ASHEE: a compressible, equilibrium-Eulerian model for volcanic ash plumes

A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations for a mixture of gases and solid particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model, valid for low concentration regimes and small particles Stokes $St<0.2$. When $St < 0.001$ the model reduces to the dusty-gas one. The new model is significantly faster than the Eulerian model while retaining the capability to describe gas-particle non-equilibrium. Direct numerical simulation accurately reproduce the dynamics of isotropic turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration of particles by turbulence, verifying the model reliability and suitability for the simulation of high-Reynolds number and high-temperature regimes. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous properties. The self-similar radial profile and the development of large-scale structures are reproduced, including the rate of entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal, and maximum plume height. Coarse particles partially decouple from the gas within eddies, modifying the turbulent structure, and preferentially concentrate at the eddy periphery, eventually being lost from the plume margins due to the gravity. By these mechanisms, gas-particle non-equilibrium is able to influence the large-scale behavior of volcanic plumes.Comment: 29 pages, 22 figure

Effect of particle inertia on the turbulence in a suspension

We propose a one-fluid analytical model for a turbulently flowing dilute suspension, based on modified Navier-Stokes equation with a $k$-dependent effective density of suspension, $\rho_ {eff}(k)$, and an additional damping term $\propto \gamma_ p(k)$, representing the fluid-particle friction (described by Stokes law). The statistical description of turbulence within the model is simplified by a modification of the usual closure procedure based on the Richardson-Kolmogorov picture of turbulence with a differential approximation for the energy transfer term. The resulting ordinary differential equation for the energy budget is solved analytically for various important limiting cases and numerically in the general case. In the inertial interval of scales we describe analytically two competing effects: the energy suppression due to the fluid particle friction and the energy enhancement during the cascade process due to decrease of the effective density of the small scale motions. An additional suppression or enhancement of the energy density may occur in the viscous subrange, caused by the variation of the extent of the inertial interval due to the combined effect of the fluid-particle friction and the decrease of the kinematic viscosity of the suspensions. The analytical description of the complicated interplay of these effects supported by numerical calculations is presented. Our findings allow one to rationalize the qualitative picture of the isotropic homogeneous turbulence of dilute suspensions as observed in direct numerical simulations.Comment: 21 pages, 5 figues,included, PRE, submitte

DNS of compressible multiphase flows through the Eulerian approach

In this paper we present three multiphase flow models suitable for the study of the dynamics of compressible dispersed multiphase flows. We adopt the Eulerian approach because we focus our attention to dispersed (concentration smaller than 0.001) and small particles (the Stokes number has to be smaller than 0.2). We apply these models to the compressible ($\text{Ma} = 0.2,\,0.5$) homogeneous and isotropic decaying turbulence inside a periodic three-dimensional box ($256^3$ cells) using a numerical solver based on the OpenFOAM$^{R}$ C++ libraries. In order to validate our simulations in the single-phase case we compare the energy spectrum obtained with our code with the one computed by an eighth order scheme getting a very good result (the relative error is very small $4*10^{-4}$). Moving to the bi-phase case, initially we insert inside the box an homogeneous distribution of particles leaving unchanged the initial velocity field. Because of the centrifugal force, turbulence induce particle preferential concentration and we study the evolution of the solid-phase density. Moreover, we do an {\em a-priori} test on the new sub-grid term of the multiphase equations comparing them with the standard sub-grid scale term of the Navier-Stokes equations.Comment: 10 pages, 5 figures, preprint. Direct and Large Eddy Simulations 9, 201

Deblocking of interacting particle assemblies: from pinning to jamming

A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either external quenched disorder, or of internal constraints. The first case belongs to the realm of the depinning transition, which, for example, is relevant for flux-lines in type II superconductors and other elastic systems moving in a random medium. The second case is usually included within the so-called jamming scenario observed, for instance, in many glassy materials as well as in plastically deforming crystals. Here we review some aspects of the rich phenomenology observed in interacting particle models. In particular, we discuss front depinning, observed when particles are injected inside a random medium from the boundary, elastic and plastic depinning in particle assemblies driven by external forces, and the rheology of systems close to the jamming transition. We emphasize similarities and differences in these phenomena.Comment: 20 pages, 8 figures, submitted for a special issue of the Brazilian Journal of Physics entitled: Statistical Mechanics of Irreversible Stochastic Models - I

A statistical mechanics approach to mixing in stratified fluids

Predicting how much mixing occurs when a given amount of energy is injected into a Boussinesq fluid is a longstanding problem in stratified turbulence. The huge number of degrees of freedom involved in those processes renders extremely difficult a deterministic approach to the problem. Here we present a statistical mechanics approach yielding prediction for a cumulative, global mixing efficiency as a function of a global Richardson number and the background buoyancy profile.Comment: Accepted in Journal of Fluid Mechanic