k-ε model for predicting transitional boundary-layer flows under zero-pressure gradient

A modified k-epsilon model is proposed for calculation of transitional boundary-layer flows. To develop the eddy viscosity model for the problem, the flow is divided into three regions: the pretransition region, transition region, and fully turbulent region. In the pretransition region, because the turbulence does not yet attain its equilibrium state in which the eddy viscosity is proportional to the distance from the wall, it is postulated that a viscous sublayer structure prevails across the boundary layer so that the eddy viscosity is proportional to the cube of the wall distance. Further it is assumed that as the turbulent spots which have appeared at the onset of transition grow with the downstream distance in the transition region, dependence of the eddy viscosity on the wall distance changes gradually from that in the pretransition region to that in the fully turbulent state. A universal downstream variation of intermittency factor in the transition region is employed to represent such a transition eddy viscosity in the transition region. In addition, the model constant C-epsilon1 in the standard k-epsilon model is modified to take into account the particular characteristics of turbulence in the transition region. In the present test calculations, because the governing equations are integrated from a point close to the leading edge in the pretransition region, the initial and boundary conditions of k and epsilon at the onset of transition are automatically supplied. The proposed model is applied to calculate three benchmark cases of the transitional boundary-layer flows with different freestream turbulent intensity (1-6%) under zero-pressure gradient. It was found that the profiles of mean velocity and turbulent intensity, local maximum of velocity fluctuations, their locations as well as the streamwise variation of integral properties such as skin friction, shape factor, and maximum velocity fluctuations are very satisfactorily predicted throughout the flow regions.