基于ν_(t)尺度方程的雷诺应力模型初步研究  

Preliminary study on Reynolds stress model based on ν_(t)-scale equation

作　　者：陈彦君 王圣业 符翔 刘伟[1] Chen Yan-Jun;Wang Sheng-Ye;Fu Xiang;Liu Wei(College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]国防科技大学空天科学学院,长沙410073

出　　处：《物理学报》2022年第16期233-241,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12002379);湖南省自然科学基金(批准号:2020JJ5648);国防科技大学科研计划(批准号:ZK20-43);国家专项工程(批准号:GJXM92579)资助的课题。

摘　　要：雷诺应力模型一直是湍流模式理论研究的前沿和难点,而提高数值鲁棒性是其广泛开展工程应用的关键.借鉴经典的k-k L湍流模型,本文构造了一种新的ν_(t)尺度方程,并将其用于耦合SSG/LRR模式从而形成SSG/LRR-ν_(t)雷诺应力模型.通过零压力梯度湍流平板边界层、翼型尾迹流、超声速方腔流和NACA0012翼型45°迎角分离流动4个标准算例对新模型进行了验证与确认.同时,为了测试模型的数值鲁棒性,采用高精度数值格式对模型方程进行了离散求解,并与SA涡粘模型和SSG/LRR-ω雷诺应力模型进行对比.结果表明:ν_(t)尺度方程在黏性壁面边界严格为零,相比传统的ω尺度,具有更好的数值鲁棒性,从而可实现新模型与高精度数值格式的匹配并获得更好的网格收敛效率;新模型具备雷诺应力模型的传统优势,可对拐角流动进行很好的模拟;具备尺度自适应能力,对于非定常分离流动的模拟存在一定的潜力.Reynolds stress model has always been the frontier and challenging problem in turbulence model theory research,where improving numerical robustness is the key to its wide application in engineering.Referring to the classical k-kL turbulence model,a new vt-scale equation is constructed and used to couple the SSG/LRR model to form a so-called SSG/LRR-v_(t) Reynolds stress model.Four benchmark cases,including zero pressure gradient turbulent plate boundary layer,airfoil wake flow,supersonic square duck flow and separated flow over NACA0012 airfoil at 45 degree angle of attack,are carried out to test the new turbulence model.At the same time,high-order numerical schemes are used to discretize the turbulence equations in order to assess its numerical robustness.The results are compared with those of SA eddy viscosity model and SSG/LRR-ωReynolds stress model.It is shown that the vt-scale equation is strictly equal to zero at the viscous wall boundary.Compared with the traditional ω-scale,it has better numerical robustness.Along with this,the new model can be matched with the high-order numerical schemes and obtain a better efficiency in the mesh convergence.Moreover,the new model has the inherent advantage of Reynolds stress model in simulating the corner flow and has the potential in scale adaptive simulation of unsteady separated flow.

关 键 词：湍流流动 雷诺应力模型 分离流动 加权紧致非线性格式 

分 类 号：O357.5[理学—流体力学]