On a Proper Tensorial Subgrid Heat Flux Model

Abstract

In this work, we aim to shed light to the following research question: can we find a nonlinear tensorial subgrid-scale (SGS) heat flux model with good physical and numerical properties, such that we can obtain satisfactory predictions for buoyancy-driven turbulent flows?This is motivated by our findings showing that the classical (linear) eddy-diffusivity assumption, qeddy T , fails to provide a reasonable approximation for the actual SGS heat flux, q= uT uT : namely, a priori analysis for airfilled Rayleigh-Bénard convection (RBC) clearly shows a strong misalignment. In the quest for more accurate models, we firstly study and confirm the suitability of the eddy-viscosity assumption for RBC carrying out a posteriori tests for different models at very low Prandtl numbers (liquid sodium, Pr= 0.005) where no heat flux SGS activity is expected. Then, different (nonlinear) tensor-diffusivity SGS heat flux models are studied a priori using DNS data of an air-filled (Pr= 0.7) RBC at Rayleigh numbers up to 1011. Apart from having good alignment trends with the actual SGS heat flux, we also restrict ourselves to models that are numerically stable per se and have the proper cubic near-wall behavior. This analysis leads to a new family of SGS heat flux models based on the symmetric positive semi-definite tensor GGTwhere G u, i.e. q GGTT , and the invariants of the GGTtensor. Finally, relevant numerical aspects regarding the implementation of this type of models are discussed in detail. A list of physical and numerical properties is identified and subsequently imposed, leading to a symmetrypreserving discretization that is based on discrete operators already available in any CFD code.