First-harmonic balance for fast evaluation of power-law fluid flow enhancement under periodic pressure gradient

Abstract

This work considers rectilinear laminar flow of power-law liquids under a periodic pressure gradient. In contrast to Newtonian flow, previous studies have shown that the interaction between nonlinearities by non-Newtonian rheology and exogenous periodic forcing can yield important changes in the flow patterns, such as mean flowrate enhancement for shear-thinning fluid whereas flowrate reduction for shear-thickening fluid relative to non-forcing conditions. The aim of this work was to evaluate the ability of first-harmonic approximation for estimating mean flowrate enhancement/reductions under periodic pressure gradient oscillations. The first-harmonic balance involves the projection of nonlinearities on a first-harmonic Fourier basis, which reduces the governing partial differential equation into three ordinary boundary-value problems that should be solved numerically. The results showed that the predictions from the first-harmonic balance were in good agreement, both qualitative and quantitative, with direct numerical simulations of the governing partial differential equation. The advantage of the former over the latter is the computational burden since numerical computations for the first-harmonic equations does not depend of the forcing frequency.