Testing of Model Equations for the Mean Dissipation using Kolmogorov Flows
Testing of Model Equations for the Mean Dissipation using Kolmogorov Flows
复制标题
使用柯尔莫哥洛夫流测试平均耗散模型方程
DOI：
10.1007/s10494-010-9273-4
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
N. Peters
中科院分区：
文献类型：
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作者：
P. Schaefer;M. Gampert;J. Goebbert;Lipo Wang;N. Peters
在体积为（2π）3的周期盒中，施加U(y) = fsin (y)的y方向平均速度剖面，在110 ~ 190之间的三个不同雷诺数下对Kolmogorov流动进行直接数值模拟（DNS）。经过几次积分后，紊流在统计上是稳定的。在此基础上，对两方程RANS （Reynolds average Navier-Stokes）湍流模型中平均耗散ε的两种不同模型方程进行了比较。k-ε-模型的高雷诺数版本（Jones and Launder, Int J Heat Mass Transfer 15:301 - 314,1972）被称为标准模型，以及Menter等人（2006）的新模型，被称为Menter - egorov模型，根据DNS结果进行了测试。对两种模型进行了数值求解，发现标准模型不能提供稳定的解，而门特-叶格罗夫模型可以。此外，在动能k和耗散ε的平均分布上，模型解与DNS数据有较好的定量一致性。此外，基于流动固有几何的分析，称为耗散元素（Wang and Peters, J Fluid Mech, 608:113 - 138,2008），被用于检验Menter-Egorov ε模型方程。通过对耗散单元长度的概率密度函数（pdf）的演化方程取适当的矩，推导出ε的演化表达式。与模型方程逐项比较，可以预测常数，随着雷诺数的增加，该常数接近经验值。
Direct Numerical Simulations (DNS) of Kolmogorov flows are performed at three different Reynolds numbers Reλ between 110 and 190 by imposing a mean velocity profile in y-direction of the form U(y) = F sin(y) in a periodic box of volume (2π)3. After a few integral times the turbulent flow turns out to be statistically steady. Profiles of mean quantities are then obtained by averaging over planes at constant y. Based on these profiles two different model equations for the mean dissipation ε in the context of two-equation RANS (Reynolds Averaged Navier–Stokes) modelling of turbulence are compared to each other. The high Reynolds number version of the k-ε-model (Jones and Launder, Int J Heat Mass Transfer 15:301–314, 1972), to be called the standard model and a new model by Menter et al. (2006), to be called the Menter–Egorov model, are tested against the DNS results. Both models are solved numerically and it is found that the standard model does not provide a steady solution for the present case, while the Menter–Egorov model does. In addition a fairly good quantitative agreement of the model solution and the DNS data is found for the averaged profiles of the kinetic energy k and the dissipation ε. Furthermore, an analysis based on flow-inherent geometries, called dissipation elements (Wang and Peters, J Fluid Mech 608:113–138, 2008), is used to examine the Menter–Egorov ε model equation. An expression for the evolution of ε is derived by taking appropriate moments of the equation for the evolution of the probability density function (pdf) of the length of dissipation elements. A term-by-term comparison with the model equation allows a prediction of the constants, which with increasing Reynolds number approach the empirical values.