Modeling of the Energy Equation for LES of Flows at Supercritical Pressure

Abstract

A database of transitional Direct Numerical Simulation (DNS) realizations of a supercritical mixing layer is analyzed for understanding small-scale behavior and examining Subgrid Scale (SGS) models duplicating that behavior. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier Stokes, total energy and species equations coupled to a real gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The Large Eddy Simulation (LES) equations are derived from the DNS ones through Altering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The focus is here on the energy equation. The magnitude of all terms in this filtered DNS equation is analyzed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there is a new term that must be modeled in this equation. This new term can be thought to result from the filtering of the strongly nonlinear equation of state, and is associated with high density-gradient magnitude regions both found in DNS and observed experimentally in fully-turbulent high-pressure flows. A priori modeling approaches for the energy-equation additional term are proposed, all of which must ultimately be tested in LES to show viability.