二维非定常N-S方程及两方程湍流模型耦合求解技术研究

【作者】 成水燕；

【导师】 李杰；

【作者基本信息】 西北工业大学 ， 流体力学， 2006， 硕士

【摘要】 现代飞行器设计迫切需要计算流体力学为其提供准确、高效和实用的气动力数据以及流场分析工具,数值求解Euler方程已无法满足现代飞行器设计过程中对气动力特性模拟的精度要求。从理论上讲,求解N-S方程可以比较真实地模拟流动的粘性效应,提供比较准确详实的流场信息。计算机软、硬件技术日新月异、计算流体力学数值方法日益发展完善,使数值求解N-S方程组成为可能。 本文主要发展了计算翼型跨音速定常及非定常粘性绕流的数值模拟方法。基于雷诺平均的思想,出现在RANS方程中的雷诺应力项一般采用统计意义下的湍流模型进行封闭。文中湍流模型分别采用B-L零方程模型及k-ε、k-ω两种线性涡粘两方程模型,对N-S方程的几种数值求解方法进行了探讨。 在空间离散上,基于有限体积法,采用迎风型通量矢量分裂类Van Leer格式,并引入三阶MUSCL插值方法和连续可微的van Albada通量限制器,使格式具有高阶精度,且具有良好的稳定性和收敛性;在时间推进上,分别采用显式四步Runge-Kutta和隐式LU-SGS推进方法,对主控方程与湍流模型方程进行耦合求解,虽然本文工作侧重于定常绕流的数值模拟,但从原理上说,本文所开发的LU-SGS定常计算程序只需略做修改即可实现非定常流动模拟;边界条件采用虚拟网格技术作为统一的边界处理方式,有效地提高了编程和计算效率。 飞行器定常、非定常气动力的准确数值模拟,特别是跨音速范围内的数值求解及研究,一直以来都是飞行器设计工作者面对的重要研究课题。本文主要针对NACA0012、RAE2822翼型的定常粘性流场进行数值模拟;在此基础上,以NACA0012翼型为例,对非定常粘性流场进行了数值求解。计算网格采用贴体结构粘性网格,其中非定常算例采用了刚性运动网恪的处理方法。文中对比分析了不同方法、不同湍流模型之间的差异,获得了比较理想的计算结果,验证了本文数值求解技术的可行性以及计算程序的正确性。更多还原

【Abstract】 In modern aircraft design, there is a pressing demand for accurate, efficient and applied aerodynamic data and computational analysis tools. However, the Euler equations are not satisfied all the requirement for simulating the precision of aeroelastic problems. It’s necessary to solve N-S equations to simulate viscous effects, offer more accurate and more detailed flow-fields information. It is possible to solve N-S equations with the improvement of the hardware and software in computer fields, and the development of numeric methods in computational fluid dynamics domains.The present work is mainly focused on developing airfoils numerical simulation methods for steady and unsteady transonic flow. With the numerical solution of RANS equations, the applications of B-L zero-equation 、 k-ε and k-ω two-equation linear eddy turbulence models are discussed.On the basis of a finite volume method, the spatial discrete scheme about the convection terms of N-S equations: the Van Leer scheme of flux vector splitting, is studied. To get higher order accuracy、well stability and astringency, the MUSCL interpolation function and the continuous differential van Albada limiter are applied for Van Leer. In this paper, two time stepping schemes, explicit four-stage Runge-Kutta scheme and implicit LU-SGS scheme, are employed to solve the governing equations. Boundary conditions are treated by adopting "ghost" cells, thecomputational efficiency is improved and the program’s complexity is reduced, too. In aircraft design, accurate numerical simulation for steady and unsteady flows.especially for transonic flows, is a crucial problem for designers. To confirm the validity and reliability of developed flow solvers, test cases of steady viscous flows around NACA0012 and RAE2822 airfoils, are given in this paper. On the base of steady computation, unsteady viscous flows about NACA0012 airfoil, are simulated. The structured viscous grid is used. The unsteady viscous motorial grid is fixed relative to airfoils. Numerical results are in good agreement with the experimental data. The method and the procedure presented in this dissertation are verified.更多还原