Steady and Unsteady Flow Modelling Using the k-#8730;kL Model

In the last two years, the first two authors have re-visited the principle formulation of two-equation turbulence models. The investigations were motivated by the unphysical solution produced by standard two-equation models when operated in unsteady mode (URANS). The re-evaluation of Rotta's theory for the derivation of a length scale equation resulted in a new term in the equation for the turbulent length scale. This term introduces the second spatial derivative of the velocity field into the two-equation model. As a result, the von Karman length scale appears as a natural scale-determining quantity and allows the model to adapt to nonhomogenous and unsteady flows more accurately. Particularly the behaviour for unsteady flows changes dramatically from the standard URANS formulations and exhibits the LES-like behaviour. This ability to adjust to steady and unsteady flows automatically was termed Scale-Adaptive Simulation (SAS).