ODTLES SIMULATIONS OF TURBULENT FLOWS THROUGH HEATED CHANNELS AND DUCTS

Abstract

A widely occurring problem in fluid dynamics either in engineering or e.g. hydrology is the turbulent transport through channels and ducts. ODTLES, a stochastic based multi-scale and multi-dimensional model, is a promising tool to describe these flows even including scalar properties like temperature. We are quantifying the ability of ODTLES to describe the heated channel flow with respect to the Prandtl number and the flow through squared ducts with respect to the Reynolds number. INTRODUCTION An interesting challenge in classical mechanics is the description of a turbulent fluid. A key difficulty in modelling these flows is their multi-scale nature. Even fundamental problems like the flow through a channel or duct are still under study and have been investigated by several groups in experiments (e.g. Hirota et al. (1997)) and numerical studies (e.g. Kawamura et al. (1999), Pinelli et al. (2010)). Direct Numerical Simulations (DNSs) are widely used to investigate these fundamental problems because they are solving the governing physical incompressible Navier-Stokes equations without assumptions. So DNSs can yield the complex statistics of moderate Reynolds number channel and duct flows, but are limited mostly to fundamental research due to the wide range of spatial and temporal scales emerging in technical and meteorological flows. These problems are for example treated by modeling small scales in Large-Eddy-Simulations (LES). These models have issues in resolving non-isotropic flow regions (e.g. near wall and stratified flows) and turbulent backscatter effects. The disagreement in the scientific community about the influence of the latter effects (e.g. Piomelli et al. (1991)) indicates the lack of understanding. Figure 1. Coordinate system and geometry of the duct (left) and the channel (right). From this point of view, stochastic approaches based on One-Dimensional-Turbulence (ODT) (e.g. Kerstein et al. (2001), Kerstein (1999)) and multi-dimensional approaches incorporating ODT, like ODTLES (e.g. Schmidt et al. (2008) and Gonzalez-Juez et al. (2011)), are an interesting alternative. The ability of ODT to resolve molecular effects (as DNSs) and to describe even non isotropic 3D turbulence using a stochastic process distinguishes ODT and ODTLES from techniques such as LES and ReynoldsAveraged-Navier-Stokes (RANS) models. NUMERICAL METHODOLOGY We are considering incompressible flows in a channel and a duct (see fig. 1). The square duct is bounded by walls at the faces normal to x3 = {−h,h} and x2 = {−h,h}, the channel by walls at x2 = {0,2h}. All other boundary conditions are considered periodic to mimic e.g. an infinite streamwise extension in the x1-direction. The turbulent channel can be described by both ODT and ODTLES, the square duct only by ODTLES due to the three dimensional non turbulent properties (e.g. secondary instabilities) of the characteristic flow. To understand the approach of ODTLES, a brief description of ODT will follow first.