A compressible fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes and dilute pyroclastic density currents. Main references are: http://www.geosci-model-dev-discuss.net/8/8895/2015/gmdd-8-8895-2015-metrics.html http://linkinghub.elsevier.com/retrieve/pii/S0377027316301688 https://doi.org/10.1038/s41467-019-10337-3 The code has been written by using the OpenFOAM libraries. 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 (volumetric concentration smaller than 1 vol.%) and small particles Stokes number St<0.2. When St<0.001, the model reduces to the dusty-gas one. The model is significantly faster than standard multiphase Eulerian models, 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, dynamic Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous properties without then need of any empirical parameters for turbulence. 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.

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