基于动态变形网格的非定常粘性流动数值分析

【作者】 黄守智；

【导师】 李杰；

【作者基本信息】 西北工业大学 ， 流体力学， 2005， 硕士

【摘要】 飞行器的定常和非定常气动力的准确数值求解,特别是跨音速范围内的准确数值求解及研究,一直以来都是飞行器设计工作者必须面对的重要研究难题。本文主要对亚音速、跨音速和超音速定常和非定常粘性绕流的数值模拟进行深入的研究。 利用代数生成法中的沿物面边界法向外推法和结合源项修正技术的偏微分方程生成法共同生成高质量的贴体正交粘性网格。以此作为初始网格,运用无限插值法(TFI)生成任意时刻的非定常动态变形网格。非定常动态变形网格的变形过程与初始网格的生成毫无关系,它维持了初始网格的整体特征,在流场剧烈变化的区域内的网格由最小程度的扭曲变形而得到。尤其重要的是,在靠近物面的区域尽量保持了网格的固定,并允许靠近远场的网格扭曲变形,或至少是在流场变化不明显的小梯度范围内变形。 对于定常和非定常绕流,本文均将Navier-Stokes方程在中心有限体积法离散格式下,利用以Runge-Kutter迭代法为内迭代的双时间推进法进行求解。所谓双时间推进指同时采用真实时间步和虚拟时间步,即在每个真实时间步上采用虚拟时间进行定常迭代,从而不但使时间迭代具有二阶精度,计算时间大大缩短,而且非定常与定常程序相差不大,使程序修改简洁、方便。湍流计算采用了Baldwin-Lonax代数紊流模型。运用当地时间步长和隐式残值光顺等加速技术,加速了收敛过程;用虚拟边界改进了边界域的处理,提高了效率。 以NACA0012、RAE2822、NACA64A010翼型为例,进行亚音速、跨音速定常和非定常粘性绕流数值模拟,计算结果同实验结果进行比较,吻合良好,验证了本文方法及程序的正确性更多还原

【Abstract】 In aircraft design, efficacious and accurate numerical simulation for steady or unsteady flow, especially for transonic flow is a crucial problem for designers. And the research of this dissertation is focused on how to efficaciously accurately simulate numerically the unsteady subsonic and transonic viscous flows.Solving the elliptic grid generation together with an algebraic method marching along the normal-to-wall direction, viscous grids around complex geometries are generated. By using TFI of displacements, we can get the unsteady viscous grid in any time. And the grid deformation process becomes completely independent of the generation of the initial grid; an important feature of the deforming grid procedure is that it must maintain the overall quality of the initial grid by introducing minimal distortion of the cells in the regions where the flow is likely to be changing rapidly. It is particularly important to keep the grid as rigid as possible in the near-wall regions and allow cell distortion towards the far-field, or at least in the regions of low gradients where the flow is not changing rapidly.The steady and unsteady viscous flow solvers based on Jameson’s cell-centred finite volume method, and Jameson’s dual method with Runge-Kutter scheme as inner iteration scheme have been development in this dissertation. In dual time method, there are real time and the pseudo-time, at each real time step marches the solution in a pseudo-time to steady state through an explicit time marching scheme, and the equation have two-order accuracy in time. We can make the solver more laconic and spend less time to get the numerical result. Baldwin-Lomax turbulence model is implemented in Navier-Stokes flow solver. In order to efficacious simulate the Navier-Stokes flow, some standard convergence acceleration techniques, such as local time stepping and implicit residual smoothing, and "ghost" cells which make complex boundary conditions simply have been used.To confirm the validity, effectivity and reliability of developed flow solvers, testcases of steady/unsteady subsonic and transonic flow of NACA0012、 RAE2822、 NACA64A010 airfoils. The result of flow field computation is good agreement with experiment; the method and the procedure presented in this paper are verified.更多还原