Development of Models for Mixtures of Fluids and Granular Sediments

Abstract

Mixtures of fluids and granular sediments play an important role in many industrial, geotechnical, and aerospace engineering problems, from waste management and transportation (liquid–sediment mixtures) to dust kick-up below helicopter rotors (gas–sediment mixtures). These mixed flows often involve bulk motion of hundreds of billions of individual sediment particles and can contain both highly turbulent regions and static, non-flowing regions. To avoid tracking individual grain–grain interactions and pore-scale fluid flows, it is desirable to model these problems using continuum techniques, where microscopic grain-scale properties are homogenized into bulk descriptions of the mixture’s behavior. This approach offers exceptional scaling; however, it requires the development of material constitutive models and simulation techniques that are capable of capturing the breadth of phenomena exhibited by submerged granular sediments under different loading conditions. When compacted, the friction between grains manifests as a bulk yield stress, resulting in solid-like behavior. When this yield stress is exceeded, the microscopic reorganization of grains can produce critical state behavior as the material transitions to a flowing, fluid-like state. Additionally, in unconfined flows, grains can become disconnected from each other and begin interacting through infrequent, inelastic collisions: behaving more like a granular gas. This breadth of different material behaviors is also coupled to the motion of the fluid filling the pore space between grains. A complete continuum modeling framework should be able to describe, predict, and simulate this wide range of behaviors, smoothly transitioning between these different flow regimes. Recently developed continuum modeling frameworks that use the material point method (MPM) have shown substantial promise; however, existing approaches are limited in the range of material behaviors that are considered and types of engineering applications that can be addressed. In this thesis, a continuum modeling framework for fluid–sediment mixtures is developed that incorporates a new granular material model and addresses several of the numerical limitations associated with the MPM. This granular material model is designed to capture the important behaviors described above and can also be extended to capture other non-trivial mixture phenomena, such as that observed in shear-thickening suspensions (e.g., cornstarch–water mixtures). Additionally, this thesis considers techniques for mitigating simulation error in the material point representation of the pore fluid, including direct changes to the MPM as well as combining the MPM with a more common numerical solver, such as the finite volume method (FVM). The modeling framework developed in this thesis is shown to be predictive for a wide range of mixed flows, including both liquid–sediment and gas–sediment problems.Ph.D