Influence of grain-size distribution on the dynamics of underexpanded volcanic jets

• We identify two regimes of overpressured volcanic jets solely related to grain-size.
• Supersonic jets laden with fine particles (Stokes number St < 1) develop a Mach shock.
• The Mach shock is obliterated in presence of coarse particles (St > 1).
• In polydisperse mixtures the effective St depends on the fine/coarse mass ratio.
• In presence of fines, St < 1 also for coarse grains and the Mach shock is retrieved.

The dynamics of underexpanded volcanic jets is studied by means of a Eulerian multiphase flow model, accounting for kinetic and thermal non-equilibrium between gas and particles. Two-dimensional numerical simulations are analysed in terms of the scaling properties of the gas–solid flow based on the particle Stokes number St, defined as the ratio of the particle relaxation time τs and a typical flow time scale, here taken as the formation time of the jet Mach disk τM. For monodisperse mixtures, fine particles with St ≪ 1 are tightly coupled to the gas during decompression and the typical flow patterns of supersonic free jets are reproduced. The multiphase flow model, in this case, gives results comparable to a dusty-gas model. However, for St ≫ 1 we demonstrate that the effects of particle inertia and gas–particle drag are so relevant that the shock wave structure associated with gas decompression is obliterated, although the mixture velocity remains supersonic. We are therefore able to identify two different regimes of jet decompression (with/without Mach disk) that appear to be associated exclusively with the size of the ejected particles. For bidisperse mixtures, multiphase flow numerical simulations show that the features of underexpanded jet depend on the relative mass load of fine and coarse particles. A scaling analysis has been performed by means of a hybrid multiphase flow model, in which fine particles are mixed with the gas (in a dusty-gas approximation), while coarse particles are modelled as a disperse phase, with a modified Stokes number accounting for the mixture properties of the carrier pseudofluid. Both scaling analysis and numerical simulations with the hybrid model corroborate the analysis based on the Stokes number for bidisperse underexpanded jets, although particle–particle momentum exchange between particles of different size can affect the multiphase flow dynamics, especially in regimes with St ~ 1. We finally extend our analysis to polydisperse mixtures, by defining a threshold between fine and coarse particles on the basis of their Stokes number. Numerical simulations and scaling analysis based on the hybrid model (in which all fine particles are mixed with the gas in the dusty-gas approximation and the coarsest particles are described by a single hydraulically equivalent disperse phase) demonstrate that the total particle size distribution can have a significant effect on the jet decompression dynamics, potentially affecting the stability and large-scale behaviour of the volcanic column.

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