基于端壁L形凹槽的扩压叶栅角区分离控制

doi:10.7527/S1000-6893.2023.29206

Abstract

Abstract:

To overcome the shortcomings of current vortex generator techniques used to control corner separation in compressors， we investigate the mitigation of corner separations using the streamwise vortex generated by the L-shaped endwall groove in a high-speed compressor cascade. First of all， a convenient and universal parametric modeling method for the L-shaped endwall groove has been proposed by introducing the standard modeling space and function superposition strategy， and the L-shaped endwall groove optimization was conducted based on this method. The simulated flow fields of the baseline cascade and a Pareto-optimal case have been compared. It was found that the groove separation vortex generated by the L-shaped groove could effectively block the endwall cross flow， cut off the supply of low momentum endwall fluid to the corner region， and therefore significantly mitigated the reverse flow in the corner region and avoid the formation of the corner separation vortex， remarkably improving the cascade performance within a wide range of incidence. Calculated results of different Pareto-optimal cases have been compared. The results show that the strength of the groove separation vortex determines the control effect of the groove on the endwall cross flow and the severity of additional loss and blockage caused by the groove， and thus is the key factor influencing the control effect of the L-shaped endwall groove. Secondly， the influence of design parameters on the L-shaped endwall groove and its mechanism have been analyzed through the combined use of the Sobol indices-based sensitivity analysis method and conventional control variate method. It was found that the control effect of the endwall groove was significantly influenced by four design parameters including the pitchwise location of the groove， groove depth， the width and length of the upstream groove. The pitchwise location of the groove determined the distance between the groove separation vortex and suction-side corner region， while the other three mainly influenced the strength of the groove separation vortex. Finally， a guideline for selecting design parameters of the L-shaped endwall groove has been summarized based on the above analyses.

Key words: compressor cascade, corner separation, L-shaped endwall groove, groove separation vortex, design parameter

CLC Number:

V231.3

Bo WANG, Yanhui WU, Lingju HUANG, Zixu WANG. Corner separation control in compressor cascade based on L-shaped endwall groove[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(10): 129206.

Figures/Tables 34

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Fig.A1

Table A1

Shape-defining functions of upstream pitchwise groove

函数名		函数表达式	表达式区间
切向控制函数 $f Y 1 Y$	$L 1 > 0.5 W 2$	0	$Y < D - L 1$
		$0.5 c o s 2 π W 2 (Y + L 1 - D) - 0.5$	$D - L 1 ≤ Y ≤ D - L 1 + 0.5 W 2$
		-1	$D - L 1 + 0.5 W 2 < Y < D + 0.5 W 2$
		$0.5 c o s 2 π W 2 (Y - D) - 0.5$	$D + 0.5 W 2 ≤ Y ≤ D + W 2$
		0	$Y > D + W 2$
	$L 1 ≤ 0.5 W 2$	0	$Y < D - L 1$
		$L 1 W 2 c o s π L 1 (Y + L 1 - D) - L 1 W 2$	$D - L 1 ≤ Y ≤ D$
		$0.5 c o s 2 π W 2 (Y - D) - 0.5 + L 1 W 2 c o s 2 π W 2 (Y - D + 0.5 W 2) - L 1 W 2$	$D < Y < D + 0.5 W 2$
		$0.5 c o s 2 π W 2 (Y - D) - 0.5$	$D + 0.5 W 2 ≤ Y ≤ D + W 2$
		0	$Y > D + W 2$
流向控制函数 $f Z 1 Z$		0	$Z < - W 1$
		$0.5 c o s 2 π W 1 Z - 0.5$	$- W 1 ≤ Z ≤ 0$
		0	$Z > 0$

Table A1

Fig.A2

Table A2

Shape-defining functions of inter-passage streamwise groove

函数名		函数表达式	表达式区间
流向控制函数 $f Z 2 Z$	$L 2 > 0.5 W 1$	0	$Z < - 0.5 W 1$
		$0.5 c o s 2 π W 1 (Z + 0.5 W 1) - 0.5$	$- 0.5 W 1 ≤ Z ≤ 0$
		$0.5 c o s π L 2 (Z + L 2) - 0.5$	$0 < Z ≤ L 2$
		0	$Z > L 2$
	$L 2 ≤ 0.5 W 1$	0	$Z < - 0.5 W 1$
		$L 2 W 1 c o s 2 π W 1 (Z + 0.5 W 1) - L 2 W 1$	$- 0.5 W 1 ≤ Z ≤ 0$
		$L 2 W 1 c o s π L 2 (Z + L 2) - L 2 W 1$	$0 < Z ≤ L 2$
		0	$Z > L 2$
切向控制函数 $f Y 2 Y$		0	$Y < D$
		$0.5 c o s 2 π W 2 (Y - D) - 0.5$	$D ≤ Y ≤ D + W 2$
		0	$Y > D + W 2$

Table A2

References 30

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设计参数	无量纲化方式
上游切向凹槽宽度w₁	W₁=w₁/c_z
上游切向凹槽长度l₁	L₁=l₁/s
通道内流向凹槽宽度w₂	W₂=w₂/s
通道内流向凹槽长度l₂	L₂=l₂/c_z
凹槽切向位置（通道内凹槽与叶片中弧线之间的距离）d	D=d/s
凹槽深度h_depth	H_depth=h_depth/δ

参数	数值
弦长 c/m	0.04
弯角φ/（°）	48
安装角γ/（°）	22.5
设计进气角β_1d/（°）	42
设计出气角β_2d/（°）	6
设计偏转角Δβ_d= β_1d-β_2d/（°）	36
展弦比h/c	1
栅距/弦长s/c	0.55
来流马赫数Ma₁	0.67
雷诺数Re₁	5.6×10⁵

设计变量	取值范围
W₁	［0.015，0.2］
L₁	［0，1］
W₂	［0.07，1］
L₂	［0，1.2］
D	［0，1］
H_depth	［0.02，0.5］

方案	设计参数						目标函数相对变化量
方案	W₁	L₁	W₂	L₂	D	H_depth	Y_p_，1/%	C_p_，2/%
A	0.2	0.153 8	0.433 0	1.162 5	0	0.497 8	-20.64	+14.62
B	0.2	0.207 2	0.387 9	0.973 7	0.002	0.473 8	-19.64	+17.06
C	0.174 8	0.267 0	0.371 0	0.927 4	0	0.495 6	-17.69	+17.94

设计变量	取值范围
W₁	［0.050 2，0.2］
L₁	［0，0.5］
W₂	［0.085，0.5］
L₂	［0.4，1.4］
D	［0，0.5］
H_depth	［0，0.5］

Corner separation control in compressor cascade based on L-shaped endwall groove

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