基于浸没边界法的雨滴作用下微型扑翼飞行器数值模拟方法研究

This project aims to develop an efficient computational platform for simulating flapping-wing micro air vehicle (MAV) under complex rain conditions by combining the immersed boundary method (IBM), diffuse interface (DI) method and the block-structured adaptive mesh refinement (AMR) technique. In the numerical platform, a new IBM method will be proposed to accurately deal with the gradient boundary condition of the order parameter and chemical potential in the DI method, which overcomes the difficulty faced by the IBM in dealing with the Neumann conditions; to effectively track the interface of rain drops, a mass-conserved DI method will be presented; based on the IBM and the DI method and by introducing the order parameter, vorticity and physical locations of moving boundaries as indicator for grid refinement, a block-structured AMR technique will be presented. This project innovatively develops and combines the IBM, the DI method and the block-structured AMR technique to build an efficient numerical platform for effective simulation of flapping-wing MAV with rain effects, which provides an advanced numerical tool and powerful technological support for evaluating the aerodynamic performance and flight safety of MAV.

针对雨滴作用下微型扑翼飞行器动边界流动问题，耦合浸没边界法、扩散界面法和块结构自适应网格技术，发展有效求解含有多相流的动边界问题数值模拟方法。基于壁面单侧物理量修正思想，提出能够精确满足多相流模拟中相变量和化学势梯度边界条件的浸没边界法，从而有效处理雨滴在微型扑翼飞行器表面的边界条件；发展能满足质量守恒的扩散界面法，实现雨滴界面位置的有效追踪；结合浸没边界法和质量守恒扩散界面法，综合相变量、涡量和动边界等作为指示因子并应用高阶守恒型插值方法，发展具有一致收敛性的二维和三维块结构自适应网格技术。本项目深入发展耦合浸没边界法、扩散界面法和块结构网格技术，并创新性的将之结合，建立有效模拟雨滴作用下微型扑翼飞行器多相流动边界流动的耦合算法，能够为复杂环境下微型飞行器气动性能和飞行安全的评估提供先进的数值模拟方法和有力的技术支撑。

雨滴作用下微型扑翼飞行器多相流流固耦合这一关键科学问题，涉及到了流体力学、多相流动力学、固体力学以及结构和材料等多学科交叉，相关的数值模拟方法并不成熟。本项目针对雨滴作用下微型扑翼飞行器动边界流动问题，在浸没边界法、扩散界面法和自适应网格技术等三方面进行了积极的探索。提出了能满足第二类边界条件的浸没边界法、发展了能满足质量守恒和保持界面形状的扩散界面方法，建立块结构自适应网格算法和程序。通过模拟液滴撞击液膜、拉普拉斯定律、单个扑翼、蜻蜓飞行、液滴与翼型相互作用、液滴与圆球相互碰撞等多相流问题、复杂外形和动边界问题的数值模拟，验证了算法的正确性。这些研究工作为深入研究雨滴作用下微型扑翼飞行器多相流流固耦合问题提供了一定的研究基础，也为相关的科学工程问题建立了有效的数值模拟方法和工具。