考虑孔隙气压致流化的非等容稳定颗粒模型
Non-isochoric stable granular models taking into account fluidisation by pore gas pressure
AI总结：
本文研究高体积浓度固气混合物的非等容模型，通过孔隙气压方程和剪胀函数降低颗粒摩擦，推导出线性稳定且能量耗散的流化颗粒模型，确保模型适定并正确反映颗粒流物理。
摘要：
本文研究了高体积浓度下固体颗粒与气体混合物的非等容模型。本研究的动机之一涉及地球物理学，特别是火山碎屑密度流，它们正是火山碎屑、岩石碎块与空气的混合物。它们是极具破坏力的现象，能够摧毁城市化地区，并已知能传播很长的距离，甚至在几乎平坦的地形上也是如此。孔隙气压导致的这些致密颗粒流的流化，是能够解释这种行为的一种机制，因此必须在模型中加以考虑。从气固混合模型出发，通过状态方程引入气体的可压缩性，我们将气相质量守恒方程改写为关于孔隙气压的方程，其净效应是降低颗粒间的摩擦。固相动量方程由通用的本构律补充，如 Schaeffer et al (2019, Journal of Fluid Mechanics, 874, 926-951) 中所述，通过屈服函数和剪胀函数来具体化。因此，反映颗粒流膨胀或压缩能力的速度场散度，取决于体积分数、压力、应变率和惯性数。此外，我们要求剪胀函数描述颗粒材料在等容平衡状态（即恒定体积）附近的体积变化率。该性质确保作为质量守恒方程解的体积分数始终为正且有限。我们还要求非等容流化模型是线性稳定的，并且（随时间）耗散能量。在这一理论框架下，我们推导了对应于经典流变学（如 Drucker-Prager 和 $μ$(I)，含或不含膨胀效应）的剪胀模型。本研究的主要结果是表明，有可能获得非等容且流化的颗粒模型，这些模型满足正确描述颗粒流物理性质所需的所有属性，并且是适定的，至少是线性稳定的。
英文摘要：
In this paper, we study non-isochoric models for mixtures of solid particles, at high volume concentration, and a gas. One of the motivations of this work concerns geophysics and more particularly the pyroclastic density currents which are precisely mixtures of pyroclast and lithic fragments and air. They are extremely destructive phenomena, capable of devastating urbanised areas, and are known to propagate over long distances, even over almost flat topography. Fluidisation of these dense granular flows by pore gas pressure is one response that could explain this behaviour and must therefore be taken into account in the models. Starting from a gas-solid mixing model and invoking the compressibility of the gas, through a law of state, we rewrite the conservation of mass equation of the gas phase into an equation on the pore gas pressure whose net effect is to reduce the friction between the particles. The momentum equation of the solid phase is completed by generic constitutive laws, specified as in Schaeffer et al (2019, Journal of Fluid Mechanics, 874, 926-951) by a yield function and a dilatancy function. Therefore, the divergence of the velocity field, which reflects the ability of the granular flow to expand or compress, depends on the volume fraction, pressure, strain rate and inertial number. In addition, we require the dilatancy function to describe the rate of volume change of the granular material near an isochoric equilibrium state, i.e. at constant volume. This property ensures that the volume fraction, which is the solution to the conservation of mass equation, is positive and finite at all times. We also require that the non-isochoric fluidised model is linearly stable and dissipates energy (over time). In this theoretical framework, we derive the dilatancy models corresponding to classical rheologies such as Drucker-Prager and $μ$(I) (with or without expansion effects). The main result of this work is to show that it is possible to obtain non-isochoric and fluidised granular models satisfying all the properties necessary to correctly account for the physics of granular flows and being well-posed, at least linearly stable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
