Khim B. Khattri
An innovative and full-dimensional simulation of two-phase debris flows
Depth-averaged models and simulations have been largely successful in describing granular avalanches and debris flows [4, 6, 10]. However, their success is limited to the prediction of flow depths and mean velocities as these models are restricted by hydrostatic assumptions, and thus could not fully be applied when topography changes are large, in the vicinity of the flow obstacle interactions, for strongly converging and diverging flows, in flow initiations and also during the deposition processes. Also, the full dynamical and internal pressure cannot be obtained. Therefore, in general, we need a physically complete description of the flow dynamics without reduction of the information through the flow depth. This includes the full evolution of the flow dynamical quantities, e.g., the distribution of particle concentration in all flow directions, through various channels in process engineering scenarios, in hydraulic channels, power generating plants, and irrigation systems, and largely so, for natural mass flows down mountain slopes. Recently, Domnik and Pudasaini (2012) and Domnik et al. (2013) [1, 2] advanced fundamentally by developing new theoretical models and simulation methods to describe full-dimensional innovative pressure- and rate-dependent Coulomb-viscoplastic model equations for effectively single-phase granular flows by retaining all the flow physics. Similarly, Pudasaini (2012) [8] presented a generalized three-dimensional and real two-phase solid-fluid mixture mass flow model. Although a physically complete description of the mixture flow dynamics with a non-depth-averaged model and simulation is required, this is still lacking for a real two-phase mass flow. Thus, motivated by the recent advancements in the physical-mathematical modeling and efficient simulation techniques, here, we explore an opportunity to combine these innovative methods and aim to present a novel and unified modeling and simulation framework for a full-dimensional, real two-phase mass flows down channels and slopes. The model and simulation results will be calibrated and validated against suitable data for solid-fluid mixture flows down slopes and channels.
The anticipated results may contribute significantly to our understanding of the very complex dynamics of mixing and separation between phases, depth-stratification of the dynamic quantities, such as the particle concentration, pressure, and velocity. This is necessary for the full understanding of mixture flows in natural slopes, in the form of landslides, debris flows and particle transports, both in the subaerial and submarine environments, that determine the evolution of morphodynamics of mountain slopes and vallyes. The same applies for particle-laden flows, and sediment transport in hydraulic channels and plants, and also the two-phase flows in chemical plants and process engineering.
References:
1. B. Domnik and S. P. Pudasaini. Full two-dimensional rapid chute flows of simple viscosplastic granuular materials with a pressure-dependent dynamic slip-velocity and their numerical simulations. J. Non-Newtonian Fluid of Mechanics, 173-174:72-86, 2012.
2. B. Domnik, S. P. Pudasaini, R. Katzenbach, and S. A. Miller. Coupling of full two-dimensional and depth-averaged models for granular flows. J. Non-Newtonian Fluid Mechanics, 201:56-68, 2013.
3. K. B. Khattri. Sub-diffusive and Sub-advective Viscous Fluid Flows in Debris and Porous Media. M. Phil. Dissertation, Kathmandu University, School of Science, Dhulikhel, Kavre, Nepal, 2014.
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6. S. P. Pudasaini and K. Hutter. Avalanche Dynamics: Dynamics of Rapid Flows of Dense Granular Avalanches. Springer, Berlin, New York, 2007.
7. S. P. Pudasaini, K. Hutter, S.S. Hsiau, Y. Wang S.C. Tai, and R. Katzenbach. Rapid flow of dry granular materials down inclined chutes impinging on rigid walls. Phys. Fluids, 19(053302), 2007.
8. S. P. Pudasaini. A general two-phase debris flow model. Journal of Geophysical Research, 117:F03010, 2012. doi:10.1029/2011JF002186.
9. S. P. Pudasaini. Dynamics of submarine debris flow and tsunami. Acta Mechanica, 225(8), 2423-2434, 2014.
10. Y. C. Tai, S. Noelle, J. M. N. T. Gray, and K. Hutter. Shock-capturing and front-tracking methods for granular avalanches. J. Comput. Phys., 175:269-301, 2002.