High load compressor cascade

The datum profile investigated in this work is cut-off at the mid-span of a certain axial compressor rotor. Limited by the test facility, chord length was scaled down to 0.5 times for a higher aspect ratio. Table 1 lists the design parameters for the profile after scaling. Cascade tests were performed on a variable density plane cascade wind tunnel at China Aerodynamics Research and Development Center (CARDC). Detailed test introduction, including test facilities parameters, measurement methods, test conditions, etc., and test results have been published by Wang et al. (2024).

Slot design

In order to introduce a suitable jet flow near the end-wall to control the corner separation, the slot design was carried out. The design parameters of slot are presented in Figure 1. The aim of slotting is to control the flow in the mid-span of the cascades to be close to two-dimensional flow so as to reflect the real performance of profiles in the test, not to improve the performance of the cascade. Therefore, a complex geometry of slots is not necessary, although it may have a good effect in reducing the loss of cascades. Straight slots were chosen because they have the advantage of simple structure and few parameters while satisfying the aim. A blade end slot (covering 10% of the span from the end-wall) was selected to control the separation near the end-wall without affecting the performance of the mid-span of the cascade. Some literatures (Ma et al., 2021; Ramzi et al., 2011; Rockenbach, 1968) suggested that slot should be near the separation start point. However, it mainly reduces the trailing edge separation of the 2D blade, and the effect on the end-wall separation was not obvious (Ramzi and AbdErrahmane, 2013; Rockenbach, 1968). In order for the slot jet flow to impact the center of separation, the outlet of the slot was set at 80% chordwise position. The width of the slot was set to 1.1% of the chord length, and the angle from the axis was 48.8 deg.

Figure 1.

Slot configuration.

CFD modelling

ANSYS CFX was used in this study to solve the Navier-Stokes equation. Quasi-2D profile, 3D datum cascade and 3D slotted cascades were calculated. The single-passage is adopted due to the periodicity of the cascade. Half of blade passage in the spanwise direction was considered because the flow in cascade symmetrically along the plane of 50% span. Extension sections with 1- and 2-times chord length were arranged upstream and downstream of the cascade. The measuring position of the inlet and outlet flow was 50% chord length away from the leading and trailing edge, which is the same as the measurements in test.

The total pressure and static temperature at the inlet boundary and the static pressure at the outlet boundary measured in the test were set in the simulation, which ensured that the inlet Mach number was consistent with the test value. No-slip and adiabatic conditions were imposed on all solid walls, including surface of blade and slot and end-wall. For 3D simulation, 50% span section was set to symmetric plane. For the quasi-2D calculation, the upper and lower end-walls were set as periodic boundaries, and the flow of the two-dimensional profile was simulated by an infinite cascade. The SST turbulence model was used to account for the turbulence flow. The free stream turbulence intensity was set as Tu = 1% at the inlet according to test.

Mesh

The meshes for the simulation were generated using the NUMECA Autogrid5. Figure 2 shows the meshes for datum cascade and 3D slotted cascades. The structured multi-block O4H grid was used for the datum blade. For quasi-2D and 3D datum cascades, a series of grids with different densities and distributions were compared with guarantee grid independence. The final grid for the datum blade has 2.3 million grid points with 77 nodes in the spanwise direction. A H-block grids was added for the slot on the basis of the datum blade mesh. About 0.12 million grid points were chosen, which satisfies grid independence. The meshes were added to the main flow passage to ensure the one-to-one correspondence of the mesh nodes at the junction and optimize the local mesh expansion ratio (mainly for the boundary layer mesh in slot). The final grid for the slotted blade has 3.8 million grid points. The y⁺ calculated was less than 1 for all simulations.

Figure 2.

Meshes of datum cascade (left) and slotted cascade (right).

Validation of simulations

Comparisons were made between test results and simulation results. The total pressure loss coefficient ω, defined by Equation (1), was compared in Figure 3. In Equation (1), P¯t,2 means outlet total pressure, P¯t,1 means inlet total pressure and P¯s,1 means inlet static pressure, which are all massflow-average results.

Figure 3.

Comparison of total pressure loss coefficients (left) and static pressure coefficients (right) between test and CFD of datum cascade.

Within positive and negative stall boundaries (twice the minimum loss conditions) except for the incidence angle of −3 deg, the deviations of total pressure loss ω between simulation and test results are less than 5%. When incidence angle is −3 deg, there is a shock in the passage due to the large negative incidence angle, shown in Figure 4. Static pressure coefficient distribution Cp, defined by Equation (2), on the blade surface at the mid-span of the simulation and tests were also shown in Figure 3. In Equation (2), Ps means local static pressure. P¯s,1 means inlet static pressure and P¯t,1 means inlet total pressure, which are both massflow-average results.

Figure 4.

Mach number contour at 50% span of CFD result when incidence is −3 deg.

The intensity of the shock wave in the simulation result is greater than the test results. The difference in the loss when incidence angle is −3 deg was mainly produced in the shock wave. The streamlines on blade surface of test and simulation were also compared in Figure 5. The simulation of different incedences can well predict the region of separation. Based on the above comparison, simulations in this paper are reliable.

Figure 5.

Streamlines of test and CFD of datum cascade.

Mid-span performance

For cascade test, the performance at mid-span was of interest. In order to obtain the performance of the 2D profile in test, the flow and performance at mid-span of cascade should be closer to the 2D results. Figure 6 shows the total pressure loss ω and deviation angle δ for 2D profile, and mid-span of 3D datum and slotted cascade. It can be seen that there is a large deviation in the prediction of the total pressure loss ω of the 2D profile by the 3D prototype cascade. When i=+1∘ (minimum loss condition), the relative deviation between results of the 3D datum cascade and the 2D profile is 1.08%. When i=−3∘ (negative incidence condition), the relative deviation between the two is 26.39%. When i=+9∘ (positive incidence condition), the relative between the two is 22.27%. The same goes for deviation angle δ. At different incidences, the predicted errors of deviation angle δ of 3D datum cascade for the 2D profile results are around 1.5–2 degrees. The performance difference shows that for this profile, the test results of the 3D datum cascade are difficult to accurately predict the performance of profile due to the influence of end-wall separation. Especially in the positive incidence conditions, which are more dangerous conditions, the results of the 3D datum cascade may underestimate the loss of the profile, making the expectations too optimistic, thus affecting the blade design.

Figure 6.

Performance varying with incidence at mid-span (left: total pressure loss, middle: deviation angle, right: AVDR).

The slotted cascade better predicts the performance of the 2D profile compared to the datum cascade. When i=+1∘, the predicted total pressure loss ω of the slotted cascade is basically consistent with that of the datum cascade. When i=−3∘, the relative deviation of the calculated total pressure loss ω between slotted cascade and 2D profile is reduced to 7.28%. When i=+9∘, the relative deviation between the two is reduced to 4.48%. The situation where losses may be underestimated under positive incidence conditions has been improved. The maximum deviation angle δ is also reduced to 0.7 deg, among which the errors at the minimum loss condition and the positive incidence condition are both less than 0.5 deg. In the entire range of incidence angles, the test results using 3D slotted cascades can better obtain the performance of this profile.

Figure 6 also shows the changes in AVDR under different incidence angles. AVDR is defined by Equation (3), in which ρ¯1 and ρ¯2 means inlet and out density, V¯z,1 means inlet and outlet axial velocity, which are both massflow-average results. The larger AVDR of the three-dimensional cascade, the stronger influence of the three-dimensional flow, and the stronger the end-wall blockage on the flow passage in the blade. AVDR of the two-dimensional blade is 1. The results show that the AVDR of the datum cascade is above 1.1 and increases with the increase of the incidence. AVDR of slotted blades is all reduced, which is around 1.05, except for the large negative incidences. The flow in the slotted cascade is closer to two-dimensional flow.

Streamlines and Mach number contours at mid-span at typical incidence angles are compared in Figure 7, to analyse the effect of slotting on the flow in the cascade. The results show that the flow of the slotted blade in the blade is closer to the 2D profile flow. When i=+9∘, due to large positive incidence angle, the two-dimensional profile flow has a large trailing edge separation on suction surface. In the 3D datum cascade, the trailing edge separation is significantly reduced. This is because the AVDR of the 3D datum cascade is large, the flow channel in the blade is compressed, the flow is accelerated, and the trailing edge separation on the suction surface is suppressed. After blade slotting, the AVDR decreases, the flow acceleration in the blade weakens, and the trailing edge separation on the suction surface returns to the state of the 2D profile flow. The increase in separation causes the high total pressure loss and deviation angle at mid-span, which return to the level of the 2D profile. When i=+1∘, the flow changes caused by slotting are similar to those of i=+9∘. However, since the trailing edge separation on suction surface of the 2D profile flow is small when i=+1∘, the flow changes among the three are very small, and the overall performance is basically unchanged. When i=−3∘, a compression wave appears in the 2D profile channel. The flow acceleration caused by AVDR leads to enhanced compression waves and increased loss. After slotting, the AVDR is reduced, the compression wave intensity is reduced, and the loss is reduced.

Figure 7.

Mach number contours and Streamlines under typical incidences: (a) 2D, +9 deg, (b) datum, +9 deg, (c) slot, +9 deg, (d) 2D, +1 deg, (e) datum, +1 deg, (f) slot, +1 deg, (g) 2D, −3 deg, (h) datum, −3 deg, (i) slot, −3 deg.

Comprehensively, blade end slot on cascade reduces the AVDR, restores the flow in cascade to 2D flow, and better predicts the performance of the 2D profile.

3D flow structures

The three-dimensional flow structure of datum cascade and slotted cascade when i=+9∘ are exhibited, and the effect of blade end slots is analysed entropy contours and streamlines for 5% span is shown in Figure 8. Separation and the slot jet can be observed. A large separation occurs near the trailing edge on the suction surface of the datum cascade. In the slotted cascade, driven by the pressure difference from the pressure surface to the suction surface, the slot jet rushes into the separation zone on the suction surface along the slot direction and flows downstream of the blade along the suction surface. The high-energy fluid of the jet accelerates the low-energy fluid in the separation. The higher axial momentum slot jet carries drive the backflow near the trailing edge to flow downstream of the blade and clears the flow passage. The jet “disperses” the corner separation near suction surface and reduces end-wall blockage.

Figure 8.

Entropy contours and Streamlines at 5% span when incidence is +9 deg (a) datum, (b) slot.

Figure 9 shows the pressure gradient contours and streamlines on the blade and end wall surfaces, reflecting the flow and separation on the wall. The pressure gradient in the blade height direction (X direction), dp/dx, is contoured on the blade surface, and the pressure gradient in the circumferential direction (Y direction), dp/dy, on the end-wall. Red indicates a positive pressure gradient and blue indicates a negative pressure gradient.

Figure 9.

Pressure gradient contours and Streamlines on blade surface and end-wall when incidence is +9 deg (a) datum, (b) slot.

Corner separation occurs in the corner near the suction surface of the datum cascade. Driven by the positive pressure gradient in Y direction on the end-wall near the trailing edge, the end-wall boundary layer mixes with the trailing edge separation, forming a backflow near the end-wall at outlet and blocking the flow. The blockage causes a large negative pressure gradient in X direction on the front blade surface, pushing the incoming flow upstream to move toward the mid-span starting from the position about 40% of the chord. Finally, the flow channel at mid-span is squeezed.

The slot jet of the slotted cascade changes the three-dimensional flow in the corner. The jet changes the positive pressure gradient in Y direction at the end-wall, pushing the low-energy fluid away from the blade surface and relieving the blockage of the slot outlet and its downstream. The newly formed separation upstream of the slot outlet is suppressed by the jet, failed to form a large separation. The separation in the corner zone is suppressed, which reduces the blockage in the end-wall. The upstream flow is driven by less pressure difference toward the mid-span, and the flow is squeezed less. Since the flow is not significantly accelerated, a large trailing edge separation reappears at mid-span, which is the flow phenomenon that should appear in two-dimensional flow of this profile.

Vorticity magnitude contours and 3D streamlines for different S3 stream surfaces are shown in Figure 10, and the development of vortices in the blade passage can be observed. In the datum cascade, the suction surface leg of horseshoe vortex begins to move upward at position about 40% of the chord, and is drawn into the trailing edge separation. The end-wall boundary layer is involved in the separation and flows back downstream of the trailing edge, aggravating the blockage. The low-energy fluid in the corner area continues to accumulate, forming corner separation covering ranges about 35% span. In the slotted cascade, upstream of the slot outlet, the horseshoe vortex also moves upward to form a local vortex. However, it is pushed away from the blade surface under the impact of the slot jet, and then flows downstream along the mainstream direction after being accelerated. Near 10% span, that is, at the upper end of the slot, the slot jet flow is small. It separates and mixes with the trailing edge boundary layer to form a new separation. Since this separation is caused by the disturbance of the slot jet to the trailing edge separation, the separation range is small and the location is close to the downstream, so it has little impact on the flow above 20% span.

Figure 10.

Vorticity magnitude contours on S3 stream surfaces and 3D Streamlines when incidence is +9 deg (a) datum, (b) slot.

The yaw angle is resolved by the arc tangent ratio of the circumferential velocity to the streamwise velocity.

Figure 11 shows the yaw angle contours of the S3 stream surface at 20% chord downstream of the trailing edge. In the corner area of the datum cascade, a recirculation zone covering about 15% span appears, and a narrow trailing edge separation occurs above 20% span. In the corner area of the slotted cascade, the original separation area disappears and two new separations appear. The passage vortex formed between the suction surface leg of horseshoe vortex and the end wall boundary layer near the end wall (below 5% span). Due to the push of the slot jet, the passage vortex fails to mix with the trailing edge separation and fails to develop upward along the blade surface. The slot jet and trailing edge boundary layer form a vortex at about 10% span. The two separations failed to mix and develop under the splitting of the slot jet. Above 20% span, a wide trailing edge separation appears, which is the trailing edge separation of the 2D profile at this incidence (i=+9∘).

Figure 11.

Yaw angle distribution on S3 stream surface (20%c downstream the TE) when incidence is +9 deg (a) datum, (b) slot.