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

TL;DR

This paper introduces a novel non-local fractional calculus-based closure model for RANS equations to better capture turbulence non-locality, demonstrating high accuracy across different flow types without extra coefficients.

Contribution

It formulates and analyzes a non-local fractional calculus model for RANS turbulence, advancing beyond traditional local models with minimal error and applicability to complex flows.

Findings

Less than 1% error in flow predictions

Effective modeling in wall units without extra coefficients

Scaling laws and asymptotic relationships established

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.