*4.1.1. Loosely-coupled analysis strategy*

The loosely-coupled analysis strategy for the fluid-thermal-structural coupling problem on the basis of the static trajectory is shown in **Figure 11**. ∆*t* F is the time step in flow-field calculation, ∆*t* TS is the time step in thermal-structure volumetric coupling calculation of solid; ∆*t* C is the time step in fluid-solid coupling surficial calculation and can be set as several times the time step in thermal-structure volumetric coupling calculation of solid, that is ∆*t* C = *n* ∙ ∆*t*TS ( *n* = 1, 2, 3, ⋯).

The loosely-coupled analysis strategy can be summarized as:

**1.** At the initial time *t*<sup>0</sup> , an initial constant temperature or temperature field distribution as well as the initial load and displacement constraints is given to the solid structure first. Then the wall temperature and displacement of the solid structure are transferred to the fluid domain by the information transfer method of the interface. The wall temperature is used for the boundary condition in the flowfield calculation, while the displacement is used to update the flow-field grid;

*4.1.2. Tightly-coupled analysis strategy*

By introducing sub-iteration into each computational time step of coupling in the looselycoupled analysis strategy, the tightly-coupled analysis strategy for fluid-thermal-structural

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The coupling analysis strategy is to discretize the sustained dynamic trajectory into a set of a

As for the fuselage-engine-integrated design, the waverider forebody is utilized for pre-compression in order to produce lift and at the same time obtain the flow rate required by the engine inlet. In this case, both the waverider forebody and the cowl leading edge are on windward side where the most severe aeroheating takes place. As shown in **Figure 13**, the forebody precompression oblique shock and the cowl leading edge shock may intersect with each other, which leads to shock interaction and thus aggravates aeroheating near the cowl leading edge, even more severe than that at the nose leading edge. Case 1 is defined as over-ideal state, in which the incident shock enters the cowl and the cowl leading edge is under the farfield freestream condition. Case 2 is defined as ideal state, in which the incident shock arrives exactly at the inlet cowl and interacts with the shock at the cowl leading edge; Case 3 is defined

coupling problems based on the static trajectory is shown in **Figure 12**.

**Figure 11.** Loosely-coupled analysis strategy for fluid-thermal-structural coupling problem.

**4.3. Fluid-thermal-structural coupling analysis of inlet cowl leading edge**

**4.2. Coupling analysis strategies based on dynamic trajectory**

finite number of quasi-static trajectories in chronological order.


Modeling and Analysis of Fluid-Thermal-Structure Coupling Problems for Hypersonic Vehicles http://dx.doi.org/10.5772/intechopen.70658 123

**Figure 11.** Loosely-coupled analysis strategy for fluid-thermal-structural coupling problem.

#### *4.1.2. Tightly-coupled analysis strategy*

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 loosely-coupled analysis strategy for the fluid-thermal-structural coupling problem on

the time step in fluid-solid coupling surficial calculation and can be set as several times the

time step in thermal-structure volumetric coupling calculation of solid, that is ∆*t*

TS is the time step in thermal-structure volumetric coupling calculation of solid; ∆*t*

well as the initial load and displacement constraints is given to the solid structure first. Then the wall temperature and displacement of the solid structure are transferred to the fluid domain by the information transfer method of the interface. The wall temperature is used for the boundary condition in the flowfield calculation, while the displacement is

**2.** By calculating the steady flowfield in the fluid domain based on the imposed boundary condition of temperature and the updated flow-field grid, the wall heat flux and the wall

**3.** The wall heat flux and the wall pressure of the steady flowfield are transferred to the solid domain as the heat load and force load respectively for the thermo-structural dynamic

**4.** Transient thermo-structural dynamic calculation can be done in the solid domain based on the imposed heat and force load to obtain the response parameters of the solid struc-

the fluid domain by the information transfer method of the interface. The wall temperature is used for the boundary condition for flowfield calculation, while the displacement is used

**6.** When the calculation in one coupling time step has been completed, the calculation will

calculation of solid by the information transfer method of the interface;

tural heat/force coupling as the time advances from *t*<sup>0</sup>

**5.** The wall temperature and displacement of the solid structure at *t*<sup>0</sup>

continue in the next time step until all the time steps are covered.

F

, an initial constant temperature or temperature field distribution as

to *t*<sup>0</sup>

 + ∆*t*C and finally reaches

 + ∆*t*C are transferred to

is the time step in flow-field calcula-

C is

C = *n* ∙ ∆*t*TS (

the fluid-solid coupling interface.

122 Advances in Some Hypersonic Vehicles Technologies

*4.1.1. Loosely-coupled analysis strategy*

used to update the flow-field grid;

pressure can finally be obtained;

to update the flow-field grid;

tion, ∆*t*

*t*0  + ∆*t*C;

*n* = 1, 2, 3, ⋯).

**1.** At the initial time *t*<sup>0</sup>

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

the basis of the static trajectory is shown in **Figure 11**. ∆*t*

The loosely-coupled analysis strategy can be summarized as:

By introducing sub-iteration into each computational time step of coupling in the looselycoupled analysis strategy, the tightly-coupled analysis strategy for fluid-thermal-structural coupling problems based on the static trajectory is shown in **Figure 12**.

#### **4.2. Coupling analysis strategies based on dynamic trajectory**

The coupling analysis strategy is to discretize the sustained dynamic trajectory into a set of a finite number of quasi-static trajectories in chronological order.

#### **4.3. Fluid-thermal-structural coupling analysis of inlet cowl leading edge**

As for the fuselage-engine-integrated design, the waverider forebody is utilized for pre-compression in order to produce lift and at the same time obtain the flow rate required by the engine inlet. In this case, both the waverider forebody and the cowl leading edge are on windward side where the most severe aeroheating takes place. As shown in **Figure 13**, the forebody precompression oblique shock and the cowl leading edge shock may intersect with each other, which leads to shock interaction and thus aggravates aeroheating near the cowl leading edge, even more severe than that at the nose leading edge. Case 1 is defined as over-ideal state, in which the incident shock enters the cowl and the cowl leading edge is under the farfield freestream condition. Case 2 is defined as ideal state, in which the incident shock arrives exactly at the inlet cowl and interacts with the shock at the cowl leading edge; Case 3 is defined

force/thermal load of the external flowfield are taken into consideration and the wall radiation effect is also considered with the surface emissivity *ε* = 1.0 in the coupling calculation and analysis. A pressure load *p*∞ = 1197 Pa is imposed on the inner wall, the fixed support is selected for

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It can be intuitively seen from **Figure 14** that under the effect of the striking of the extremely densified heat flux due to shock interaction, the heat rapidly accumulates within the structure nearby the struck point, causing a leading increase in the temperature of the point. As the heat accumulates at the point over time, the structure temperature is also increasing and at the same time the heat is gradually transferred to internal area in depth. Hence, the temperature distribution is also gradually expanding from the struck point to internal structure area in depth. Simultaneously, the amplitude of overall temperature distribution within the structure declines much if wall radiation effect is taken into account because it effectively limits the heat entering the internal structure. **Figure 15** shows that the earliest stress concentration occurs within the structure near the struck point on the wall. The stress distribution is also gradually expanding to the internal structure area in depth over time. Simultaneously it is also shown that the amplitude of overall stress distribution inside the structure declines if wall radiation

both ends of the model.

effect is taken into account.

**Figure 14.** The structure temperature within the inlet cowl leading edge model.

**Figure 15.** The structural stress within the inlet cowl leading edge model.

**Figure 12.** Tightly-coupled analysis strategy for fluid-thermal-structural coupling problem.

**Figure 13.** The shock interaction phenomena near the inlet cowl leading edge.

as under-ideal state, in which the incident shock outside has not reached the cowl and the cowl leading edge is under the downstream shock freestream condition.

The cylindrical leading edge model is used as the inlet cowl leading edge model, which utilize titanium alloy (Ti-6Al-2Sn-4Zr-2Mo) as the material. Sustained coupling calculation time of 11 seconds is selected for the fluid-thermal-structural coupling calculation and analysis of the engine cowl leading edge model; the loosely-coupled analysis strategy is employed for calculation and its fluid-solid surficial coupling calculation time step adopts the adaptive strategy. High temperature chemical non-equilibrium gas model is adopted for the calculation of the external fluid domain, non-catalytic wall is selected as the wall catalytic condition. The initial temperature for calculation of thermal-structural coupling within the solid domain is 300 K with zero initial stress and the reference temperature of thermal stress is 300 K. The aerodynamic force/thermal load of the external flowfield are taken into consideration and the wall radiation effect is also considered with the surface emissivity *ε* = 1.0 in the coupling calculation and analysis. A pressure load *p*∞ = 1197 Pa is imposed on the inner wall, the fixed support is selected for both ends of the model.

It can be intuitively seen from **Figure 14** that under the effect of the striking of the extremely densified heat flux due to shock interaction, the heat rapidly accumulates within the structure nearby the struck point, causing a leading increase in the temperature of the point. As the heat accumulates at the point over time, the structure temperature is also increasing and at the same time the heat is gradually transferred to internal area in depth. Hence, the temperature distribution is also gradually expanding from the struck point to internal structure area in depth. Simultaneously, the amplitude of overall temperature distribution within the structure declines much if wall radiation effect is taken into account because it effectively limits the heat entering the internal structure. **Figure 15** shows that the earliest stress concentration occurs within the structure near the struck point on the wall. The stress distribution is also gradually expanding to the internal structure area in depth over time. Simultaneously it is also shown that the amplitude of overall stress distribution inside the structure declines if wall radiation effect is taken into account.

**Figure 14.** The structure temperature within the inlet cowl leading edge model.

as under-ideal state, in which the incident shock outside has not reached the cowl and the cowl

The cylindrical leading edge model is used as the inlet cowl leading edge model, which utilize titanium alloy (Ti-6Al-2Sn-4Zr-2Mo) as the material. Sustained coupling calculation time of 11 seconds is selected for the fluid-thermal-structural coupling calculation and analysis of the engine cowl leading edge model; the loosely-coupled analysis strategy is employed for calculation and its fluid-solid surficial coupling calculation time step adopts the adaptive strategy. High temperature chemical non-equilibrium gas model is adopted for the calculation of the external fluid domain, non-catalytic wall is selected as the wall catalytic condition. The initial temperature for calculation of thermal-structural coupling within the solid domain is 300 K with zero initial stress and the reference temperature of thermal stress is 300 K. The aerodynamic

leading edge is under the downstream shock freestream condition.

**Figure 12.** Tightly-coupled analysis strategy for fluid-thermal-structural coupling problem.

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**Figure 13.** The shock interaction phenomena near the inlet cowl leading edge.

**Figure 15.** The structural stress within the inlet cowl leading edge model.

In general, the aerodynamic force and thermal load have a great impact on the inlet cowl leading edge, which suffices to cause thermal and dynamic damage to thermal protection structures despite the short imposing time in actual flight, presenting severe challenge for material selection and structure design of thermal protection. As for the air-breathing hypersonic vehicles, the impact of shock interaction is common in the surrounding flowfield. Therefore, thermal protection design of local leading edges (structures such as the tail and rudders) on the windward side wrapped by the nose shocks should be done carefully besides the nose and the engine cowl leading edge.
