A new flow analysis technique: Fourier-Averaged Navier-Stokes equations

Abstract

This dissertation introduces a new flow analysis technique based on the Fourier-Averaged Navier- Stokes (FANS) equations. It details their application to educing the effect of fluid forces on flow physics. The derivation and interpretation of the method is described, and details of how to calculate key terms are presented. The method is then applied to several case studies to illustrate its applicability, interpretability, and limitations across flows of different complexities. Three of these case studies are used to evaluate the characteristics of FANS and verify that the method is interpretable. Specifically, conclusions are made from FANS and these conclusions are compared to known physics and the findings of other methods. These cases consist of 2D laminar vortex shedding over a square cylinder, axisymmetric swirling jet flow, and irregular asymmetric vortex shedding over a pair of square cylinders. FANS is shown to be simple to calculate and easy to interpret for analysing fluid flows with increasing complexity, including cases with broadband spectrum. The final case study looks at 3D flow over normally-oriented, thin flat plates. This case illustrates the practicality of FANS in exploring unknown physics in a fully 3D, nonperiodic flow. Three flat plates with varying end conditions are compared to investigate the effect of end plates on the fluctuating and mean flow. FANS shows the effect of friction from the end plates on dampening transverse velocity fluctuations. It also shows how interaction between the rollers with the boundary layer induces coherent spanwise flow at the shedding frequency. Overall, the proposed method is shown to be applicable in investigating the physics of flows with cyclic characteristics, including those with nonperiodic behaviour.