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

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2010
auteur(s) Thompson Roney L.; Mompean Gilmar
journal (abréviation) International Journal of Engineering Science (Int J Comput Eng Sci)
volume (numéro) 48 (11)
pages 1633 – 1640
résumé In formulating polynomial representations of turbulent stress anisotropy tensors, it is necessary to impose equilibrium conditions on the turbulent eld 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 di usion 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 hy- pothesis is performed in order to improve the physical interpretation of this as- sumption. One important result of the analysis is that previous turbulent weak- equilibrium hypothesis available in the literature impose that the ow 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 ows, is natural that at equilibrium conditions such motion occurs. However, the eigenval- ues of the Reynolds stress can change in time on turbulent extensional ows due to action of the mean ow in a di erent 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.
mots clés Turbulent equilibrium assumption, Coaxial-orthogonal tensor decomposition, Reynolds stress evolution
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