The principle of pressure decomposed for flow over a flat plate and its application on the magnetic fluids

Abstract

According to the diffusion-parabolized Navier-Stokes (DPNS) equations theory and the physical characteristic analysis of the boundary layer of flat plate flow, it is first put foreword that the velocity grade and the pressure grade are different in different layer of the boundary layer and outlet flow field in the tangential direction of the wall surface, which is different from the Prandtl’s boundary layer theory using an unitary freestream velocity grade and an unitary pressure grade, and we call it as the trible grades theory. According to the trible grades theory of pressure and the Prandtl’s boundary layer theory, the principle of pressure decomposed is obtained. Accordingly, the Navier-Stokes ferrohydrodynamic (FH) equations are simplified, the principle of pressure decomposed of the magnetic fluid is obtained, there are three fluid flows which are controlled by three basic equations: the Euler FH (EFH) equations, diffusion-parabolized FH (DPFH) equations and Navier-Stokes FH (NSFH) equations. The three basic equations have different mathematical characteristics; there is a great disparity in domains of the three basic flows and the domains of EFH equations and DPFH equations are very small. Therefore, adopting EFH-DPFH-NSFH equations system to analyze and compute high Re number magnetic fluid flows over bodies is a logical approach. Our results show that if the discrete grids are not fine enough, numerically simulating the viscous magnetic fluid with the full NSFH equations are equivalent to simulating the magnetic fluid with DPFH equations or with EFH-DPFH-NSFH equations system.