基于GKS的高超声速飞行器非巡航过程下流场/结构温度场一体化数值模拟方法研究

Non-cruise flight conditions have always been a key and complex issue in the research of hypersonic vehicles, during which the flow and fluid-thermal coupling show significant unsteadiness. Considering that gas-kinetic scheme (GKS) shows unique advantages in simulation of hypersonic flows, this project proposes a GKS-based synchronization method for fluid-thermal coupling in hypersonic flows during non-cruise conditions. Without losses of the merits of the original GKS, in order to reduce its computation and complexity, a novel GKS is constructed by simplifying the equilibrium state of the gas distribution function. The JFNK (Jacobian-free Newton-Krylov) algorithm is further employed to develop an efficient implicit GKS. For solving moving boundary problems which commonly exist in hypersonic flight, the original GKS is developed into a version in a non-inertial frame of reference and a version on moving grids. By using a synchronization algorithm, the BGK model is derived for the fluid-thermal coupled system and a generalized GKS is developed. On the above basis, for accurately simulating non-cruise conditions, the whole dynamic process is decomposed into three situations: attitude change, velocity change and height change. Then the dynamic mesh method, the non-inertial reference fame method and the source term method are respectively adopted to account for them. Finally, by considering them in combination and using the GKS-based synchronization method, the unsteady fluid-thermal coupling during non-cruise conditions is investigated. The research of this proposal can provide an advanced and useful tool for hypersonic aerodynamic design and also lay a technique foundation for aeroelastic analysis and thermal production.

非巡航过程是高超声速飞行器关键而复杂的飞行状态，该过程下流场及流固热耦合的非定常特征显著。鉴于气体动理学格式（GKS）在高超声速流动计算上展现的特有优势，本项目开展基于GKS的非巡航过程下流场/结构温度场一体化数值模拟方法研究。通过构造基于简化分布函数的高效隐式GKS，克服原始格式计算量大且对于高超声速复杂问题收敛率较低的缺点。建立非惯性系下和动网格系统下的GKS，将其应用范围拓展至马赫数和姿态变化等复杂动边界问题。基于一体化方法求解流固热耦合问题，构造针对统一耦合系统方程的BGK模型和相应的一体化GKS。分别采用非惯性系、动网格以及添加源项的方法来模拟非巡航过程中马赫数、姿态和高度变化，进而结合发展的一体化GKS，实现非巡航过程下流场/结构温度场耦合的精确模拟。本项目研究能为高超声速飞行器气动设计、热防护以及热气动弹性等问题提供先进的数值策略和技术基础。

流固热耦合是高超声速飞行器设计发展过程中的关键科学问题，而非巡航过程是其关键而复杂的飞行状态，该过程下流场及流固热耦合的非定常特征突出。本项目研究基于气体动理学格式（GKS）的高超声速飞行器非巡航过程下流场/结构温度场一体化数值模拟方法。构造出基于圆函数平衡态分布函数形式的隐式GKS-JFNK，显著降低计算复杂度及提高计算效率；针对非巡航过程下的变马赫数、变姿态等复杂动边界问题，构造出非惯性系和动网格系统下的GKS；在此基础上提出统一流固热耦合系统方程的BGK模型以及建立起相应的一体化GKS，最终实现高超声速飞行器非巡航过程下流场/结构温度场耦合的精确模拟。本项目研究成果能为高超声速飞行器气动设计、热防护和热气动弹性等问题提供理论和技术支撑。