Model Reduction Based on a Numerical Length Scale Analysis

Abstract

For the time being, the required computational cost to solve the 3D time dependent flow prevents the use of such methods for internal flows at high Reynolds number in complex geometries. In this work we present a method based on a numerical length scale analysis to get a rational reduction of the full 3D governing equations for turbulent pipe flows. The length scale analysis quantifies the terms of the governing equations after changing the coordinate system into a curvilinear coordinate system with one coordinate aligned with the flow path. By retaining the most important terms or neglecting the (significantly) smallest terms, different reductions may be attained. The results for a double bent pipe, used to illustrate the approach, show that the most significant component of the viscous terms is the normal component. The convective terms are all important. The normal component is significant in the bends of the pipe due to centrifugal forces, while the spanwise component is most significant after the second bend due to a swirling motion.