**4. Modeling and analysis of fluid-thermal-structural coupling problem**

During the sustained flight of an actual hypersonic vehicle within the atmosphere, the strong two-way coupling of aerothermal environment with thermal response within solid structures causes the heat distribution in the form of transient temperature field. It not only has dynamic effects on the properties of solid structures also causes thermal stress due to the temperature gradient. Meanwhile, the resultant thermal strain from the thermal stress influences the heat distribution through the deformation of the solid structures. The large structural deformation even affects the aerodynamic forces/heat in the external flowfield. On the other hand, the aerodynamic forces lead to the structural stress and structural within solid structures, which can also affect aerodynamic forces/heat in the external flowfield in the form of structural deformation.

The fluid-thermal-structural coupling model is shown in **Figure 10**. The volumetric coupling of the aerodynamic forces and aerodynamic heat of the flowfield within the fluid is described by unified fluid governing equations, which is solved by computational fluid dynamics (CFD) to obtain the parameters of aerodynamic forces/heat. The thermal load (wall heat flux *q*) and force load (wall pressure *p*) are imposed on the solid through the fluid-solid coupling interface. Within the solid, the thermal response is described by governing equations of heat conduction, while the stress/strain are described by governing equations of thermoelastics.

**Figure 10.** Fluid-thermal-structural coupling model.

to optimize the integrated design of thermal protection and to study new concepts and methods of thermal protection by accurately predicting and analyzing the temporal and spatial distribution characteristics and the transmission of heat within the vehicle solid

**Figure 9.** The temperature distribution of the I-I section plane within the solid structure. (a) *t* = 25 s, (b) *t* = 55 s, (c) *t* = 100 s,

The preliminary analysis and research on coupling characteristic and influencing factors of the hypersonic fluid-thermal coupling problem reveal the spatial-temporal distribution characteristics of the fluid-solid heat transfer coupling and the influence of wall radiation effect on the sustained flight conditions. There is a close coupling between the aeroheating of the flowfield and the heat transfer of the structure. The heat distribution and transfer within the structure change with the dynamic trajectory, which displays the spatial and temporal characteristics of multi-physics coupling. The integrated analysis method and the program platform

structure for guidance.

(d) *t* = 150 s, (e) *t* = 180 s, and (f) *t* = 210 s.

120 Advances in Some Hypersonic Vehicles Technologies

Considering the effects of the temperature-deformation coupling, the parameters within the solid can be obtained by solving the governing equations of heat conduction and thermoelastics with HyCCD platform. The temperature condition (the wall temperature *T*) and structural deformation condition (the surface displacement **u**) are provided for the fluid through the fluid-solid coupling interface.

### **4.1. Coupling analysis strategies based on static flight trajectory**
