Fig.1

Schematic diagram for topology optimization of compressible flow based on variable density

Fig.2

Design domain and boundary conditions for four-channel problem

Fig.3

Comparison of topology optimization results for four-channel design domain

Fig.4

Design domain， mesh and initial flow field for shrink-expand channel

Fig.5

Topological optimized configuration and flow field for shrink-expand channel （objective is minimization of energy dissipation）

Fig.6

Topological optimized configuration and flow field for shrink-expand channel （objective is minimization of velocity decay）

Table 1

Performance comparison before and after shrink-expand channel optimization

Fig.7

Schematic diagram and mesh of design domain for two-dimensional cascade flow channel

Table 2

Boundary conditions of design domain for topology optimization of stator cascade flow channel

Fig.8

Convergence history of normalized objective function and evolution of topology configuration at 50% span

Fig.9

Comparison of entropy distribution before and after optimization in cascade flow channel at section of 50% span

Fig.10

Isentropic Mach number of blade surface before and after optimization on cascade flow channel at 50% span

Fig.11

Convergence process of objective-configurations in design domain at 10% span and 90% span

Fig.12

Comparison of stator before and after optimization

Table 3

Comparison of turbine performance indica-tors before and after blade topology optimization

Fig.13

Schematic diagram and mesh of rotor blade tip design domain

Fig.14

Distribution rules of total pressure loss coefficient-volume constraint at rotor blade tip Section 1

Fig.15

Curved blade tip configuration after topology optimization

Fig.16

Comparison of tip flow fields at 30%， 50%， and 70% axial chord positions of rotor blade before and after optimization

Fig.17

Schematic diagram of shape-topology para-meterized fluid topology optimization method

Fig.18

Shape-topology parameterization system

Fig.19

Computational performance at different grid numbers

Fig.20

Workflow of sampling-data acquisition

Fig.21

Multi-objective optimization flow based on deep surrogate model

Table 4

Initial conditions for design scenarios

Fig.22

Performance comparison of DNN surrogate model in low speed-high-load scenario

Fig.23

Static pressure ratio iteration and topology selection process

Fig.24

Non-dominated solution set distribution of total pressure loss coefficient-static pressure ratio

Fig.25

Comparison of flow fields for configurations before and after optimization