守恒型可压缩一维湍流方法及其在超声速标量混合层中的应用

doi:10.7527/S1000-6893.2021.26364

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守恒型可压缩一维湍流方法及其在超声速标量混合层中的应用

陈崇沛¹, 梁剑寒¹, 关清帝¹, 高天运^1,2

1. 国防科技大学空天科学学院临近空间技术研究所, 长沙 410073;
2. 国防科技大学国际关系学院, 南京 210039

收稿日期:2021-09-01 修回日期:2021-09-14 发布日期:2021-10-09
通讯作者: 梁剑寒 E-mail:jhleon@vip.sina.com

Conservative compressible one-dimensional turbulence method and its application in supersonic scalar mixing layer

CHEN Chongpei¹, LIANG Jianhan¹, GUAN Qingdi¹, GAO Tianyun^1,2

1. Science and Technology on Scramjet Laboratory, College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China;
2. International Studies College, National University of Defense Technology, Nanjing 210039, China

Received:2021-09-01 Revised:2021-09-14 Published:2021-10-09

摘要/Abstract

摘要： 一维湍流（ODT）方法是一种能在一维计算域上遵循湍流基本物理规律的湍流建模方法。通过结合确定性和随机性求解方法，能够在一维计算域上准确捕捉到湍流统计规律，且降维建模可显著减小计算量。ODT方法主要被广泛用于不可压湍流和湍流燃烧研究，若要将其拓展用于模拟高速可压缩湍流，需对建模方法进行深度改进。相比于不可压ODT方法，本文基于欧拉参考框架，针对可压缩湍流的特性，将因变量由原始变量改为有利于减小可压缩湍流模拟误差的守恒通量，并加入了组分求解模块。对确定性和随机性求解模块均进行了相应的深度改进，开发出具有标量混合模拟功能的守恒型可压缩ODT方法。在确定性模块中改为求解以守恒通量为变量的一维截断控制方程，在随机性模块中构造一维涡时，将三联映射的作用对象也相应地由原始变量改为守恒通量，并选用了可保证变密度情况下动量守恒的双核变换。通过模拟空间发展超声速平面湍流混合层并将自相似阶段结果与实验结果比对，验证该方法对可压缩剪切湍流场中标量混合的捕捉精度。守恒型可压缩ODT方法模拟得到的速度场和组分场的平均剖面和脉动强度分布与实验结果准确吻合，精度明显优于传统的耦合梯度扩散亚格子模型的大涡模拟方法（LES-GRAD.DIFF.）以及耦合线性涡（LEM）亚格子模型的大涡模拟方法（LES-LEM），且该方法的降维处理使其在降低计算成本方面具有显著优势。

关键词: 一维湍流(ODT), 可压缩湍流, 数值模拟, 守恒型, 混合层, 标量混合

Abstract: The One-Dimensional Turbulence (ODT) method is a turbulence modeling method that follows the basic physical laws of turbulence in the one-dimensional computational domain. The statistical laws of turbulence can be accurately captured in the one-dimensional computational domain by combining deterministic and stochastic solving methods, and modeling in the reduced dimension can significantly reduce the amount of computation. The ODT method is widely used in the study of incompressible turbulence and turbulent combustion, but needs to be further improved to simulate high-speed compressible turbulent flows. Different from the incompressible ODT method, in this paper, the dependent variables are changed from the original variables to the conservative fluxes based on the Euler reference frame, which is beneficial to reducing the error of compressible turbulence simulation. A component solution module is also proposed in this research. A conservative compressible ODT method capable of simulating scalar mixing is developed by further improving both deterministic and stochastic solving modules in a corresponding manner. In the deterministic module, the one-dimensional truncated governing equations solved are adjusted as the ones with conservative fluxes as dependent variables, and the triplet mapped object is correspondingly changed from the original variables to the conservative fluxes, and simultaneously the kernel transformation with two kernels is selected to ensure momentum conservation for variable density when one-dimensional eddies are constructed in the stochastic module. The accuracy of the method for capturing scalar mixing in the compressible shear turbulent field was verified by simulating the spatially developing supersonic plane turbulent mixing layer and comparing the results of the self-similar stage with the experimental results. The mean profile and the fluctuation intensity profile of velocity field and component field captured by the method proposed are in excellent agreement with experimental results. The accuracy of the proposed method is obviously better than that of the Large Eddy Simulation with the Gradient Diffusion sub-grid closure (LES-GRAD.DIFF.) and that of the Large Eddy Simulation coupled with the Linear Eddy Mixing (LEM) model (LES-LEM), and the dimensionality reduction of the method proposed gives it a significant advantage in reducing computational cost.

Key words: One-Dimensional Turbulence (ODT), compressible turbulent flow, numerical simulation, conservative, mixing layer, scalar mixing

中图分类号:

V231.21

陈崇沛, 梁剑寒, 关清帝, 高天运. 守恒型可压缩一维湍流方法及其在超声速标量混合层中的应用[J]. 航空学报, 2021, 42(S1): 726364-726364.

CHEN Chongpei, LIANG Jianhan, GUAN Qingdi, GAO Tianyun. Conservative compressible one-dimensional turbulence method and its application in supersonic scalar mixing layer[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(S1): 726364-726364.

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守恒型可压缩一维湍流方法及其在超声速标量混合层中的应用

Conservative compressible one-dimensional turbulence method and its application in supersonic scalar mixing layer

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