Behavior of a Vorticity-Influenced Asymmetric Stress Tensor in Fluid Flow

摘要

The Navier Stokes momentum equations describe the general movement of a Newtonian fluid. In classic derivation of these equations, an entity called the stress tensor is postulated to exist. Classic thought allowed the stress to depend on dilation and deformation but assumed no effect of vorticity on stress. Because the complete Navier Stokes equations had not yielded to numerical solution until the last few years, it has been impractical to test the validity of assuming no influence of vorticity on stress. However, the arrival of powerful computers has now made their numerical solution possible. Consequently, an investigation was made into the relative behavior of the classic stress tensor as compared to a vorticity influenced stress tensor. In this work, a vorticity influenced stress tensor is derived. Behavior of its principal axes is examined. Within the context of a linearized one dimensional momentum equation, the asymmetric stress tensor is shown to display a forcing function behavior in phase space under some conditions. Classic heuristic arguments are discussed for assuming no influence of vorticity on stress. Lastly, the behavior of a two dimensional, low speed free shear layer is computed as it transitions from laminar to turbulent flow under the influence of the Stokesian tensor and then the vorticity-influenced tensor. The MacCormack, two dimensional, explicit, time accurate, compressible code is used for this study. Results show that the two vorticity fields differ by a maximum of about one percent in the vicinity of some vortical structures.