Shear stress calculation in asymmetric turbulent flows: a combined ARS-model

Extended expressions for the primary turbulent shear stresses are proposed, which can be regarded as an eddy-diffusivity or mixing length model. The new formulae, containing second derivatives of the mean velocity, were incorporated into an existing algebraic Reynolds stress (ARS) closure by simply relating the new variables to quantities calculated within this model, such as turbulent kinetic energy and dissipation. With this combined model, the negative turbulence energy production in regions near the velocity maximum in asymmetric turbulent flows could be captured very well. This is demonstrated for several cases of channel flow, where asymmetry is caused by unequal wall roughness or system rotation. In addition, a short validation is given for wholly symmetrical flow. The presented results are compared with measurements and computations (DNS, secondorder closure) from the available literature and previous calculations as well.