A low Reynolds number dissipation rate equation model using the dissipation rate tensor equation and elliptic-blending equation

Abstract

The purpose of this study is to theoretically supplement the dissipation rate equation model that has been adopted and used for the elliptic-blending second-moment closure widely and currently used for analysis of turbulent flow, and eventually to enhance the theoretical validity of the model. The new dissipation rate equation model was derived by using the dissipation rate equation in terms of length scale that can be applied both in the near-wall region and to homogeneous flow and by using the dissipation rate tensor equation model. The newly derived dissipation rate equation model is applied in the existing elliptic-blending model as it is. To test the model equation we conducted a numerical analysis of non-rotating and rotating channel flows, channel flow with uniform transpiration, square duct flow, and 3-dimensional curved duct flow before comparing the analysis results with DNS data and the measurements. In regard to all flow fields adopted in this study, the expected results showed a high satisfaction in comparison with DNS data and measurements, thereby proving the theoretical validity of the new model.