Fig.1

NACA0012 airfoil fluid field mesh

Fig.2

Buffet lift coefficient curves at 5.0° angle of attack with different mesh amounts

Table 1

Mesh parameters for mesh independence verification

Table 2

Comparison of 5.0° angle of attack buffet simulation results with Ref.［22］

Fig.3

Comparison of buffet lift coefficient curves for 5.0° angle of attack， Mach number 0.7

Table 3

Verification of time independence in simulation for 5.0° angle of attack， Mach number 0.7

Fig.4

5.5° angle of attack airfoil transonic buffet lift coefficient curve

Fig.5

Periodic changes in transonic buffet flow field

Fig.6

Schematic diagram of skin vibration

Fig.7

Block diagram of system under forced vibration

Fig.8

Block diagram of a system under fluid-structure interaction

Fig.9

Single-degree-of-freedom pitch airfoil structural model

Table 4

Dimensionless parameter value for pitch airfoil structure

Fig.10

Comparison of lift coefficient curve results from single-degree-of-freedom pitch airfoil fluid-structure interaction simulation at Ma=0.7， 4.5° angle of attack， ks =0.13

Table 5

Buffet lift coefficient amplitude and reduced frequnce of single-degree-of-freedom pitch airfoil fluid-structure interaction simulation at Ma=0.7， 4.5° angle of attack and kb =0.13

Fig.11

Two-degree-of-freedom airfoil structure model

Table 6

Dimensionless parameter value for two-degree-of-freedom airfoil structure

Fig.12

Comparison of control effects with different scale factors

Fig.13

Comparison of control effect of different delay times

Fig.14

Lift coefficient， skin vibration position and drag coefficient curves at P=0.006 and 1/4T delay time

Fig.15

Control effect for different skin vibration zone lengths

Fig.16

Effect of skin vibration position on control performance

Fig.17

Buffet response before and after control under forced vibration

Fig.18

Lift coefficient curve for buffet control under fluid-structure interaction

Fig.19

Buffet response before and after control under fluid-structure interaction

Fig.20

Mach number and streamline diagram of transonic buffet flow field of airfoil

Fig.21

Fluid-structure interaction and structural response to forced vibration before control

Fig.22

Sink and float displacement PSD analysis before control

Fig.23

Structural response of fluid-structure interaction and forced vibration after control

Fig.24

Root mean square of pressure coefficient fluctuations on the upper wing surfaces before and after control

Fig.25

Space-time contour of the upper surface pressure coefficient before and after control

Table 7

Comparison of shock wave moment and separation zone variation before and after control

Fig.26

Phase relationship between skin movement and shock wave movement/separation zone movement at different delay time controls

Fig.27

Flow separation under different delay time controls