MoST-DFG Collaboration - Theoretical, numerical and experimental investigations of gravity-driven fluid-granular mixture flows

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Fluid-granular mixture flows are motivated by various applications in industrial processes and predictions of natural hazards such as debris flows. A debris flow represents a gravity-driven flow of sediment particles and water, which fills the interstices of granular material partially or excessively. Despite the past developments in modeling, computing and experimenting geophysical mass flows, the prediction of such fluid-granular multiphase flows is still a most challenging topic mainly in two aspects (i) theoretical and numerical modeling and (ii) experimental investigation. On the one hand, in most continuum models, such mixture flows are often treated as a single-phase medium, even though they are clearly two-phase mixture. In such single-phase approaches, the debris mixture is considered either as a non-Newtonian fluid including some plastic behavior or as a Coulomb continuum where the effect of the interstitial fluid is incorporated parametrically or as a mixture with the same constituent velocities. Very rarely multi-constituent mixture models are constructed and applied to debris flows. A few existing models consider such multiphase concepts as fluid-saturated granular mixtures, although natural granular flows are often not fully saturated or else over-saturated by water. On the other hand, the simultaneous measurement of velocities and volume fractions of all constituents in a fluid-granular mixture flow is also a difficult task. Although many experimental studies discuss the effect of the interstitial fluid on the granular flow, only the dynamics of the granular medium is measured, because of the difficulty in measuring the dynamics of the fluid phase in a granular-fluid mixture.With this project, we will attempt to develop a fluid-granular two-phase model, which is able to describe such under-saturated and over-saturated mixtures and their transition by means of a two-layer approach, in which the fluid-saturated granular lower layer is overlain by either the pure granular upper layer, for the under-saturated case, or the pure fluid, for the over-saturated case. For experimental investigations, the indirect image measurement technique will be developed, by coupling PIV and PTV, to measure the fluid velocities, the granular positions, velocities and volume fractions during the dynamic mixture flow. In this coupling method, PIV will be used for simultaneously measuring the fluid velocities, and PTV for measuring the velocities of granules. The benefits are that the accuracy of the PIV method is high for discriminating the seeding particles that identifying the fluid phase, while the PTV can offer more detailed information about granular velocities than PIV. The theoretical model will be examined numerically by the discontinuous Galerkin (DG) method of an arbitrary high-order accuracy in terms of gravity-driven flows of various under- or over-saturated granular-fluid mixtures and validated by experimental results.