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Figure 4. Application of a chamfer on the RC inner wall edge showing the mitigation of the blockage at the channel outlet. (a) Overview of the recirculation channel flow structure. (b) Improving the inner float shape. (c) Comparison of the y velocity distribution at the recirculation channel outlet. The overview of the recirculation channel flow structure is shown in Figure 4a by Mach numbet grayscale iso-levels, captured by two-dimensional (2D) simulations. The flow conditions of this 2D calculation are specified by the results of corresponding 3D calculations on the computational domain of Figure 2. In the absence of any casing treatment, the pressure difference across the blade thickness, which is modeled by imposing different pressures along the left and right boundaries of the computational domain of Figure 4a, generates a leakage flow over the tip clearance. In the simulation shown in Figure 4a, the right-hand side boundary is set at a higher pressure than the left boundary so that the elevated pressure to the right of the modeled blade thickness creates a leakage jet over it that runs from right to left, as indicated by the white arrow. By applying the recirculation channel over the rotor blade, the fluid is sucked at the channel inlet and it is injected into the main passage at the channel outlet. The leakage flow from the rotor tip is diverted downwards, which indicates a significant interaction from the confluence of the two flows. As a result of the channel activation, the tip flow over the tip clearance directed towards the left computational domain boundary is substantially obstructed

Figure 4 Application of a chamfer on the RC inner wall edge showing the mitigation of the blockage at the channel outlet. (a) Overview of the recirculation channel flow structure. (b) Improving the inner float shape. (c) Comparison of the y velocity distribution at the recirculation channel outlet. The overview of the recirculation channel flow structure is shown in Figure 4a by Mach numbet grayscale iso-levels, captured by two-dimensional (2D) simulations. The flow conditions of this 2D calculation are specified by the results of corresponding 3D calculations on the computational domain of Figure 2. In the absence of any casing treatment, the pressure difference across the blade thickness, which is modeled by imposing different pressures along the left and right boundaries of the computational domain of Figure 4a, generates a leakage flow over the tip clearance. In the simulation shown in Figure 4a, the right-hand side boundary is set at a higher pressure than the left boundary so that the elevated pressure to the right of the modeled blade thickness creates a leakage jet over it that runs from right to left, as indicated by the white arrow. By applying the recirculation channel over the rotor blade, the fluid is sucked at the channel inlet and it is injected into the main passage at the channel outlet. The leakage flow from the rotor tip is diverted downwards, which indicates a significant interaction from the confluence of the two flows. As a result of the channel activation, the tip flow over the tip clearance directed towards the left computational domain boundary is substantially obstructed

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Table 1. Overall parameters of NASA rotor 37. 2.3. Numerical Modelling
Table 1. Overall parameters of NASA rotor 37. 2.3. Numerical Modelling
flow from the tip clearance reaching at the adjacent rotor blade is the main driver of rotor tip stall inception in axial compressors. Rotor tip leakage from the blade pressure side to its suction side is caused by the pressure difference across the rotor blade thickness. Mitigating the rotor tip leakage is expected to delay the spike type stall inception. Figure 1 illustrates the authors’ own take of the axisymmetric recirculation channel (RC) concept applied to an axial compressor rotor. This concept broadly draws from a detail of a one-way valve by Tesla [17]. The RC is placed over the rotor shroud wall at approximately 0.2 blade axial chords downstream from the leading edge (LE) of the blade. A recirculating flow is induced in this recirculation channel (RC) by the pressure difference between the suction side and the pressure side of a rotor blade. This pressure difference is enhanced by the axial pressure gradient through the rotor passage. The induced flow is intended to seal the tip leakage flow near the casing wall. The channel outlet is of a subsonic nozzle shape to obtain a high momentum from a small recirculation mass flow rate. Figure 1. The concept of the recirculating type casing treatment over the rotor blade tip clearance.
flow from the tip clearance reaching at the adjacent rotor blade is the main driver of rotor tip stall inception in axial compressors. Rotor tip leakage from the blade pressure side to its suction side is caused by the pressure difference across the rotor blade thickness. Mitigating the rotor tip leakage is expected to delay the spike type stall inception. Figure 1 illustrates the authors’ own take of the axisymmetric recirculation channel (RC) concept applied to an axial compressor rotor. This concept broadly draws from a detail of a one-way valve by Tesla [17]. The RC is placed over the rotor shroud wall at approximately 0.2 blade axial chords downstream from the leading edge (LE) of the blade. A recirculating flow is induced in this recirculation channel (RC) by the pressure difference between the suction side and the pressure side of a rotor blade. This pressure difference is enhanced by the axial pressure gradient through the rotor passage. The induced flow is intended to seal the tip leakage flow near the casing wall. The channel outlet is of a subsonic nozzle shape to obtain a high momentum from a small recirculation mass flow rate. Figure 1. The concept of the recirculating type casing treatment over the rotor blade tip clearance.
Figure 2. Three-dimensional computational domain and mesh with the recirculation channel (RC) over the rotor blades. The computational mesh is coarsened by a factor of two in the direction of each coordinate, for graphical rendering purpose. CFD (ANSYS, Inc., Canonsburg, PA, USA) is used for generating the structured mesh. Only one blade-to-blade passage is modeled to reduce the computational cost. This configuration corresponds to 1/36th of the compressor full annulus. The structured mesh for the recirculation channel is first generated as a separate mesh and then it is appended to the main passage mesh by defining the interface between the two. A constant height for the first cell height normal to the solid boundary wall is set to 5 x 10~° m throughout the computational domain. This achieved an average near-wall resolution of y+ ~ 1.5. Figure 2. Three-dimensional computational domain and mesh with the recirculation channel (RC) wall is set to 5 x 10°” m throughout the computational domain. This achieved an average near-wall
Figure 2. Three-dimensional computational domain and mesh with the recirculation channel (RC) over the rotor blades. The computational mesh is coarsened by a factor of two in the direction of each coordinate, for graphical rendering purpose. CFD (ANSYS, Inc., Canonsburg, PA, USA) is used for generating the structured mesh. Only one blade-to-blade passage is modeled to reduce the computational cost. This configuration corresponds to 1/36th of the compressor full annulus. The structured mesh for the recirculation channel is first generated as a separate mesh and then it is appended to the main passage mesh by defining the interface between the two. A constant height for the first cell height normal to the solid boundary wall is set to 5 x 10~° m throughout the computational domain. This achieved an average near-wall resolution of y+ ~ 1.5. Figure 2. Three-dimensional computational domain and mesh with the recirculation channel (RC) wall is set to 5 x 10°” m throughout the computational domain. This achieved an average near-wall
Table 2. Flow conditions used for the numerical modeling. The inflow is turbulent and uniform inflow k and « fields are prescribed based on the turbulence intensity and on the turbulent length scale values of Table 2. The static pressure at the computational domain outlet of Figure 2 is specified as the outflow boundary condition. For steady RANS simulations, the static pressure is imposed under the condition of radial equilibrium. For time-dependent RANS, a macroscopic pressure resistance model defined in Equation (3) is applied at the outlet boundary in order to model the pressure drop during the stall inception process [27,28].
Table 2. Flow conditions used for the numerical modeling. The inflow is turbulent and uniform inflow k and « fields are prescribed based on the turbulence intensity and on the turbulent length scale values of Table 2. The static pressure at the computational domain outlet of Figure 2 is specified as the outflow boundary condition. For steady RANS simulations, the static pressure is imposed under the condition of radial equilibrium. For time-dependent RANS, a macroscopic pressure resistance model defined in Equation (3) is applied at the outlet boundary in order to model the pressure drop during the stall inception process [27,28].
Figure 3. Circumferentially mass-averaged radial profiles at Station 1 and Station 4 showing the comparison between computational fluid dynamics (CFD) and experimental data. Experimental data from [18,29]. Figure 3 compares the radial profiles of circumferentially mass-averaged total pressure at Station 1 and at Station 4, tangential velocity at Station 4, and flow angle at Station 4, between CFD and experiment. The radial profiles calculated by the steady RANS are drawn in Figure 3 by black solid lines. The radial profiles predicted by the time-dependent RANS are shown by gray dashed lines in the same figure. For time-dependent RANS, the radial profiles are calculated by the average of four equispaced time points during one pitch blade rotation at increments At = 27(36 x 5w3). Figure 3 indicates that both steady and time-dependent RANS models with the realizable k-e turbulence closure model are capable of modeling the performance of the NASA rotor 37 for the purpose of evaluating different casing treatments.
Figure 3. Circumferentially mass-averaged radial profiles at Station 1 and Station 4 showing the comparison between computational fluid dynamics (CFD) and experimental data. Experimental data from [18,29]. Figure 3 compares the radial profiles of circumferentially mass-averaged total pressure at Station 1 and at Station 4, tangential velocity at Station 4, and flow angle at Station 4, between CFD and experiment. The radial profiles calculated by the steady RANS are drawn in Figure 3 by black solid lines. The radial profiles predicted by the time-dependent RANS are shown by gray dashed lines in the same figure. For time-dependent RANS, the radial profiles are calculated by the average of four equispaced time points during one pitch blade rotation at increments At = 27(36 x 5w3). Figure 3 indicates that both steady and time-dependent RANS models with the realizable k-e turbulence closure model are capable of modeling the performance of the NASA rotor 37 for the purpose of evaluating different casing treatments.
Figure 5. Schematic of locating the RC at different axial positions on the meridional plane. As stated in Section 2, the RC is designed to activate recirculating flow by the pressure difference between the channel inlet and the channel outlet. The static pressure at the channel inlet and at the channel outlet depends on the axial location of the RC. Hence, the axial position of the RC is likely to be an important factor in determining the RC performance. Therefore, a parametric study on the RC axial position is carried out to evaluate its effect on the compressor performance. Six different RC axial positions are tested, as shown by the meridional plane schematic of Figure 5. Table 3 lists the axial location and the axial length of each of them. The Case #0 RC in Figure 5 is located as in Figure 1. This datum recirculation channel is applied at about 0.2 axial chord lengths axially downstream from the blade leading edge, which is where the circumferential groove design gave the best stall margin in [8]. The stall inception is determined numerically for all six cases by progressively increasing the exit pressure boundary condition.
Figure 5. Schematic of locating the RC at different axial positions on the meridional plane. As stated in Section 2, the RC is designed to activate recirculating flow by the pressure difference between the channel inlet and the channel outlet. The static pressure at the channel inlet and at the channel outlet depends on the axial location of the RC. Hence, the axial position of the RC is likely to be an important factor in determining the RC performance. Therefore, a parametric study on the RC axial position is carried out to evaluate its effect on the compressor performance. Six different RC axial positions are tested, as shown by the meridional plane schematic of Figure 5. Table 3 lists the axial location and the axial length of each of them. The Case #0 RC in Figure 5 is located as in Figure 1. This datum recirculation channel is applied at about 0.2 axial chord lengths axially downstream from the blade leading edge, which is where the circumferential groove design gave the best stall margin in [8]. The stall inception is determined numerically for all six cases by progressively increasing the exit pressure boundary condition.
Table 3. Parametric study of the recirculation channel location on the rotor shroud wall.
Table 3. Parametric study of the recirculation channel location on the rotor shroud wall.
Figure 6. Overall compressor performance characteristics showing the influence of the RC location. (a) Influence of the RC location on the total pressure ratio across the rotor at different normalized mass flor rates. (b) Influence of the RC location on the rotor adiabatic efficiency ad different normalized mass flow rates. Figure 6 shows the com parison of the compressor performance characteristics among the six tes cases. Figure 6a uses the same legend and abscissa as Figure 6b. The total pressure ratio in Figure 6a i calculated by the ratio of the total pressure predicted at the Station 4 to the reference upstream tote pressure given in [18]. The adiabatic efficiency is calculated by Equation (2). The choked mass flow rat Mehoked predicted in the CFD of the baseline (BL) case is used to normalize the mass flow rate value of the abscissa. The final increment of the back pressure to detect the stall inception is 0.3% of th atmospheric pressure in all t he calcu case is marked by the gray-fi led sym the arrow for each case at the bottom the widest operating range. The pred ations. The predicted limit of the stable operating range for eac! bol. The stable operating range in mass flow rate is highlighted b of Figure 6a. Among these test cases, Case #0 is predicted to hav icted stable operating range of the compressor rotor decreases a the RC is moved axially either way from the Case #0 position. Figure 6b shows that the rotor adiabati efficiency is substantially unaffected by the presence of the RC, unlike with the casing treatments [6,7
Figure 6. Overall compressor performance characteristics showing the influence of the RC location. (a) Influence of the RC location on the total pressure ratio across the rotor at different normalized mass flor rates. (b) Influence of the RC location on the rotor adiabatic efficiency ad different normalized mass flow rates. Figure 6 shows the com parison of the compressor performance characteristics among the six tes cases. Figure 6a uses the same legend and abscissa as Figure 6b. The total pressure ratio in Figure 6a i calculated by the ratio of the total pressure predicted at the Station 4 to the reference upstream tote pressure given in [18]. The adiabatic efficiency is calculated by Equation (2). The choked mass flow rat Mehoked predicted in the CFD of the baseline (BL) case is used to normalize the mass flow rate value of the abscissa. The final increment of the back pressure to detect the stall inception is 0.3% of th atmospheric pressure in all t he calcu case is marked by the gray-fi led sym the arrow for each case at the bottom the widest operating range. The pred ations. The predicted limit of the stable operating range for eac! bol. The stable operating range in mass flow rate is highlighted b of Figure 6a. Among these test cases, Case #0 is predicted to hav icted stable operating range of the compressor rotor decreases a the RC is moved axially either way from the Case #0 position. Figure 6b shows that the rotor adiabati efficiency is substantially unaffected by the presence of the RC, unlike with the casing treatments [6,7
Figure 7. Changes in the compressor performance and in the intensity of the injected momentum over the compressor operating range. (a) Comparison of the axial compressor rotor overall characteristics: stall margin (ASM), outlet static pressure change at the near-stall (NS) condition (AP), and rotor adiabatic half-stage efficiency at peak efficiency (PE) condition (An). (b) Variation in the injected flow momentum M with outflow pressure and RC axial position. Figure 7. Changes in the compressor performance and in the intensity of the injected momentum over Figure 7a summarizes the variation of the compressor performance among the test cases. All value of the ordinate are calculated as the difference from the value of the BL case. The SM is calculate by Equation (1). Figure 7b shows the variation in the injected axial momentum over the compressc operating range. The norma ized axial momentum M is calculated by M = —puyu,/ Pref (Umia) A positive momentum means flow injection from the RC toward the main flow passage. All the cas« except Case #1.-2 provides a be in Case #1.-2 is much smaller work as intended in Figure 4. Case #0 adiabatic efficiency a the P the intensity of the injected momen E condition are the highest among inception. This feature shows an interesting and welcome self-regulating channel. Similarly, in Cases #1.1 to compressor loading. At the same bac .3, the intensity of the injected mo k pressure setting, the intensity of th to decrease monotonically as the RC is placed axially more downstream RC upstream than in Case #0 genera injection occurs at low loading condi static pressure value 122 kPa. Above ter SM than the BL case. As shown in Figure 7b, the injected momentur than in the other cases, which indicates t Both the Case #0 outlet pressure at the NS operating condition and th hat Case #1.-2 RC does nx the test cases. In Figure 7 tum in Case #0 increases almost monotonically up to the sta property of the recirculatio mentum tends to rise wit e injected momentum tenc han in Case #0. Placing tt tes a different trend. In Case #1.-1, significant axial momentu1 ions. M increases with the outlet static pressure up to the outl 22 kPa, the axial momentum injection intensity starts to decreas At the NS condition of Case #1.-1, the intensity of the injected momentum is almost same as that « Case #0. This may explain why the operating range of Case #1.-1 is not wider than that of Case # although intense injection occurs in Case #1.-1 at low loading conditions. This difference is investigate further by the analysis of the corresponding flow structures presented in the next chapter. Figure 8a shows the distribution of the normalized momentum injected in the axial direction at the RC inlet and at the RC outlet. In all the cases shown in Figure 8a, the peak of the injected momentum
Figure 7. Changes in the compressor performance and in the intensity of the injected momentum over the compressor operating range. (a) Comparison of the axial compressor rotor overall characteristics: stall margin (ASM), outlet static pressure change at the near-stall (NS) condition (AP), and rotor adiabatic half-stage efficiency at peak efficiency (PE) condition (An). (b) Variation in the injected flow momentum M with outflow pressure and RC axial position. Figure 7. Changes in the compressor performance and in the intensity of the injected momentum over Figure 7a summarizes the variation of the compressor performance among the test cases. All value of the ordinate are calculated as the difference from the value of the BL case. The SM is calculate by Equation (1). Figure 7b shows the variation in the injected axial momentum over the compressc operating range. The norma ized axial momentum M is calculated by M = —puyu,/ Pref (Umia) A positive momentum means flow injection from the RC toward the main flow passage. All the cas« except Case #1.-2 provides a be in Case #1.-2 is much smaller work as intended in Figure 4. Case #0 adiabatic efficiency a the P the intensity of the injected momen E condition are the highest among inception. This feature shows an interesting and welcome self-regulating channel. Similarly, in Cases #1.1 to compressor loading. At the same bac .3, the intensity of the injected mo k pressure setting, the intensity of th to decrease monotonically as the RC is placed axially more downstream RC upstream than in Case #0 genera injection occurs at low loading condi static pressure value 122 kPa. Above ter SM than the BL case. As shown in Figure 7b, the injected momentur than in the other cases, which indicates t Both the Case #0 outlet pressure at the NS operating condition and th hat Case #1.-2 RC does nx the test cases. In Figure 7 tum in Case #0 increases almost monotonically up to the sta property of the recirculatio mentum tends to rise wit e injected momentum tenc han in Case #0. Placing tt tes a different trend. In Case #1.-1, significant axial momentu1 ions. M increases with the outlet static pressure up to the outl 22 kPa, the axial momentum injection intensity starts to decreas At the NS condition of Case #1.-1, the intensity of the injected momentum is almost same as that « Case #0. This may explain why the operating range of Case #1.-1 is not wider than that of Case # although intense injection occurs in Case #1.-1 at low loading conditions. This difference is investigate further by the analysis of the corresponding flow structures presented in the next chapter. Figure 8a shows the distribution of the normalized momentum injected in the axial direction at the RC inlet and at the RC outlet. In all the cases shown in Figure 8a, the peak of the injected momentum
Figure 8. Distributions of the normalized momentum injected in the axial direction. View from above the casing, approximately in the cascade plane. (a) Distribution of the injected normalized momentum in the axial direction at the inlet and at the outlet of the RC. (b) Absolute velocity streamlines inside the recirculation channel (Case #1.-1, OP-A, top view). in the axial direction is predicted at the channel outlet near the blade suction surface. The most intense flow injection is predicted at this point in Case #1.-1 at the operating condition OP-A. This reduces by increasing the compressor loading to the condition OP-B. Figure 8b visualizes the streamlines inside the RC, which are drawn from the absolute velocity field of Case #1.-1 at OP-A. In Figure 8b, the inner and outer walls of the casing channel are displayed transparent to show the trajectory of the streamlines. The streamlines related to the intense flow injection of Figure 8a come from the PS of the rotor blade. This indicates the recirculation flow inside the casing channel is driven by the pressure difference between the blade SS and the blade PS. Figure 9 shows the static pressure distribution at the RC inlet and outlet. This is mainly determined by the positioning of the main passage flow structures, such as the passage shock front. In Case #1.-1, high static pressure sits in at the channel inlet at the operating condition OP-A because of the RC inlet being just behind the leading edge shock. This high pressure promotes the recirculating flow inside the casing channel. By increasing the compressor loading to the operating condition OP-B, the location of the passage shock front shifts upstream of the compressor rotor leading edge, pulling the high static pressure behind the shock with it, away from the channel inlet. This causes the static pressure at the channel inlet to decrease, as shown in Figure 9. This is likely to be the main reason for the decrease in axial momentum injection at the high loading condition in Case #1.-1 shown in Figure 8a. The predicted static pressure distribution at the channel outlet across one blade pitch is shown for Case#0 and Case #1.1 in Figure 9. A region of high pressure, encircled by a dashed line ellipse for Case #1.-1 in Figure 9, is located close to the blade pressure side. This location is pitchwise just ahead of the advancing blade that pressurizes air by a scooping action. The pressure difference between the channel inlet and the channel outlet across the blade thickness created by this action is lower with a casing treatment located more downstream, as shown by Case #0 and Case #1.1 in Figure 9. This is likely to be the reason why the momentum injection in Figure 7 is lower in Case #1.1, Case #1.2, and the Case #1.3 than in Case #0 at the same operating condition.
Figure 8. Distributions of the normalized momentum injected in the axial direction. View from above the casing, approximately in the cascade plane. (a) Distribution of the injected normalized momentum in the axial direction at the inlet and at the outlet of the RC. (b) Absolute velocity streamlines inside the recirculation channel (Case #1.-1, OP-A, top view). in the axial direction is predicted at the channel outlet near the blade suction surface. The most intense flow injection is predicted at this point in Case #1.-1 at the operating condition OP-A. This reduces by increasing the compressor loading to the condition OP-B. Figure 8b visualizes the streamlines inside the RC, which are drawn from the absolute velocity field of Case #1.-1 at OP-A. In Figure 8b, the inner and outer walls of the casing channel are displayed transparent to show the trajectory of the streamlines. The streamlines related to the intense flow injection of Figure 8a come from the PS of the rotor blade. This indicates the recirculation flow inside the casing channel is driven by the pressure difference between the blade SS and the blade PS. Figure 9 shows the static pressure distribution at the RC inlet and outlet. This is mainly determined by the positioning of the main passage flow structures, such as the passage shock front. In Case #1.-1, high static pressure sits in at the channel inlet at the operating condition OP-A because of the RC inlet being just behind the leading edge shock. This high pressure promotes the recirculating flow inside the casing channel. By increasing the compressor loading to the operating condition OP-B, the location of the passage shock front shifts upstream of the compressor rotor leading edge, pulling the high static pressure behind the shock with it, away from the channel inlet. This causes the static pressure at the channel inlet to decrease, as shown in Figure 9. This is likely to be the main reason for the decrease in axial momentum injection at the high loading condition in Case #1.-1 shown in Figure 8a. The predicted static pressure distribution at the channel outlet across one blade pitch is shown for Case#0 and Case #1.1 in Figure 9. A region of high pressure, encircled by a dashed line ellipse for Case #1.-1 in Figure 9, is located close to the blade pressure side. This location is pitchwise just ahead of the advancing blade that pressurizes air by a scooping action. The pressure difference between the channel inlet and the channel outlet across the blade thickness created by this action is lower with a casing treatment located more downstream, as shown by Case #0 and Case #1.1 in Figure 9. This is likely to be the reason why the momentum injection in Figure 7 is lower in Case #1.1, Case #1.2, and the Case #1.3 than in Case #0 at the same operating condition.
Figure 9. Distributions of the static pressure across the RC openings. View from above the casing, approximately in the cascade plane.
Figure 9. Distributions of the static pressure across the RC openings. View from above the casing, approximately in the cascade plane.
Figure 10. Surface streamlines and specific entropy color iso-levels near the casing wall showing how the confluence line (interface) around the rotor leading edge (LE) changes with a RC. View of the cascade plane close to the casing. (a) BL (OP-A, NS). (b) Case #1.-1 (OP-A). (c) Case #0 (OP-A). (d) Case #1.1 (OP-A).
Figure 10. Surface streamlines and specific entropy color iso-levels near the casing wall showing how the confluence line (interface) around the rotor leading edge (LE) changes with a RC. View of the cascade plane close to the casing. (a) BL (OP-A, NS). (b) Case #1.-1 (OP-A). (c) Case #0 (OP-A). (d) Case #1.1 (OP-A).
Figure 11. Visualization of the flow blockage mitigation on the shroud surface by the RC for different RC axial locations. Passage viewed from the hub towards the casing approximately in the radial direction. (a) BL (OP-A, NS). (b) Case #1.-1 (OP-A). (c) Case #1.-1 (OP-B, NS). (d) Case #0 (OP-A). (e) Case #0 (OP-B). (f) Case #1.1 (OP-A). (g) Case #1.1 (OP-B, NS). radial direction just below the RC outlet in the two-dimensional numerical prediction of Figure 4a. At the higher loading condition (OP-B), the volume of separated flow near the casing is larger than that at OP-A for the three cases (Case #1.-1, Case #0, and Case #1.1). This most likely causes a higher blockage. The size of the volume of separated flow in Case #1.1 is larger than that of Case #0 and a larger blockage appears to be generated around the blade LE on the blade pressure side in Case #1.1. This is consistent with the earlier stall inception predicted in Case #1.1 in Figure 6a than in Case #0.
Figure 11. Visualization of the flow blockage mitigation on the shroud surface by the RC for different RC axial locations. Passage viewed from the hub towards the casing approximately in the radial direction. (a) BL (OP-A, NS). (b) Case #1.-1 (OP-A). (c) Case #1.-1 (OP-B, NS). (d) Case #0 (OP-A). (e) Case #0 (OP-B). (f) Case #1.1 (OP-A). (g) Case #1.1 (OP-B, NS). radial direction just below the RC outlet in the two-dimensional numerical prediction of Figure 4a. At the higher loading condition (OP-B), the volume of separated flow near the casing is larger than that at OP-A for the three cases (Case #1.-1, Case #0, and Case #1.1). This most likely causes a higher blockage. The size of the volume of separated flow in Case #1.1 is larger than that of Case #0 and a larger blockage appears to be generated around the blade LE on the blade pressure side in Case #1.1. This is consistent with the earlier stall inception predicted in Case #1.1 in Figure 6a than in Case #0.
Figure 12 shows how the blade loading near the casing is changed by the action of the RC. Specifically, Figure 12 shows the normalized static pressure distribution at 0.98 span from the rotor blade root. Figure 12a compares the blade loadings among four cases at the operating condition OP-A, which corresponds to the stable operating range limit of the BL case. Figure 12a shows that adding the RC reduces the sharpness of the normalized static pressure peak on the PS leading edge. The flow induced through the channel requires a positive pressure difference between the channel inlet and outlet. The broadening of the pressure peak towards the blade trailing edge provides pressure at the channel inlet and therefore benefits the production of the controlling flow through the RC. Over the blade suction side, Figure 12a shows that adding the RC moves the axial location where the passage shock impinges on the blade surface from about 0.46 axial chords to about 0.49 axial chords. The pressure rise across the shock, as indicated by the vertical arrow in Figure 12a, slightly increases. Figure 12b shows corresponding results of blade loading at the operating condition OP-B. This figure does not include the result of the BL case, as the BL case stalls at a lower pressure ratio and therefore never reaches this operating condition. Figure 12b shows that changing the RC axial position affects the location where the passage shock impinges on the blade suction side (SS). This is displayed in Figure 12b by the sharp rise in static pressure that takes place between 0.4 and 0.5 axial chords. Specifically, Case #0 gives the most downstream shock impingement location, whereas both Case#1.-1 and Case #1.1 locate the passage shock wave upstream. In all three RC cases, the static pressure on the blade SS increases at the RC, where indicated py the filled arrow for each case in Figure 12b. This shows a local reduction in the blade loading by flow injection between 0.1 and 0.3 axial chords. In spite of this localized reduction in blade loading, Figure 12 shows that introducing the RC maintains and possibly increases the rotor tip blade loading. This effect is quite different with respect to more conventional rotor tip treatments that off-load the rotor tip to reduce secondary flow losses and increase the stall margin, such as circumferential lean, sweep, or taper. This sets the RC treatment described in this work apart from three-dimensional blade treatment reported in the literature, as it enables to gain stall margin without compromising on performance, by retaining good blade loading in the rotor tip region. Figure 12 indicates that the largest area endorsed by the normalized pressure distribution, hence the highest loading, is achieved at both OP-A and OP-B with the RC positioned as in Case #0.
Figure 12 shows how the blade loading near the casing is changed by the action of the RC. Specifically, Figure 12 shows the normalized static pressure distribution at 0.98 span from the rotor blade root. Figure 12a compares the blade loadings among four cases at the operating condition OP-A, which corresponds to the stable operating range limit of the BL case. Figure 12a shows that adding the RC reduces the sharpness of the normalized static pressure peak on the PS leading edge. The flow induced through the channel requires a positive pressure difference between the channel inlet and outlet. The broadening of the pressure peak towards the blade trailing edge provides pressure at the channel inlet and therefore benefits the production of the controlling flow through the RC. Over the blade suction side, Figure 12a shows that adding the RC moves the axial location where the passage shock impinges on the blade surface from about 0.46 axial chords to about 0.49 axial chords. The pressure rise across the shock, as indicated by the vertical arrow in Figure 12a, slightly increases. Figure 12b shows corresponding results of blade loading at the operating condition OP-B. This figure does not include the result of the BL case, as the BL case stalls at a lower pressure ratio and therefore never reaches this operating condition. Figure 12b shows that changing the RC axial position affects the location where the passage shock impinges on the blade suction side (SS). This is displayed in Figure 12b by the sharp rise in static pressure that takes place between 0.4 and 0.5 axial chords. Specifically, Case #0 gives the most downstream shock impingement location, whereas both Case#1.-1 and Case #1.1 locate the passage shock wave upstream. In all three RC cases, the static pressure on the blade SS increases at the RC, where indicated py the filled arrow for each case in Figure 12b. This shows a local reduction in the blade loading by flow injection between 0.1 and 0.3 axial chords. In spite of this localized reduction in blade loading, Figure 12 shows that introducing the RC maintains and possibly increases the rotor tip blade loading. This effect is quite different with respect to more conventional rotor tip treatments that off-load the rotor tip to reduce secondary flow losses and increase the stall margin, such as circumferential lean, sweep, or taper. This sets the RC treatment described in this work apart from three-dimensional blade treatment reported in the literature, as it enables to gain stall margin without compromising on performance, by retaining good blade loading in the rotor tip region. Figure 12 indicates that the largest area endorsed by the normalized pressure distribution, hence the highest loading, is achieved at both OP-A and OP-B with the RC positioned as in Case #0.
Figure 13. Comparison of overall compressor performance characteristics between steady Reynolds Averaged Navier Stokes (RANS) simulations and time-dependent RANS simulations. The parametric study on the axial position of the recirculation channel has shown that the RC placed 0.18 axial chords length downstream from the blade tip leading edge provides the best compressor stall margin improvement among the test cases. Since the stall inception of axial compressors is an inherently unsteady process [30], it is of interest to confirm the effectiveness of the RC treatment by performing time-dependent RANS simulations using the time-resolved numerical approach and boundary conditions described in Section 2.3. Due to their computational cost, time-dependent RANS simulations were performed only for the BL case and Case #0. Figure 13 compares the overal compressor performance characteristics predicted by steady RANS simulations and by time-dependent RANS simulations. Both in the BL case and in Case #0, the total pressure ratio and the adiabatic efficiency obtained by the time-dependent RANS simulations closely follow the trends obtained by the steady RANS simulations. For both the BL case and Case #0, the incipient stall operating condition is obtained by unsteady RANS simulations at a slightly lower normalized mass flow rate than by steady RANS simulations. The stall margin improvement from the BL case to Case #0 predicted by time-dependent RANS simulations is 5.80%, which is close to 5.60% predicted by the steady RANS simulations. This provides confidence that the performance improvements provided by the RC treatment as predicted by steady RANS are retained in the time-resolved flow. It provides additional numerical validation of the RC concept and of the projected performance for stall margin and adiabatic efficiency.
Figure 13. Comparison of overall compressor performance characteristics between steady Reynolds Averaged Navier Stokes (RANS) simulations and time-dependent RANS simulations. The parametric study on the axial position of the recirculation channel has shown that the RC placed 0.18 axial chords length downstream from the blade tip leading edge provides the best compressor stall margin improvement among the test cases. Since the stall inception of axial compressors is an inherently unsteady process [30], it is of interest to confirm the effectiveness of the RC treatment by performing time-dependent RANS simulations using the time-resolved numerical approach and boundary conditions described in Section 2.3. Due to their computational cost, time-dependent RANS simulations were performed only for the BL case and Case #0. Figure 13 compares the overal compressor performance characteristics predicted by steady RANS simulations and by time-dependent RANS simulations. Both in the BL case and in Case #0, the total pressure ratio and the adiabatic efficiency obtained by the time-dependent RANS simulations closely follow the trends obtained by the steady RANS simulations. For both the BL case and Case #0, the incipient stall operating condition is obtained by unsteady RANS simulations at a slightly lower normalized mass flow rate than by steady RANS simulations. The stall margin improvement from the BL case to Case #0 predicted by time-dependent RANS simulations is 5.80%, which is close to 5.60% predicted by the steady RANS simulations. This provides confidence that the performance improvements provided by the RC treatment as predicted by steady RANS are retained in the time-resolved flow. It provides additional numerical validation of the RC concept and of the projected performance for stall margin and adiabatic efficiency.
Related topics:
PhysicsMechanicsAxial CompressorsAxial CompressorParameter Optimizationcasing treatment
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