Numerical simulations of free-surface flows of a Carbopol solution.
Abstract not provided.
McConnell, Joshua↗
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Free-Surface Liquid Lithium Flow Modeling and Stability Analysis for Fusion Applications
Liquid metal plasma facing components are considered an attractive design choice for fusion devices including pilot plants. Virtual prototyping of such devices includes modeling of free-surface flow of the electrically conductive liquid, which requires computational fluid dynamics (CFD) and magnetohydrodynamics (MHD) simulations. Numerical tools capable of simulating flows and heat transfer in the free-surface MHD flow were developed at PPPL based on the customized ANSYS CFX. Here, MHD is introduced using a magnetic vector potential approach. Free-surface flow capabilities are available in the code and were tested. Special stabilization procedures were derived and applied to improve convergence of the momentum equations with the source terms due to the Lorentz force and surface tension. Important characteristics of the fusion-relevant liquid metal flow is free surface smoothness and stability. Heat flux from the plasma impacts the liquid surface at a very acute angle, so any change of the free surface from axisymmetry can dramatically increase the local heat flux density and thus create excessive evaporation of liquid lithium into the plasma, which is detrimental to operations. Stability analysis of the liquid metal film flow was performed to determine applicable flow regimes. Thin film flow along horizontal wall is considered. Effects of gravity, magnetic field, and surface tension are included in the analysis.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A weighted Shifted Boundary Method for free surface flow problems
The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods and was recently introduced for the Poisson, linear advection/diffusion, Stokes, Navier-Stokes, acoustics, and shallow-water equations. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Navier-Stokes flows with moving free-surfaces, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach prevents spurious pressure oscillations in time, which would otherwise be produced if the total active fluid volume were to change abruptly over a time step. In fact, the proposed weighted SBM method induces small mass (i.e., volume) conservation errors, which converge quadratically in the case of piecewise-linear finite element interpolations, as the grid is refined. Finally, we present an extensive set of two- and three-dimensional tests to demonstrate the robustness and accuracy of the method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Magneto-Stokes flow in a shallow free-surface annulus
In this study, we analyse ‘magneto-Stokes’ flow, a fundamental magnetohydrodynamic (MHD) flow that shares the cylindrical-annular geometry of the Taylor–Couette cell but uses applied electromagnetic forces to circulate a free-surface layer of electrolyte at low Reynolds numbers. The first complete, analytical solution for time-dependent magneto-Stokes flow is presented and validated with coupled laboratory and numerical experiments. Three regimes are distinguished (shallow-layer, transitional and deep-layer flow regimes), and their influence on the efficiency of microscale mixing is clarified. The solution in the shallow-layer limit belongs to a newly identified class of MHD potential flows, and thus induces mixing without the aid of axial vorticity. We show that these shallow-layer magneto-Stokes flows can still augment mixing in distinct Taylor dispersion and advection-dominated mixing regimes. The existence of enhanced mixing across all three distinguished flow regimes is predicted by asymptotic scaling laws and supported by three-dimensional numerical simulations. Mixing enhancement is initiated with the least electromagnetic forcing in channels with order-unity depth-to-gap-width ratios. If the strength of the electromagnetic forcing is not a constraint, then shallow-layer flows can still yield the shortest mixing times in the advection-dominated limit. Our robust description of momentum evolution and mixing of passive tracers makes the annular magneto-Stokes system fit for use as an MHD reference flow.
58 GEOSCIENCES↗
FreeMHD: Validation and verification of the open-source, multi-domain, multi-phase solver for electrically conductive flows
The extreme heat fluxes in the divertor region of tokamaks may require an alternative to solid plasma-facing components, for the extraction of heat and the protection of the surrounding walls. Flowing liquid metals are proposed as an alternative, but raise additional challenges that require investigation and numerical simulations. Free surface designs are desirable for plasma-facing components, but steady flow profiles and surface stability must be ensured to limit undesirable interactions with the plasma. Previous studies have mainly used steady-state, 2D, or simplified models for internal flows and have not been able to adequately model free-surface liquid metal (LM) experiments. Therefore, FreeMHD has been recently developed as an open-source magnetohydrodynamics (MHD) solver for free-surface electrically conductive flows subject to a strong external magnetic field. The FreeMHD solver computes incompressible free-surface flows with multi-region coupling for the investigation of MHD phenomena involving fluid and solid domains. The model utilizes the finite-volume OpenFOAM framework under the low magnetic Reynolds number approximation. FreeMHD is validated using analytical solutions for the velocity profiles of closed channel flows with various Hartmann numbers and wall conductance ratios. Next, experimental measurements are then used to verify FreeMHD, through a series of cases involving dam breaking, 3D magnetic fields, and free-surface LM flows. These results demonstrate that FreeMHD is a reliable tool for the design of LM systems under free surface conditions at the reactor scale. Furthermore, it is flexible, computationally inexpensive, and can be used to solve fully 3D transient MHD flows.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Quasi-periodic travelling gravity–capillary waves
We present a numerical study of spatially quasi-periodic travelling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wavenumbers satisfying the dispersion relation is irrational. We propose a conformal mapping formulation of the water wave equations that employs a quasi-periodic variant of the Hilbert transform to compute the normal velocity of the fluid from its velocity potential on the free surface. We develop a Fourier pseudo-spectral discretization of the travelling water wave equations in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on the torus. This leads to an overdetermined nonlinear least-squares problem that we solve using a variant of the Levenberg–Marquardt method. We investigate various properties of quasi-periodic travelling waves, including Fourier resonances, time evolution in conformal space on the torus, asymmetric wave crests, capillary wave patterns that change from one gravity wave trough to the next without repeating and the dependence of wave speed and surface tension on the amplitude parameters that describe a two-parameter family of waves.
97 MATHEMATICS AND COMPUTING↗
Hyporheic Exchange in Sand Dunes Under a Freely Deforming River Water Surface
Bedform-driven hyporheic exchange is conditioned by the head gradients at the sediment-water interface. Local exchange phenomena between the surface and the subsurface are often driven by the dynamic forces related to the velocity distributions around sediment waves. In open channels, the static forces are represented by the water depth, yet most computational fluid dynamics models use a rigid-lid approximation. Here, we investigated whether and when the deformation of the river’s free-surface influences bedform-driven hyporheic exchange. This was done through simulations of coupled open channel and hyporheic flows with the air-water interface modeled either as a free-surface or a rigid-lid across increasing subcritical Froude numbers from ~0.05 to ~0.95. The normalized hyporheic flux was higher when considering free-surface deformation across most of the range of Froude numbers considered. When the Froude number was larger than 0.6 and smaller than 0.85, both hydrostatic and nonhydrostatic-driven fluxes increased significantly compared to the rigid-lid approach and the total flux was about five times that predicted with the rigid-lid. These results indicate that bedform-driven hyporheic fluxes are underestimated in most studies that use a rigid-lid assumption in subcritical flows.
58 GEOSCIENCES↗
Experimental characterization of extreme temperature granular flows for solar thermal energy transport and storage
High-temperature, dense granular flows along an inclined plane were considered for solar thermal energy transport and storage with sintered bauxite particles. A series of experiments was performed for particle inlet temperatures of ~ 200, 400, 600, and 800 °C to understand the mechanisms of granular flows at extreme temperatures. Mass flow rates were measured using a load cell and free-surface velocities were measured and computed using particle image velocimetry. Surface temperatures were measured using infrared cameras. A significant decrease in steady-state particle mass flow rate was observed with increasing temperature due to changing flow properties. A decrease in bulk particle free-surface velocities was observed at higher temperatures. Free-surface velocity measurement error between experiments were within 20% of the average. The particle surface temperatures decreased from inlet to outlet with larger gradients at higher temperatures observed due to increasing convection and radiative heat losses. Here, a decrease in temperature was observed along the side walls due to a decrease in particle velocities.
14 SOLAR ENERGY↗
Molten Salt Tritium Transport Experiment: A Versatile Fluoride Salt Loop for Validation of Tritium Transport Phenomena
Tritium is generated in Molten Salt Reactors (MSRs) from neutron capture by lithium and other constituents of the molten salt FLiBe. Tritium is a unique radionuclide as it readily permeates through hot structural materials. Thus, any material in contact with tritium laden molten salt is a potential pathway for release. Understanding tritium transport and devising adequate control strategies is necessary for the safe operation of MSRs. The Molten Salt Tritium Transport Experiment (MSTTE) is a forced-convection fluoride salt loop with the capability to inject hydrogen isotopes into flowing molten salt and to measure transport phenomena such as permeation through metals and evolution from free-surfaces. MSTTE is designed to be versatile to test potential control technology in future campaigns. This report focuses on the current design and analysis of MSTTE. Custom designed and fabricated experiment components such as the hydrogen injection system, permeation test section, diagnostics, and gas distribution system are discussed in detail. System-level tritium transport modeling using the System Analysis Module investigates experiment parameters such as hydrogen source terms, salt flow rate, and salt temperature. Computational fluid dynamics of the salt flow in the permeation test section informs design choices to establish fully developed flow in the measured permeation zone.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Percheron Power Archimedes Screw Turbine Analysis (Abstract)
The development of the Percheron Power (Percheron) composite Archimedes screw turbine (AST) is based upon employing newly developed theoretical mathematical models for optimizing the water volume carried through the AST for a given diameter, combined with minimizing efficiency losses due to bypass flow and friction. The key feasibility issues associated with producing the composite blades will be to understand the strength, fatigue, and wear performance of the AST blades and associated components, and how these factors change along the length of the turbine. To get to this understanding of material property requirements, Percheron needs free-surface computational fluid dynamics (CFD) models of the AST designs and to perform interactive modeling between the turbine blade optimization and component design based on finite element method stress analysis (FEA). The workscope and analyses requested by Percheron in the Small Business Voucher (SBV) program are well aligned with PNNL capability and recent work experience in performing CFD and FEA analysis for hydropower and marine energy turbines. The CFD analysis will provide estimates of power, efficiency, and surface forces on the blades. The forces on the blade will be transferred to the FEA analysis that will be used to evaluate the material stresses. The CFD and FEA analyses will be repeated for different AST designs provided to PNNL by Percheron. The work conducted in this SBV project will complement the existing Percheron FOA project by providing better defined parameters for design and material selection for the turbine unit prior to manufacture of initial test units.
42 ENGINEERING↗
Bounds on the Rate-Dependent Plastic Flow of Tantalum up to 75 GPa
In this study we report on the continued development of thermodynamics-based analysis of shock waves propagation with the objective of extracting information related to materials strength at high strain rates and pressures. Building on previous results reported for peak stresses of 10 GPa and 25 GPa, we present a series of three-step gas-gun shock experiments designed to explore the pressure and strain rate dependence of plastic flow in polycrystalline tantalum. These experiments at nominal peak stresses of 50 GPa and 75 GPa show the irreversible deformation before pullback to be almost entirely confined to the shock loading, with negligible plastic relaxation on the post-shock plateau. We also add a reverse-ballistics shot at 25 GPa, which was designed to reveal the pullback response with negligible interference from free-surface effects. General thermodynamic considerations allow us to place bounds on the plastic behavior even for parts of the curve that change far too rapidly for the velocimetric time resolution of (conservatively) ~ 5 ns. To analyze the data, we found it necessary to substantially improve the interpolation/extrapolation scheme in order to improve its robustness, flexibility and range of applicability. We describe the new scheme based on splines, as well as an extension of free-surface corrections to the post-shock rarefaction waves. Reanalysis with the new scheme produces results essentially within the error bars previously reported, showing that the known systematic errors associated with free-surface effects are relatively inconsequential for determining thermodynamic paths.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Effect of surface defects on damage and failure of dynamically driven cylindrical shells
Here, in this work, expanding cylinder experiments are performed using a gas gun on the aluminum 6061 alloy to understand the dynamic deformation and failure behavior of this material in the presence of surface defects in the form of scratches. The experiments are then modeled with the modified Tepla (for tensile plasticity) model, which is equipped with the damage yield function of Gurson [“Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media,” (1977)] and Tvergaard and Needleman [Acta Metall. 32(1), 157–169 (1984)], over-stress viscosity [F. Addessio and J. Johnson, J. Appl. Phys. 74(3), 1640–1648 (1993)], and the underlying viscoplastic model of Preston et al. [J. Appl. Phys. 93(1), 211–220 (2003)] (Preston–Tonks–Wallace model) for the dense material. The Tepla model parameters were calibrated using the Bayesian approach against experimentally measured free-surface velocity data obtained from plate impact experiments on the aluminum 6061 alloy. The evolution of radial expansion and shapes of the deformed cylinder from the simulations on a pristine cylinder wall and a cylinder wall with a longitudinal surface defect shows excellent agreement with the corresponding experimental results. Finally, the role of surface defect size and cylinder wall geometry on the dynamic strength of the cylinder wall was also investigated through a series of simulations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Experimental and numerical study of heat transfer characteristics of single-phase free-surface fan jet impingement with automatic transmission fluid
Not Available
Feng, Xuhui (ORCID:0000000261559356)↗