Non-linear eddy-viscosity modelling of separated flows

The paper reviews some recent developments in the area of non-linear eddy-viscosity modelling and investigates the performance of several model variants when these are applied to flows with complex strain. The formulation of this type of model has been motivated by the desire to combine the advantageous numerical properties and economy of linear Boussinesq-viscosity models with the superior predictive performance of second-moment closure which is mathematically complex and numerically challenging. The rationale, fundamental principles and inherent properties of non-linear stress-strain relationships are considered first in general terms, with particular emphasis being placed on the mechanisms by which normal-stress anisotropy and sensitivity to curvature strain are represented. This is followed by a review of several particular model forms and the principal elements of their derivation. The models are then applied to four two-dimensional flows featuring, inter alia, strong curvature, irrotational straining, separation from curved surfaces and transition. The computational results presented demonstrate that the models possess predictive characteristics which are qualitatively similar to those of second-moment closure. However, quantitative agreement between predictions and reality varies considerably among the models, and this reflects the strong reliance of the models on the quality of the closure approximations adopted and their sensitivity to the details of the calibration process.