Nonlinear eddy diffusivity model for wall-bounded flow with arbitrary rotating axes

Abstract

Rotating flows have been encountered in many engineering-relevant applications such as a flow in turbomachinery. Recently, rotating channel flows with arbitrary rotating axes have been investigated by direct numerical simulation (DNS). Although numerical studies of spanwise rotating channel flow have been reported, there are few reports on streamwise and wall-normal rotating channel flows. In the present study, first, we conducted DNS of various rotational channel flows in order to understand phenomena of rotating wall-bounded flows and to make databases for turbulence modelling. It is found from the DNS results that cases of streamwise rotating channel flow which have a mean spanwise velocity caused by rotation involve the counter gradient turbulent diffusion. Thus, since it is well-known that the conventional eddy diffusivity turbulence model (EDM) cannot predict this case, we have to consider the reconstruction of a nonlinear eddy viscosity turbulence model (NLEDM) based on a cubic model. Consequently, we evaluated existing nonlinear eddy viscosity turbulence models based on our DNS of streamwise and wall-normal rotating channel flows. Using the results of evaluation, we have improved the modeled expression for Reynolds stress, in which a new cubic-type nonlinear eddy viscosity model has been proposed. The proposed nonlinear two-equation turbulence model can accurately predict rotating channel flows with arbitrary rotating axes.