【作者】 成娟；

【导师】 黄明恪；

【作者基本信息】 南京航空航天大学 ， 流体力学， 2001， 博士

【摘要】 气体流场的数值模拟（CFD）方法，由于具有高效、快捷以及费用低的特点，在飞机设计中正得到越来越多的重视与应用。如何模拟具有复杂外形飞行器的有粘、有旋、非线性的真实流场是当今CFD方法的发展方向。 本文的主要工作是研究如何运用非结构网格对复杂流场进行Navier-Stokes方程计算。实现N-S方程计算的困难在于：1．网格生成。2．N-S方程数值解法。3．湍流模型。 围绕以上几方面的问题，本文作了较为系统的研究，主要的研究工作有： 1．提出一种非结构网格自适应的新策略。这种新的自适应方法不同于传统的自适应法如加点法、修改背景网格法。它在网格需要加密处，布置一些小的三角形单元，并以这些单元的边作为初始推进波阵面的一部分。在推进过程中，小单元附近自然生长出尺寸逐渐变大的单元。数值算例显示新的自适应方法是非常成功的。 2．根据物理学中的弹簧原理，提出一种半非结构网格生成的新方法，即挤压法。它首先在流场内运用推进波阵面技术生成无粘非结构网格；然后利用弹簧原理，移动各网格点的位置，在物面附近挤出一附面层厚度的距离；再在附面层内利用结构网格生成质量较高的大长宽比的网格。挤压法的优点是能实现附面层内外网格的光滑过渡。 3．将Jameson的格心有限体积法推广到N-S方程中，成功地实现了非结构网格上的三维有粘流场流动计算。 4．为了湍流模型方程数值格式的稳定性，湍流模型的源项须作小心的处理。本文对各种源项的性质作了详尽的理论分析，从理论上推导出每种源项应采取的数值处理方法。 5．在非结构网格上构造格心显式格式求解Baldwin-Barth—方程湍流模型，并运用Von Neumann稳定性分析方法，给出了格式稳定性条件。实际湍流数值模拟结果理想。更多还原

【Abstract】 With the property of efficiency, rapid speed and low cost, computational fluid dynamics methods are paid more attention on and are used more on the aircraft design. How to simulate viscous, rotate and nonlinear true flow field around complex aircraft is the development direction of CFD. The main research of this paper is how to simulate complicated flow by using Navier- Stokes equation. The difficulties of numerical computation are as follows: 1. Mesh generation. 2. Numerical method of N-S equation. 3. Turbulence models. Focusing on these questions, relatively systematic research is given in this paper. The main achievements of work are: 1. A new method for adaptive refinement of unstructured grids is presented. This new adaptive method is different from traditional adaptive methods such as adding point, modiI~ying background grid. Some small triangle units are arranged on the place where mesh needs to be refined, and all the sides of these units are regarded as a part of the initial front. During the advancing process, near the above-mentioned units, the cells are naturally generated from small to large. Numerical examples show the success of the new method. 2. Based on the spring principle of physics, a new method of generating semi- unstructured grids is proposed. At first, inviscid unstructured grids are generated by the advancing front. Then moving the position of cell nodes by the spring principle, a distance of boundary layer thickness is squeezed out near the surface of wall. At last, high aspect ratio structured grids of good quality are created in the boundary layer field. The advantage of this new method is that it can ensure a smooth transition from a viscous highly stretched mesh to an inviscid regular mesh. 3. We extend Jameson cell-center finite volume method to N-S equation ,3D viscous flow numerical simulation is successfully carried out on unstructured grids. 4. The source terms in turbulence equations need to be discretized correctly in order to obtain a stable numerical scheme. In this paper, the recommendation of how to treat the source term is gained by the detailed theoretical analysis done on a kind of source terms. 5. An explicit finite difference scheme is constructed to simulate Baldwin-Barth one-equation turbulence model. By using Von Neumann analysis method, its stability condition is obtained. The result of turbulent simulation is satisfactory.更多还原