A Priori Assessment of Subgrid-Scale Models and Numerical Error in Forced Convective Flow at High Prandtl Numbers

Abstract

The accurate modelling of the subgrid-scale (sgs) fluxes of momentum and heat near heated/cooled walls still represents a challenging task in Large-Eddy Simulations (LES). This is specially the case at molecular Prandtl numbers (Pr) well beyond unity, where the relevant length scales of the smallest turbulent thermal structures locally differ significantly from their dynamical counterparts. This disparity strongly conflicts with the Reynolds analogy between the transport of momentum and heat, which is inherently assumed by most sgs models for the turbulent heat flux. The present study carries out an extensive a priori analysis on data from fully resolved Direct Numerical Simulation (DNS) fields of fully developed heated turbulent pipe flow at high molecular Prandtl numbers \(Pr=10/20\), considering three popular modelling candidates for subgrid-scale closure. Aside from assessing the models’ capabilities to describe quantitatively the unresolved turbulent fluxes, a special focus is also put on the role of the numerical error, which arises from the discretization of the filtered advective fluxes on a coarse LES grid. The present analysis extends here previous studies on subgrid-scale momentum transport in isothermal mixing layer and channel flow carried out by [1] and [6], respectively, to the subgrid-scale transport of heat at high Prandtl numbers. The statistical dependence between the individual contributions (resolved, subgrid-scale, numerical discretization error) constituting the filtered advective flux terms in the LES formulation is investigated in terms of corresponding cross-correlations, as well.