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Assessment of alternative scale-providing variables in a Reynolds-stress model using high-order methods

利用高阶方法在雷诺应力模型中评估替代尺度提供变量

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Abstract

This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes (RANS) equations, which are coupled with the turbulence model equations. Three alternative scale-providing variables for the specific dissipation rate (ω) are implemented in the framework of the Reynolds stress model (RSM) for improving its robustness. Specifically, \(g\left( { = 1/\sqrt \omega } \right)\) has natural boundary conditions and reduced spatial gradients, and a new numerical constraint is imposed on it; \(\tilde \omega \left( { = \ln \omega } \right)\) can preserve positivity and also has reduced spatial gradients; the eddy viscosity νt also has natural boundary conditions and its equation is improved in this work. The solution polynomials of the mean-flow and turbulence-model equations are both reconstructed by the weighted compact nonlinear scheme (WCNS). Moreover, several numerical techniques are introduced to improve the numerical stability of the equation system. A range of canonical as well as industrial turbulent flows are simulated to assess the accuracy and robustness of the scale-transformed models. Numerical results show that the scale-transformed models have significantly improved robustness compared to the ω model and still keep the characteristics of RSM. Therefore, the high-order discretization of the RANS and RSM equations, which number 12 in total, can be successfully achieved.

摘要

本文的背景是对耦合湍流模型方程的雷诺平均Navier-Stokes (RANS)方程进行高阶有限差分离散. 为提高鲁棒性, 在雷诺应力模型(RSM)的框架中实现了三个比耗散率(ω)的替代尺度提供变量. 具体来说, \(g\left( { = 1/\sqrt \omega } \right)\) 具有自然边界条件和较小的空间梯度, 并对其施加了新的数值约束; \(\tilde \omega \left( { = \ln \omega } \right)\) 具有保正性, 同时也减少了空间梯度; 涡黏性νt 也有自然边界条件, 并本文中对其方程进行了改进. 平均流动方程和湍流模型方程的解多项式均由加权紧致非线性格式(WCNS)重构. 此外, 还引入了几种数值技术来提高方程组的数值稳定性. 对一系列规范和工业湍流开展模拟以评估尺度转换后模型的准确性和鲁棒性. 数值结果表明, 尺度转换后的模型与ω模型相比具有显着提高的鲁棒性, 并且仍然保持RSM的特征. 因此得以成功实现总数12个方程的RANS和RSM的高阶离散.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 12002379), the Natural Science Foundation of Hunan Province in China (Grant No. 2020JJ5648), the Scientific Research Project of National University of Defense Technology (Grant No. ZK20-43), and the National Key Project (Grant No. GJXM92579).

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Authors and Affiliations

  1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, China

    Xiang Fu  (符翔), Shengye Wang  (王圣业) & Xiaogang Deng  (邓小刚)

  2. Chinese Academy of Military Science, Beijing, 100071, China

    Xiaogang Deng  (邓小刚)

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  1. Xiang Fu  (符翔)
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Correspondence to Shengye Wang  (王圣业).

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Shengye Wang and Xiang Fu designed the research. Xiang Fu wrote the first draft of the manuscript. Xiang Fu set up the experiment set-up and processed the experiment data. Shengye Wang helped organize the manuscript. Shengye Wang and Xiaogang Deng revised and edited the final version. Shengye Wang and Xiaogang Deng acquired of the financial support for the project leading to this publication.

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Fu, X., Wang, S. & Deng, X. Assessment of alternative scale-providing variables in a Reynolds-stress model using high-order methods. Acta Mech. Sin. 38, 322151 (2022). https://doi.org/10.1007/s10409-022-22151-x

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