表征高超声速绕流稀薄度的广义判据及其应用研究

As a hypersonic flow transits from continuous to more and more rarefied, classical aerodynamic force/heating prediction theories based on the continuum hypothesis become invalid gradually. Due to the complex physical factors involved, it is very difficult to establish systematic analytic theories in this transition flow regime. As a result, numerical methods and empirical fitting formula are excessively relied in the engineering practice. In the applicant's earlier studies, a feasible way has been found to carry on theoretical analyses in this flow regime. A rarefaction criterion, named Wr, has been introduced based on a theoretical modeling study of the non-Fourier aero-heating on the stagnation points of sharpened noses. An effective bridge function with physical meanings has also been built based on Wr to predict the stagnation point heat fluxes. In the present project, the theoretical modeling tradition will be inherited to extend the physical meanings of Wr to the downstream region of the stagnation point and to the field of aerodynamic force analysis. Generalized rarefaction criteria will be derived to characterize the aerodynamic force/heating features in hypersonic rarefied flows over bodies, to theoretically find the aerodynamic force/heating prediction formula for the whole flow regime, and finally to establish a systemic engineering theory framework. The Direct Simulation Monte Carlo (DSMC) method will also be employed to verify the conclusions of the analytical method. The expected results of this project will have both high academic significance and application value.

高超声速绕流从连续态到稀薄态的过渡过程中，基于连续介质假设的经典气动力/热预测理论逐渐失效。由于涉及诸多复杂物理因素，在过渡领域内很难建立系统的解析理论，目前工程上主要依赖数值方法和拟合公式。申请者在前期研究中，已找到一条在该领域内建立解析理论的道路。我们通过模型理论分析研究了尖化前缘驻点区域的非线性气动加热特征，提出了一个衡量稀薄气体效应影响的判据Wr，并基于Wr构建了具有物理意义的驻点热流预测桥函数。在当前项目中，我们将继续采用模型理论分析的手段，尝试把参数Wr的物理意义向驻点下游区域以及气动力研究领域进行推广，寻找表征高超声速绕流稀薄度的广义判据；同时结合直接模拟蒙特卡洛（DSMC）数值结果验证，研究高超声速稀薄流动中气动力/热随稀薄度广义判据的变化特征，构建从连续到稀薄整个流动领域内的气动力/热预测公式，形成系统的工程理论框架体系。该研究同时具有较高的学术意义和重要的应用价值。

本项目是我们前期项目研究结果的深化和扩展。在前期研究中，我们基于non-Fourier传热模型，在高超声速微钝前缘驻点推导出一个具有实际物理意义的稀薄流动判据Wr。本项目的研究结果发现，该判据具有更广的物理意义和应用范围。首先，我们基于non-Fourier传热模型和non-Newtonian剪切模型，发现判据Wr同样可以用来表征高超声速平板前缘的流动稀薄度，预测稀薄气体效应对热流和摩阻分布的影响，我们进一步构建了热流-摩阻的广义比拟关系；其次，我们研究了钝头体下游弯曲壁面的热流和摩阻分布，以及稀薄气体效应的影响，发现此时仍然存在热流-摩阻的广义比拟关系。这样，我们基于该判据把基于层流平板边界层假设的经典Reynolds比拟关系，推广至稀薄流动条件和弯曲壁面都适用的广义Reynolds比拟关系。另外，我们也进一步研究了高超声速尖前缘流动中稀薄气体效应和非平衡真实气体效应的耦合问题，发现稀薄流动判据Wr在预测非平衡真实气体效应对驻点气动加热影响中也有关键作用，我们建立了驻点气动加热受稀薄气体效应和非平衡真实气体效应的解析预测算式，并对该模型理论结果向驻点下游区域的推广进行了讨论。这些研究把驻点附近气动加热研究中提出的稀薄流动判据推广应用于驻点下游区域的气动力-热研究之中，这个基于非线性本构关系提出的特征参数确实是表征高超声速绕流稀薄度的广义判据，具有重要的学术意义和应用价值。我们部分研究结果已在航天工程单位得到应用，其中一个合作研究项目获得军队科技进步二等奖（本项目负责人排名3/10）。