Compressible heat transfer computations by an adaptive finite element method

Abstract

This paper presents adaptive finite element computations of laminar jet impingement heat transfer. Variable fluid properties and compressibility effects are considered. A unified formulation of the equations is used to treat the simultaneous presence of three flow regimes: incompressible ( ρ= constant), compressible ( ρ= ρ( p, T)), and anelastic ( ρ= ρ( T)). The error estimator uses a local least squares projection method and accounts for errors in velocity, pressure and temperature. The performance of the methodology is verified by solving a problem possessing a closed form solution. Several applications are then considered. We study two different gases (air and CO 2), different conditions (heated, cooled or constant properties), compressibility and inlet velocity profile effects. Heat transfer is a key element of the study. Results indicate that the methodology can produce grid independent solutions even for derived quantities and in thin boundary layers.