考虑振动非平衡的可压缩库埃特流动及其传热

新型近空间高超声速飞行器大多具有尖头薄翼的外形, 驻点下游机身附近的强剪切流动及气动加热具有显著的非平衡特征. 由于加热总量预估和实验测热数据辨识的需要, 工程上越来越关注强剪切非平衡流动及气动加热预测问题. 本文结合理论建模和直接模拟蒙特卡洛数值模拟, 研究了振动非平衡条件下的可压缩库埃特流动的气动力/热问题. 首先基于参考温度方法, 在量热完全气体模型下, 得到了可压缩库埃特流动参考温度的理论公式. 然后分析了振动非平衡过程对于参考温度和雷诺比拟关系的影响, 得到了表征振动非平衡强弱程度的无量纲判据, 并利用该判据构建了考虑振动非平衡效应的摩阻与热流预测理论. 最后用DSMC (direct?simulation?Monte?Carlo)计算数据对理论分析结果进行了验证与标定. 理论和数值结果表明, 振动非平衡效应会导致可压缩库埃特流动的摩阻减小, 但热流和摩阻仍然满足雷诺比拟关系, 只是比拟系数需要引入振动能传热影响的修正. 该研究可以加深对强剪切流动中振动非平衡效应的认识, 其中的非平衡流动判据也可进一步推广用于研究更为实际的气动加热问题. 

COMPRESSIBLE COUETTE FLOW AND ITS HEAT TRANSFER UNDER VIBRATIONAL NONEQUILIBRIUM EFFECTS

Most of the new-generation hypersonic cruise vehicles have sharp leading edges and thin wings, and the flow and heat transfer downstream the stagnation point are characterized by the strong shear effects and significant nonequilibrium effects. Because of the demand on the total heat load prediction and the experimental data identification,there is an increasing engineering interest in the strongly sheared nonequilibrium flow and aerodynamic heating problems. In this paper, the theoretical modeling method, as well as the direct simulation Monte Carlo(DSMC) method,is used to study the aerodynamic force and heating performance of the compressible Couette flow under the vibrational nonequilibrium effects. Firstly, based on the reference temperature method, a theoretical formula of the reference temperature for the compressible Couette flow is deduced under the calorically perfect gas model. Then, analyses are conducted of the vibrational nonequilibrium effects on the reference temperature and the Reynolds analogy. The dimensionless criterion for the vibrational nonequilibrium effects is proposed, and the criterion is further employed to design formulas for prediction of the skin-friction and heat transfer. Finally, the theoretical results are validated and calibrated by the DSMC results. Both the analytical and numerical results in this study indicate that, the vibrational nonequilibrium effects reduce the skin-friction of the compressible Couette flow, but meanwhile, the Reynolds analogy is still valid as long as the analogy ratio is corrected to take into account of the vibrational energy transfer. The present study could enrich our understanding of the vibrational nonequilibrium shear flow, and specifically, the nonequilibrium flow criterion could be extended to investigate more practical aerodynamic heating problems which significantly involve the thermal nonequilibrium effects.