A model is developed for describing mixing of several species under high-pressure conditions. The model includes the Peng-Robinson equation of state, a full massdiffusion matrix, a full thermal-diffusion-factor matrix necessary to incorporate the Soret and Dufour effects and both thermal conductivity and viscosity computed for the species mixture using mixing rules. Direct numerical simulations (DNSs) are conducted in a temporal mixing layer configuration. The initial mean flow is perturbed using an analytical perturbation which is consistent with the definition of vorticity and is divergence free. Simulations are performed for a set of five species relevant to hydrocarbon combustion and an ensemble of realizations is created to explore the effect of the initial Reynolds number and of the initial pressure. Each simulation reaches a transitional state having turbulent characteristics and most of the data analysis is performed on that state. A mathematical reformulation of the flux terms in the conservation equations allows the definition of effective species-specific Schmidt numbers (Sc) and of an effective Prandtl number (Pr) based on effective speciesspecific diffusivities and an effective thermal conductivity, respectively. Because these effective species-specific diffusivities and the effective thermal conductivity are not directly computable from the DNS solution, we develop models for both of these quantities that prove very accurate when compared with the DNS database. For two of the five species, values of the effective species-specific diffusivities are negative at some locations indicating that these species experience spinodal decomposition; we determine the necessary and sufficient condition for spinodal decomposition to occur. We also show that flows displaying spinodal decomposition have enhanced vortical characteristics and trace this aspect to the specific features of high-density-gradient magnitude regions formed in the flows. The largest values of the effective speciesspecific Sc numbers can be well in excess of those known for gases but almost two orders of magnitude smaller than those of liquids at atmospheric pressure. The effective thermal conductivity also exhibits negative values at some locations and the effective Pr displays values that can be as high as those of a liquid refrigerant. Examination of the equivalence ratio indicates that the stoichiometric region is thin and coincides with regions where the mixture effective species-specific Lewis number values are well in excess of unity. Very lean and very rich regions coexist in the vicinity of the stoichiometric region. Analysis of the dissipation indicates that it is † Email address for correspondence: josette.bellan@jpl.nasa.govMulti-species supercritical-pressure mixing 579 dominated by mass diffusion, with viscous dissipation being the smallest among the three dissipation modes. The sum of the heat and species (i.e. scalar) dissipation is functionally modelled using the effective species-specific diffusivities and the effective the...

This paper presents a statistical approach, known as mesoscopic Eulerian formalism (Février et al., J Fluid Mech 533:1-46, 2005), which is extended in order to model a cloud of inertial evaporating droplets interacting with a turbulent carrier flow. This approach is checked in a non-isothermal droplet-laden turbulent planar jet by means of a priori tests. The "measurement" of the mesoscopic particlevelocity and particle-temperature moments is accomplished by using the Eulerian particle fields computed from a Direct Numerical Simulation (DNS) coupled with a Lagrangian approach for the droplets. The results of this work show the ability of such an approach to describe the evaporating dispersed phase interacting with turbulent flows.

International audienceAn algebraic-closure-based moment method (ACBMM) is developed for unsteady Eulerian particle simulations, coupled with direct numerical simulations (DNSs) of fluid turbulent flows, in very dilute regime and up to large Stokes numbers StK (based on the Kolmogorov timescale) or moderate Stokes numbers St (based on the turbulent macroscale seen by the particles). The proposed method is developed in the frame of a conditional statistical approach which provides a local and instantaneous characterization of the dispersed-phase dynamic accounting for the effect of crossing between particle trajectories which becomes substantial for StK > 1. The computed Eulerian quantities are low-order moments of the conditional probability density function (PDF) and the corresponding governing equations are derived from the PDF kinetic equation in the general frame of the kinetic theory of gases. At the first order, the computation of the mesoscopic particle number density and velocity requires the modeling of the second-order moment tensor appearing in the particle momentum equation and referred to as random uncorrelated motion (RUM) particle kinetic stress tensor. The current work proposes a variety of different algebraic closures for the deviatoric part of the tensor. An evaluation of some effective propositions is given by performing an a priori analysis using particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal particle-laden turbulent planar jet. Several million-particle simulations are analyzed in order to assess the models for various Stokes numbers. It is apparent that the most fruitful are explicit algebraic stress models (2UEASM) which are based on an equilibrium assumption of RUM anisotropy for which explicit solutions are provided by means of a polynomial representation for tensor functions. These models compare very well with Eulerian-Lagrangian DNSs and properly represent all crucial trends extracted from such simulations