钝头体中的广义雷诺比拟关系

钝头体壁面的摩阻和热流分布规律不同,平板流动中的雷诺比拟关系在钝头体壁面失效. 文章在前期高超声速广义雷诺比拟理论研究工作的基础上,利用数值仿真的方法对不同外形和来流参数条件下的钝头体广义雷诺比拟关系开展进一步研究. 通过建立钝头体绕流边界层的理论分析模型,得到了钝头体壁面雷诺比拟系数的线性分布预示公式. 采用数值求解 N-S 方程的方法,计算了圆柱和幂次体壁面的摩阻和热流以及二者之间的比拟系数. 通过与前期数值和理论结果对比,以及计算收敛性和网格无关性检验,对数值方法进行了验证. 通过在不同雷诺数 ($Re_\infty = 3.98\times 10^2 \sim 1.59\times 10^6$) 和马赫数 ($M_\infty = 3\sim 12$) 条件下的计算结果对比分析雷诺比拟系数的分布,总结了钝头体中广义雷诺比拟关系受外形和来流条件的影响,评估了广义雷诺比拟理论的适用性. 研究发现,在较高雷诺数条件下,离驻点较远的下游 ($\theta > 60^\circ$) 部位,雷诺比拟系数的分布不同程度地偏离理论预示的线性规律. 相比于圆柱外形,幂次体壁面的雷诺比拟系数分布的线性规律相对较好,其分布斜率略低于圆柱壁面的结果. 研究表明,如果针对实际外形和雷诺数进行适当修正,可以提高广义雷诺比拟关系的预示精度. 

GENERAL REYNOLDS ANALOGY RELATION ON BLUNT-NOSED BODIES

The classical Reynolds analogy relation fail on blunt-nosed bodies, as the distributions of skin frictions on curved wall surfaces differ from that on heat fluxes. With a theoretical research background on hypersonic Reynolds analogy relations, numerical simulations are presented in this paper to study the general Reynolds analogy relation on blunt-nosed bodies, as circular cylinder and power-law body, under different incoming flows. A linear relation of Reynolds analogy is obtained by theoretical analysis on the boundary layer along those surfaces. Also, numerical methods are applied to obtain solutions of N-S equations, from which skin frictions and heat fluxes and their analogy coefficients around cylinders and power-law bodies are calculated. The methods are validated by comparing the distribution of Reynolds analogy coefficients and the stagnation point heat transfer rate with former numerical and theoretical results. The convergence and grid independence are verified for the TVD method. The variation of Reynolds analogy relations are investigated in the range of $Re_\infty = 3.98\times 10^2 \sim 1.59\times 10^6$ and $M_\infty = 3\sim 12$. The present study shows that the general Reynolds analogy relation predicts the ratio between skin frictions and heat fluxes on regimes near the stagnations point for hypersonic flows. Downstream the stagnation point of circular cylinders (where $\theta > 60^\circ$), the Reynolds analogy relation deviates from the theoretical linear relationship in varying degrees with the growing of Reynolds number. Numerical results demonstrate that, comparing with the general Reynolds analogy relations on circular cylinders, Reynolds analogy coefficients are lower and fit linear distributions better for power-law bodies. Analyses indicate that modifications based on the shape of noses or the Reynolds number may improve the accuracy of theoretical predictions.