The development and application of two-time-scale turbulence models for non-equilibrium flows

摘要

This study re-visits the largely overlooked, but highly promising, topic of multi-scale BANS modelling for non equilibrium turbulent flows. The paper presents the development of BANS models which, at an effective-viscosity level, involve two transport equations for the turbulent kinetic energy; one for the energy of the large scale, energy-producing, eddies and one for that of the smaller eddies, which, through continuous break-up, transfer turbulence energy to the dissipative scales. Two transport equations for the transfer-rate of the turbulent kinetic energy are also necessary, one for the rate of energy transfer from the large to the smaller scales and one for the rate of transfer from the smaller to the dissipative scales, the latter being of course the dissipation rate of turbulence. The two-time-scale model of Hanjalic et al. (1980) has been the starting point of the current developments. The coefficients of the terms which appear in these models have been determined from asymptotic analyses of decaying grid turbulence, homogeneous shear flows and local-equilibrium boundary-layer flows. The models were subsequently further developed to become more responsive to strong non-equilibrium features, such as those caused by strong shear. It has been identified that in general, models which have been optimised to satisfy equilibrium flows (as is usually done) are unable to capture the strong changes the flows are subjected to due to highly non-equilibrium effects, thus needing further development. Within the two-time-scale framework, it has been found possible to overcome this problem, by exploiting the additional information available on the turbulence spectrum. In a further departure from the development of earlier effective-viscosity two-time scale models, here the eddy viscosity expression is made sensitive to the local strain rate, as was also the case in single scale models developed by Craft et al. (1996).