A coupled finite volume and material point method for two-phase simulation of liquid-sediment and gas-sediment flows

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. This breadth of phenomena necessitates the use of continuum simulation methods, such as the material point method (MPM), which can accurately capture these large deformations while also tracking the Lagrangian features of the flow (e.g.\ the granular surface, elastic stress, etc.). Recent works using two-phase MPM frameworks to simulate these mixtures have shown substantial promise; however, these approaches are hindered by the numerical limitations of MPM when simulating pure fluids. In addition to the well-known particle ringing instability and difficulty defining inflow/outflow boundary conditions, MPM has a tendency to accumulate quadrature errors as materials deform, increasing the rate of overall error growth as simulations progress. In this work, we present an improved, two-phase continuum simulation framework that uses the finite volume method (FVM) to solve the fluid phase equations of motion and MPM to solve the solid phase equations of motion, substantially reducing the effect of these errors and providing better accuracy and stability for long-duration simulations of these mixtures

A predictive model for fluid-saturated, brittle granular materials during high-velocity impact events

Granular materials -- aggregates of many discrete, disconnected solid particles -- are ubiquitous in natural and industrial settings. Predictive models for their behavior have wide ranging applications, e.g. in defense, mining, construction, pharmaceuticals, and the exploration of planetary surfaces. In many of these applications, granular materials mix and interact with liquids and gases, changing their effective behavior in non-intuitive ways. Although such materials have been studied for more than a century, a unified description of their behaviors remains elusive. In this work, we develop a model for granular materials and mixtures that is usable under particularly challenging conditions: high-velocity impact events. This model combines descriptions for the many deformation mechanisms that are activated during impact -- particle fracture and breakage; pore collapse and dilation; shock loading; and pore fluid coupling -- within a thermo-mechanical framework based on poromechanics and mixture theory. This approach allows for simultaneous modeling of the granular material and the pore fluid, and includes both their independent motions and their complex interactions. A general form of the model is presented alongside its specific application to two types of sands that have been studied in the literature. The model predictions are shown to closely match experimental observation of these materials through several GPa stresses, and simulations are shown to capture the different dynamic responses of dry and fully-saturated sand to projectile impacts at 1.3 km/s

Development of Models for Mixtures of Fluids and Granular Sediments

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

A coupled, two-phase fluid-sediment material model and mixture theory implemented using the material point method

Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 115-118).A thermodynamically consistent constitutive model for fluid-saturated sediments, spanning dense to dilute regimes is developed from the integral form of the basic balance laws for two-phase mixtures. This model is formulated to capture the (i) viscous inertial rheology of wet grains under steady shear, (ii) the critical state behavior of granular materials under shear, (iii) the viscous thickening of fluid due to the presence of suspended grains, and (iv) the Darcy-like drag interaction for both dense and dilute mixtures. The full constitutive model is combined with the basic equations of motion for each mixture phase and implemented in the material point method (MPM) to accurately model the coupled dynamics of the combined system. Qualitative results show the breadth of problems, which this model can address. Quantitative results demonstrate the accuracy of this model as compared with analytical models and experimental observations.by Aaron S. Baumgarten.S.M

A general fluid–sediment mixture model and constitutive theory validated in many flow regimes

We present a thermodynamically consistent constitutive model for fluid-saturated sediments, spanning dense to dilute regimes, developed from the basic balance laws for two-phase mixtures. The model can represent various limiting cases, such as pure fluid and dry grains. It is formulated to capture a number of key behaviours such as: (i) viscous inertial rheology of submerged wet grains under steady shearing flows, (ii) the critical state behaviour of grains, which causes granular Reynolds dilation/contraction due to shear, (iii) the change in the effective viscosity of the fluid due to the presence of suspended grains and (iv) the Darcy-like drag interaction observed in both dense and dilute mixtures, which gives rise to complex fluid-grain interactions under dilation and flow. The full constitutive model is combined with the basic equations of motion for each mixture phase and implemented in the material point method (MPM) to accurately model the coupled dynamics of the mixed system. Qualitative results show the breadth of problems which this model can address. Quantitative results demonstrate the accuracy of this model as compared with analytical limits and experimental observations of fluid and grain behaviours in inhomogeneous geometries. ©2018 Cambridge University Press.Army Research Office (W911NF-16-1-0440)NSF (CBET-1253228

Proposed definition of competencies for surgical neuro-oncology training

Objective: The aim of this work is to define competencies and entrustable professional activities (EPAs) to be imparted within the framework of surgical neuro-oncological residency and fellowship training as well as the education of medical students. Improved and specific training in surgical neuro-oncology promotes neuro-oncological expertise, quality of surgical neuro-oncological treatment and may also contribute to further development of neuro-oncological techniques and treatment protocols. Specific curricula for a surgical neuro-oncologic education have not yet been established. Methods: We used a consensus-building approach to propose skills, competencies and EPAs to be imparted within the framework of surgical neuro-oncological training. We developed competencies and EPAs suitable for training in surgical neuro-oncology. Result: In total, 70 competencies and 8 EPAs for training in surgical neuro-oncology were proposed. EPAs were defined for the management of the deteriorating patient, the management of patients with the diagnosis of a brain tumour, tumour-based resections, function-based surgical resections of brain tumours, the postoperative management of patients, the collaboration as a member of an interdisciplinary and/or -professional team and finally for the care of palliative and dying patients and their families. Conclusions and Relevance: The present work should subsequently initiate a discussion about the proposed competencies and EPAs and, together with the following discussion, contribute to the creation of new training concepts in surgical neuro-oncology