines of bowed cascades with suction.The figure shows that the high loss region decreases as the bow angle of the cascade increases,and that it is smaller than the linear cascade with suction.This result indicates that the endwall loss decreases.In the corner of 10°bowed cascade,3D streamlines form a vortex,which further proves the open corner separation in 10°bowed cascade.The corner separation is smaller than the linear cascade with suction.

As the bow angle increases up to 20°,3D streamlines flow smoothlydownstream,and no severecornervortexis observed,which indicates that the open corner separation is removed by the bowed cascade.

Fig.22 compares the overall loss,mid-span loss,and endwall loss of the linear cascade with suction and bowed cascades at different suction coefficients.Fig.23 shows the pitchwise averaged loss of different cascades at the suction coefficient of 1.92%.The endwall loss is defined as the mass flow averaged loss coefficient of 20%mass flow near the endwall.Mid-span loss is defined as the mass flow averaged loss coeff icient of 60%mass flow in the mid-span.

Without boundary layer suction,the overall loss of the cascade first decreases and then increases as the bow angle of the cascade increases.The 10°bowed cascade has the lowest overall loss because the bowed blade improves the flow filed near the endwall,but deteriorates the mid-span flow filed.The reduction of endwall loss is more than the increment of mid-span loss.The mid-span loss increases with the bow angle,and the endwall loss decreases as bow angle increases to 30°.The reduction of endwall loss from 20°to 30°bow angle is much smaller than that from 0°to 10°.The endwall loss of 40°bow angle is more than that of 30°bow angle.

As suction coefficient increases,the overall loss of linear cascade with suction and 10°bowed cascade first decreases and then increases slightly.The overall loss of the cascade with larger bow angle keeps decreasing at the suction coefficient range in this study.The cascade with 20°bow angle exhibits the minimum loss of all the cascades at most of the suction coefficient ranges.

Mid-span loss of the linear cascade with suction and the cascade with 10°bow angle firstdecreasesand then remainsunchanged asthesuction coefficientincreases.Meanwhile,mid-span losses of 20–40°bow angles keep decreasing at the mass flow range in this study.Mid-span losses of the linear cascade with suction and 40°bowed cascade are the minimum and maximum of all the cascades respectively,because the bowed cascade transfers the low energy fluid to the mid-span.

The endwall loss of all the cascades increases with the suction coef ficient.At the same suction coef ficient,the endwall loss of the bowed cascade is smaller than that of the linear cascade with suction.The cascade with 40°bow angle has the smallest endwall loss.Moreover,the growth rate of the endwall loss of bowed cascade is lower than that of the linear cascade with suction because the bowed cascade decreases the spanwise static pressure gradient.

Fig.23 shows the same trend as Fig.22(b)and(c).From 0%to approximately 20%span,the loss coefficient decreases as the bow angle increases.From 20%to approximately 40%span,the loss coefficient increases with the bow angle because the bowed cascade moves the low energy fluid towards the mid-span.From approximately 40%to 50%spans,the loss coefficient remains unchanged as bow angle increases.

Fig.24 shows the velocity vectors and Mach number contours at the cascade outlet.The figures show only the lower half of the cascade outlet.Fig.24(a)shows a passage vortex near the endwall and a concentration shedding vortex(CSV)above the passage vortex(PV).

After boundary layer suction of the baseline linear cascade,the passage vortex nearly disappears,as shown in Fig.24(b).The concentration shedding vortex enlarges,and the center of the vortex moves towards the endwall because the inverse‘C’shaped static pressure reduces the migration of low energy fluid towards the mid-span.The low Mach number region near the endwall increases,which indicates the increase of low energy fluid at the suction surface/endwall corner.

Bowed cascade increases the static pressure gradient near the endwall,leading to the enlargement of the passage vortex.The low Mach number region near the endwall decreases as bow angle increases.The low Mach number region close to the endwall of 40°bowed cascade almost vanishes;it migrates towards the mid-span.

4.4.Influence of slot length on effectiveness of coupled local suction and bowed blade

In addition,in order to investigate the influence of slot length on the effectiveness of coupled local suction and bowed blade,two suction slots with different lengths are designed and investigated.The suction slots distribute from 25%to 75%and 15%to 85%spans.The slot distributing from 25%to 75%span is a bit far from the suction corner.Considering that a slot distributing throughout the whole blade span will weaken the strength of the blade significantly,we do not investigate longer slot in the study,e.g.,Brian et al.4utilized part span slot for both the rotor and stator of an aspirated compressor in the experiment.

Fig.25 compares the suction surface limiting streamlines of bowed cascades with the suction slot distributing from 25%to 75%span;the suction coefficient is 1.92%.Compared with Fig.13,the mid-span separations are all removed.However,the flow field in the corner is deteriorated obviously.The open corner separation enlarges at the bow angle of 10°.The open corner separation remains at the bow angle of 30°.As the bow angle approaches 40°,the open corner separation is replaced by a closed corner separation.The corner shape factor is larger than that in Fig.16(d).

In Fig.26,the limiting streamlines on the suction surface of bowed cascades with the suction slot distributing from 15%to 85%span are provided;the suction coefficient is also 1.92%.Local boundary layer suction effectively removes the midspan separations.The open corner separation of all the cascades in Fig.26 vanishes;moreover,compared with the bowed cascade with the suction slot distributing from 20%to 80%span as shown in Fig.16,the corner shape factor decreases,indicating lower endwall loss.

Figs.27 and 28 provide the variations of overall loss with the increase of suction coefficient.With the suction slot distributing from 25%to 75%span,the overall losses of the bowed cascades are lower than those of the linear cascade with suction.The optimal bow angle is 20°.The minimum loss is lower than that of the linear cascade with the suction slot distributing from 15%to 85%and 20%to 80%spans.Therefore,a shorter suction slot coupled with bowed blade is able to achieve the effect of a longer suction slot in the linear cascade.However,as the open corner separation exists even at the opti-mal bow angle,the reduction of overall loss coefficient is lower than the coupled suction schemes with longer suction slots.

As the coupled suction scheme with the suction slot distributing from 15%to 85%span effectively eliminates the open corner separation,the overall loss of the cascade reduces significantly.The optimal bow angle is also 20°.The minimum overall loss is lower than that of the coupled suction schemes with the suction slot distributing from 25%to 75%and 20%to 80%spans.

Figs.29 and 30 provide the variations of endwall loss and mid-span loss with the increase of bow angle for different suction slots.The suction coefficient is 1.92%for each condition.The coupled suction scheme with the shortest suction slot exhibits the highest endwall loss and mid-span loss because of the open corner separation under most conditions.

In conclusion,shorter suction slot far from the suction corner tends to induce open corner separation,which deteriorates the near endwall flow field,whereas longer suction slot that extends to the suction corner is apt to avoid open corner separation,which deteriorates the near endwall flow filed less.Therefore,longer suction slot is easier to balance the suction technique and bowed blade,and exhibits lower overall loss coefficient.In the design process of coupled mid-span suction and bowed blade,the slot length should be sufficiently long to eliminate the open corner separation at the optimal bow angle;the strength of the blade is also to be considered,so a suction slot distributing throughout the whole span is not suggested.In this study,a suction slot distributing from 20%to 80%span can effectively eliminate the mid-span trailing edge separation and the open corner separation at the optimal bow angle.

In Fig.29,the slop of endwall loss curve for 20–80%span suction is approximately the same before 20°bow angle;the decrement is much smaller while the bow angle is higher than 20°,and the endwall loss almost does not change from 30°to 40°bow angle.The variations of endwall loss for 15–85%span suction are similar with those for 20%–80%span suction.The variations are related to the forms of corner separation.At low bow angles,as there is much low energy fluid in the open corner separation region,bowed blade decreases the endwall loss obviously,whereas at high bow angles,as there is little low energy fluid in the closed corner separation region,the increase of bow angle does not improve the endwall flow filed much.However,as the bowed blade increases the loading of mid-span,and enlarged surface area increases the fraction loss19,the mid-span loss keeps increasing.Moreover,the mag-nitude of the slop of the mid-span loss curves increases with the bow angle.Therefore,in the design process of coupled suction cascade,the bow angle should be sufficiently high to eliminate the low energy fluid near the endwall,but it should also be not so high as to avoid excessive mid-span loss.For the cascade in the study,20°is the optimal bow angle.

4.5.Validity of coupled method under different inlet boundary layer characteristics

This study presents the total pressure boundary layer on the cascade inlet to validate the effectiveness of coupled method under different inlet boundary layer characteristics.The definition of the total pressure boundary layer is expressed as follows

whereP*is local total pressure;P*0the baseline inlet total pressure and total pressure of the inlet bulk flow in the cascade with inlet boundary layer;ΔP*the difference between the total pressure of the bulk flow and the endwall;ΔLthe thickness of the boundary layer;xthe position of the blade span.

The study investigates the influence of two different schemes of the inlet boundary layer,as shown in Fig.31.Boundary-05 scheme has a total pressure boundary layer thickness of 5%span,whereas Boundary-10 scheme has a thickness of 10%span.The inlet mass flow averaged Mach number stays the same as the baseline linear cascade.The suction slot is the same as that of Sections 4.1 and 4.3.

Fig.32 shows the overall loss coefficient,mid-span loss coefficient and endwall loss coefficient of Boundary-05 scheme,respectively.Fig.33 shows the loss coefficients of Boundary-10 scheme.ThelosscoefficientsoftheBoundary-05 and Boundary-10 schemes show similar variations as the suction coefficient increases.

For the Boundary-05 scheme,the overall loss shows similar variations as the clean inlet cascade.The overall loss of the linear cascade of the Boundary-05 scheme first decreases and then increases slightly as the suction coefficient increases.The overall loss of the 10°bowed cascade and other bowed cascades keeps decreasing in the suction coefficient region,which indicates more low energy fluid migrating to the mid-span.At the highest suction coefficient,the losses of all the bowed cascades are lower than the linear cascade.The 20°bowed cascade has the lowest overall loss at the highest suction coefficient.Compared with the linear cascade at the same suction coeff icient,the 20°bowed cascade decreases by 22.6%.Mid-span loss variations are similar to the clean inlet cascade.Endwall loss of the cascades increases with the suction coefficient,but with a smaller increment.

For the Boundary-10 scheme,the bowed cascades still improve the performance of the cascade effectively.The overall loss of the linear cascade of Boundary-10 scheme first decreases and then increases significantly.The overall loss of the linearcascadeislowerthan theclean inletand Boundary-05 scheme,and keeps reducing until the suction coefficient reaches 1.44%.The overall loss of the bowed cascade keeps decreasing at the suction coefficient range in the study.The overall loss of 10°,20°and 30°bowed cascades is lower than that of the linear cascade in most of the suction coefficient regions.The variation of mid-span loss is similar to that of the clean inlet cascade.The endwall loss of the linear cascade shows more difference than that of the clean inlet cascade,and increases slightly with the suction coefficient.

5.Conclusions

(1)A coupled local tailored boundary layer suction and positive bowed blade method is developed based on the investigation of the mid-span local boundary layer suction and bowed blade separately.

(2)Mid-span local boundary layer suction can effectively eliminate mid-span trailing edge separation.However,the open corner separation is more severe than baseline linear cascade because of the spanwise inverse ‘C”shaped static pressure distribution.The positive bowed cascades exhibit an opposite characteristic;they effectively improve the near endwall flow field,but enlarge the mid-span separation because of the spanwise ‘C”shaped static pressure distribution.

(3)The coupled method can effectively improve the near endwall flow field and the mid-span flow fields.The open corner separation is replaced by closed corner separation at 20°or higher bow angles.The corner shape factor decreases as the bow angle increases.Mid-span trailing edge separation is removed by local boundary layer suction.The static pressure near the trailing edge increases significantly.The 20°bowed cascade has the lowest overall loss at the maximum suction coefficient.

(4)For the linear cascade with suction and coupled controlled cascades,mid-span loss decreases as the suction coefficient increases,whereas mid-span loss increases with the bow angle.Endwall loss increases in different degrees as the suction coefficient increases.As bow angle increases,endwall loss decreases significantly.The endwall loss of coupled cascade is higher than that of the bowed cascade without boundary layer suction because of the weak spanwise inverse ‘C” shaped static pressure distribution.The coupled method can also improve the flow field of the cascade effectively under different inlet boundary layer conditions.

Acknowledgements

This study was supported by China Postdoctoral Science Foundation and a key project of the National Natural Science FoundationofChina(No.51236006).Theauthorswouldliketothank Dr.Zhou Chao for the help during the writing of the paper.

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10 December 2015;revised 9 May 2016;accepted 19 October 2016

Available online 21 December 2016

Ⓒ2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is anopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.

E-mail address:zycao@pku.edu.cn(Z.Cao).

Peer review under responsibility of Editorial Committee of CJA.