Comparison of aerodynamic characteristics between a novel highly loaded injected blade with curvature induced pressure-recovery concept and one with conventional design

Zhiyun CAO,Cho ZHOU,b,c,*,Zhili SUN

aState Key Laboratory for Turbulence and Complex Systems,College of Engineering,Peking University,Beijing 100871,China

bBIC-ESAT,Peking University,Beijing 100871,China

cCollaborative Innovation Center of Advanced Aero-Engine,Beijing 100083,China

Comparison of aerodynamic characteristics between a novel highly loaded injected blade with curvature induced pressure-recovery concept and one with conventional design

Zhiyuan CAOa,Chao ZHOUa,b,c,*,Zhili SUNa

aState Key Laboratory for Turbulence and Complex Systems,College of Engineering,Peking University,Beijing 100871,China

bBIC-ESAT,Peking University,Beijing 100871,China

cCollaborative Innovation Center of Advanced Aero-Engine,Beijing 100083,China

Available online 8 May 2017

*Corresponding author at:State Key Laboratory for Turbulence and Complex Systems,College of Engineering,Peking University,Beijing 100871,China.

E-mail address:czhou@pku.edu.cn(C.ZHOU).

Peer review under responsibility of Editorial Committee of CJA.

Production and hosting by Elsevier

http://dx.doi.org/10.1016/j.cja.2017.03.018

1000-9361©2017 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

This paper introduces a novel design method of highly loaded compressor blades with air injection.CFD methods were firstly validated with existing data and then used to develop and investigate the new method based on a compressor cascade.A compressor blade is designed with a curvature induced pressure-recovery concept.A rapid drop of the local curvature on the blade suction surface results in a sudden increase in the local pressure,which is referred to as a curvature induced ‘Shock’.An injection slot downstream from the ‘Shock’is used to prevent‘Shock’induced separation,thus reducing the loss.As a result,the compressor blade achieves high loading with acceptable loss.First,the design concept based on a 2D compressor blade profile is introduced.Then,a 3D cascade model is investigated with uniform air injection along the span.The effects of the incidence are also investigated on emphasis in the current study.The mid-span flow field of the 3D injected cascade shows excellent agreement with the 2D designed flow field.For the highly loaded cascade without injection,the flow separates immediately downstream from the ‘Shock’;the initial location of separation shows little change in a large incidence range.Thus air injection with the same injection configuration effectively removes the flow separation downstream from the curvature induced ‘Shock’and reduces the size of the separation zone at different incidences.Near the endwall,the flow within the incoming passage vortex mixes with the injected flow.As a result,the size of the passage vortex reduces significantly downstream from the injection slot.After air injec-

Axial compressor;

Air injection;

Curvature induced ‘Shock’;Flow control;

Separation tion,the loss coefficients along spanwise reduces significantly and the flow turning angle increases.©2017 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1.Introduction

The development of future aero-engines requires a higher thrust-weight ratio and higher efficiency.It challenges one of the main components of an aero-engine,axial compressor,by increasing the stage loading1,which requests an increase of the compressor blade loading and normally results higher losses.2The stage loading of a conventional blade design is limited by the separated flows in the compressor.3–6For example,Dickens and Day2showed that significant separations occur in the stator of a highly loaded compressor design.

Controlling these separations and the loss is the key to improve aerodynamic performance,e.g.,the turning angle and efficiency,of highly loaded compressors.7–23Flow control methods are used to mitigate the negative effects due to the flow separation of highly loaded compressors,e.g.,air injection or blowing is used on the blade suction side surface to control local flow separations.15–23In the experimental studies by Culley et al.15and Kirtley et al.16,streamwise blowing air was applied on the suction surface of a compressor cascade.The blowing air reenergized the laminar boundary layers,which suppressed the flow separation,thus reducing the losses of blade rows.They believed that air blowing delays separation by reenergizing the inner boundary layer with high-momentum fluid transported from freestream.Sarimurat and Dang17investigated steady blowing on a low-speed compressor cascade by an analytical model.The influences of the momentum,the velocity magnitude,and the angle of the blowing flow on the performance of the boundary layer were investigated.Feng et al.18experimentally studied the effects of air injection near the suction surface corner on the flow separation and losses of a highly loaded compressor cascade.The results show that air injection improves the flow field at the suction surface/endwall corner.The energy loss coefficients reduces by 5.5%at most.Nerger et al.19conducted active flow control by means of endwall and suction surface blowing on a controlled diffusion cascade.The suction surface blowing reduces the boundary layer separation effectively.In the investigation work of Vorreiter et al.20,circulation control was conducted by an active blowing method on a linear compressor cascade to inhibit boundary layer separation.Then the result of the cascade was transferred to a four-stage high-speed compressor.Circulation control or active blowing was applied in the first stator.For their numerical investigation results,the performances of the cascade and the compressor show impressive benefits by air blowing.Guendogdu et al.21further investigated air injection flow control on a high-speed compressor.Their intent was to reduce the number of stator vanes.The results show that the solidity of the stator can be decreased by 25%by active injection flow control with a blowing rate of 0.5%of the main mass flow.Furthermore,impulsive suction surface injection22,23has also been investigated.

Most studies have developed flow injection methods to control the blade surface separation based on an existing compressor blade.However,the distributions of the flow within the blade passage are significantly different for cases with or without blade surface injections.It’s necessary to design the injected airfoil in conjunction with flow control.

In this paper,an exploration of the design of a highly loaded injected compressor blade is reported.The investigation aims at the design of a highly loaded compressor blade in conjunction with local air injection.The blade is designed by a curvature induced pressure-recovery concept,which will be discussed in the following.The airfoil is divided into three sections:a highly loaded section from the leading edge to about 74%axial chord;a curvature induced ‘Shock’section near 74%axial chord;and a flow controlled section from 74%to the trailing edge.The low adverse pressure gradient level on the suction surface of the highly loaded section prevents the flow from separating in a rather large incidence range.Thus the injection slot downstream from the ‘Shock’is effective in a large incidence range to remove the ‘Shock’induced separation.As a result,the compressor blade achieves high loading with an acceptable loss.3D flow field simulations are performed in the investigation,which further validates the novel design method.

2.Numerical method and validations

The analysis code employed is ANSYS FLUENT,a fully three-dimensional Reynolds-Averaged Navier–Stokes(RANS)solver.The code uses a finite volume method.Calculations were carried out using a second order accurate in space and turbulence numeric based on a density-based solver.The transition shear stress turbulence(SST)model is adopted for accounting for the transportation of the turbulence shear stress and modelling highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients.‘O’type mesh around the blade surface and ‘H’type mesh in other domains are created for the calculations.

In order to validate the numerical method on capturing the near wall flow field and the corner separation,the experimental results from an NACA 64A-905 compressor cascade are adopted to compare with the numerical results.Fig.124shows the comparison of the surface flow field of the compressor cascade.It shows that the limiting streamlines of the numerical results agree excellently with those of the experimental results;the onset position and region of corner separation are accurately captured.

The airfoil designed in the following section features high loading.However,there is little detailed highly loaded compressor cascade data published for validation.Considering the diffusion flow in the compressor cascade is similar to the local diffusion near the rear of the suction surface in the highly loaded turbine cascade,a widely investigated highly loaded turbine cascade T106C is adopted to validate the diffusion flow in the highly loaded compressor cascade.The surface static pressure coefficients comparison of a T106C cascade is shown in Fig.2,Cptis surface static pressure coefficients for turbine cascade,Sis blade surface coordinate measured from leading edge andSois overall surface length of blade suction/pressure side.The surface static pressure of numerical simulations matches well with that of experimental data.The separation position on the suction surface is also accurately simulated.

3.2D highly loaded injected compressor blade design

3.1.Curvature induced pressure-recovery concept

The ‘velocity discontinuity’concept is firstly introduced by Goldstein26for external airfoil design to increase the aerodynamic loading.The design concept achieves a rapid pressure recovery over a small segment of suction surface at the rear part of an airfoil;and it establishes a novel loading distribution along chordwise.Thus the airfoil section before the rapid pressure recovery position,that is most part of the chord,exhibits high loading.The ‘velocity discontinuity’is formed under a local finite-discontinuous change in the streamline curvature to induce a consequently rapid increase in the local suction surface static pressure.As the rapid increase of the static pressure of the suction surface is similar to the characteristic of shock,the ‘velocity discontinuity’concept can be called as curvature induced ‘Shock’.This method is not so often used in turbomachinery designs.Only one example found so far is that Power et al.27designed a highly loaded cascade by a curvature induced pressure-recovery concept with boundary layer suction.

In order to validate the local ‘velocity discontinuity’induced by a curvature drop,the suction surface of a conventional loaded cascade is redesigned firstly.The profiles of an original conventional loaded blade and a redesigned blade with a local curvature drop are shown in Fig.3,CL means conventional loaded cascade.The cross area of the local stream-tube close to the suction surface undergoes a mild change initially and then experiences a rapid dilation across the curvature rapid drop.Therefore,the rapid drop of the local curvature implies a significant static pressure increase.The curvature drop is located at 55%axial chord.The curvature of the suction surface returns to normal after the local curvature rapid variation.For this conventional loaded blade,only a small part of the suction surface profile near the local curvature drop is redesigned.As a consequence,the profiles of the redesigned conventional loaded blade and the original conventional loaded blade almost overlap with each other except for the local curvature drop region;thus they share similar loading,i.e.,the conventional loading.

In this paper,the authors focus on the investigation of the typical flow conditions of the middle-stage and rear-stage in multi-stage axial compressors,whose blades operate at subsonic inlet flows.In order to validate the local‘velocity discontinuity’under different subsonic inlet flow conditions,numerical calculations were conducted from a very low inlet Mach number of 0.1 to a relatively high inlet Mach number of 0.7.The surface static pressure coefficients of the original conventional loaded cascade and the redesigned conventional loaded cascade are compared in Fig.4,Cpcis surface static pressure coefficients for compressor cascade.The static pressure coefficients experiences a rapid increase across the ‘Shock’for each of the three inlet Mach number conditions in the figure,the same as the variations of the static pressure across a regular shock.Therefore,the local curvature rapid drop is able to introduce ‘velocity discontinuity’in the investigated inlet Mach number range.

However,as the blade loading and the ‘Shock’strength are not so high,the redesigned conventional loaded blade exhibits no ‘Shock’induced separation.The static pressure increases progressively at the rear part of the suction surface,indicating that there is no flow separation downstream from the ‘Shock’.The flow fields near the local curvature drop of the redesigned conventional loaded cascade are compared with those of the original conventional loaded cascade in Fig.5,which further illustrates that there is no flow separation downstream from the ‘Shock’for this design.

However,just as similar as a regular shock,the strong static pressure gradient across the ‘Shock’leads to thickening of the local boundary layer.The boundary layer will separate if the‘Shock’wave strength is too strong.Thus air injection flow control downstream from the ‘Shock’is utilized in the design of a highly loaded cascade in the following to delay ‘Shock’induced separation on the suction surface.

3.2.2D highly loaded injected diffusion cascade

Firstly,a highly loaded airfoil is designed by the curvature induced ‘Shock’concept,which will result in a separation on the suction side surface.The airfoil is designed in conjunction with air injection.Then,air injection is utilized immediately downstream from the curvature induced ‘Shock’to control flow separation.

3.2.1.2D airfoil design

This paper discusses a highly loaded airfoil designed by the curvature induced pressure-recovery concept.The suction surface static pressure distribution is carefully designed by an inverse design method of MISES.The surface static pressure coefficients of the inviscid calculation of MISES is shown in Fig.6.The curvature induced ‘Shock’is at 74%axial chord.Viscid results of MISES and FLUENT are both compared with the MISES inviscid results in the figure.The static pressure coefficients of the three curves agree well with each other at the forepart before the ‘Shock’.Because there is severe flow separation after the ‘Shock’,which will be presented later,the‘Shock’of the viscid results differs a little from that of the inviscid results;the inviscid and viscid results from MISES see discrepancy after the ‘Shock’.It’s because the calculation methods of inviscid and viscid flow fields are different,and inviscid is just an assumption for the fluid.However,as it’s almost impossible to carry out the inverse design by the viscid method of MISES when there is severe flow separation,the inviscid method is still implemented during the inverse design.On one hand,as MISES is a coupled Euler/boundary-layer flow solver,whilst FLUENT is a Reynolds Averaged Navier-Stokes solver in conjunction with a turbulence model,their abilities on flow field simulation are different;on the other hand,it’s difficult to predict severe flow separations until nowadays.Therefore,despite the discrepancy,the viscid results of MISES and FLUENT show acceptable agreement;the discrepancy does not affect the conclusions of this paper;the design of a highly loaded injected blade by the inviscid method is successful.

The existence of the ‘Shock’makes a highly loaded blade easy to be achieved.The deceleration process is divided into three parts:the first is from the peak velocity position to the‘Shock’;the second is the deceleration across the ‘Shock’;the last is from the ‘Shock’to the trailing edge.The ‘Shock’shares a large part of the deceleration on the suction surface;thus the deceleration upstream from the ‘Shock’can be reduced significantly,which results in high loading upstream from the‘Shock’.However,just as a regular shock wave,the strong pressure recovery across the curvature induced ‘Shock’can also lead to flow separation.In this investigation,air injection is performed immediately downstream from the ‘Shock’on the suction surface to control flow separation.

The baseline highly loaded airfoil is shown in Fig.7.The lower pressure gradient upstream from the local curvature drop leads to a mild increase of the curvature.It forms a thicker airfoil which is good for the design of inner injection plenum and blade strength.The rapid drop of the local curvature is seen at 74%axial chord on the suction surface.

Table 1 shows the 2D airfoil design point operating conditions.It indicates that a highly loaded blade with an ultra-high camber angle of 69.35°and a Leiblien diffusion factor of 0.61 is designed.

Fig.8 shows the Mach number contours of the baseline highly loaded cascade at different incidences without air injection.This figure shows how to design a highly loaded airfoil in conjunction with air injection by the curvature induced ‘Shock’pressure-recovery concept.

At 0°incidence in Fig.8(a),the suction surface flow accelerates to a peak velocity soon after the leading edge,and then decelerates mildly toward the ‘Shock’.The Mach number shows significant decrement near the location of the local curvature rapid drop,which is the curvature induced ‘Shock’.Severe flow separation is observed downstream from the ‘Shock’.Air injection should be performed immediately downstream from the ‘Shock’.Therefore,in the design of a highly loaded airfoil by the novel pressure-recovery concept,the air injection position is associated with the curvature induced ‘Shock’.

Fig.8(b)further shows that the separation of a highly loaded airfoil originates from the same position in a rather large positive incidence range.Thus the injection slot designed at the design incidence will be effective in a large incidence range.In Fig.8(b),the deceleration upstream from the ‘Shock’is more than that at 0°incidence.However,the adverse pressure gradient is still not severe enough to introduce flow separation before the location of the curvature rapid drop.Flow separation is also found downstream from the ‘Shock’,the same as that under the 0°incidence condition.The flow separations of 0°incidence and 6°incidence only differ in the separation area,while their onset positions are the same.Therefore,the appropriate injection position of a larger incidence is the same as that under the 0°incidence condition.

In conclusion,the highly loaded airfoil designed by the curvature induced ‘Shock’concept contains three parts:the upstream highly loaded section,the curvature induced ‘Shock’section,and the downstream flow controlled section.The highly loaded section has a low deceleration on the suction surface,which results in excellent performance in a large incidence range.The rapid drop of the local curvature leads to the curvature induced ‘Shock’.The ‘Shock’shares a large part of the deceleration on the suction surface,so the flow separation doesn’t move upstream in a large incidence range.In consequence,the highly loaded airfoil is designed in conjunction with air injection;air injection should be applied right downstream from the ‘Shock’,and it works effectively in a large incidence range.

Table 1 2D airfoil design point operating conditions.

3.2.2.Injection configuration design

Fig.9 shows the injection slot designed for controlling the‘Shock’induced flow separation.The injection slot locates right downstream from the ‘Shock’.Fig.9(a)shows the conventional injection slot configuration.The baseline highly loaded blade is slotted in order to design the injection slot.The major disadvantage of this injection configuration is that the curvatures of the injection slot and the suction surface downstream are discontinuous.The angle between the injection slot and the downstream suction surface will surely reduce the injection efficiency.Moreover,the injection direction is detrimental for the flow turning of the primary flow.

The injection configuration shown in Fig.9(b)aims at improving the injection efficiency.Because the flow separation downstream from the ‘Shock’is so severe that the modification of the rear part of the suction surface will not deteriorate the flow field much,or it will have no deteriorative effect.Therefore,in this investigation,the suction surface from the injection slot to the trailing edge is redesigned by a high-order Bezier curve,which is shown in detail in Fig.10,HL means highly loaded cascade and SS means suction surface.

In the Fig.10,the injection slot inlet is alongY-axis;thus the injection direction is alongZ-axis.The upside of the injection slot is parallel toZ-axis.The position ofP1on the slot inlet is determined by the width of the injection slot.P2toP5are moved downward from the original suction surface,and the displacements reduce fromP2toP5.Theirycoordinates are all lower than that ofP1.P6andP7are on the original suction surface.A high-order Bezier curve is designed to go through these points,so the downside of the injection slot is merged with the suction surface,and they form a smooth surface.The curvature changes smoothly from the injection slot to the trailing edge.Thus the injection air can blow directly downstream along the surface.

The loss coefficients of the baseline highly loaded cascade without injection and the redesigned highly loaded cascade are compared in Fig.11,which shows no significant increment of loss coefficients after the redesign of the rear suction surface.

In summary of the injection slot configuration design,the injection slot starts from the ending point of the local curvature drop on the suction surface,where the ‘Shock’induced separation forms.As the separation on the suction surface doesn’t move upstream in a large incidence range,the injection slot is also effective in a large incidence range.It’s in this way that the injection slot is in conjunction with the highly loaded airfoil design.The width of the injection slot inlet is determined by the injection mass flow,peak injection velocity at the injection slot inlet,and density.The injection mass flow is 4.75%of the cascade inlet mass flow in the paper.In the design process,the allowable injection mass flow should be enlarged.As a higher injection velocity means a higher total pressure bled from further aft of the multistage compressor,which results in more cost of injection flow,the peak injection velocity is limited to the velocity of the cascade inlet.The density is assumed as the value near the ‘Shock’of baseline cascade.Thus the injection mass flow,the peak injection velocity,and the density determine the width of the injection slot.Moreover,the suction surface downstream from the local curvature drop is redesigned together with the injection slot by a high-order Bezier curve for better injection efficiency.

During calculations,air injection is implemented by presenting a high total pressure on the inlet of the injection slot,which is the same as a practical implementation.Injection mass flow is achieved by modifying the presented total pressure.

Fig.12 confirms the effect of the injection configuration designed in Fig.9.It shows the comparison of Mach number contours between different injection configurations at 0°incidence.The applied injection mass flows are 4.75%of the cascade inlet mass flow at the design condition.The following injection mass flows are all normalized by the cascade inlet mass flow.With the conventional injection slot,the injection air has a large incidence angle toward the suction surface,and thus it cannot effectively remove the flow separation.On the contrary,for the redesigned suction surface/injection slot,the injection air flows attached to the suction surface.Flow separation is removed obviously by the redesigned injection configuration.Downstream from the ‘Shock’,the air continues to decelerate steadily toward the trailing edge.

Fig.13 compares the static pressure coefficients of the highly loaded blade with/without air injection.After air injection with the redesigned slot/suction surface,the surface static pressure upstream from the‘Shock’is the same as that without injection;whilst the surface static pressure distribution downstream from the ‘Shock’improves significantly.From the‘Shock’to the trailing edge,the static pressures on both the suction and pressure surfaces increase progressively.The highly loaded injected cascade with the redesigned slot/suction surface is also called as a novel injected cascade in the following.

Fig.14 shows the Mach number of the novel injected cascade at 6°incidence.Compared with Fig.8(b),as the suction surface flow separates from the same position,air injection with the same injection configuration as that at 0°incidence effectively removes the separation completely.It proves that the injection slot designed at the design condition performs excellently at different incidence angles.

The variation of the 2D novel injected cascade loss coefficient versus the incidence angle is presented in Fig.11,together with the baseline highly loaded cascade without injection,the redesigned highly loaded cascade without injection,and a conventional designed highly loaded cascade without or with injection.They share the same chord,inlet blade angle,and outlet blade angle as those of the highly loaded injected blade;the solidity of the conventional highly loaded cascade is lower than that of the highly loaded injected cascade so as to achieve the same diffusion factor of 0.61.The position and length of the injection slot are the same as those of the novel highly loaded injected cascade,as well as the injection mass flow.

The loss coefficients is defined in Eq.(1)in terms of ωaandaccounts for the loss of the bulk flow,while ωiis the injection loss coefficients accounting for mixing the injection mass flow with the free-stream.ωaand ωiare defined in Eqs.(2)and(3),respectively,wherept1is the cascade inlet stagnation pressure,pt2is the stagnation pressure at the cascade exit plane,ptiis the stagnation pressure at the injection slot inlet,ρ1is the cascade inlet density,V1is the cascade inlet velocity,m1is the cascade inlet mass flow,andmiis the injection mass flow.

The applied injection mass flows are held constant at these operating conditions in Fig.11 which are 4.75%of the cascade inlet mass flow at the design condition.The simulations predict a minimum loss coefficients value of 0.0365 at an incidence of 2°for the novel injected cascade.At 0°incidence,the loss coefficient of the novel injected cascade is 65.4%lower than that of the redesigned highly loaded cascade without injection.This novel injected cascade can also reduce the loss by more than 33.3%in the incidence angle range of-12°to 8°.Compared with the conventional highly loaded cascade without injection,the loss coefficients of the novel injected cascade also sees a remarkable decrement,especially at large positive and negative incidences.The loss coefficients reduces by 38.9%at 0°incidence compared with that of the conventional highly loaded cascade without injection.

The loss coefficients of the conventional highly loaded cascade without injection is lower than that of the redesigned cascade in the incidence angle range below 7°,but higher in the incidence angle range of 7°–12°.It is the result of the mildly increasing curvature of the front section of the redesigned cascade which keeps the separation at the rear part of the suction surface in a relatively large incidence range;whilst the separation of the conventional highly loaded cascade without injection moves upstream as the incidence angle increases,which results in a higher loss in the incidence angle range of 7°–12°.

The loss coefficients of the conventional highly loaded cascade with injection also decreases substantially more than that of the conventional highly loaded cascade without injection.While compared with the novel injected cascade,the loss coefficients is higher in most of the incidence angle range,except for the incidence range of-4°to 0°where the loss coefficients is slightly lower.At large positive incidence angles,i.e.,from 8°to 12°incidence,the loss coefficients of the conventional highly loaded cascade with injection is much higher than that of the novel injected cascade.The reason is also the mildly increasing curvature of the front section on the suction surface of the novel injected cascade which keeps the separation at the rear part of the suction surface in a large incidence angle range;whilst the separation on the conventional highly loaded cascade moves upstream significantly as the incidence angle increases,which is hard to be removed by the same injection slot.Therefore,for the novel injected cascade,the range of incidence angles where the loss coefficients remains relatively flat is larger than that of the conventional highly loaded cascade with injection,indicating an increase in the effective operating incidence range.

Fig.15 shows the Mach number contours of the conventional highly loaded cascade with injection and the novel injected cascade at incidence angles of 0°and 8°.It confirms the results in Fig.11.

At 0°incidence,air injection can effectively remove the trailing edge separation in the conventional highly loaded cascade,which is similar to the novel injected cascade in Fig.12(b).On the contrary,since the onset of separation for the conventional highly loaded cascade moves upstream remarkably and the separation enlarges substantially at 8°incidence,air injection at the same position with the novel injected cascade is invalid in suppressing the severe separation.The novel injected cascade can still effectively remove the separation at 8°incidence,as shown in Fig.15(c).

In summary,the novel injected cascade designed by the curvature induced ‘Shock’concept can result in a high aerodynamic loading,a low loss,and a large effective operating incidence range.The mildly increasing curvature of the front section exhibits well at larger incidences as the curvature keeps the pressure gradient not too high to induce a severe separation upstream from the curvature rapid drop location.Thus,the loss coefficients is not so high even at 8°incidence.The novel injected cascade exhibits pretty good aerodynamic performance in a significant incidence range.

4.Substantiation of the novel injected blade on a 3D cascade

In order to substantiate the novel injected cascade,a 3D cascade model is investigated with uniform air injection along the span.The aspect ratio of the 3D cascade is 1.54.The flow field is calculated by the RANS method.The operating conditions are the same as those in the 3rd section.The inlet Mach number is 0.3,and the incidence angles are 0°and 6°,respectively.

3D meshes of the injected linear cascade are created by a structured mesh-generation tool.An ‘O’type block is created around the blade surface for high mesh quality;an ‘H’type block is utilized to model the other regions of the cascade passage and the injection slot.The mesh of the blade surface and the endwall for the injected cascade are illustrated in Fig.16.The total number of nodes is about 4.27 million.In the calculations,the injection mass flows are uniform along spanwise.

4.1.Design condition discussions

Fig.17 compares the mid-span Mach number contours of the 3D linear cascade with and without air injection at 0°incidence.The mid-span flow field is similar to the 2D cascade flow field.While without injection,the suction surface experiences mild deceleration upstream from the curvature induced‘Shock’.The flow separates downstream from the ‘Shock’.Air injection with the same mass flow coefficients as in 2D calculations removes the flow separation at mid-span effectively.The deceleration across the ‘Shock’increases.The exit Mach number is lower than that of the flow field without injection,which indicates that the diffusion ability of the cascade increases.

Fig.18 compares the limiting streamlines/static pressure contours on the suction surface of the linear cascade with and without air injection at 0°incidence.The static pressure is normalized by the inlet total pressure.The injection mass flow coefficients is 4.75%.For both figures,it’s demonstrated that the static pressure increases mildly upstream from the injection slot.Then it shows a rapid increase across the injection slot,which is the designed curvature induced ‘Shock’.For the cascade without injection,the static pressure downstream from the injection slot doesn’t increase,whilst the static pressure of the cascade with injection increases progressively from the injection slot toward the trailing edge.At the trailing edge,the static pressure of the cascade with injection is much higher than that of the cascade without injection.

As the adverse pressure gradient upstream from the ‘Shock’is not severe,boundary layer transition doesn’t occur until approaching the curvature induced ‘Shock’,where a laminar separation line shows up.Without injection,the flow downstream from the injection slot separates,similar to the 2D flow field.The concentration of low-energy fluid toward the suction surface/endwall corner results in the formation of 3D corner separation.After air injection is applied,the laminar separation moves downstream,and the separation downstream from the ‘Shock’almost removes completely.The limiting streamlines downstream from the injection slot flow chordwise toward the trailing edge;barely any spanwise flow is seen.Besides,the 3D corner separation reduces remarkably.

Fig.19 illustrates the Mach number contours and secondary flows at different axial sections.The flow fields with and without injection are compared in the figure.In the 3D cascade without air injection,there are separations in both the mid-span and suction surface/endwall corner.Although the numerical codes at present may be insufficient to model the severe flow separation,it does show the flow trends in the highly loaded cascade,because it’s widely believed that the flow will stall in the cascade with a Leiblien diffusion factor higher than 0.6.As a result of the blockage of the separations,the Mach numbers of other regions are still high.It’s because the loading is so high that the cascade is obliged to shut down part of the flow area by flow separation,and thus reduces the adverse pressure gradient by increasing the velocities in other regions.

After air injection,the flow separation is blown off significantly.The blue region which stands for the low Mach number at the mid-span is removed completely;the low-Mach number region in the suction surface/endwall corner also reduces remarkably.In Fig.19(b),the passage vortex increases as the axial section goes downstream toward the injection slot location.The passage vortex in the sixth section of the figure is the maximum.As the low-energy fluid is blown off by the injection flow,the passage vortex after the sixth axial section reduces significantly.

Fig.20 illustrates the pitchwise mass flow weighted loss coefficients distribution along spanwise.The results of the linear cascade with and without injection are compared in the figure.The loss coefficients distributions along spanwise of the cascade with and without injection are similar.From 50%to about 70%spans,the loss coefficients keeps constant,but it increases rapidly from 70%to 100%spans,which is caused by the endwall secondary loss.After air injection,the loss coefficients at all spans reduces remarkably.In the mid-span,the constant loss coefficients region increases as the injection mass flow increases.The reason is that the spanwise migration of endwall secondary flows decreases as the endwall secondary flow reduces.

Fig.20(b)illustrates the pitchwise mass flow weighted outlet flow angles distribution along spanwise.The results of the linear cascade with and without injection are compared.The spanwise distribution of outlet flow angles is also similar to those of the cascade with and without air injection.From 50%to about 70%spans,the loss coefficients almost keep constant.The fluid exhibits underturning near 87%span;whilst it shows overturning near the endwall.After air injection,the outlet flow angles at all spans decrease,which indicates that the flow turning angles increase.

4.2.Off design condition discussions

Fig.21 compares the mid-span Mach number contours of the 3D linear cascade with and without air injection at 6°inci-dence.At a higher incidence than the design condition shown in Fig.17,the flow decelerates more near the leading edge;thus results in a higher adverse pressure gradient near the leading edge.A higher adverse pressure gradient will probably lead flow transition.However,as the suction surface curvature upstream from the ‘Shock’varies little,the Mach number reduces mildly after the deceleration near the leading edge.The flow still separates downstream from the rapid drop of the local curvature.The injection slot should also be settled downstream from the ‘Shock’,which is the same as the design condition.

After air injection with the same mass flow coefficients as in 2D calculations,the mid-span separation is removed effectively.The deceleration across the ‘Shock’increases.The exit Mach number is lower than those of the flow field without injection and the flow field of 0°incidence,which indicates that the diffusion ability of the cascade increases.

Fig.22 compares the limiting streamlines/static pressure contours on the suction surface of the linear cascade with and without air injection at 6°incidence.The static pressure is also normalized by the inlet total pressure.Compared with Fig.18,the static pressure near the leading edge at 6°incidence increases more than that of the flow field at 0°incidence.An increased adverse pressure gradient near the leading edge results in the flow transition;flow separation and reattachment are found near the leading edge.Downstream from the reattachment line,the pressure increases mildly toward the‘Shock’;the adverse pressure gradient is not large enough to introduce flow separation.In Fig.22(a),the flow separates near the injection slot,where the rapid drop of the local curvature introduces a severe adverse gradient.The separation line is farther downstream than in Fig.18(a),which is because the turbulent boundary layer can sustain a stronger adverse pressure gradient than the laminar boundary.Downstream from the ‘Shock’on the suction surface is the separation region.

After air injection is applied,the separation line at the midspan near the injection slot removes completely;the corner separation reduces significantly.The flow separation downstream from the ‘Shock’removes.Besides,the static pressure increases gradually toward the trailing edge.The static pressure is higher than that of the cascade without air injection.

Fig.23 illustrates the Mach number contours and secondary flows at different axial sections.The flow fields at 6°incidence with and without injection are compared in the figure.The flow field without injection is similar to the flow field at 0°incidence shown in Fig.19(a),but with more low-Mach number regions.A high diffusion factor introduces large flow separations in both the mid-span and suction surface/endwall corner.

After air injection is adopted,the flow separation is blown off significantly.The low-energy fluid in the mid-span almost removes completely.The blue region that represents lowenergy fluid in the corner removes remarkably.However,the low-energy fluid in the corner is more than that in the flow field at 0°incidence.It’s because of the higher diffusion at 6°incidence.Air injection also reduces the passage vortex downstream from the injection slot effectively.

In conclusion,the highly loaded blade designed by the curvature induced ‘Shock’concept has a large effective incidence range.At 6°incidence,although the separation enlarges,the initial location of flow separation doesn’t change.Air injection downstream from the rapid drop of the local curvature exhibits well in a large incidence range.

5.Conclusions

(1)A novel design method of highly loaded compressor blades with air injection is introduced in the paper.A highly loaded compressor blade is designed by a curvature induced pressure-recovery concept in conjunction with air injection.The highly loaded blade is characterized by high loading at the front section,a curvature induced ‘Shock’at 74%axial chord,and air injection immediately downstream from the ‘Shock’to prevent‘Shock’induced separation.

(2)The curvature induced ‘Shock’shares a large part of the deceleration on the suction surface.The low diffusion level on the suction surface upstream from the curvature induced ‘Shock’results in high loading.As a result,the highly loaded blade has a camber angle of 69.35°and a diffusion factor of 0.61 at the design operating condition.Besides,the high loading section exhibits excellent performance at various incidences.The flow separates at the same location,which locates immediately downstream from the ‘Shock’,in a large incidence range.Thus the location where air injection should be settled is certain in the design process.Therefore,air injection has been taken into account in the airfoil design process by the curvature induced ‘Shock’concept.

(3)Air injection with the same injection configuration effectively removes the flow separation downstream from the curvature induced ‘Shock’and reduces the size of the separation zone at various incidences.The compressor blade achieves high loading with acceptable loss.The loss coefficients along spanwise of a 3D cascade reduces significantly and the flow turning angle increases remarkably after air injection.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China(Nos.51576003 and 11521091)and China Postdoctoral Science Foundation(No.2016M600015).

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31 January 2016;revised 19 April 2016;accepted 17 July 2016