Fig.1

Geometry of the first stage of GE-E3

Table 1

Boundary conditions

Fig.2

Validation for film cooling effectiveness on squealer tip

Fig.3

Validation for heat transfer coefficient on squealer tip without film holes

Fig.4

Configuration of the structural grid

Table 2

Mesh independence validation

Fig.5

Parameterization method for cooling hole outlets assisted by camber lines

Fig.6

Parameterization method for combined inclination of an oval hole

Table 3

Range of design variables

Fig.7

Update strategy of the candidate list

Fig.8

Evolutionary strategy

Fig.9

Flowchart of AHEA

Fig.10

Local search strategy of surrogate model

Fig.11

Hierarchical equivariant probability calculation based on non-dominated sorting

Fig.12

Flowchart of MAHEA

Table 4

Tests for convergence accuracy of single objective functions

Fig.13

Tests for convergence rate of single objective functions

Fig.14

Test results of bi-objective function ZDT1

Fig.15

Test results of tri-objective function DTLZ1

Fig.16

Automatic optimization framework

Fig.17

Distribution of samples in mixed optimization

Table 5

Results of variable optimization

Fig.18

Comparation of geometry structures

Fig.19

Structure of flow field on squealer tip

Fig.20

Distribution of jet streamline and vortex core on squealer tip

Fig.21

Distribution of film cooling effectiveness on squealer tip

Fig.22

Comparison of average film cooling effectiveness on squealer tip

Fig.23

Distribution of heat transfer coefficient on squealer tip

Fig.24

Comparison of average heat transfer coefficient on squealer tip

Fig.25

Distribution of leakage flow along axial chord length

Fig.26

Comparison of efficiency and total pressure loss