两方程湍流模型的应用研究

【作者】 张强；

【导师】 杨永；

【作者基本信息】 西北工业大学 ， 流体力学， 2004， 硕士

【摘要】 现代飞机设计迫切需要计算流体力学为其提供准确、高效、实用的气动数据和流场分析工具，已经不再满足于仅采用Euler方程进行数值模拟。它要求数值求解Navier-Stokes(NS)方程以模拟粘性效应，提供更加准确而详实的流场信息。尽管求解雷诺平均NS方程(RANS)是解决现代空气动力学问题物理上最可信的方法，但它也有一个缺点：平均流动中湍流脉动量的影响是未知的。湍流脉动的影响作为一个新的附加项—雷诺应力，出现在RANS方程中，它是扰动速度分量二阶关联张量的散度。本文的目的就是把两方程湍流模型应用于NS方程计算，以模拟湍流脉动对平均运动的影响。 文中详细讨论了四种涡粘模型(Eddy Viscosity Model)和三种显式代数应力模型(Explicit Algebraic Stress Model)在数值求解雷诺平均NS方程(RANS)中的应用。所涉及到的两方程湍流模型一般包含两部分：一是尺度标定模型，它给出了湍流的标量信息，如两方程模型的尺度因子κ，ε或者ω。另一个是构成模型，即决定应力张量、应变率张量和两个湍流尺度因子之间的函数关系式，它决定了雷诺应力。如果构成模型是线性的，则为Boussinesq涡粘模型(EVM)，如果构成模型是非线性的代数关系式，则为显式代数应力模型(EASM)。 本文是在欧拉方程求解器的基础上，通过加入粘性(耗散)项，把流场的主控方程由欧拉方程(Euler)改为NS方程，然后引入两方程湍流模型，使其封闭。为了得到更准确的计算结果，采用了改进的Jameson二阶、四阶人工粘性；采用隐式残值光顺技术和当地时间步长加速收敛。 加入两方程湍流模型后，通过对平板、翼型、ONERA M6机翼等绕流流场的数值计算，验证了加入的各湍流模型的准确性，测试了它们对不同湍流流场的预测能力。更多还原

【Abstract】 In modern aircraft design, there is an urgent requirement for accurate, efficient and easy-use aerodynamic data and computational analysis tools. However, the Euler codes cannot satisfy all the demands for simulating the complex flow-fields. It’s necessary to solve Navier-Stokes (NS) equations to give viscous effects, more accurate and more detailed information of flow-fields. Although being superior over the other methods in terms of physical realism, the RANS methods, however, involve one major weakness-the effects of the turbulent motion of the mean flow are unknown and must be modeled. The influence of turbulence is seen as a new term in the equations. This term is the divergence of a second-order correlation tensor of the fluctuating parts of each velocity component. This correlation tensor is known as the Reynolds stress tensor, and it is the object that needs to be modeled. The main focus of this study is on two-equation turbulence models.The two-equation turbulence models can be thought to consist of two more or less separate parts: the scale determining model, which provides scalar information about the turbulence, and the constitutive model, which determines the Reynolds stress tensor. If the two-equation turbulence models employ a linear relationship between the Reynolds stress and the mean strain-rate tensors, this relationship is known as the generalized Boussinesq model, the two-equation models can be extended for a wider range of applicability by developing more advanced nonlinear algebraic relations between the stress tensor and the mean-velocity gradient and the turbulent scales, this is known as explicit algebraic stress models (EASM).The NS solver is developed from Euler equation code by adding viscous terms and two-equation turbulence models. In order to get a better result, the improved Jameson second and forth artificial dissipation is used, the implicit residual averaging and local time step techniques are employed to accelerate the convergence processing. We studied four eddy viscosity models (EVM) and three nonlinear EASM models in detail.The two-equation turbulence models are validated through simulating the flow fields over flat plate, airfoils and ONERA M6 wing. The capabilities of different turbulence models are accessed in this study.更多还原