Partially Lagging One-Equation Turbulence Model

A partially lagging one-equation eddy viscosity model, based on the transformation of the k-epsilon turbulence closure through Bradshaw et al. ("Calculation of Boundary Layer Development Using the Turbulent Energy Equation," Journal of Fluid Mechanics, Vol. 23, No. 3, 1967, pp. 593-616), is proposed. The model attempts to account for the turbulence history effects by spatially lagging the destruction/diffusion terms. The amount of relaxation is based on the von Karman length scale. The present model does not assume equal diffusion coefficients of the k and epsilon equations; therefore, third-order velocity gradients emerge. The performance of the present model is assessed against the Spalart-Allmaras model (" A One-Equation Turbulence Model for Aerodynamic Flows," AIAA Paper 1992-0439, 1992) and the one-equation model proposed by Menter (" Eddy Viscosity Transport Equations and Their Relation to the k-epsilon Model," Journal of Fluids Engineering, Vol. 119, 1997, pp. 876-884), which is based on Bradshaw et al. (" Calculation of Boundary Layer Development Using the Turbulent Energy Equation," Journal of Fluid Mechanics, Vol. 23, No. 3, 1967, pp. 593-616), and the assumption of equal diffusion coefficients. The behavior of the one-equation transformed model without the presence of third-order velocity gradients is also examined. The proposed model is validated through a comparison to a wide class of internal and external turbulent flows.