Some Consequences of Material Frame Indifference on Engineering Flow Calculations

Abstract

The principle of material frame indifference (MFI) is a fundamental and controversial principle of continuum mechanics which has been invoked to derive recent nonlinear algebraic models for stresses of viscoelastic liquids (Mompean, Thompson, and Souza Mendes [2003]) and for Newtonian turbulent fluids (Rumsey, Gatski, and Morrison [2000]). The purpose of the present study is to identify regions of a flow field where MFI should be considered. Such regions are identified by computing the angular velocity of the principal directions of the rate-of-deformation tensor in order to obtain a Euclidean objective vorticity tensor. The method is applied to the planar flow through an abrupt 4:1 contraction. The main results are: (i) MFI should be taken into account in regions characterized by the transition between two different viscometric kinematics and significant velocities (ii) MFI can be safely ignored in regions of pure viscometric behavior as well as in recirculation regions.