The Basic k-ϵ Model and a New Model Based on General Statistical Descriptions of Anisotropic Inhomogeneous Turbulence Compared with DNS of Channel Flow at High Reynolds Number

J. J. H. Brouwers
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Abstract

Predictions are presented of mean values of statistical variables of large-scale turbulent flow of the widely used basic k-ϵ model, and of a new model, which is based on general statistical descriptions of turbulence. The predictions are verified against published results of direct numerical simulations (DNSs) of Navier–Stokes equations. The verification concerns turbulent channel flow at shear Reynolds numbers of 950, 2000, and 104. The basic k-ϵ model is largely based on empirical formulations accompanied by calibration constants. This contrasts with the new model, where descriptions of leading statistical quantities are based on the general principles of statistical turbulence at a large Reynolds number and stochastic theory. Predicted values of major output variables such as turbulent viscosity, diffusivity of passive admixture, temperature, and fluid velocities compare well with DNS for the new model. Significant differences are seen for the basic k-ϵ model.
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基本 k-ϵ 模型和基于各向异性非均质湍流一般统计描述的新模型与高雷诺数通道流 DNS 的比较
对广泛使用的基本 k-ϵ 模型和基于湍流一般统计描述的新模型的大尺度湍流统计变量平均值进行了预测。预测结果与已公布的纳维-斯托克斯方程直接数值模拟(DNS)结果进行了验证。验证涉及剪切雷诺数为 950、2000 和 104 时的湍流通道流动。基本 k-ϵ 模型主要基于经验公式,并附有校准常数。而新模型对主要统计量的描述是基于大雷诺数统计湍流的一般原理和随机理论。主要输出变量的预测值,如湍流粘度、被动混合的扩散率、温度和流体速度,与新模型的 DNS 比较良好。基本 k-ϵ 模型与 DNS 有显著差异。
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