Calculation Model of Temperature Response of Active Cooling Lattice Sandwich Panel for Thermal Protection
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摘要: 针对点阵夹层结构主动热防护问题，建立了夹层结构面板和芯体导热与冷却剂对流耦合的非稳态传热理论模型，利用有限体积法离散控制方程并在MATLAB中进行了迭代求解；模型首次考虑了面板与夹芯杆之间的收缩热阻，并利用分离变量法得到了收缩热阻的近似解析解；基于单胞模型和周期性边界条件，模拟得到了模型所需的表面对流传热系数hb和hfin；最后，选取多单胞计算工况进行数值模拟和理论模型对比，并讨论了收缩热阻对模型预测精度的影响。结果表明：理论模型能够准确预测夹层结构及内部流体的温度变化，理论与仿真之间的最大误差不超过1%；随着外加热流密度不断增大，忽略收缩热阻使得计算结果造成的误差不断增大；与数值模拟相比，理论模型可显著减少计算时间并节省计算资源，尤其适用于非均匀、非稳态复杂热载荷下点阵夹层结构的温度响应计算。Abstract: Aiming at the active thermal protection with lattice sandwich structure, an unsteady heat transfer theoretical model which couples facesheet and core heat conduction and coolant convection in the sandwich structure was established, the model equations were discretized by finite volume method and solved iteratively in Matlab; the constriction thermal resistance between the facesheet and the lattice strut was considered for the first time in the model, and the approximate analytical solution of the constriction thermal resistance was obtained using the method of separation of variables; based on the unit-cell model and periodic boundary conditions, the heat transfer coefficients hb and hfin required by the model were first obtained by numerical simulation. Finally, a case study with a multi-cells structure was carried out to compare the numerical and theoretical results, and the influence of constriction thermal resistance on the prediction accuracy was discussed. The results show that the theoretical model can accurately predict the temperature variation of the sandwich structure and the internal fluid, and the maximum deviation between theory and simulation is less than 1%. As the external heat flux increases, the error of theoretical prediction increases when the constriction resistance is ignored. Compared with the numerical simulation, the theoretical model can significantly reduce the calculation time and save calculation resources, thus it is especially suitable for actively cooled lattice sandwich structure subjected to complex, non-uniform and unsteady thermal load.
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图 1 金字塔型点阵金属夹芯结构的强制对流换热示意图
Figure 1. Schematic of forced convection heat transfer of pyramidal lattice metal sandwich structure
图 2 点阵夹层结构及内部流体的离散示意图
Figure 2. Discrete diagram of lattice sandwich structure and internal fluid
图 3 周期性流动传热数值模拟：(a) 计算域及边界条件；(b) 网格
Figure 3. Numerical simulation of periodic flow and heat transfer: (a) computational domain and boundary conditions; (b) mesh
图 4 不同Red下夹芯杆表面的对流换热系数
Figure 4. Heat transfer coefficient on the surface of lattice strut under different Red
图 5 求解收缩热阻的等效模型
Figure 5. Equivalent model for solving constriction thermal resistance
图 6 含多个单胞点阵夹层结构数值模拟计算域及边界条件
Figure 6. Numerical simulation domain and boundary conditions for multi-cell lattice sandwich structure
图 7 加热面平均温度随网格数量的变化曲线
Figure 7. Variation curve of the average temperature of heating surface with the number of meshes
图 8 RLV再入过程中表面的入射热通量随时间的变化曲线
Figure 8. Incident heat flux profile with re-entry time on the RLV surface
图 9 结构最大温度与流体出口温度的变化曲线：(a) 结构最大温度；(b) 流体出口温度
Figure 9. Variation curves of the maximum temperature of the sandwich structure and the outlet temperature of fluid with time: (a) maximum temperature of the sandwich structure; (b) outlet temperature of fluid
图 10 不同热流密度下结构的最大温度
Figure 10. The maximum temperature of the structure under different heat flux
图 11 不同流体进口速度下收缩热阻随导热率的变化曲线
Figure 11. Variation curves of constriction thermal resistance with thermal conductivity under different fluid inlet velocities
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