A New Segmented Suction Slot Design Based on the Performance of Compressor Cascade

Abstract

To develop an effective suction slot arrangement, computational fluid dynamics simulation software and a high subsonic compressor cascade were used to simulate different suction slots. Based on the effects of various suction slots on the cascade performance under various operating conditions, a novel segmented suction slot structure Seg₃ was proposed. The results of the study revealed that in the vicinity of the operating conditions ($\text{incidence}\le 4°$), a full-blade height suction slot should be installed at least 5% of the chord length downstream of the corner separation point to effectively remove the separation. For small and medium incidences, the best performance was observed for suction slot SS₅, which was located at 60% of the chord length downstream of the leading edge. Analyzing the effects of SS₅ and Seg₃ on the cascade performance revealed that when the incidence was less than 4°, the reductions in the total pressure loss coefficients for ζ_suc of SS₅ and Seg₃ both exceeded 8.2%. When the incidence was 4° or greater, the ζ_suc increased slightly for SS₅, whereas it decreased for Seg₃, and the ζ_suc was reduced. For a 3° incidence, for example, Seg₃ reduced the ζ_suc and passage blockage by 12.74% and 8.41%, respectively, and increased the static pressure rise coefficient by 18.55% from the baseline values. Thus, the segmented suction slot proposed in this paper outperformed conventional full-blade height suction slots.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Highly-loaded compressors have attracted considerable attention for use in aeroengine designs because they can achieve high-pressure ratios. However, the flow fields inside highly-loaded compressor are complex. The 3D corner regions near the blade suction side in a highly-loaded compressor tend to accumulate low-velocity fluids. Experimental studies [1–4] have revealed that with an increase in the aerodynamic load, the axial reverse pressure gradient increases, and more low-velocity fluids accumulate; these fluids adversely affect the performance of the entire compressor stage. Therefore, eliminating accumulations of the low-velocity fluids and controlling the corner separation are critical in developing highly-loaded axial compressors.

Numerous active and passive flow control methods are used in the aerospace industry to control the performance degradation caused by airflow separation inside compressors [4–6]. Among them, boundary layer suction technology exhibits considerable advantages. This technology is typically applied to aspirate low-velocity fluids near the end wall and reduce the flow loss [7]. The technology is typically adopted in stator passages. The main types of suction technology applied in fans/compressors are holes and slots.

In 1998, the US Air Force Scientific Research Bureau carried out large-scale model verification of the suction fan at Massachusetts Institute of Technology and completed the detailed design and test of the suction fan. Since then, the suction hole has been gradually studied in the fan/compressor. Research shows that [8], as the blade blowing and suction technology is applied to tests, when the tangential speed of the high-performance fan blade tip is 450 m/s, the pressurization ratio can reach 3.4. Through the verification of tests and computer numerical simulation analysis, the boundary layer suction hole technology has achieved its expected goal. Kerrebrock et al. [9] introduced the transonic/supersonic fan stage series. As the suction hole is adopted, when the tangential speed of the blade tip is 457.2 m/s, the pressurization ratio of the rotor can reach 3.7. The paper proposed aspirated compressors and revealed that the aspirated technology could aspirate low-velocity fluids and improve the pressurization capacity of compressors. Foreign research on the blowing/suction technology of compressor blades is based on the experimental demonstration stage, which is relatively mature.

At present, the researches on suction slots are also gradually developing. Gbadebo et al. [10] analyzed the effects of different suction slot positions on the corner region separation of the compressor blade suction surface. They revealed that these two positions exhibited strong capabilities of reducing the total pressure loss and decreasing the passage blockage. According to Gbadebo, Chen et al. [11, 12] comprehensively analyzed the effects of end-wall suction slot position on the cascade performance and concluded that the axial range of the slots should include the starting point of the corner separation. Researchers have also investigated the effect of the amount of gas suctioned by the suction slots on the cascades’ performance. Gmelin et al. [13] revealed that the total pressure loss decreased with an increase in the suction flow rate, and the static pressure increased. Moreover, a suction flow ratio of 1% was adopted in most studies [14, 15], because larger suction volumes consume more external energy. Therefore, to ensure that the results of this study can be compared, with previously published results, suction slots with a suction flow ratio of 1% were used to improve the cascade performance, and the 1% suction flow rate was obtained from the plenum outlet.

Researchers have also investigated the suction slot distribution. Chen et al. [12] proposed a segmented end-wall suction slot design. The authors believed that the formation of the three-dimensional corner separation in cascades is produced by the confluence of the suction side branch of the horseshoe vortex and the pressure surface branch of the adjacent blade in the blade passage. This phenomenon occurs under the pitch pressure gradient under the blade suction side/end-wall corner region. Based on the horseshoe vortex formation process, a segmented suction slot design was proposed. Studies have revealed that this design can reduce the total pressure loss in a cascade by 11.2% and increase the static pressure by 9.84%. Ma et al. [16] proposed a novel segmented suction slot design for blade suction sides and revealed that with increases in the incidence, the corner separation range near the suction side gradually expands along the span and chord directions. Furthermore, the separation point also continues to move forward, and before a stall occurs, this separation range always includes the corner region formed by the end-wall and the blade’s trailing edge. They then proposed a segmented suction scheme for the blade suction side. The study revealed that this design could increase the cascade stall incidence from 8° to 10°.

This study considered a high subsonic cascade, and the correlation between the position of the suction slot and the corner separation in the compressor cascade was discussed. A superior segmented suction slot design was proposed based on the performance characteristics of a suction slot with a full-blade height. This study achieved three primary objectives:

(1) A quantitative method was proposed to express the relationship between the corner separation point and the suction slot. Relationships between the optimal positions of the suction slots and the separation point were discussed for a variety of operating conditions

(2) The effects of the axial position of the suction slot on the cascade performance were analyzed for various incidences, and suggestions regarding the axial placement of the suction slot were provided

(3) A segmented suction slot design for the blade suction side that was based on the performance of a suction slot with a full-blade height was proposed

2. Axial Compressor Cascade and Suction Methods

A subsonic axial compressor cascade was used during this study. The cascade profile was derived from the NACA-65 K48 airfoil [11]. Chen et al. [11, 12] conducted aerodynamic experiments with the baseline using oil flow visualization technology in the high subsonic cascade experimental wind tunnel at the Institute of Propulsion Technology in the German Aerospace Center. The inlet of the wind tunnel was connected to a 40 mm $\text{width}\times 90\text{mm}$ (length) rectangular nozzle. The contraction ratio of the nozzle was 1 : 218, so the Mach number (Ma) of the cascade inflow could be accelerated to 0.7. The detailed aerodynamic and geometric parameters are presented in Section 2.1.

2.1. Compressor Cascade

The cascade had a designed Mach number of 0.67 and a Reynolds number of 560,000. Table 1 presents the actual geometric dimensions and the primary aerodynamic parameters used in the experiment. The parameters in the table are illustrated in Figure 1, which depicts the two-dimensional arrangement and crucial geometric and aerodynamic parameters. In the figure, $t$ represents the pitch, LE is the blade’s leading edge, and TE is the trailing edge. The measurement cross-section in the experiment was located 0.4 C downstream of the TE.

Table 1

Geometric and aerodynamic parameters of the compressor cascade [11].

Parameter	Value
Inflow Mach number ($\text{Ma}$)	0.67
Inlet airflow angle (${\beta }_1$)	132°
Outlet airflow angle (${\beta }_2$)	90°
Mounting angle ($\gamma$)	112.5°
Blade chord length ($C$)	40 mm
Full-blade height ($h$)	40 mm
Pitch ($t$)	22 mm

[figure(s) omitted; refer to PDF]

2.2. Introduction of the Suction Slot

At a large incidence, the boundary layer of the inner end wall of the cascade passage is pushed to the blade suction side under the high transverse pressure gradient, and a flow separation is formed in the corner region. Opening suction slots on the suction side of the blade can absorb the accumulated low-velocity fluids near the slots, which improves the flow field performance.

A full-blade height suction slot was investigated during this study. Figures 2 and 3 display schematics of the cascade with a slot. Figure 2 displays a 3D geometric model of the cascade with a suction slot and a plenum chamber. To simulate the actual nonuniform suction of the suction slot, actual suction blades were simulated inside the blades, and a plenum chamber was established. To ensure that the flow at the outlet of the plenum chamber did not affect the flow between the suction slot and the blade suction side, the length of the plenum outlet was extended to 0.5 h.

[figure(s) omitted; refer to PDF]

Figure 3 presents a two-dimensional schematic of the suction cascade. This study investigated the effects of different positions of the spanwise suction slot on the cascade performance. Therefore, the axial distance, $Z_{\text{SS}}$ (along the $z$-axis, with $\text{SS}$ representing the suction slot), from the center point (red dot in Figure 3) of the spanwise slot to the LE was used to describe the position of the suction slot. The width of the suction slot is represented by $W_{\text{SS}}$ ($W$ denotes width). In this study, $W_{\text{SS}}=0.01C$.

3. Numerical Simulation Method

3.1. Computational Domain and Boundary Conditions

The commercial software ANSYS CFX was used to perform numerical simulations. The IGG-Autogrid5 generated the calculation mesh. The calculation domain, boundary conditions, and meshing method are displayed in Figure 4. Considering that the blades of the axial compressor cascade were vertically symmetric, half of the blade was generated in the computational domain to reduce the computation costs. The solid wall in the flow field was defined as a no-slip boundary, while the upper surfaces of the passage, the suction slot, and the plenum chamber were defined as symmetry boundaries. The inlet was a total pressure boundary. The incidence was adjusted by changing the airflow angle. The static pressure at the outlet was set to 101325 Pa. To ensure that the outlet airflow was fully mixed, the outlet boundary was extended to 250% of the axial chord length downstream of the TE. The outlet of the plenum chamber was defined as a static pressure boundary. The suction flow was changed by adjusting static pressure, and a translation period was used for the periodic boundary.

[figure(s) omitted; refer to PDF]

To ensure that the $Y+$ value was less than 1, the element height of the first layer was set to 1e-6 m. The mesh had an expansion ratio in the boundary layer of 1.1, and the nodes were 33. To ensure the mesh quality, an O-shaped topology was used around the blade. To accurately capture the flow field, the LE and TE were densified. To ensure the grid quality and calculation accuracy, a butterfly topology was used for meshing inside the plenum chamber, and the mesh was locally densified around the suction slot. The locally adjusted mesh portions are presented in the enlarged views within Figure 4.

3.2. Mesh and Numerical Model Verification

The authors referred to the numerical simulations from Chen et al. [12] for the cascade parameters, and the SST k–ω model was used as the turbulence model. Grid independence verification is critical for ensuring the accuracy of results while conserving computing resources. In this study, eight sets of meshes were used for verification. The mesh set with the minimum number of nodes had 0.54 million nodes. The number of nodes increased along three directions (the meshes in the boundary layer were fixed). The increase in the number of nodes for each successive mesh was guaranteed to be approximately 600,000 (O-shaped meshes surrounded the blades, so achieving the same number was difficult). The final numbers of nodes were 0.54 million, 1 million, 1.63 million, 2.42 million, 2.98 million, 3.45 million, 3.91 million, and 4.43 million. The mass flow average total pressure loss coefficient $\zeta$ and the Ma were extracted at the measurement cross-section (40% of the axial chord length downstream of the TE) for the different mesh sets. The changes in $\zeta$ and Ma with changes in the numbers of nodes are displayed in Figure 5, which reveals that with increases in the number of nodes, $\zeta$ decreased gradually, and Ma increased gradually. For more than 3.45 million nodes, the values of $\zeta$ and Ma remained nearly unchanged. Thus, increasing the number of nodes past 3.45 million had only a limited effect on the cascade performance. Therefore, 3.45 million nodes (half-blade height) were used in the subsequent simulations. The $\zeta$ is a crucial parameter that represents the performance of the compressor cascade. It is defined by $$\begin{array}{}\text{(1)}& \zeta x,y,z=\frac{{\text{Pt}}_{\mathit{\text{in}}}-\text{Pt}x,y,z}{{\text{Pt}}_{\text{in}}-P_{\text{in}}},\end{array}$$where Pt is the total pressure, $P$ is the static pressure, the subscript in represents the inlet cross-section, and $x,y,z$ represents the set of local parameters.

[figure(s) omitted; refer to PDF]

Figure 6 presents comparisons between the numerical calculation results and the experimental data to verify the reliability of the numerical simulation method. The abscissae in the plots are both the dimensionless blade height, while ζ is in the left plot, and the outlet airflow angle is the ${\beta }_2$ in the right plot. The comparisons reveal that the flow loss could be captured by the simulations, especially its variations trend along the blade height direction. The loss was only slightly underestimated in the area near the cascade wall, which could be attributed to measurement errors in the flow field near the end wall during the experiments. Furthermore, the predications of the outlet airflow angle trend in the blade height direction were highly accurate, with only a slight overall overestimation, which had a limited effect on the flow performance estimations. Therefore, the numerical simulation methods were feasible for this study.

[figure(s) omitted; refer to PDF]

4. Analysis of the Simulation Results

4.1. Introduction of the Suction Scheme

Using boundary layer suction technology on the suction side of a blade can effectively absorb the low-velocity fluids near the walls [17, 18]. Studies have revealed that the axial positions of a suction slot considerably affect the flow loss reduction in a cascade [17]. However, limited quantitative studies have been conducted regarding the effects of the axial positions of suction slots on the aerodynamic performance of the cascade. In this study, a correlation was established between the axial position of the suction slot on the blade suction surface and the total pressure loss.

First, a design scheme for the suction slot was developed. Figure 7 displays a cross-sectional view of the cascade. Because both edges of the blade were thin, making a slot there takes work. The axial positions of the seven suction slots in the figure were set sequentially in the $Z$ direction. The $z$-axis represents the dimensionless axial distance in the cascade. The dimensionless axial chord length was equal to 1. The distances between the suction slots and the $y$-axis ranged from 0.2 to 0.8. The spacing between the slots was 0.1. The seven slots (marked in red in Figure 7), which were named SS₁–SS₇, started from an axial position of 0.2. As displayed in Figure 7, the axial distance between SS₁ and the $y$-axis was 0.2 C, and the axial distance from SS₂ to the $y$-axis was 0.3 C, the distances between the rest of the slots and the $y$-axis followed this pattern as well.

[figure(s) omitted; refer to PDF]

Part of the air flowed out from the suction slots when the boundary layer suction technology was used, so the effects of the suction slots should be considered. When calculating the total pressure loss of a cascade with suction slots, the corrected total pressure loss coefficient ${\zeta }_{\text{suc}}$ can be used: $$\begin{array}{}\text{(2)}& {\zeta }_{\text{suc}}=\frac{1‐\dot{m}\cdot {Pt}_{\text{in}}-{Pt}_{\text{out}}+\dot{m}\cdot {Pt}_{\text{in}}-{Pt}_{\text{ple}}}{{Pt}_{\text{in}}-P_{\text{in}}}.\end{array}$$

In Equation (2), subscript $\text{ple}$ denotes the outlet of the blade plenum chamber, subscript $\text{in}$ is the inlet section of the blade passage, and subscript $\text{out}$ is the outlet section of the blade passage. The $\dot{m}$ is the mass flow rate at the outlet of the plenum chamber, which could be obtained by dividing the flow rate at the outlet of the plenum chamber by the cross-sectional area of the flow field passage inlet. The readers should note that when this paper refers to the total pressure loss coefficient, the coefficient for a baseline cascade without suction slots is denoted by $\zeta$, while that for the cascade with a suction slot is denoted by ${\zeta }_{\text{suc}}$.

To obtain a correlation between the slot positions and the corner separation, the axial position coefficient $Z_{\text{SS}i}$ was used to describe the axial positions of the slots according to $$\begin{array}{}\text{(3)}& Z_{\text{SS}i}=\frac{Z_{\text{SS}}-Z_{\text{CS}}}{C}.\end{array}$$

In Equation (3), $Z_{\text{CS}}$ represents the distance between the starting point of the 3D corner separation region and the LE of the cascade under the corresponding operating conditions, and the value of subscript $i$ represents the different suction slots. $Z_{\text{CS}}$ is equal to 0.45 C under the 0° incidence design condition, as displayed in Figure 8.

[figure(s) omitted; refer to PDF]

As presented in Table 2, suction slots with negative axial position were located upstream of the starting position of the corner separation, while the other slots were located downstream of the starting position. For example, the negative value associated with SS₁ indicates that this slot was located upstream of the starting position of the corner separation and that its axial distance to the separation point was 0.25 C.

Table 2

Axial positions of the suction slots with respect to the separation point of the associated corner region.

Suction slot	SS1	SS2	SS3	SS4	SS5	SS6	SS7
$$Z_{\text{SS}i}$$	−0.25	−0.15	−0.05	0.05	0.15	0.25	0.35

4.2. Performance Analysis of the Full-Blade Height Suction Slots

Figure 9 displays the effects of the suction slots at various axial positions on the ${\zeta }_{\text{suc}}$ of the cascade under the 0° incidence design condition. The red dashed line represents the ${\zeta }_{\text{suc}}$ of the baseline, and the black mark represents the ${\zeta }_{\text{suc}}$ for the cascade with different suction slots. The blue dot in the figure represents the starting position of the corner separation region in the baseline. The values of ${\zeta }_{\text{suc}}$ in Figures 9–11 are all the average mass flow rates measured at the outlet cross-section and are expressed by $$\begin{array}{}\text{(4)}& \frac{\int {\zeta }_{\text{suc}}d\dot{m}}{\dot{m}}.\end{array}$$

[figure(s) omitted; refer to PDF]

The figures reveal that as the suction slot axial position changed from near the LE of the blade (SS₁) to near the TE of the blade (SS₇), the ζ_suc changes changed considerably, first increasing and then decreasing. For the suction slots that were upstream of the separation point of the corner separation, that is, SS₁-SS₃, the ${\zeta }_{\text{suc}}$ was greater than the baseline value (the red dashed line), and the cascade performance was adversely affected. For the suction slots that were downstream of the starting position of the corner separation, that is, SS₄–SS₇, the ζ_suc was less than the baseline value (the red dashed line). It first decreased and then increased, and its optimal location was at SS₅.

The results discussed above led to certain conclusions. First, the axial position of the full-span suction slot considerably affected the total pressure loss of the cascade. When the suction slot was located upstream of the separation point of the baseline, it adversely affected the performance of the cascade, leading to an increase in the ${\zeta }_{\text{suc}}$. According to Table 2, when a slot is located at 0.05 C downstream of the separation point of the baseline (SS₄, or $Z_{\text{SS}0}=0.05$) under the design conditions, the ${\zeta }_{\text{suc}}$ begins to decrease. The minimum value of the total pressure loss was reached at SS₅ ($Z_{\text{SS}0}=0.15$). At this location, the ${\zeta }_{\text{suc}}$ was reduced by 10.9%.

To explain these conclusions, it was critical to analyze the flow field. Figure 12 presents a comparison between the 3D flow fields of the baseline, the cascade with SS₁, and the cascade with SS₅ under the 0° incidence design condition. SS₁ and SS₅ are the two typical cases that had the largest and smallest total pressure losses, respectively. In the figure, a red line marks a suction slot on the blade suction side, and the limit streamlines are displayed on the wall. The extraction value of the blue three-dimensional iso-value surface is $v_z=-0.0001\text{m}/\text{s}$, which indicates that the airflow velocity within the range wrapped by the iso-value surface was negative along the $z$-axis, that is, the airflow through the iso-value surface was backflow, representing the airflow separation region. The contour of the $\zeta$ was extracted for the cross-section at 40% of the chord length downstream of the TE.

[figure(s) omitted; refer to PDF]

As shown in Figure 12(a), the starting position of the airflow separation in the baseline appeared at a distance equal to 45% of the chord length downstream of the LE. The flow field can be improved if the suction slots can absorb part of the separated gas. As displayed in Figure 12(b), when a suction slot on the blade suction side was located at a distance equal to 20% of the chord length downstream of the LE (SS₁), the three-dimensional flow separation area increased, typically along the z-axis, and the total pressure loss on the downstream portion of the blade also increased considerably.

Figure 12(c) shows that when the suction slot was located at 60% of the chord length downstream of the LE, the 3D corner separation region become considerably smaller in the $Z$ direction. The contour of the $\zeta$ on the downstream portion of the blade reveals that the pressure loss decreased and that the size of the high-loss area also decreased. These phenomena are crucial to improving the cascade performance.

The results discussed above also led to multiple conclusions. Suppose the suction slots are located upstream, far away from the separation point of the baseline. In that case, the airflow from the downstream part of the suction slot is sucked upstream, which causes significant backflow and intensifies the airflow separation. When the suction slot was located at a suitable position downstream of the separation point of the baseline, not only did the separation associated with the upstream suction slots nearly disappear, but the size of the airflow separation region downstream as well as the total pressure decreased.

To illustrate the relationship between the axial suction slot position and the corner separation, the effects of placing the suction slot at various axial positions on the $\zeta$ of the cascade were analyzed for 2° and 4° incidences. Figure 13 reveals that the starting positions of the 3D corner separation in the baseline for the 2° and 4° angles of attack were located at 32% and 15% of the chord length downstream of the LE, respectively.

[figure(s) omitted; refer to PDF]

Figure 10 displays the effects of placing the suction slot at various axial positions on the ${\zeta }_{\text{suc}}$ of the cascade at incidences of both 2° and 4°, respectively. The labels in the figure are the same as those in Figure 9. Figure 10(a) reveals that when the incidence was 2°, as the axial position of the suction slot moved from SS₁ to SS₇, the ${\zeta }_{\text{suc}}$ first decreased and then increased, and it reached a minimum value at SS₅, which result is consistent with that for the 0° incidence. However, when the suction slot moved backward to SS₃, the ${\zeta }_{\text{suc}}$ decreased to a value smaller than that of the baseline. This phenomenon can be attributed to the fact that for a 2° incidence, the starting position of the corner separation of the baseline moved forward to the blue dot, as displayed in Figure 10(a). At this stage, the ${\zeta }_{\text{suc}}$ decreased because the suction slot SS₃ was located behind the separation point. This situation also occurred for the 4° operating condition, as displayed in Figure 10(b). As the axial installation position of the slot moved from SS₁ to SS₇, the ${\zeta }_{\text{suc}}$ first decreased and then increased. Unlike for the 0° and 2° incidence, the ${\zeta }_{\text{suc}}$ reached the lowest value at SS₃. The total pressure loss decreased below the reference value when the suction slot was located at SS₂, just downstream of the reference corner separation point. This phenomenon confirms that when the suction slot was located downstream of the separation point in the baseline, the ${\zeta }_{\text{suc}}$ tended to decrease.

Conclusions could also be drawn from the previous discussion. At 2° and 4° incidences, when the slot was located downstream of the separation point of the baseline, and the axial distance from the separation point was 0.08 C and 0.07 C (i.e., $Z_{\text{SS}2}=0.08$ and $Z_{\text{SS}4}=0.07$), the ${\zeta }_{\text{suc}}$ exhibited a decreasing trend. When the incidence was 2° and 4°, the suction slots with the most significant decrease in the ${\zeta }_{\text{suc}}$ are suction slots that were SS₅ and SS₃ ($Z_{\text{SS}2}=0.28$, $Z_{\text{SS}4}=0.17$), which had pressure loss reductions of 8.15% and 14.41%, respectively. Suction slots SS₃, SS₄, and SS₅ exhibited certain advantages in reducing the total pressure loss of the cascade at 2° and 4° incidences. SS₄ and SS₅ considerably reduced the ${\zeta }_{\text{suc}}$ of the cascade at a 0° incidence.

The following segmented suction slot comprehensively considers the suction slot location advantages under several typical operating conditions. The advantages and characteristics of this type of structure are also discussed.

4.3. Performance Analysis of the Segmented Suction Slots

Figure 11 displays a schematic of the segmented suction slot on the blade suction side. To make the segmented suction slot comparable to the full-blade height suction slot, segments that were 33% of the blade height were placed at the original positions of SS₃, SS₄, and SS₅. The sum of the areas of the three cross-sections was equal to the cross-sectional area of the full-blade height suction slot. The suction flow rate on the outlet of the plenum was 1%. The study object when using the segmented suction slot was named Seg₃ (i.e., segmented suction with three slots). Figure 11 displays a schematic of the full-blade single-passage cascade. These settings were only intended to make the segmented suction slot intuitive. The calculation domain was still the single-passage half-blade height flow field, and the symmetry boundary condition was set for the 50% span.

Figure 14 presents the effects of suction slots SS₅ and Seg₃ on the total pressure loss at incidences of 0°–6° incidences. The upper portion of the figure shows the variations in the ${\zeta }_{\text{suc}}$ for SS₅, the middle portion presents the values of the ${\zeta }_{\text{suc}}$, and the lower portion depicts the variations in the ${\zeta }_{\text{suc}}$ for Seg₃. At minor incidences ($i<3°$), SS₅ and Seg₃ both exhibited considerable abilities to reduce the total pressure loss, especially at the designed operating condition (0° incidence) and at 3° incidence. For 0° and 3° incidence, SS₅ reduced the ${\zeta }_{\text{suc}}$ by 10.9% and 9.9%, respectively, and Seg₃ reduced the ${\zeta }_{\text{suc}}$ by 11.2% and 12.7%, respectively, with respect to the baseline values.

[figure(s) omitted; refer to PDF]

At incidences with less than 4°, the reductions in the total pressure loss for SS₅ and Seg₃ exceeded 8.2%, which represents a significant reduction. At $\text{incidences}\ge 4°$, the reductions in the ${\zeta }_{\text{suc}}$ were small, and the ${\zeta }_{\text{suc}}$ for SS₅ actually increased slightly. Seg₃ reduced the ${\zeta }_{\text{suc}}$ slightly at large incidences. Multiple conclusions could be drawn from the results discussed above.

At medium and small incidences, full-blade height suction slot SS₅, which was located downstream of the separation point of baseline’s separation point, could reduce the cascade’s total pressure loss. The segmented suction slot Seg₃ was proposed after considering that an appropriate selection of the suction slot position exhibited an excellent capability for improving the cascade performance. At large incidences, SS₅ did not improve the performance of the cascade. However, Seg₃ could reduce the total pressure loss in the cascade for large incidence. To further analyze the change of flow field characteristics, the details of three-dimensional flow fields at high incidences are given in Figures 15 and 16.

[figure(s) omitted; refer to PDF]

It is difficult to judge the stall condition of the cascade and the effect of the suction slot on the cascade performance only through the changed total pressure loss coefficient. Therefore, Figures 15 and 16 show the three-dimensional flow fields of the baseline cascade and the cascades with the SS₅, and Seg₃ at 6° and 7° incidences to analyze the effects of the suction slot on the stall characteristics. The blue three-dimensional iso-value surface indicates the airflow separation area. The contour of the $\zeta$ is extracted at a cross-section at 40% of the chord length downstream of the TE.

According to Figure 15, when the incidence increases to 6°, the suction slot does not significantly improve the accumulation of low-energy fluid. The total pressure loss on the downstream section of the blade’s trailing edge changes little, which indicates that the suction slots with different structures (SS₅ and Seg3) have a weak ability to remove an extensive range of low-energy fluid. When the incidence increases to 7°, the low-energy fluid in the baseline increases sharply, and the total pressure loss increases significantly. The flow field suddenly deteriorated at this time, indicating that the corner stall had occurred. For Figures 16(b) and 16(c), the full-blade high suction slot and segmented suction slot did not delay the occurrence of corner stall, and the sudden increase of separation area and the sharp increase of total pressure loss still occurred at the 7° incidence. Therefore, these two suction slots could not effectively improve the stall characteristic.

To discuss the performance advantages of segmented suction slot Seg₃, which was proposed after considering the effects of suction slot position, the compressor performance was quantitatively analyzed using multiple parameters, including the static pressure rise coefficient, the total pressure loss coefficient, and the blockage.

The static pressure rise coefficient is a critical parameter for evaluating compressor performance. It reflects the capability of the cascade and stator to increase the static pressure, expressed by $C_p$, according to $$\begin{array}{}\text{(5)}& C_{p}x,y,z=\frac{Px,y,z-P_{\text{in}}}{{Pt}_{\text{in}}-P_{\text{in}}}.\end{array}$$

The blockage evaluation method proposed by Khalid [19] was used to obtain the blockage distribution in the cascade passages. He proposed using the scalar $\nabla \rho v_m$ to evaluate the blockage; however, the local blockage boundary should be reflected on the plane perpendicular to the axial direction. Therefore, the gradient magnitude should be obtained from the gradient components of $\nabla \rho v_m$ on the axial plane in the span and circumferential directions. For a Cartesian coordinate system, this gradient can be expressed as ${\nabla \rho vm}_{x,y}$. Khalid revealed that after the blockage equation has been nondimensionalized, the contours equal to two are defined as the blockage boundary. The area with contours more significant than two is the blockage area. After nondimensionalization, the blockage boundary in this study was defined by $$\begin{array}{}\text{(6)}& \frac{{\nabla \rho v_m}_{x,y}}{{\rho }_{\text{in}}{v}_{\text{in},C}/C}=2,\end{array}$$where ${\rho }_{\text{in}}$ represents the average density at the inlet cross-section, $v_m$ is the velocity component of the airflow in the primary flow direction, and $v_{\mathit{\text{in}},C}$ is the average axial velocity at the inlet cross-section.

The blockage area in the passage cross-section at the TE is represented by $A_{\text{blo}}$, which denotes the extent of the blockage of the flow field passage.

Figure 17 displays a comparison between the flow fields of the baseline cascade and the cascades with SS₅ and Seg₃ at 3° incidence. In each image, the airflow in the blue three-dimensional iso-surface is the backflow, which represents the airflow separation area. A cross-section at 40% of the chord length downstream of the TE was considered. The contour of the $\zeta$ was extracted at this position. The passage blockage at the TE cross-section is represented by a gray area in Figure 18, where SS represents the suction side and PS represents the pressure surface. Table 3 summarizes the performance parameters of the three cases, which are used to analyze the cascade performance from Figure 17. Here, $\zeta$ represents the mass flow rate’s average total pressure loss coefficient as expressed in Equation (4). Furthermore, $C_p$ represents the average static pressure rise coefficient of the mass flow rate and is expressed by $$\begin{array}{}\text{(7)}& \frac{\int C_{p}d\dot{m}}{\dot{m}}.\end{array}$$

[figure(s) omitted; refer to PDF]

Table 3

Performance parameters of the baseline cascade and cascades with SS₅ and Seg₃.

Case	${\zeta }_{\text{suc}}$	$C_p$	$A_{\text{blo}}$ (cm2)
Baseline	0.09445	0.4678	2.033
SS5	0.08505	0.5426	1.893
Seg3	0.08242	0.5546	1.862

The bar graph in Figure 19 reveals the variations in the three performance parameters, ${\zeta }_{suc}$, $C_p$, and $A_{b\text{lo}}$, for cascades with SS₅ and Seg₃ relative to the baseline values and based on Table 3.

[figure(s) omitted; refer to PDF]

Figure 17 reveals that the 3D corner separation was effectively reduced from that of the baseline cascade because of the effect of full-blade height suction slot SS₅, especially since the separation upstream of the slot almost disappeared. The contour of the $\zeta$ and the blockage (Figure 18) reveals that the high loss in the core area of the total pressure loss decreased significantly and that the range of the maximum blockage in the pitch direction in the passage also decreased. Finally, with respect to the baseline values, ${\zeta }_{\text{suc}}$ was reduced by 9.95%, the passage blockage was reduced by 6.89%, and the static pressure rise coefficient increased by 15.99% (Figure 19).

Figure 17 reveals that the separation region decreased more for Seg₃ than for SS₅. The separation nearly disappeared within a distance equal to one-third of the blade span height from the end wall; this result can be attributed to the suction slot distribution characteristics. Although additional separations occurred near the middle of the blade span, the overall flow loss decreased considerably, especially the high flow loss in the core area of the total pressure loss. The range of the maximum blockage in the pitch direction in the passage also decreased markedly. Finally, with respect to the baseline values, the ${\zeta }_{\text{suc}}$ was reduced by 12.74%, the passage blockage was reduced by 8.41%, and the static pressure rise coefficient increased by 18.55% (Figure 19).

5. Conclusions

A high subsonic cascade was used as a case study to comprehensively investigate the effects of changing the axial position of a full-blade height suction slot on the cascade performance. The optimal axial position of the slot was quantitatively analyzed using the starting position in a corner region separation of the baseline cascade as a reference. The study produced three primary conclusions:

(1) At medium and small incidences, as the axial position of the slot changed from the front to the back of the blade surface, the total pressure loss first decreased and then increased. At 0° and 2° incidences, the optimal location of the suction slot was 60% of the chord length downstream of the LE (SS₅). Placing a suction slot at this location reduced the total pressure loss coefficient (${\zeta }_{\text{suc}}$) for the 0° and 2° incidences by 10.9% and 8.2%, respectively, from the baseline values. For a 4° incidence, the optimal location of the suction slot was 50% of the chord length downstream of the LE (SS₄); placing the suction slot at this location reduced the ${\zeta }_{\text{suc}}$ by 14.41% from the baseline value

(2) The relationship between the location of a slot and the corner separation point at different working conditions was also investigated. At incidences of 0°, 2°, and 4°, when the suction slot was located downstream of the separation point of the baseline cascade, ${\zeta }_{\text{suc}}$ decreased with $Z_{\text{SS}0}=0.05$, $Z_{\text{SS}2}=0.08$, and $Z_{\text{SS}4}=0.07$, respectively, and reached minimum values at $Z_{\text{SS}0}=0.15$, $Z_{\text{SS}2}=0.28$, and $Z_{\text{SS}4}=0.17$, respectively. At medium and small incidences, a full-blade height suction slot should be installed downstream of the corner separation point to achieve desired results. The slot should be located at least 0.05 C downstream of the separation point to consider the effects of various operating conditions. For the best performance, the full-blade height suction slot should be installed between 0.15 C and 0.28 C downstream of the corner separation point

(3) Based on the effect of the axial position of the full-blade height suction slot on the cascade performance, a segmented suction slot Seg₃ was proposed. Comparisons between Seg₃ and SS₅ revealed that when the incidence was less than 4°, the ${\zeta }_{\text{suc}}$ reductions were more than 8.2% for both SS₅ and Seg₃. When the incidence was 4° or greater, the reduction in ${\zeta }_{\text{suc}}$ was slight, ${\zeta }_{\text{suc}}$ increased slightly for SS₅, and Seg₃ reduced ${\zeta }_{\text{suc}}$ slightly at large incidences. For an incidence of 3°, SS₅ could reduce ${\zeta }_{\text{suc}}$ by 9.95% and the passage blockage by 6.89% from the baseline values, and it could increase the static pressure rise coefficient $C_p$ by 15.99% from the baseline value. However, because of its distribution characteristics, Seg₃ could nearly eliminate the separation within a distance equal to one-third of the blade span from the end wall. Therefore, ${\zeta }_{\text{suc}}$ and the passage blockage were reduced by 12.74% and 8.41%, respectively, and the $C_p$ increased by 18.55% from the baseline values

These nondimensional analysis results can be used to establish a standardized guide for the selection of the suction slot axial position. When designing suction slots for other axial compressor cascades, finding the position of the corresponding separation point for the same operating condition is necessary. The suction slot position can be then estimated using Conclusion 2. The conclusions of this study should be verified theoretically using numerous cascade models.

Acknowledgments

This research was funded by the Sichuan Natural Science Foundation for Distinguished Young Scholars (through grant no. 23NSFSC2925), by the Key Laboratory of Flight Techniques and Flight Safety, CAAC (through grant no. FZ2022KF02), and by the National Natural Science Foundation of China (through grant no. U2133209).

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