Fig.1

Modeling process of L-shaped endwall groove based on function superposition

Fig.2

Sketch of domain mapping relationship

Table 1

Design parameters of L-shaped endwall groove and their normalization method

Fig.3

Definition of L-shaped endwall groove in normalized orthonormal domain

Fig.4

Definition of L-shaped endwall groove in real endwall domain

Fig.5

Cascade geometry

Table 2

Geometric and aerodynamic parameters of cascade

Fig.6

Computational domain and mesh

Fig.7

Calculated and measured results for flow field characteristics

Fig.8

Numerical and experimental results for spanwise distributions of total pressure loss coefficient and outlet flow angle at 0.4cz downstream of trailing edge

Fig.9

Optimization strategy

Table 3

Range of design variables during DOE stage

Fig.10

Distribution of objective functions during optimization process

Table 4

Design parameters and relative variation of objective functions for Cases A-C

Fig.11

L-shaped grooves of Cases A-C

Fig.12

Comparison of incidence characteristics for baseline cascade and Pareto-optimal cases

Fig.13

Vortical structures extracted by Q=7×107 s-2 isosurface in baseline cascade and Case B

Fig.14

Limiting streamlines on walls， vortex core lines， streamlines on planes cross vortex， and reversed-flow regions（Uz /U1=-0.001 isosurface） in baseline cascade and Case B

Fig.15

Distributions of low-velocity and high entropy production regions in baseline cascade and Case B

Fig.16

Normalized vorticity contours on planes cross inter-passage grooves of different controlled cascades

Fig.17

Axial distribution of normalized viscous entropy generation rate and blockage area at OP1

Fig.18

Limiting streamlines and spanwise wall shear stress coefficient on blade suction side of different controlled cascades at OP2

Fig.19

Axial distribution of normalized viscous entropy generation rate and blockage area at OP2

Fig.20

Schematic diagram for flow control effects of L-shaped endwall groove

Table 5

Range of design parameters for sub-design space Γ

Fig.21

Primary and total-effect sensitivity indices of design parameters at different conditions

Fig.22

Variation of cascade aerodynamic performance parameters with groove pitchwise location D

Fig.23

Velocity contours， limiting streamlines on wall， vortex core lines and reversed flow regions in controlled cascades with different D

Fig.24

Variation of cascade aerodynamic performance parameters with groove depth Hdepth， width of upstream pitchwise groove W1 and length of upstream pitchwise groove L1

Fig.25

Normalized pitchwise vorticity contours on plane cross upstream grooves with different groove depth Hdepth， width of upstream pitchwise groove W1 and length of upstream pitchwise groove L1

Fig.A1

Definition of upstream pitchwise groove in normalized orthonormal domain

Table A1

Shape-defining functions of upstream pitchwise groove

Fig.A2

Definition of inter-passage streamwise groove in normalized orthonormal domain

Table A2

Shape-defining functions of inter-passage streamwise groove