An alternative assessment of weak-equilibrium conditions in turbulent closure modeling

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• 作者：R.L. Thompson ; G. Mompean
• 关键词：Turbulent equilibrium assumption ; Coaxial-orthogonal tensor decomposition ; Reynolds stress evolution
• 刊名：International Journal of Engineering Science
• 出版年：2010
• 出版时间：November 2010
• 年：2010
• 卷：48
• 期：11
• 页码：1633-1640
• 全文大小：210 K

文摘

In formulating polynomial representations of turbulent stress anisotropy tensors, it is necessary to impose equilibrium conditions on the turbulent field in order to reduce the governing transport equations to a set of implicit algebraic equations. Imposing these conditions on the anisotropy tensor rather than the turbulent stress tensor directly results in a set of weak-equilibrium conditions on the evolution of the anisotropy tensor. A second kind of assumption is a requirement that the turbulent transport and viscous diffusion be related to the anisotropy tensor in a manner consistent with both the dynamics and related tensorial properties.

In the study reported here, an alternative analysis of the weak-equilibrium hypothesis is performed in order to improve the physical interpretation of this assumption. One important result of the analysis is that previous turbulent weak-equilibrium hypothesis available in the literature impose that the flow has reached a Motion With Constant Relative Principle Anisotropic-Reynolds-Stress History, which means that the eigenvalues of the anisotropic Reynolds stress tensor do not change in time. Since virtually every geometry used to test this kind of hypothesis do not have a change on the cross sectional area and lead to viscometric flows, is natural that at equilibrium conditions such motion occurs. However, the eigenvalues of the Reynolds stress can change in time on turbulent extensional flows due to action of the mean flow in a different process from a turbulent relaxation. In this case, the extended weak-equilibrium assumption has to be related to an objective time derivative which is not purely co-rotational.