【作者】 李晨辉； 高振勋； 郭培旭； 蒋崇文；

【Author】 Li Chenhui;Gao Zhenxun;Guo Peixu;Jiang Chongwen;School of Aeronautic Science and Engineering,Beihang University;Laboratory of Aero-thermal Protection Technology for Aerospace Vehicles, China Aerospace Science and Technology Corporation;

【机构】 北京航空航天大学航空科学于工程学院； 中国航天科技集团航天飞行器气动热防护实验室；

【摘要】 由Wilcox提出的动量厚度雷诺数与最大涡量雷诺数之间的关系式被广泛应用于转捩模型边界层动量厚度的当地化建模中,但其在可压缩流动中的适用性有待进一步研究。通过求解可压缩平板边界层的自相似解,对超声速边界层中涡量雷诺数与动量厚度雷诺数之间的关系进行了分析,研究发现超声速流动中动量厚度雷诺数与最大涡量雷诺数之间依然保持正比关系,但其比例系数与不可压时相差较大。在此基础上,利用大量自相似解结果建立了以涡量雷诺数最大值处马赫数、静温与壁温之比为自变量的修正关系式。随后,研究了流向压力梯度对前述关系的影响,结果表明在常见的压力梯度范围内,忽略压力梯度造成的误差不会超过10%。最后,将建立的动量厚度雷诺数修正关系式应用于γ-Reθ模型的转捩触发函数Fonset中,获得了适用于超声速流动的γ-Reθ转捩模型,利用其对高超声速平板边界层转捩实验开展数值模拟研究,转捩预测结果与实验结果符合较好,验证了本文动量厚度雷诺数修正关系式的可靠性。更多还原

【Abstract】 The correlation of momentum thickness Reynolds number and maximum vorticity Reynolds number proposed by Wilcox is widely used in the localization of momentum thickness in transition model.However, its applicability in compressible flow needs further research. The correlation is study by solving the self-similar solution of compressible boundary layer equations. It is found that the correlation of momentum thickness Reynolds number and maximum vorticity Reynolds number is still proportional, but the coefficient is quite different from that in incompressible flow. On this basis, a modified correlation with Mach number at the maximum of vorticity Reynolds number and the ratio of wall temperature to temperature at the maximum of vorticity Reynolds number as independent variables is established. The influence of pressure gradient on the above relationship is analyzed and the results show that the error caused by neglecting the pressure gradient will not exceed 10% within the usual range. Finally, the modified momentum thickness Reynolds number correlation is applied to improve the γ-Reθ transition model for compressible flow. Simulations on boundary layer transition of a flat plate is carried out. The predicted results by the improved γ-Reθ model show a good agreement with experimental data in different hypersonic conditions, which demonstrates that the modified momentum thickness Reynolds number correlation is reliable.更多还原