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Multiphase modeling of geophysical granular gravity currents with a comprehensive granular kinetic-collisional and plastic rheological model. Pyroclastic flow dynamic and depositional processes. -- (undated)
Sebastien Dartevelle, (Michigan) sdarteve@mtu.edu
We focus on the dynamic and depositional processes of granular gravity currents in volcanology and geophysics. Geophysical granular flows such as pyroclastic-flows and -surges (i) are multiphase flows, (ii) are very dissipative over many different scales, (iii) display a wide range of grain concentrations, and (iv), as a final result of these previous features, display complex nonlinear, non-uniform, and unsteady rheologies. Therefore our objectives are twofold, (i) setting up a hydrodynamic model which acknowledges the multiphase nature of granular flows and (ii) defining a comprehensive rheological model which accounts for all the different forms of viscous dissipations within granular flows at any concentration. Three important regimes within multiphase granular flows must be acknowledged: kinetic (pure free flights of grain), kinetic-collisional and frictional. The momentum and energy transfer will be different according to the granular regimes; i.e., strain-rate dependent in the kinetic and kinetic-collisional cases and strain-rate independent in the frictional (high concentration) case. The kinetic-collisional viscous regime is defined from the Boltzmann's kinetic theory of dense gas modified to account for inelastic collisions between grains and the presence of the gas phase (the "Lun et al." model). The frictional viscous regime is defined from the plastic potential and the critical state theories which account for compressibility of granular matter (e.g., dilatancy, consolidation and critical state). Yield functions are represented by a family of nested ellipsoids in the principal stress space, each one corresponding to an unique granular concentration. This compressible plastic model allows to simulate depositional processes ("Pitman-Schaeffer-Gray-Stiles" or the "Roscoe et al." model). This comprehensive granular rheological model is used in an Eulerian-Eulerian multiphase computer codes initially developed by the U.S. Department of Energy (DOE) laboratories and further adapted for typical geophysical and atmospherical application: (G)MFIX (Geophysical) Multiphase Flow with Interphase eXchange. Such multiphase flow approach allied with a comprehensive rheological model allows to reinterpret geophysical granular gravity currents in the light of kinetic-collisional and plastic rheologies. For instance, very diluted granular flows (e.g., pyroclastic surges) display a large span of granular viscosities (between 0.001 and 1 Pa.s) owing the large mean-free path of the grain and the high "granular-temperature" (i.e., turbulent flow). More concentrated flow (between 1 and 50 vol.%) have very low viscosities (<~0.001 Pa.s) because of the inelastic nature of collisions between grains. Frictional flows (>50 vol.%) display infinite plastic viscosities as their yield strength exponentially increase with grain-concentrations. Pyroclastic-flow and -surge simulations generated by "collapsing fountain" at the vent show that both diluted and concentrated end-members are closely tight together, e.g., an initially diluted flow may generate a denser basal underflow which will eventually outrun the expanded (diluted) head of the flow. We further illustrate evidences of vertical and lateral flowtransformation processes between diluted and concentrated flows, particularly laterally from a turbulent "maintained over-time fluidized zone" near source. We will illustrate that complex lateral and vertical flow transformations occur between the diluted and concentrated part of the flow and that sharp concentration gradient develops between pyroclastic flows and surges. This would suggest there is no continuum between the end-members of the flow. Most importantly, the plastic rheological model in the granular phase allows the multiphase flow model to simulate depositional processes. Our simulations suggest that a progressive vertical aggradation occurs instead of an "en masse" freezing. Fresh sediments is continuously supplied by either overlying surges or by upstream concentrated (frictional)pyroclastic-flows.