Generalized Hydrodynamic Equations for Viscous Flows - Simulation versus Experimental Data

Generalized hydrodynamic equations (GHE) proposed by Alexeev (1994), have been explored for simulations of viscous flows for a wide range of problems and flow parameters, including high Reynolds numbers flows with thin boundary layers. These GHE is not a turbulence model, and no additional equations are introduced. Spacial fluctuations (small flow scales) can be successfully captured with GHE, and the derived small scale of turbulent flow compares well with observed one in the experiments by Koseff and Street (1984). In this paper, we review numerical solutions using GHE for several viscous flow problems and compare numerical results with experimental data for the cases we considered in the range of Reynolds number from Re = 10(-6), to 3200, and to 1,000,000. The method is reviewed and numerical solutions are compared with the experimental data for a 3D driven cavity flow at Re = 3200 and 10,000, 2D backward facing step flow at Re = 44,000, 2D channel flow at Re number up to 10(6); and a 3D thermal convection in a cylinder at Ra = 1000 to 150,000. Comparison with the analytical asymptotic solution is provided for a thermal convection, in the electrically conducting fluid suppressed by a strong magnetic field at Hartman numbers Ha up to 20,000 (Re = 10(-5)). In all the cases considered, GHE results compare favorably with experimental data. 2D and 3D Naver-Stokes solutions and k-epsilon model solutions are also provided, and they are outperformed by GHE results.