摘要
湍流边界层流动是一种广泛存在于飞行器内部和外部的流动现象,是基础理论和模型验证的重要研究对象.能够捕捉大部分流动细节且计算量适中的大涡模拟(large-eddy simulation, LES)方法在湍流数值模拟中得到了越来越广泛的应用.文章基于格心有限差分方法,使用4阶紧致中心格式离散N-S方程无黏项,分别应用5种不同的亚格子(subgrid-scale, SGS)模型,即隐式, SM(Smagorinsky model), DSM(dynamic Smagorinsky model), WALE(wall-adapting local eddy-viscosity model)和CSM(coherent structures model),对Re=3 000, Ma=0.5的等温壁面槽道流动进行了大涡模拟研究.与实验值和直接数值模拟(direct numerical simulation, DNS)结果对比后发现,流场平均温度、平均密度等热力学量以及平均流向速度对亚格子模型不敏感,不适宜作为判断模型优劣的判据.亚格子模型在壁面附近的耗散越大,壁面摩擦速度以及阻力系数就越小.对于与速度相关的脉动量来说,不同模型得到的结果在壁面和脉动峰值附近误差比较大,中心线附近较小;显式模型结果在流向速度峰值处均高于参考值,而在展向和壁面法向速度脉动峰值处则均偏低.考虑显式的4种模型在壁面附近的涡黏系数分布, DSM和CSM曲线满足涡黏系数与无量纲壁面距离3次方成正比的分布规律, SM曲线斜率偏小而WALE曲线斜率偏大.
Turbulent boundary layer flow is a basic phenomenon that exists widely inside and outside the aircraft. This phenomenon is of primordial interest for fundamental research as well as for numerical modeling. Large-eddy simulation(LES) has been widely applied to simulate turbulent flow due to its ability to capture main flow details and moderate computational cost. Based on cell-centered finite difference method , the 4 th -order compact center scheme was used to discretize convective Fluxes. Five different subgrid-scale(SGS) models were applied to simulate the isothermal-wall channel flow at Re =3 000 , Ma =0.5 , namely the implicit model , the Smagorinsky model(SM), the dynamic Smagorinsky model(DSM), the wall-adapting local eddy-viscosity model(WALE) and coherent structures model(CSM). Compared to experimental and direct numerical simulation(DNS) results , it′s found that there is no evident discrepancy in mean temperature , mean density and mean streamwise velocity between different SGS models. These quantities , therefore , are not proper to distinguish SGS models. The greater dissipative the SGS model is , the smaller the wall friction velocity and friction coefficient are. As for fluctuating quantities associated with velocity , the error of results obtained by different models is larger near the wall and the peak , while smaller near the center line. Results from all explicit models are higher than reference value at the peak of fluctuating velocity in streamwise direction , while lower in spanwise and wall-normal directions. Considering eddy viscosity coefficient , DSM and CSM satisfy the relation that the eddy viscosity is proportional to the cube of dimensionless distance from the wall , and the slope of SM is smaller while the slope of WALE is larger.
作者
洪正
叶正寅
HONG Zheng;YE Zheng-yin(School of Aeronautics , Northwestern Polytechnical University , Xi′an 710072 , China)
出处
《气体物理》
2019年第1期33-44,共12页
Physics of Gases
基金
国家自然科学基金(11732013)
关键词
槽道流
N-S方程
大涡模拟
格心有限差分法
亚格子模型
channel flow
N-S equation
large-eddy simulation
cell-centered finite difference method
subgrid-scale model
