Fractional models of Reynolds-averaged Navier-Stokes equations for Turbulent flows

Abstract

Its is a well known fact that Turbulence exhibits non-locality, however, modeling has largely received local treatment following the work of Prandl over mixing-length model. Thus, in this article we report our findings by formulating a non-local closure model for Reynolds-averaged Navier-Stokes (RANS) equation using Fractional Calculus. Two model formulations are studied, namely one- and two-sided for Channel, Pipe and Couette flow, where the results shown have less 1% error. The motivation of two-sided model lies in recognising the fact that non-locality at a given spatial location is an aggregate of all directions. Furthermore, scaling laws and asymptotic relationship for Couette, Channel and Pipe flow is reported. It is to be noted that modeling in wall units, no additional coefficient appears, thus there models could be applied to complex flows with ease.