Multiscale model for turbulent flows

A is devised for computing general turbulent flows. The is an improvement over two-equation turbulence models in a critically important manner, that is, the new accounts for disalignment of the Reynolds-stress-tensor and the mean-strain-rate-tensor principal axes. The improved representation of the Reynolds-stress tensor has been accomplished through the introduction of a multiscale description of the turbulence, i.e., two energy scales are used corresponding to upper and lower partitions of the turbulence energy spectrum. A novel feature of the formulation is that the differential equation for the Reynolds-stress tensor is of first order, which in effect corresponds to what can be termed an algebraic stress model with convective terms. As a consequence of its mathematical simplicity, the is very efficient and easy to implement computationally. The is applied to a wide range of turbulent flows including homogeneous turbulence, compressible and incompressible two-dimensional boundary layers, and unsteady boundary layers including periodic separation and reattachment. Comparisons with corresponding experimental data show that the reproducesall salient features of the flows considered/Perturbation analysis of the viscous sublayer shows that integration through the sublayer can be accomplished with no special viscous modifications to the closure coefficients appearing in the model.