Heat and fluid flow in additive manufacturing—Part I: Modeling of powder bed fusion
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Here, we continue our development of phase field model benchmark problems with the addition of a third set, complimenting our previously developed problems for diffusion, precipitation, dendritic growth and linear elasticity. These benchmark problems are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from the phase field community. The first problem in this third set targets Stokes flow, with a particular emphasis on flow around an obstruction placed asymmetrically in the domain. While Stokes flow is not traditionally in the canon of phase field problems, it is a class of problems gaining importance in areas such as filtration and water purification. The second problem deals with coupled Cahn-Hilliard diffusion and electrostatic forces, which is an important area in energy storage and battery sciences. We present our own solutions and discuss sources of numerical errors for the Stokes problem as well as simple checks to avoid fundamental issues in the coupled diffusion-electrostatics problem. The latter problem contains some subtleties that we expand on in an Appendix.
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A new 3D multiphase numerical capability is presented here for simulating multiphase flow regimes at all Mach numbers (M). The new method is a semi-implicit extension of the finite volume discrete equation method (DEM) of Chinnaya et al. (2004), which originally used explicit time-stepping. The capability is also developed to work with another extension of the DEM to moving grids for arbitrary Lagrangian-Eularian (ALE) methods detailed in Dunn (2011). Rather than solving all phase equations simultaneously, the DEM reduces the equations to a system of single-phase Riemann solves, where each phase has its own velocity and thermodynamic state. Exchanges between the phases are modeled through source terms accounting for the phase interactions. Furthermore, since the original multiphase scheme uses an explicit time-advancement scheme, it has time step restrictions dictated by the speed of sound, which limits the model's ability to simulate weakly compressible flows which typically need to be integrated for longer time periods. Here, we extend the current multiphase formulation by implementing a pressure-correcting step to enable implicit calculations and remove acoustic time step limitations. The new semi-implicit algorithm allows use of relatively large time steps compared to an explicit method. Validation and benefits of the new implicit time-step method are illustrated using several examples including weakly compressible flows and strong shock waves. The scheme presented here is general and may be used for a variety of applications which require capabilities for handling multiphase flow at a wide range of Mach numbers. However, the goal of this research is to simulate all stages of high energy explosions, including the shock formation (high Mach numbers) and evolution of the buoyant cloud (low Mach numbers).
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This work investigates the injection-induced seismic response of a heterogeneous fault plane, featuring low-permeability asperities embedded into a high-permeability damage zone. We simulate the pressure evolution with a hydrogeological simulator, accounting for the heterogeneous fault plane. Seismicity occurs then on the asperities, represented as unstable patches reactivating by means of the Mohr-Coulomb criterion. The hydrological and seismic modules are implicitly coupled to account for effects of asperity reactivation on the permeability. Results show that permeability changes may cause at a later time a change in seismicity propagation. Finally, we also investigated such effects by varying the density of asperities.
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Physical properties of the sediment directly overlying a gas hydrate reservoir provide important controls on the effectiveness of depressurizing that reservoir to extract methane from gas hydrate as an energy resource. The permeability of overlying sediment determines if a gas hydrate reservoir’s upper contact will provide an effective seal that enables efficient reservoir depressurization. Compressibility, stiffness and strength indicate how overlying sediment will deform as the in situ stress changes during production, providing engineering data for well designs. Assessing these properties requires minimally-disturbed sediment. India’s National Gas Hydrates Program Expedition 2 (NGHP-02) provided an opportunity to study these seal sediment properties, reducing disturbance from gas exsolution and bubble growth by collecting a pressure core from the seal sediment just above the primary gas hydrate reservoir at Site NGHP-02-08 in Area C of the Krishna-Godavari Basin. The effective stress chamber (ESC) and the direct shear chamber (DSC) devices in the suite of Pressure Core Characterization Tools (PCCTs) were used to measure permeability, compressibility, stiffness and shear strength at the in situ vertical stress. Geotechnical properties of the predominantly fine-grained seal layer at in situ vertical stress are in typical clay sediment ranges, with low measured permeability (0.02 mD), high compressibility (C c = 0.26 – 0.33) and low shear strength (404 kPa). Though pressure and temperature were maintained throughout the collection and measurement process to stabilize gas hydrate, the lack of effective stress in the pressure core storage chamber and the chamber pressurization with methane-free water caused core expansion and gas hydrate in a thin coarser-grained layer to dissolve. The PCCTs can reapply in situ stress with incremental loading steps during a consolidation test to account for sediment compaction. Lastly, gas hydrate dissolution can be limited by storing cores just above freezing temperatures, and by using solid spacers to reduce the storage chamber’s free volume.
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