Comprehensive Approaches to Multiphase Flows in Geophysics--Application to Nonisothermal, Nonhomogenous, Unsteady, Large-Scale, Turbulent Dusty Clouds. I. /Hydrodynamic and Thermodynamic RANS and LES Models

摘要

The objective of this manuscript is to fully derive a geophysical multiphase model able to ''accommodate'' different multiphase turbulence approaches; viz., the Reynolds Averaged Navier-Stokes (RANS), the Large Eddy Simulation (LES), or hybrid RANSLES. This manuscript is the first part of a larger geophysical multiphase project--lead by LANL--that aims to develop comprehensive modeling tools for large-scale, atmospheric, transient-buoyancy dusty jets and plume (e.g., plinian clouds, nuclear ''mushrooms'', ''supercell'' forest fire plumes) and for boundary-dominated geophysical multiphase gravity currents (e.g., dusty surges, diluted pyroclastic flows, dusty gravity currents in street canyons). LES is a partially deterministic approach constructed on either a spatial- or a temporal-separation between the large and small scales of the flow, whereas RANS is an entirely probabilistic approach constructed on a statistical separation between an ensemble-averaged mean and higher-order statistical moments (the so-called ''fluctuating parts''). Within this specific multiphase context, both turbulence approaches are built up upon the same phasic binary-valued ''function of presence''. This function of presence formally describes the occurrence--or not--of any phase at a given position and time and, therefore, allows to derive the same basic multiphase Navier-Stokes model for either the RANS or the LES frameworks. The only differences between these turbulence frameworks are the closures for the various ''turbulence'' terms involving the unknown variables from the fluctuating (RANS) or from the subgrid (LES) parts. Even though the hydrodynamic and thermodynamic models for RANS and LES have the same set of Partial Differential Equations, the physical interpretations of these PDEs cannot be the same, i.e., RANS models an averaged field, while LES simulates a filtered field. In this manuscript, we also demonstrate that this multiphase model fully fulfills the second law of thermodynamics and fulfills the necessary requirements for a well-posed initial-value problem. In the next manuscripts, we will further develop specific closures for multiphase RANS, LES, and hybrid-LES.