The rotational energy of diatomic gases would be activated by the process of intermolecular collisions in high-temperature hypersonic flows. In this paper, a multi-temperature nonlinear coupled constitutive model has been proposed for simulating the transfer of energy between translational and rotational motions in hypersonic non-equilibrium flows. In this model, the nonlinear coupled constitutive equations are modified by introducing a rotational energy relaxation model and a changeable viscosity ratio related to local temperature. To confirm its accuracy, the new model is applied to investigate steady shock wave structures and high-speed gas flows around a cylinder and across a flat plate. The computational results are compared with the multi-temperature Navier–Stokes (NS) equations, the direct simulation Monte Carlo (DSMC) solutions, and the experiment data. The final results show the new model would reproduce the NS results at low Knudsen numbers but behave quite differently from the NS results as the non-equilibrium degree is enhanced. The new model is in better agreement with the DSMC solutions and the experimental data than the NS solutions in the far-from-equilibrium regions, which demonstrates the potential of the new relaxation model in the simulation of hypersonic non-equilibrium flows.

中文翻译：

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高超音速双原子气流非线性耦合本构关系的多温度模型

双原子气体的旋转能量将通过高温高超音速流中的分子间碰撞过程而被激活。本文提出了一种多温度非线性耦合本构模型，用于模拟高超声速非平衡流中平移运动与旋转运动之间的能量传递。在该模型中，通过引入旋转能量松弛模型和与局部温度有关的可变粘度比来修改非线性耦合本构方程。为了证实其准确性，该新模型被用于研究稳定的冲击波结构以及高速气体在气缸周围和平板上的流动。将计算结果与多温度Navier–Stokes（NS）方程，直接模拟Monte Carlo（DSMC）解决方案进行比较，和实验数据。最终结果表明，新模型将以低Knudsen数重现NS结果，但随着非平衡度的提高，其行为与NS结果有很大不同。与NS解决方案相比，该新模型与DSMC解决方案和实验数据在远离平衡区域的一致性更好，这表明新松弛​​模型在高超声速非平衡流模拟中的潜力。