Pipe Flow and Wall Turbulence Using a Modified Navier—Stokes Equation

Abstract

We use a derived incompressible modified Navier-Stokes equation to model pipe flow and wall turbulence.We reproduce the observed flattened paraboloid velocity profiles of turbulence that cannot be obtained directly using standard incompressible Navier-Stokes equation. The solutions found are in harmony with multi-valued velocity fields as a definition of turbulence. Repeating the procedure for the flow of turbulent fluid between two parallel flat plates we find similar flattened velocity profiles. We extend the analysis to the turbulent flow along a single wall and compare the results with experimental data and the established controversial von Karman logarithmic law of the wall.

A frequency quantum interpretation of the surface renewal model of mass transfer

“…For example, Llaguno & Muriel [ 24 ] explained the multilevel turbulent data of the flow of nitrogen at room temperature obtained in a specially constructed experimental apparatus by postulating transitions between different rotational energy levels of the nitrogen molecule, which are caused by intermolecular collisions. By introducing a modification (postulated to arise from inelastic interactions of quantum origin among fluid molecules, which may be in different excited states) to the incompressible Navier–Stokes equation, Jirkovsky & Muriel [ 25 ] were able to derive the flattened paraboloid velocity profile in the turbulent flow of a fluid in a pipe and between two parallel plates, and also to fit the experimentally observed velocity profile with a single exponential-type equation in the near wall (viscous and buffer sublayers), intermediate and far away region in the turbulent flow of water in a channel. We note that the universal velocity profile for turbulent flow in a pipe is conventionally represented by three separate expressions depending upon the distance from the wall [ 26 ].…”