MoST-DFG Collaboration - Theoretische, numerische und experimentelle Untersuchungen von schwerkraftgetriebenen Fluid-Granulat-Strömungen
Zusammenfassung der Projektergebnisse
The project aims to theoretically, numerically and experimentally investigate the flow dynamics of general granular-fluid mixtures. Different from single-medium flows, such as pure granular or pure fluid flows, granular-fluid mixtures exhibit complex interactions between the solid and fluid phases. Another important characteristic of these flows is the phase separation between grains and fluid during motion, which leads to the occurrence, transition and even disappearance of different flow regimes. These include single-layer flow regimes of pure grains, pure fluid, and saturated granular-fluid mixtures, as well as the two-layer flow regimes of under-saturated and over-saturated mixtures. We started with a comprehensive mixture theory for saturated granular-fluid mixtures and established the mass and momentum balance equations for the solid and fluid phases. The single-phase balance equations for pure granular and pure fluid flows can be obtained by simplifying the balance equations for saturated mixtures. By depth integration of these balance equations, together with the application of the corresponding boundary conditions and jump conditions, if any, we derived the depth-averaged model for different flow regimes. The proposed model accounts for the effects of the granular dilatancy and the induced excess pore fluid pressure in the saturated mixture region. In the under-saturated or over-saturated mixture regimes, the granular or fluid mass and momentum transfer cross the interface are considered. For numerical simulations, we implemented the depth-averaged models for pure granular flows and saturated mixtures within the in-house developed BoSSS solver. To validate the numerical implementation, the simulations of the collapse of a pure granular column on a slope were conducted and compared with the analytical solutions. Convergence studies were also performed, demonstrating the expected convergence behaviour. Furthermore, we numerically investigated the flow dynamics of pure grains and saturated mixtures, where a finite mass of material flows down a slope transitioning into a horizontal surface. To simulate the occurrence of different flow regimes in granular-fluid mixtures, the two-layer structure depth-averaged model was solved numerically using a high-resolution second-order centralupwind scheme. Although this numerical scheme does not achieve the arbitrary numerical accuracy of the DG method, it offers a simpler implementation and allows faster validation of our theoretical model. This numerical scheme has been widely used in studies of granular flows. To validate the proposed depth-averaged model, the Taiwanese cooperation partner conducted the experiments on the collapse of granular columns under different initial water-saturation conditions, including the initially under-saturated, saturated, and over-saturated granular-water mixture columns. Their experiments measured the temporal evolution of layer depths for both grains and water, as well as the particle velocities using PIV technology. The experimental results were compared with our numerical simulations to evaluate the effectiveness of the model. Additionally, to demonstrate the robustness of the numerical implementation and to evaluate the performance of the proposed model, we conducted numerical simulations for a range of scenarios and compared them with previous experimental studies. These include: (i) landslides of dry grains and initially saturated grain-water mixture, (ii) collapse of granular columns in a viscous fluid, and (iii) dry particles sliding into water, inducing water free-surface waves. The numerical results show that our model effectively captures these flow dynamics, highlighting the ability of the proposed depth-averaged model to predict of the flow behaviour of real geophysical flows. Future research should extend the proposed theoretical model to the study of real geophysical flows, such as landslides, avalanches, and debris flows, to support the development of effective hazard prevention and mitigation strategies.
Projektbezogene Publikationen (Auswahl)
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A depth-averaged description of granular-fluid mixture flows with a compressible µ(I) rheology. In GAMM Annual Meeting, August 2022, Aachen, Germany
W. Sun & Y. Wang
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A Depth‐Averaged Description of Submarine Avalanche Flows and Induced Surface Waves. Journal of Geophysical Research: Earth Surface, 128(4).
Sun, W.; Meng, X.; Wang, Y.; Hsiau, S. S. & You, Z.
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Modeling Phase Separation in Grain‐Fluid Mixture Flows by a Depth‐Averaged Approach With Dilatancy Effects. Journal of Geophysical Research: Earth Surface, 129(12).
Sun, Weihang & Wang, Yongqi
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Experimental and numerical investigation of the granular column collapse under different initial water-saturation conditions. Computers and Geotechnics, 181, 107136.
Hsiau, Shu-San; Sun, Weihang; Sheng, Li-Tsung; Chou, Shih-Hao; Wang, Jun-Yi & Wang, Yongqi
