笛卡尔网格下不同湍流模型的壁面函数方法研究  

STUDY ON WALL FUNCTION METHOD OF DIFFERENT TURBULENCE MODELS BASED ON CARTESIAN GRID

作　　者：罗灿炎 毕林 徐晶磊[3] 周丹[1] 袁先旭 唐志共 LUO Can-yan;BI Lin;XU Jing-lei;ZHOU Dan;YUAN Xian-xu;TANG Zhi-gong(Key Laboratory of Traffic Safety on Track of Ministry of Education,Central South University,Changsha 410075,China;State Key Laboratory of Aerodynamics,Mianyang 621000,China;School of Energy and Power Engineering,Beihang University,Beijing 100083,China)

机构地区：[1]中南大学,轨道交通安全教育部重点实验室,长沙410075 [2]空天飞行空气动力科学与技术全国重点实验室,绵阳621000 [3]北京航空航天大学能源与动力工程学院,北京100083

出　　处：《工程力学》2024年第8期11-22,共12页Engineering Mechanics

基　　金：国家重点研发计划项目(2019YFA0405204);国家数值风洞工程项目(NNW2018-ZT1A02);中南大学研究生自主探索创新项目(2020zzts544)。

摘　　要：自适应笛卡尔网格湍流模拟时,网格数目呈雷诺数的指数方量级增长,带来网格规模“灾难”问题。壁面函数方法可以将壁面第一层网格尺度放宽1~2个量级,是有效的解决办法之一,然而,由于笛卡尔网格的非贴体特性,壁面函数的实现及其与不同湍流模型的匹配是关键。针对这一问题,从经典的Spalding壁面函数出发,采用显式赋初值的方式,解决了壁面摩擦速度迭代求解初值敏感及分层壁面函数速度不光滑问题;基于切应力恒定的壁面条件,构造了多层虚拟网格的切向速度和湍流粘性系数,实现了笛卡尔网格下的壁面函数方法;采用结构系综理论,通过DNS数据标定,构造了湍动能随湍流粘性比率变化的关系式,实现了壁面函数与KDO湍流模型的匹配,并以平板T3b、湍流凸包和跨音速NACA0012翼型绕流为算例,与常用的SST、SA湍流模型壁面函数方法进行了对比分析。结果表明:该文提出的KDO湍流模型壁面函数法准确、可靠,且因其形式简单、计算量相对较小,有较大的推广应用价值。In adaptive Cartesian mesh turbulence simulation,the number of grids increases exponentially with Reynolds number,resulting in the"disaster"of grid number.The wall function is one of the effective solutions,which can reduce the scale of the first layer grid by 1-2 orders of magnitude.However,due to the non-body fitted characteristics of Cartesian grids,the realization of the wall function and its matching with different turbulence models are key.In order to solve this problem,starting from the classical Spalding wall function,an explicit assignment of initial value was adopted to solve the problem of sensitive initial value iterative solution of wall friction velocity and non-smooth velocity of layered wall function.Based on the wall condition of constant shear stress,the tangential velocity and turbulent viscosity coefficient of multi-layer ghost cell were constructed,and the wall function method was implemented in Cartesian grid.Using the structure ensemble theory and through the DNS data calibration,the relation formula of turbulent kinetic energy was constructed,which changes with turbulent viscosity ratio and wall function,and achieves KDO matching of turbulence model.Taking flat T3b,turbulent bump and transonic flow around NACA0012 airfoil as examples,the commonly used SST,SA turbulence model wall function methods were analyzed.The results show that the wall function method of KDO turbulence model is accurate,reliable,and has great application value because of its simple form and relatively small computation cost.

关 键 词：壁面函数 湍流模型 自适应笛卡尔网格 浸入边界 虚拟单元法 

分 类 号：O35[理学—流体力学]