Numerical Simulation of Flow in Centrifugal Compressor with a Single Circumferential Groove*

（School of Energy and Power Engineering,Xi'an Jiaotong University,Xi'an,China,chenxuefei.168@stu.xjtu.edu.cn,glqin@mail.xjtu.edu.cn）

Abstract：Enhancing stall margin has a great importance for the development of turbo compressors. The application of circumferential grooved casing treatment(CGCT)is a useful method of increasing the stable operating range of the compressor,and the effectiveness of this kind of casing treatment have been proved by numerous experiments.In this paper,a single circumferential casing groove is placed along the shroud side of the vaned diffuser.To clarify the effect of circumferential groove on the centrifugal compressor stability and corresponding flow mechanism,numerical investigations with different radial location,axial depth and radial width were carried out to compare the results.The computational fluid dynamics(CFD)analyses results show that the centrifugal compressor with a single circumferential groove in diffuser passage can extend stable operating range while the efficiency over the whole operating range decreases a little.Efforts were made to study blade level flow mechanisms to determine how the circumferential groove impacts the compressor's stall margin(SM)and performance.Some comparisons of the flow features with different parameter of grooved casing treatment are performed, and the results indicate that the low energy flow in the tip clearance is sucked into the groove and the area of the low energy fluid region shrinks,which helps to improve the stall margin of the centrifugal compressor.The numerical results showed that a combination of position,width and depth of circumferential groove will maximize stall margin improvement(SMI)of the centrifugal compressor.

Keywords：Circumferential Groove,Centrifugal Compressor,Vane Diffuser,Stall Margin Improvement

Nomenclature

CGCT circumferential groove casing treatment

SMI stall margin improvement

SW smooth wall

Mmass flow

πstatic pressure ratio

ηefficiency

Фstable working range

ΔSMcomprehensive improvement of stall margin

Δηefficiency improvement

Subscripts

mmass

surgesurge point condition

polpolytropic

desdesign point

swsmooth wall case

ctcasing treatment case

1 Introduction

With the development of the modern engines,the design of modern compressor is focused on reducing stage numbers,which often leads to the problem of how to prevent flow instabilities in the compressor.A number of devices and methods have been carried out to enhance the stable operating range and overcome the problem of stall and surge.[1-2]Among then,circumferential grooved casing treatment(CGCT)has been proved to be a good choice on enhancing stall margin(SM)and improving efficiency of compressors.

The open literatures about circumferential groove casing treatment(CGCT)mainly dealt with axial compressors.Many experimental investigations have proven that circumferential grooved casing treatments have the capacity to expand the stable operating range of axial compressors for ro-tor tip stall since the early 1970s[3-8].Compared with other kinds of casing treatment such as slot casing treatment[9-11],grooved casing treatments generally generate moderate stall margin improvement with small efficiency loss.Due to its simple configuration,grooved casing treatment is manufactured more easily than slot casing treatment or self-recirculating casing treatment[12].In order to solve the shortage of stall margin,a designer may only require a small or moderate stall margin improvement(SMI)for those compressors,which would not have high efficiency loss after applying casing treatment.Moreover,some compressors cannot use other kinds of casing treatment due to the mechanical restriction.Therefore,grooved casing treatments are useful to satisfy the demands of SMI,efficiency and mechanical restriction potentially.

There is a focus on uncovering the effect of singlegroove location[13-14]and groove depth[4,13,15,16]on the axial compressor stability in the majority of grooved casing treatment investigations.The influence of the axial location of single groove on stall margin improvement(SMI)was investigated by Houghton[13]on a single stage,low speed,and vertical axial compressor.The results show that the maximum SMI of 4.5%with 6mm groove depth is obtained when the upstream edge of the groove is 50%axial chord of the rotor blade tip aft of the blade leading edge.The groove generates a small SMI of about 1%when its upstream edge is 18%or 85%axial chord of the rotor blade tip aft of the blade leading edge.Li[14]used experimental method to examine the effect of the location of single groove in a low-speed axial compressor.The results indicate that the groove obtains a maximum SMI of more than 5%when the groove location is near 56.1%axial chord of the rotor blade tip.The best groove location is similar to that presented by Houghton.Baily[4]assessed the effect of different groove depth on the stable operating range of an axial flow compressor.He found that the effect made by deep grooves is more obvious than that made by shallow grooves.The experimental and numerical investigation by Houghton[13]points out that from 0%to 55%of the axial chord of the rotor blade tip,the stall margin generated by the deep groove with 6mm depth is 1%more than that generated by the shallow groove with 3mm depth.Martin16 conducted an experimental investigation of groove depth on a transonic compressor.The results indicate that for the deep grooves with 12mm depth,the stable operating range of the compressor is wider than that for shallow grooves with 3mm depth at three off-design speeds and design speed.Rabe[15]evaluated the experimental results of different depth groove casing treatments.He found that shallow grooves with 1.25mm depth can enlarge the flow range more effectively than deep grooves with 20.32mm depth on a transonic compressor rotor.

Most recently,circumferential grooved casing treatment was also used to enhance the SM of centrifugal compressors.Hu[17]used numerical method to examine the performance of a centrifugal compressor with circumferential grooved casing treatment.The results indicated that the reverse flow of the blade tip leakage to the impeller inlet was reduced with the existence of CGCT and the occurrence of stall was delayed.Gao[18]numerically studied the mechanism of SMI of a low-speed centrifugal compressor with circumferential grooved casing treatment.The results concluded that CGCT could control the development of blade tip leakage vortex(BTLV)and delay the occurrence of stall.The results on SMI of CGCT is similar to that presented by Hu.[17]Halawa[18]used numerical method to study the groove parameters on the performance of NASA CC3 centrifugal compressor.The results showed that when the aspect ratio was less than one,the reinjected groove flow is relatively weak.When the aspect ratio was equal to one,there is enough space for the flow to circulate and the reinjected groove flow generated higher velocities.When the aspect ratio was more than one,the reinjected flow velocity was increased slightly and the total area at which the flow was injected from groove increases.The results also showed that the full blades leading edge is the best location for the SMI.The SM increases and the isentropic efficiency decreases by increasing the number of grooves.

Traditionally,the CGCT is always placed over the rotor of the compressors.Spakovszky[19-20]observed rotating stall in vaned diffusers of centrifugal compressors.Thus,in this article,a circumferentially grooved casing treatment configuration[21-22]is proposed and investigated as a control method to increase the SM.In this configuration,one CGCT is placed along the shroud side of the diffuser passage to enhance the SM of the compressor.It is important that the effect of groove parameters on a compressor stable operating range should be confirmed to design a CGCT effectively.Furthermore,the fundamental flow mechanism,which is how the CGCT affects the centrifugal compressor stability,is not fully understood.This paper presents the effect of numerical investigation of groove parameters on the stability of a single-stage,high speed centrifugal compressor.CFD analysis is performed under stage environment in order to find the optimumal location of the CGCT in consideration of SMI and efficiency gain at design point,and the influence of groove radial width and axial depth to the CGCT configuration is also studied.Also,the numerical investigations attempt to uncover the flow mechanism by which CGCT provide an improvement of the stall margin of the present centrifugal compressor.The numerical cases with CGCT in vaned diffuser are carried out to compare the results.

2 Analysis Model

As previously explained,all experimental and numerical work is conducted on the single-stage,high speed,low flow rate centrifugal compressor.The design specifications of the impeller and diffuser are summarized in Table 1.The past numerical simulations indicate that there is a vortex in the diffuser passage of the compressor with smooth wall casing near stall condition[23].The overall performance obtained through the experiments and the flow passage data were referred for the validation of numerical simulations,which will be presented as follows.

Tab.1 Geometrical parameters of the compressor.

3 Numerical methods

3.1 Numerical Scheme

The NUMECA software was used to perform the numerical work.The Spalart-Allmaras turbulence model was applied during solving the steady-state Navier-Stokes equations in a relative coordinate system.A four-step Runge-Kutta algorithm was chosen for Time integration,and the spatial discretization was done by using a second-order upwind TVD scheme.In order to reduce the calculated time,local time stepping,residual smoothing and multi-grid techniques were applied.

At the inlet,total pressure and total temperature with axial-flow direction was applied for boundary condition.The real air is considered as working fluid.All solid boundaries are set to no-slip and no-heat transfer wall conditions.Blades and wheel are set as rotating parts and the design speed of the compressor is 30 215 r/min.The mass flow rate is specified at the outlet of the compressor stage for boundary condition.The mass flow ratio is degressively increased and reduced to simulate the whole performance curve of the compressor.When the simulation near the stall point,the last convergent solution with the lowest mass flow is used as the initial solution,the near stall performance characteristics of the compressor is simulated by decreasing the outlet mass flow until the convergent solution no longer exists.In calculation of this paper,the last converged solution before the numerical instability is defined as the near-stall point.

3.2 Computational Grid

In calculation of this paper,steady three-dimensional Navier-Stokes flow simulations were conducted to the whole centrifugal compressor.The computational grid of the impeller and diffuser stage is generated with the auto-grid generation software AutoGrid5 of NUMECA.The H&I topology structure is used in grid generation of impeller with the total number of nodes is 1 223 952.Proper grid encryption was presented in the leading edge and trailing edge of blade.The HOH topology was chosen to mesh the vane diffuser passage with the grid number of 202 223 and 198 695 respectively.The grids of CGCT is generated by ZR Effect function in Autogrid5 of NUMECA.The grids of CGCT and blade channel are connected by full no-matching boundary(FNMB).Each groove consists of 41 circumferential,37 axial and 37 radial points,and the groove gird was clustered near the tip clearance and groove wall,the total number of nodes is 56 129.Figure 1 displays the computational grid of the stage,the mesh of diffuser passage with one CGCT.

Fig.1 Computational grid in detail

3.3 Validation

The experimental and numerical investigations were conducted at design speeds without CGCT.The comparisons between the experiment and numerical performances are shown in Figure 2.It can be seen that the experimental stall limit agrees well with that in the calculation for smooth wall.Moreover,the variational trend of the mass flow of near stall point for the calculations agrees well with that for the experiment at the design rotating speeds.The detailed comparisons show that for smooth wall(SW),the predicted mass flow rates near stall limit is slightly lower than that in the experiment at the design speed.

Fig.2.Characteristics plot of smooth wall compressor

It can be found that there are some disagreements between the experimental and calculated pressure ratio lines and efficiency lines in Figure 2.The predicted pressure ratios for all cases are higher than the experimental data in the whole operating range at design speed.Besides,the predicted efficiency for each case is also higher than the experimental data in the whole operating mass flow regions.These disagreements are made by some factors,such as the insufficiency of the used turbulence model,the deviation of the real blade geometry,which can cause these disagreements.On top of that,because the centers of the rotor shroud and rotating axis may not same in the experiments,the size of the rotor tip clearance cannot keep a fixed value along circumferential direction.The size of the rotor tip clearance is uniform in the simulations along circumferential direction.In the experiments,the outlet total pressure probe is fixed in a certain circumferential position.Thus,the discrepancy of the rotor tip clearance between the calculations and experiments must make disagreement in the stage performance.With the overall trend of characteristics plot of the compressor is apparent,the computational method and simulation mesh is able to predict the flow parameters with sufficient reliability.

4 Results and Discussion

4.1 Design of Circumferential Groove

Flow analysis of the SW stage showed that the flow separation at the shroud side of the diffuser passage,the inflow diffuses in the impeller passage and interacts with the tip gap flow[21]In this paper,the CGCT slot position was designed in the shroud side of diffuser[23].

In order to find the optimal radial location of the CGCT,a series of slot position of CGCT were designed along the shroud side of the diffuser and numerical simulations were carried out.The CGCT in the simulations with radial width of 6mm and axial depth of 6mm as initial.Figure 3 shows the radial locations of different CGCT.For the purpose of highlight the CGCT geometry characteristics,the CGCT naming rules would be designed as"axial depth_radial width_the maximum absolute value of coordinates Y".Such as the number 1 CGCT in Figure 3 is named as“6_6_131”.

Fig.3 The slot location of circumferential grooves

In order to evaluate the effects of CGCT on the compressor stability quantitatively,stable working rangeФ,comprehensive improvement of stall margin ΔSM,polytropic efficiency improvement at designed pointΔηpolwere evaluated in present work.WhereM,πandηare the mass flow,the pressure ratio and the efficiency respectively,and subscriptsw,ct,desandstalldenote smooth wall,casing treatment,design point and near stall point respectively.

4.2 Impact of Groove Location on the Effect of CGCT

Table 2 shows the calculated results of ΔSM with four different locations of CGCT No.1/2/3/4 which named as“6_6_131”,“6_6_139”,“6_6_147”and“6_6_159”respectively.The influence of CGCT to compressor stage performance with different locations can be illustrated by Figure 4.

Tab.2 Specific results of different radial location of circumferential grooves

Fig.4 Effects of different radial location of circumferential grooves

Compared with the calculated results of the smooth wall(SW),which has a stable working range of 42.80%,the CGCT No.1 reached the largest stable working range of 47.48%and the largest comprehensive SMI of 9.10%.The CGCT No.2 has the best effect with the efficiency to reduce by about 0.23%compared with the CGCT No.1/3/4,and stable working range is 47.11%,SMI is 8.37%.The CGCT No.3 and No.4 has a less SMI and stable working range,and the efficiency decreases much more at design point.In addition,it can be found from Table 2 and Figure 4 that the CGCT located at the leading edge and middle part of the first vane of diffuser can get a better SMI than the other CGCT,which can be explained by the flow analysis of the SW stage,which showed that the flow separation at the leading edge of shroud side in the diffuser passage[21].

Figure 5 presents the entropy contours at 95%span in the impeller passage at design point.The entropy distribution with CGCT No.2 and No.3 shows little change compared with the SW casing stage in the whole part of the impeller passage.The CGCT No.2 and No.3 are located far from the impeller outlet,so the CGCT configurations have little influence to the performance of impeller at design point.It can be found from Figure 5 that there is a high entropy zone at the outlet part of the impeller passage.The zone with high entropy is induced by the tip clearance leakage flow mixed with the main flow.The entropy value is lowest at the inlet and increases from inlet to outlet in the impeller.

The diagrammatic sketch of circumferential cross section of CGCT is illustrated in Figure 6.Three cross sections are cut out averagely in the circumferential direction.Figure 7 shows the relative velocity vector and entropy distribution at the cross sections of CGCT No.2 and No.3 at near-stall point.It can be seen from the Figure that,there is apparently axial velocity in cross section 1 and section 3 of CGCT No.2 and No.3,which means the low momentum fluid in the tip of diffuser passage flows into the CGCT and transports along the circumferential and streamwise direction in the groove.According to the entropy distribution in Figure 7,the zone with high entropy is mainly at the upper left corner in section 1 and section 3.In section 2 of CGCT No.2 and No.3,there is almost no axial velocities,which shows the effect of lateral transportation of the low momentum fluid.The results show that the losses are mainly at the upper left corner and the top region in the CGCT.Compared the relative velocity vector and entropy distribution between CGCT No.2 and No.3,it can be found that the suction effects of CGCT No.2 are greater than the CGCT No.3 in each section,and the entropy value of CGCT No.2 are a little greater than CGCT No.3.

Figure 8 shows the relative velocity vector and entropy distribution at the inlet of groove for CGCT No.2 and No.3 at near-stall point.It can be seen from the figure that,for the treated casing diffusers,the fluid in the tip of diffuser passage is sucked into the groove,which shrinks the area of the tip fluid separate region,and the fluid velocity in the tip region increases.The entropy value at the inlet section of CGCT No.2 is greater than CGCT No.3,which has the similar results with cross sections in Figure 7.

4.3 Impact of Groove Depth on the Effect of CGCT

Table 3 shows the calculated results of ΔSMwith three different axial depth of CGCT which named as“6_6_139”,“10_6_139”,and“14_6_139"respectively.The influence of CGCT to compressor stage performance with different axial depth can be illustrated by Figure 9.

Fig.5 Entropy distribution at 95%-span in the impeller passage at design point

Fig.6 The diagrammatic sketch of circumferential cross section of CGCT

Fig.7 Relative velocity vector and entropy distribution at the cross sections of CGCT at near-stall point

Fig.8 Relative velocity vector and entropy distribution at the inlet of groove at near-stall point

Compared with the calculated results of the SW,which has a stable working range of 42.80%,the CGCT“14_6_139”reached the largest stable working range of 48.00%and the largest comprehensive SMI of 10.11%.The CGCT“6_6_139”has the best effect with the efficiency to reduce by about 0.23%compared with the deep CGCT“10_6_139”and“14_6_139”,and stable working range is 47.11%,SMI is 8.37%.The CGCT“10_6_139”has a more SMI and stable working range,but the efficiency decreases much more at design point.In addition,it can be found from Table 3 and Figure 9 that,with the circumferential groove axial depth increasing,stable working range and SMI enhanced but pressure ratio reduced and the efficiency decreases obviously.

Tab.3 Specific results of different axial depth of circumferential grooves

Fig.9 Effects of different axial depth of circumferential grooves

Figure 10 presents the axial velocity component distribution at inlet of groove at design point.In the figure,the positive velocity and the negative velocity indicate that the fluid out and into the CGCT.It can be seen that,as the axial depth increases,the flow status is similar to the cases.At the same time,as the axial depth increases,the area of the positive and negative velocity core regions increase a little,which makes the losses in the groove increase,so the efficiency decreased with the increase of axial depth of CGCT at design point.

The diagrammatic sketch of flow direction cross section of CGCT is illustrated in Figure 11.The cross section is cut out in the middle of the CGCT.Figure 12 shows the relative velocity vector and entropy distribution at the flow direction cross sections of CGCT“6_6_139”,“10_6_139”and“14_6_139”at design point.The compared results in Figure 12 show that,with the increase of groove depth,the axial velocity in the bottom of groove increases,which illustrates the suction capacity of CGCT improved.The fluid velocity is almost parallel with the SW,which suggests that the fluid in the top of the CGCT is mainly in the transport state.Besides,it can be found that the entropy increased at middle section of CGCT with the increase of groove depth,which illustrates the losses increased.As a result,it also conforms to the calculation results in Table 3 and Figure 9 that with the increase of groove depth,efficiency at design point reduced.

Figure 13 shows the relative velocity vector and entropy distribution at the inlet of the CGCT at near-stall point with different axial depth.The compared results in Figure 13 show that,the flow status at the inlet of the CGCT has little difference.For the treated casing diffusers,the fluid in the tip of diffuser passage is sucked into the CGCT,which shrinks the area of the tip fluid separate region,and the fluid velocity in the tip region increases.The entropy value at the inlet section of CGCT“14_6_139”is greater than CGCT“6_6_139”and“10_6_139”,which illustrates the suction capacity of CGCT improved and the losses increased.

Figure 14 shows the relative velocity vector and entropy distribution in CGCT at near-stall point.The CGCT with 14mm axial depth has the lowest efficiency at near-stall point,which influences by the highest total entropy value shown in Figure 14.The low momentum fluid is sucked into the CGCT with the effect of adverse pressure gradient,one counter clockwise vortex appears in the groove and the core of it locates at the centre of the groove.According to the entropy distribution in Figure 14,the zone with high entropy is mainly at the top of the CGCT.Compared the relative velocity vector and entropy distribution between CGCT with different axial depth,it can be found that the suction effect of CGCT“14_6_139”are greater than the CGCT“6_6_139”and“10_6_139”.Besides,the maximum entropy value appears in CGCT“10_6_139”rather than CGCT“14_6_139”,which makes the mixing space greaten to reduce the losses with the increased axial depth.

Fig.10 Axial velocity component distribution at inlet of groove at design point

Fig.11 The diagrammatic sketch of flow direction cross section of CGCT

Fig.12 Relative velocity vector and entropy distribution at the flow direction cross sections of CGCT at design point

Fig.13 Relative velocity vector and entropy distribution at the inlet of groove at near-stall point

Fig.14 Relative velocity vector and entropy distribution in circumferential casing grooves at near-stall point

4.4 Impact of Groove Width on the Effect of CGCT

Table 4 shows the calculated results of ΔSM with three different radial width of CGCT which named as“6_6_139”,“6_10_139”,and“6_14_139"respectively.The influence of CGCT to compressor stage performance with different radial width can be illustrated by Figure 15.

Tab.4 Specific results of different radial width of circumferential grooves

Fig.15 Effects of different radial width of circumferential grooves

Fig.16 Relative velocity vector and entropy distribution at the inlet of groove at design point

Fig.17 Axial velocity component distribution at the inlet of groove at near-stall point

Fig.18 Relative velocity vector and entropy distribution in circumferential casing grooves at near-stall point

Compared with the calculated results of the SW,the CGCT“6_14_139”reached the largest stable working range of 48%and the largest comprehensive SMI of 9.21%.The CGCT“6_6_139”has the best effect with the efficiency to reduce by about 0.23%at the design point.The CGCT“6_10_139”has a more SMI and stable working range,but the efficiency decreases much more.In addition,it can be found from Table 4 and Figure 15 that,with the circumferential groove radial width increasing,stable working range and SMI enhanced but pressure ratio reduced and the efficiency decreased obviously,which been similar with the results of groove axial depth.

Figure 16 shows the relative velocity vector and entropy distribution at the inlet of the CGCT at design point with different radial width.The compared results in Figure 16 show that,the flow status at the inlet of the CGCT has little difference.For the treated casing diffusers,the fluid in the tip of diffuser passage is sucked into the CGCT,which shrinks the area of the tip fluid separate region,and the fluid velocity in the tip region increases.The entropy value at the inlet section of CGCT“6_14_139”is greater than CGCT“6_6_139”and“6_10_139”,which illustrates the suction capacity of CGCT improved and the losses increased.

Figure 17 presents the axial velocity component distribution at inlet of CGCT at near-stall point.In the figure,the positive velocity and the negative velocity indicate that the fluid out and into the CGCT.It can be seen that,as the radial width increases,the flow status is similar to the cases with each other.At the same time,as the radial width increases,the area of the positive and negative velocity core regions increase obviously,which illustrates the suction capacity of CGCT improved and makes the losses in the groove increase,so the efficiency decreased with the increase of axial depth of CGCT at near-stall point.

Figure 18 shows the relative velocity vector and entropy distribution in CGCT at near-stall point.The CGCT with 14mm radial width has the lowest efficiency at near-stall point,which influences by the highest total entropy value shown in Figure 18.The low momentum fluid is sucked into the CGCT with the effect of adverse pressure gradient,one counter clockwise vortex appears in the groove and the core of it locates at the centre of the groove.According to the entropy distribution in Figure 18,the zone with high entropy is mainly at the bottom of the CGCT.Compared the relative velocity vector and entropy distribution between CGCT with different radial width,it can be found that the suction effect of CGCT“6_14_139”are greater than the CGCT“6_6_139”and“6_10_139”.Besides,the maximum entropy value appears in CGCT“6_14_139”,which makes the losses increased with the increased radial width.

From the above analysis,we can indicate that the CGCTs supplies a recirculation passage for the low momentum fluid near the diffuser casing wall at near-stall operating conditions.The low momentum fluid is sucked into the treated casing groove and transports along the circumferential and streamwise directions in the groove.Thus,the initiation of stall is delayed,and the overall contribution of each groove to SMI depends on the compound effect of suction-reinjection.

5 Conclusions

To evaluate the effects of CGCT on the SMI of a centrifugal compressor,an investigation is carried out with the help of numerical methods at design speed.The basic flow mechanisms of affecting the compressor SMI by changing the parameters of CGCT are clarified by analyzing the flow field in the diffuser tip passage in detail.Some conclusions can be summarized as follows:

1)The application of CGCT makes the area of the tip fluid separate region shrinks and the fluid velocity in the diffuser tip region increases.The CGCT helps to delay the initiation of stall,which makes the compressor get a larger stable working range and SMI with a little decrease in efficiency at design point.

2)The numerical investigation based on CGCT No.1“6_6_131”,which applied at the leading edge of the vaned diffuser can generate maximum SMI and stable working range,and CGCT No.2 which applied at the middle of the vaned diffuser provides more SMI than CGCT No.3 and No.4.The compressor with CGCT No.3,which applied at the trailing edge of the vaned diffuser gains minimum SMI.

3)With the axial depth and radial width of CGCT increased from 6mm to 14mm,the stable working range and SMI of the centrifugal compressor increase,while the efficiency is decreased and the decreasing amplitude is more than the SMI.

4)The evaluation based on SMI shows the optimal position for the CGCT was indicated to exist near the first half part of the vaned diffuser,and a combination of slot location,axial depth and radial width of the CGCT that will maximize both SMI and efficiency of the centrifugal compressor.