Shn MA ,Wuli CHU ,Hogung ZHANG ,Xingjun LI ,Hiyng KUANG

a School of Power and Energy,Northwestern Polytechnical University,Xi'an 710072,China

b Collaborative Innovation Center of Advanced Aero-Engine,Beijing 100083,China

KEYWORDS

Abstract In the current study,the effects of a combined application between micro-vortex generator and boundary layer suction on the flow characteristics of a high-load compressor cascade are investigated.The micro-vortex generator with a special configuration and the longitudinal suction slot are adopted.The calculated results show that a reverse flow region,which is considered the main reason for occurring stall at 7.9°incidence,grows and collapses rapidly near the leading edge and leads to two critical points occurring on the end-wall with the increasing incidence in the baseline.As the micro-vortex generator is introduced in the baseline cascade,the corner separation is switched to a trailing edge separation by the thrust from the induced vortex.Meanwhile,the occurrence of failure is delayed due to the mixed low energy fluid and main flow.The synergistic effects between the micro-vortex generator and the boundary layer suction on the performance of the cascade are superior to the baseline at all the incidence conditions before the occurrence of failure,and the sudden deterioration of the cascade occurs at 10.3°incidence.The optimal results show that the farther upstream suction position,the lower total pressure loss of the cascade with vortex generator at the near stall condition.Moreover,the induced vortex with a leg can migrate the accumulated low energy fluid backward to delay the occurrence of stall.

1.Introduction

High-load compressor has become a popular trend for aeroengines design to reach a higher pressure ratio.Meanwhile,the internal flow of the compressor becomes more complex.Especially the three-dimensional corner region between the blade suction surface and the hub where a mass of the low energy fluid is accumulated.According to a study by Sharma and Butler1,the secondary flow loss reaches up to 30-50%of the aerodynamic loss in a stator row.Extensive experimental studies2,3showed that higher adverse pressure gradient and more accumulation of the low energy fluid are inevitable with the increasing aerodynamic load.Therefore,eliminating the accumulation of the low energy fluid and controlling the separation in the corner region have become one of the focuses.

Vortex generator as a kind of passive control device has been widely applied in aircraft to reduce the boundary layer thickness and weak secondary flow4,5.Generally,vortex generator could change the flow direction of the boundary layer cross-flow near the end-wall as well as transport high-energy fluid from the main flow into the boundary layer to suppress the corner separation,which has become one of the most effective ways to improve the aerodynamic performance of a compressor.The introduction of vortex generator results in an increase in flow resistance,therefore many studies focused on a kind of micro-vortex generator6-8,and the height is between 0.1 and 0.5 in boundary layer thicknesses.Numerous studies provided that micro-vortex generator shows more advantages than traditional Vortex Generator(VG)8,9.

However,the performance of compressor cascade cannot be improved by the application of micro-vortex generator at some special conditions in the previous studies10.Operating range of the compressor performance improvement is limited.Therefore,one of the active flow control techniques11-14will be introduced to remedy the deficiency in this paper.A suction surface aspiration can be utilized to reduce the accumulation of the low energy fluid near the midspan.However,it does not work on the corner region due to the limited controlling capacity15.Because the work space of the induced vortex from micro-vortex generator is near the hub,the suction slot on the blade suction surface is selected for the following numerical investigations.

Virtually a control method of reasonable combination between active and passive is adopted to control secondary flow and reduce loss,the control method has been widely used in the aerospace area16,17.Hergt et al.18utilized experimental methods to contrast the flow characteristics of a suction slot installed on the end-wall and vortex generators attached to the blade suction surface respectively. But the synergistic effects between the active and passive control devices were not considered.Song et al.19and Ding et al.15have combined compound lean with boundary layer suction in compressor cascades.Song Yanping et al.indicated when the end-wall loss is a major part of the total pressure loss in the compressor cascade,the combination between the compound lean cascade and boundary layer suction can be used to reduce the endwall loss.Ding presented when the suction surface aspiration is introduced in a positive lean cascade,the stagnation pressure loss can be effectively reduced,and the operating range is slightly broadened only.The corner separation can be suppressed or even removed in the negative lean cascade with the end-wall aspiration near the suction surface,and the effective positive incidence is raised from 7.4°to 17.0°.

The synergistic effects of the active and passive flow control methods were considered feasible according to the summaries of predecessors.Therefore,a kind of modified micro-vortex generator and a longitudinal suction slot were combined to improve the performance of a compressor cascade.Based on the previous studies10,a kind of vane-VG with a‘‘curved trapezoidal”shape is applied in a high-load compressor cascade with a longitudinal suction slot. A response surface method is adopted to find the optimal configurations and interaction effects among the special parameters,and the main objects are achieved as follow:

(1)Reveal the stall inducements and forecast the operating ranges of the cascade with and without the different control devices.

(2)Using optimal design method to reach an optimal composite construction at the near stall condition.

(3)Explore an appropriate evaluation methodology of flow loss to estimate the advantages and disadvantages of the different control devices with different conditions.

2.Compressor cascade and flow control techniques

A typical high-load linear compressor cascade was tested in a large-scale low-speed (incompressible) wind tunnel with Ma ＜0.3.The circular-arc element was designed with a 51°flow turning angle in the design condition.Fig.1 shows a schematic of the experimental design.l means the pitch,and γ is the stagger angle.β1kand β2krepresent the inlet blade angle and outlet blade angle respectively,and C is the chord length.The main geometric and aerodynamic parameters of the cascade are provided in Table 1.A special flow phenomenon that the pitchwise pressure gradient occurs and induces more serious corner separation near the blade suction surface appears in the cascade.

A representative configuration of vane-type micro-vortex generator in the previous studies10is selected to control the corner separation between the suction surface and end-wall in this paper.The trapezoidal micro-vortex generator with a profile turning angle θVGoccupies an overwhelming superiority in reducing total pressure loss and delaying stall occurrence to compare with the traditional vane-type micro-vortex generator.The micro-vortex generator is mounted on the end-wall in front of the passage with 7%axial chord.The cascade with this type micro-vortex generator will be marked by MVG.Fig. 2(a) provides the mounting location and geometric parameters of the micro-vortex generator.The corresponding parameters of the micro-vortex generator are listed in Table 2.Here,δ means the thickness of boundary layer,d is the pitch distance of micro-vortex generator from the blade suction side.

Table 1 Geometric and aerodynamic parameters of cascade.

Fig.2 Configurations and grids of two kinds of control devices and boundary conditions of simulation.

Table 2 Parameters of installation and geometry of MVG.

A kind of full span suction slot on the blade suction surface is selected to combine the micro-vortex generator in this study,and the cascade with the combined method is expressed by COM.Fig.2(b)provides the vertical view of the aspirated compressor cascade with a plenum.To simulate the real flow that non-uniform suction power exists in the suction slot along the spanwise,the computational domains with a plenum and a slot in the cascade are necessary.ZBLSrepresents the axial length downstream of the leading edge.The included angle between the slot axis and the corresponding surface normal of the blade suction surface is defined as αBLS,and αBLSis 0°.The slot width wBLSis the distance between the two red points on the blade suction surface.wBLSis set to be 1%of the chord length C,ZBLSis 50%axial chord length Ca.

As presented in Fig.2(c),the inlet passage extends to 1.2 Caupstream of the leading edge.The outlet passage reaches 2.0 Cadownstream from the trailing edge to ensure enough mixing of the outlet flow.The gray plane delineated by red line is the position of the experimental measurement that is located 0.4 Cadownstream of the trailing edge.In view of the cascade with a symmetrical structure,the actual computational domain is generated for half-passage using a symmetry boundary at mid-span to reduce the computational cost.

3.Validation of the numerical simulation

The boundary conditions are assigned according to the experiments,and the experimentally measured temperature is set to be uniform at the inlet.The velocity profile of inlet,which is adopted to assure the realistic inlet condition,is shown in Fig.3.The thickness of the inlet end-wall boundary layer reaches 12.5%span.At outlet,the static pressure is set to atmospheric pressure.

The numerical grids of the cascade including the microvortex generator,slot and plenum were generated by software ICEM.The wall space according to the Fig.2(c),an O-type grid was generated around the blade,and a butterfly grid was embedded into the plenum to guarantee the grid quality.The H-type blocks were used to cover the upstream and downstream passages.The grids near the wall of the micro-vortex generator and suction slot were clustered.

To economize the calculating resources,it is meaningful to carry out a grid-independent verification in the investigated cascade.There were six sets of the passage grids with half span:0.6,1.0,1.6,2.1,2.5 and 2.9 million,respectively.As shown in Fig.4,the results were obtained in the baseline cascade at the design incidence.The values of ω and inlet Mach number almost keep unchanged when the mesh is further refined in this study,and 2.5 million is selected as the final counts of the mesh.

The numerical simulations were conducted using the CFX from the commercial software ANSYS. The threedimensional linear cascade is calculated by the highresolution scheme for the advection scheme and turbulence model.In view of the fact that a separation bubble is formed on the blade suction side in front of 50%C due to a transition occurs as shown in Fig.5(b),the SST with Gamma-Theta transition model is selected for simulation.

Fig.3 Inlet velocity distribution.

Based on the experimental results of the baseline20,the comparisons between the oil streak patterns and numerical limiting streamlines on the end-wall and blade suction surface are provided in Fig.5.The numerical flow field topologies match considerably with the experimental results,which are reflected by the locations of the node point N1and the reattached point N2in Fig.5(a).However,the separation field outlined by the separation line SL is smaller than the experimental result on the end-wall,and the location of the saddle S1shows a slight displacement.As presented in Fig.5(b),saddle point S2is accurately forecasted near the leading edge.The directions of the climbing flow and the reverse flow that are represented by the white arrows are also well predicted.A spanwise separation bubble attends in the simulation result,and the location is forecasted accurately,only the range is underestimated along the streamwise.Hence,we believe that the turbulent assumption is credible.

To validate the numerical method, the comparisons between the numerical and experimental results of the pitchwise averaged total pressure loss and flow angle are taken at 0.4 Cadownstream of the TE(trailing edge)in Fig.6.As shown in Fig.6(a),the simulation result of ω shows good agreement with the experimental result,particularly the locations of the peaks and valleys,which indicates that the numeral calculation of the ω is consistent with the actual flow characteristics.Fig.6(b)provides the pitch-averaged flow angle(β),the numerical distribution coincides with the experiment result although the profile shows a slight overestimation along the spanwise.The location of under-turning,that is the range of the accumulated low energy fluid near the blade suction surface,is accurately predicted.A well predicted under-turning peak can imply an accurate calculation of the secondary flow around the corner range.

As presented in Fig.7,a numerical result of the total pressure loss coefficient at the measurement plane is validated at the design condition.PS means pressure side,SS is suction side.Obviously,the numerical result presents a slight overestimation within the core region.However,the contour line of the total pressure loss is underestimated inside the range from 10%to 30%span,which is the main reason that the mass-flow averaged numerical result shows lower than the experiment in Fig.6(a).The two-equation turbulence model SST with transition model underestimated the separation region in the pitchwise,but the profile of the ω predicted by simulation is in substantial agreement with the measurement and the separation bubble is predicted by the turbulence model.Therefore,the computational model and the numerical method selected in this paper are appropriate for analyzing the aerodynamic performance of the high-load cascade.

Fig.4 Effect of number of grid nodes in baseline cascade on ω and inlet Mach number.

Fig.5 Oil-flow visualizations and numerical limiting streamlines distribution.20

Fig.6 Parameters distribution of experimental and numerical results at 0.4 Ca downstream of TE.

Fig.7 2D ω distribution of experimental(left)and numerical(right)results at 0.4 Ca downstream of TE.

4.Analysis of numerical results

4.1.Effects of micro-vortex generator on the performance of the high-load cascade

Two types of the total pressure loss coefficients are employed to evaluate the aerodynamic loss in the compressor cascade.The first is defined as follow:

where ω is normalized by the inlet dynamic pressure at the mid-span,and the(x,y,z)corresponds to a local parameter.The subscript in represents the inlet section of the computational domain,mid means the mid-span of the inlet section.ω can be easily tested in the experiment,and it is mainly used to visualize the loss for a more convenient comparison among the results.

The second total pressure loss coefficient is normalized by the mass-flow average dynamic pressure at the inlet boundary,and it can be regarded as ζ.When the coming flow with a boundary layer flows through a compressor,the high total pressure distribution will exist near the end-wall.The parameter can accurately evaluate the total pressure and dynamic pressure of the inlet boundary,and it is different from ω.The second can be calculated by

In this section,the micro-vortex generator with three vanes are introduced and calculated to reveal the flow mechanisms of the cascade.According to the Ref.10,this type of micro-vortex generator with a profile turning angle can control the secondary flow and delay the occurrence of the corner stall.As mentioned by Taylor et al.21,a rapid deterioration of the cascade performance indicates the occurrence of stall,which limits the useful working range of the cascade.Furthermore,as the incidence increases,trailing edge separation in spanwise and chordwise extent is raised further,which induces the progressive trailing edge failure.But according to the simulations in this study,a rapid deterioration of the cascade performance also occurs in the cascade with a trailing edge separation.As shown in Fig.8,a sudden failure occurs at 7.9°incidence in the baseline.With the incidence increases,a sudden rise of the ζ appears at 10.6°incidence when the micro-vortex generator is introduced in the cascade without a suction slot.The performance of the cascade with micro-vortex generator is superior to the baseline when the incidence is between 3°and 10.5°.The introduction of the micro-vortex generator causes the occurrence of failure that is delayed from 7.9°to 10.6°incidence.Detail variations of the flow reversal region and limiting streamlines with increasing incidence are shown in Fig.9.The blue region represents the flow reversal region.

Fig.8 Total pressure loss variations with incidence.

The top half of Fig.9 provides the flow characteristics of the baseline at typical incidences.SL represents the separation line on the blade suction surface.The separation bubble moves upstream and attaches to the leading edge with the increasing incidence.As the incidence is raised to 7.8°,the multi-critical point S2(N2)that is generally regarded as an origin of the corner separation moves upstream,and the flow reversal region keeps growing.However,the corner stall still does not happen.When the incidence is raised to 7.9°,an abrupt switch occurs on the end-wall.The rapid growing of the flow reversal region near the LE(leading edge)makes itself massively touching the end-wall,which leads to two critical points occurring:one is a spiral node point marked as‘‘N3”and the other is a saddle point named as‘‘S3”.The abrupt switch corresponds to the sudden rise of ζ at 7.9°incidence as shown in Fig.8.

The flow characteristics of the cascade with micro-vortex generator at typical incidences are illustrated in the bottom half of Fig.9.At the design condition,the distribution of flow reversal region is like the baseline.The separation mechanism is transformed from a corner separation into a threedimensional trailing edge separation with the increasing incidence.When the flow reversal region stays at the triangle region between the end-wall and separation line on the blade suction surface,the separation type is corner separation.As mentioned by Taylor et al.21about the trailing edge separation,when the vertically symmetrical separation lines relate to the further increasing incidence,a trailing edge separation forms and moves away from the TE.As the flow reversal region expands progressively in spanwise and chordwise,when the incidence increases to 8°,the development of flow reversal region is suppressed comparing with the baseline cascade at 7.9°incidence.The induced vortex could transport the highenergy fluid from the main flow into the boundary layer to decrease the accumulation of low energy fluid.However,as the incidence is raised to 10.6°,a sudden switch occurs on the blade suction surface.The trailing edge separation line SL vanishes,and the flow reversal region covers almost the full span.

4.2.Effects of active and passive control devices on the performance of the high-load cascade

As presented in Fig.8,the operating range of the compressor cascade is raised by the introduction of the micro-vortex generator. However, the vane-type micro-vortex generator selected in this paper cannot reduce total pressure loss when the incidence is lower than 3°.Because in those conditions,most of the low energy fluid stay on the range near the midspan,and the induced vortex shows a limited capacity to affect them.Therefore,suction technique can be utilized as an active control method to remove the high entropy fluid in the boundary layer.Generally,boundary layer suction is designed as a part of the air system to carry the low momentum fluid of the compressor passage into the gas turbine,the fluid is used as cooling air22. In this section, full span suction slot is arranged on the blade suction surface to reduce the accumulation of the low energy fluid.Meanwhile,the synergistic effects between the boundary layer suction and micro-vortex generator on aerodynamic performance of the cascade are investigated in this study.

As shown in Fig.10,the suction slot on the blade suction surface with 1%suction mass-flow ratio can drastically reduce total pressure loss,but the operating range shows a slight reduction from 7.9°to 7.8°compared with baseline.This is due to the limited capacity of the BLS(boundary layer suction)to remove the accumulated low momentum fluid in the corner region.The stall mechanism of BLS is the same as baseline.The sudden deterioration of the cascade with COM configuration occurs at 10.3°incidence,and the performance is superior to the BLS when the incidence is between 3°and 10.2°.The failure classification is trailing edge separation,and the border of the operating range shows a slight reduction from 10.5°to 10.2°compared with MVG.

Fig.9 Variations of flow reversal region and limiting streamlines at typical incidences.Top:baseline.Bottom:MVG.

Fig.10 Total pressure loss variations with incidence.

When the coming flow entrances a diffusion cascade,it will flow through the blade suction surface at velocity w1firstly and then accelerates to maximum velocity wmax.At last,it flows out the blade passage with velocity w2.The adverse pressure gradient,that is considered a main reason for thickening boundary layer even separation on a blade suction surface,is generated due to the velocity difference between wmaxand w2.This leads to the expanding degree of cascade passage is limited.Diffusion factor(DF)as a criterion not only can be applied to evaluate the expanding degree,but also be used in design criterion of blade23.The definition of DF is provided as follow

where w1represents the inlet relative velocity and w2is the exit relative velocity of a blade passage.Δwumeans the swirl velocity and τ is the solidity.DF is to build a relationship between the geometric/aerodynamic parameters of the cascade and the adverse pressure gradient.When DF ＞0.6 in a stator,the severe separation near the blade suction surface increases the total pressure loss.Therefore,0.6 is regarded the limiting value of DF in a liner compressor cascade24.

Fig.11 Diffusion factor variations with incidence.

Fig.11 provides the changes of diffusion factor with incidence.Before the occurrence of stall,the DF of the baseline shows a sudden drop at 7.5°incidence,which indicates that an unstable flow phenomenon emerges at this condition.As the boundary layer suction is utilized in the cascade,the DF shows a same trend compared with baseline.The significant rise at the positive incidences of DF are contributed to the installation of the micro-vortex generator(MVG and COM).Before the occurrence of stall(9°incidence),obvious decreases are observed in the cascade with MVG and COM.The three flow control devices show different capabilities to increase DF,and the maximum value is lower than 0.6.COM shows an excellent ability to enlarge the expanding degree of cascade passage.Because BLS and COM have similar failure mechanisms with baseline and MVG respectively,a more intuitive evaluation methodology will supersede the method of analyzing flow field to forecast the performance in the following.

The computational domain will be divided into several regions based on the different classifications of the loss mechanisms,and the definitions of those regions will be expatiated.The borders of the blocked area are determined by a quantity?(ρvm)referring to Khalid25.If the blocked area is calculated in an axial cross-section,the spanwise and pitchwise components of the gradient are utilized to obtain the gradient magnitude. Therefore, the edge is written as |? (ρvm)|x,y. The normalized formula and the criterion of the edge of the blocked area are provided as follow:

where the quantity vmis the velocity component of the main flow direction,and ρ is density.The velocity component parallel to the incoming flow is regarded as the main flow when the axial cross-section is located on the leading edge.The exit flow angle adopted in the cascade is designed to parallel to the axial direction,therefore the velocity component in the axial direction can be identified as the main flow when the axial crosssection at the trailing edge.

Fig.12 Distributions of 3D boundary layer.

As presented in Fig.12,the blocked areas are covered by the gray regions.As shown in Fig.12(a),the loss near the end-wall boundary layer is mainly due to the viscous effect of the incoming flow,and the blockage could be less impacted from the pitchwise pressure gradient near the leading edge.Therefore,the loss inside the end-wall blocked area is determined as an end-wall loss in Fig.12(a),and the region is estimated between the 0%-5%span.The loss near the mid-span of blade is mainly due to the viscous effect of the blade boundary layer loss,the end-wall boundary layer and secondary flow show slight effects on this location.Therefore,the loss region near the blade with a block thickness of the mid-span is determined as a profile loss.The blockage is adequately developed near the trailing edge,and the profile loss is calculated in the region of 15%pitch from the blade surface.The corner vortex near the blade suction surface(SS)is considered as a primary vortex structure for producing flow loss,and the corner loss is defined in the blocked area covered by the blue rectangle as presented in Fig.12(b).PS means the blade pressure surface.

Fig.13 provides the intuitional three-dimensional space classifications based on Fig.12.The loss in the flow field of the cascade was classified as five types based on the mechanisms of loss generation,and each of them corresponds to a kind of loss source.The detailed descriptions will be given:

Region I:Profile loss,from LE to TE,5%-95%full span in spanwise and 0-15%pitch perpendicular to the blade surface.Loss in this region mainly comes from the blade surface friction,and the loss is defined as ζPro.

Region II:Secondary flow loss,from LE to TE and 5%-95%full span in spanwise.In this region,the loss mainly refers to the reciprocal effect between the separation near the blade suction surface and main flow,and the loss is defined as ζSec.

Region III:Corner loss,from LE to TE,0-5%full span in spanwise and 0-15%pitch perpendicular to the blade surface.The total pressure loss in this region mainly refers to the effect including the corner vortex and boundary layer turning flow around the leading edge.The loss is defined as ζCorn.

Region IV:End-wall loss,from LE to TE and 0-5%full span in spanwise.Loss in this region mainly comes from the end-wall friction,and the loss is defined as ζWall.

Region V:Wake flow loss,from TE to outlet and full span in spanwise.In this region,the loss mainly refers to the mixing and dissipating between the main flow from the PS and the accumulated low energy fluid near the rear of blade suction surface.The loss is defined as ζWake.

The volume integral of total pressure loss is adopted to express the diverse losses in the corresponding region,and the equation can be expressed as follow

Fig.13 Five types of loss sources region.

Where region corresponds to a certain region.V means the velocity,and n is the direction vector of velocity.A is the area for calculating.The different loss types often refer to the different flow mechanisms,and each of them corresponds to a kind of loss source.A quantitative criterion of the sources caused by different types of dissipating flow is referred for evaluating the loss in the cascade according to the Ref.26.Φ can be chosen as a parameter to evaluate the loss source.A tensor form of Φ is shown in Eq.(6).The viscosity coefficient(μeff),which can be expressed as the sum of laminar viscosity coefficient(μ)and turbulent viscosity coefficient(μt),is modified in this equation.

where Φ represents the distribution of the loss source in a flow field.High dissipating function generally occurs in a strong shear velocity ranges,such as the border between the low energy fluid and the main flow.A general formula for estimating a specific loss source can be derived:

where the subscript source represents the type of loss source.In addition,Δptsourserepresents a specific source,that is normalized by the mass weighted inlet dynamic pressure.Then the loss coefficient γsourcecan be calculated.The five types of loss sources are marked by γPro,γSec,γCorn,γWalland γWakerespective correspond to the five regions.

The static pressure coefficient Cpis also an important parameter to judge the cascade performance.Here,ptand p represent the total pressure and static pressure.On the other hand,the static pressure difference between the inlet boundary and the suction surface could represent the suction power.Therefore,Cpsucis defined as follow

As the introduction of the boundary layer suction,the modified total pressure loss coefficient ζsucis considered15.The subscript suc represents the suction section on the blade suction side.A part of fluid flows out from the suction section,the loss from the main passage flow and aspirated flow should be considered.ζsucis given as:

where ˙m means the suction mass-flow ratio that is obtained by msuc/min.To avoid the effects of the suction slot and plenum configuration on suction performance, the corresponding parameters of the suction are extracted at the connected interface between the slot and the blade suction surface.

Fig.14 Static pressure coefficient variations with incidence.

Based on Fig.10,the sudden deterioration of the baseline cascade performance occurs at 7.9°incidence.However,the sudden drop of the static pressure coefficient occurs at 7.5°as shown in Fig.14,which indicates that an unstable flow phenomenon emerges at this condition.Therefore,the 7°incidence condition is identified as a near stall point with a stable flow field for the further researches of the aerodynamic performance in the cascade with different control devices.

The distributions of pitchwise-averaged ζ along spanwise of the cascade with different control devices are illustrated in Fig.15.The primary effect of micro-vortex generator on the performance of compressor is to suppress the growing low energy fluid and reduce the total pressure loss near the endwall.However,a mass of the low energy fluid is migrated upward by the induced vortex,which results in the ζ increases near the mid-span.The suction slot on the blade suction surface can reduce the total pressure loss along the full span,especially near the mid-span.Remarkably,as the micro-vortex generator is introduced in the aspirated compressor cascade,an overwhelming superiority in reducing total pressure loss along full span is illustrated in this figure.

Table 3 provides the aerodynamic performance of the cascade with three types of the control methods at near stall condition.By micro-vortex generator installed in the aspirated compressor cascade,the suction power applied to remove the same mass flow is economized.The last ten columns exhibit the loss and loss source in the special regions.The bold texts represent the optimum performance,and the italic is the deteriorating value of the certain parameter.Variations of the aerodynamic parameters in the cascade with three control methods are illustrated in Fig.16.

Fig. 15 Pitchwise averaged ζ along spanwise at near stall condition.

As the micro-vortex generator is introduced in the cascade without suction slot,the maximum reduction of total pressure loss is ζWakethat reaches 13.9%as shown in Fig.16.However,the loss sources show a degree of growth in the corner and near the end-wall regions,which originates from the shearing action between the induced vortex and main flow.The BLS shows slight superiority in loss source reduction compared with MVG at sub-regions except for γProand γSec.A portion of low energy fluid is migrated to the region near the blade surface,which is attributed to the application of the suction slot.Due to the limited capacity of BLS,secondary flow loss is hard to reduce.When the synergistic effects of the micro-vortex generator and full span suction are considered,the secondary flow loss and wake loss decrease mainly due to the micro-vortex generator,and ζ reduction reaches 14.2%.Meanwhile,the profile loss is suppressed by the boundary layer suction.

4.3.Optimal design of COM configurations

To obtain the connection and optimal design between the principal configurations of the control devices and the total pressure loss,the response surface method based on a design of experiment is adopted to analyze the relationship at 7°incidence condition.Number of vanes(NV),axial position of the suction slot(ZBLS)and pitch position of the vortex generator(d)are selected as the factors to build the sample space.The design space and the variable range are provided in Table 4.The total pressure loss including the suction flow loss is the response value,and the two-order polynomial is chosen.The method of polynomial regression is used by standard leastsquare for regression modeling.The correlation coefficient R2=0.922 guarantees the correlation of the design parameters.

Fig. 17 provides the response surface contours of the numerical results, which indicate the interaction effects between two of the factors.Based on Fig.17(a)and(b),the value of ζsucshows monotone increasing trend with increasing ZBLSregardless of the effects derived from NVand d,because the initial separation point is migrated to the region near the leading edge at the near stall condition.Suppressing the separation from the initial separation point is regarded as a critical factor for decreasing loss.Focus on the variations of ζsucin Fig.17(a)and(b),when the value of ZBLSis fixed,Nv and d decrease first and then increase.

As presented in Fig.17(c),the optimal point with the minimum ζsucis represented by the red dot.The obvious interaction effect could be found between d and NV.When d is constant, the value of ζsucshows decrease first and then increase trend. The optimal parameters and the optimal response value are listed in the up one line of Table 5.Obviously,the number of vanes must be an integer,the NV=2 or 3 will be verified respectively.The optimal response value is verified by numerical simulation,and the results are illustrated in the down two lines of Table 5.The optimal case 1(Optcase1)with NV=2 is the case that produces minimum total pressure loss including the suction flow loss and error,it be regarded as the optimal case.The 4.2%error is mainly from the value of NV,and the optimal result is considered successful.

The aerodynamic performance variations of the optimal result Optcase1at near stall condition are illustrated in Fig.18.The total pressure loss reduction reaches 16.1%and the static pressure rises by 8.5%. Unfortunately, the loss source in the corner region shows remarkable growth andreaches 24.4%,the intense shearing action between the low energy fluid and main flow indicates that more low energy fluid is accumulated in the corner region,which could be found in Fig.20(a).Moreover,the reduction of the secondary flow loss still shows a predominant superiority and reaches 30.7%.As presented in Fig.19,the total pressure loss shows an evident reduction near the mid-span in the optimal result Optcase1compared with COM.Therefore,the axial position of the suction slot is a critical parameter for decreasing loss.

Table 3 Effects of micro-vortex generator and boundary layer suction on aerodynamic performance of the compressor cascade.

Fig.16 Variations of aerodynamic parameters in cascade with three control method.

Table 4 Simple space of the three geometric parameters.

The detailed flow characteristics of the Optcase1and Optcase2are shown in Fig.20 to explore the advantages and disadvantages of them.A clear distinction that a leg of the induced vortex crosses the blade and enters the adjacent passage is revealed in the optimal case 2.Obviously,the leg is derived from the third vane,and the blue and pink induced vortices remain in the certain passage and join in the formation of passage vortex10.Meanwhile,the orange 3-D streamlines bypass the vortex core region and stay at the peripheral region,which do not work for suppressing the separation.Moreover,the accumulation of low energy fluid is migrated backward.Therefore,the induced vortex from the third vane could delay the occurrence of stall,which can be verified from Fig.21.The occurrence of failure is delayed from 10.1°to 10.3°.An advice for designing vortex generators that the induced vortex entering the certain passage can guarantee the reduction of total pressure loss,but the sacrifice of the performance can be exchanged for extending the operating range.

Fig.17 Response surfaces among the three configurations.

Table 5 Optimal configurations and optimal response values.

Fig.18 Variations of aerodynamic parameters in Optcase1 at near stall condition.

Fig. 19 Pitchwise averaged ζ along spanwise at near stall condition.

The effects of the suction slot and vortex generator on the passage flow are given in Fig.22.The axial velocity contours are captured at 30%full span of the cascade at 7°incidence.For the baseline,the reverse flow region almost occupies one third of the integrated passage along the pitchwise.The flow characteristic near the blade suction side obtains a significant improvement by applying the micro-vortex generator,and the induced vortex still displays a powerful strength to mix the main flow and low energy fluid at 30%full span.However,the boundary layer suction shows limited capability to migrate the reverse flow,and the initial separation point is migrated forward by the suction power.The aerodynamic performance will be further enhanced in the optima result.Optcase1demonstrates that the flow characteristic of the cascade could be improved by the combined method with proper configurations,and Optcase2shows a similar flow characteristic to Optcase1.

5.Conclusions

Fig.20 Flow characteristics of two types of vortex generators at 7°incidence condition.

Fig.21 Flow characteristics of two types of vortex generators at 7°incidence condition.

The investigation was carried out on a high-load linear compressor cascade with a low Mach number incoming flow.A kind of modified micro-vortex generator and a longitudinal suction slot were combined as the research objects to analyze the advantages and disadvantages of the different control strategies.The results showed that as the micro-vortex generator is introduced in the aspirated compressor cascade,the total pressure loss is reduced,and the stall occurrence is delayed.The following conclusions can be drawn through analyses of the aerodynamic performance:

Fig. 22 Axial velocity contours of 30% span at near stall condition.

(1)As the micro-vortex generator is introduced in the cascade without boundary layer suction,the corner separation is switched to trailing edge separation by the thrust from the induced vortex.Meanwhile,the occurrence of failure is delayed due to the mixed low energy fluid and main flow.However,the performance of the cascade with micro-vortex generator is inferior to the baseline when the incidence is between-1°and 3°,because in those conditions,most of the low energy fluid stay on the range near the mid-span,and the vortex shows a limited capacity to influence the low energy fluid.

(2)When the micro-vortex generator is introduced in the cascade with a radial direction boundary layer suction on the blade suction side,the occurrence of failure is delayed.Meanwhile,the performance of cascade is superior to the baseline at the all incidence conditions before the occurrence of failure,which attributes to the synergistic effects between the switched failure classification and the reduction of the low energy fluid near the midspan.The reductions of the secondary flow loss and end-wall loss are considered as a main achievement of the vortex generator,and the reductions of the profile loss and wake flow loss are contributed to the boundary layer suction.

(3)The optimal results show that the axial position of the suction slot is a critical parameter, and the farther upstream suction position can decrease the total pressure loss of the cascade with vortex generator at the near stall condition.Moreover,the induced vortex entering the certain passage can guarantee the reduction of total pressure loss.However,the induced vortex with a leg can migrate the accumulated low energy fluid backward to delay the occurrence of stall.

Acknowledgement

This study was co-supported by the National Natural Science Foundation of China(Grants Nos.51576162 and 51536006).