Turbulence calculation based on the extended Navier–Stokes equations

Abstract

In this study, phenomenological observations and the Kreuer interpretation of the origin of viscosity were used to develop a computational method for solving the turbulence problem of incompressible viscous Newtonian fluids based on extended Navier–Stokes (N–S) equations. The shear process in fluid flow was hypothesized to be accompanied by eddy formation, and the effects of eddies on the convection and diffusion were considered. The classical N–S equations were improved to obtain extended N–S equations. The extended equations are closed, and the sources of the velocity fluctuations are explicitly considered to be additional convection and diffusion. The extended equations are compatible with the classical N–S equations; thus, they can describe laminar and turbulent flows in a unified manner. In fluid flow simulations, the equations describing the mean flow quantities could be directly obtained from the extended N–S equations without any additional turbulence models. A numerical investigation was carried out to verify the extended equations by exploring the flow over a cube placed in a channel. The simulation results were compared with both the large eddy simulation and experimental results.