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DOE OSTI2022

A fast matrix-free approach to the high-order control volume finite element method with application to low-Mach flow

Here, a fast matrix-free formulation of the control volume finite element method is presented, requiring much less memory and computational work than previous efforts. The method is implemented and evaluated as a solver for low-Mach flow, including the evaluation of a preconditioning strategy for the pressure Poisson equation. The efficiency and scaling with polynomial order is evaluated on simple turbulent flows of interest, with appropriate solution quality metrics, and compared with a reference node-centered finite volume discretization. For a turbulent channel flow test, we show improvement in computational work for a given accuracy with the high-order scheme. The performance on a GPU accelerated platform is also investigated, with benefit shown for the matrix-free discretization.

42 ENGINEERING↗

DOE OSTI2024

Degradation of performance in ICF implosions due to Rayleigh–Taylor instabilities: A Hamiltonian perspective

The Rayleigh–Taylor instability (RTI) is an ubiquitous phenomenon that occurs in inertial-confinement-fusion (ICF) implosions and is recognized as an important limiting factor of ICF performance. To analytically understand the RTI dynamics and its impact on ICF capsule implosions, we develop a first-principle variational theory that describes an imploding spherical shell undergoing RTI. The model is based on a thin-shell approximation and includes the dynamical coupling between the imploding spherical shell and an adiabatically compressed fluid within its interior. Using a quasilinear analysis, we study the degradation trends of key ICF performance metrics (e.g., stagnation pressure, residual kinetic energy, and areal density) as functions of initial RTI parameters (e.g., the initial amplitude and Legendre mode), as well as the 1D implosion characteristics (e.g., the convergence ratio). We compare analytical results from the theory against nonlinear results obtained by numerically integrating the governing equations of this reduced model. Our findings emphasize the need to incorporate polar flows in the calculation of residual kinetic energy and demonstrate that higher convergence ratios in ICF implosions lead to significantly greater degradation of key performance metrics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Modeled sensitivity of multi-MA accelerator performance to electrode contaminant inventory

Significant particle-in-cell code development has enabled simulations of power flow in multi-MA accelerators to include the desorption of surface contaminants, their ionization into surface plasmas, and the impact of these plasmas on efficiency. The simulations base desorption on an Arrhenius equation, whose most significant unknown is the surface contaminant inventory. The sensitivity of power-flow simulations to this inventory is studied here using Sandia National Laboratories' Z accelerator with a 7-nH MagLIF load [Phys. Plasmas 17, 056303 (2010)]. Simulations are conducted in 3D cylindrical coordinates for the current-adder, or “convolute,” region of Z and in 2D for the final feed only. Simulated contaminant inventories are varied from 1 to 32 monolayers (MLs) in 2D, and 2 to 4 ML in 3D. The results reveal sensitivities to the local ratio of E/B⁠. The high B-field, low E-field region near the short-circuit load is insensitive to the contaminant inventory, where assumed values of 4–32 ML change the load current by ≤ 2%, and agree with experiment to within 2% at peak current. A 1-ML value is the outlier, increasing the load current by 5%, but still within measurement uncertainty. In contrast, the relatively higher E-field, lower B-field convolute region has slower contaminant desorption and higher-magnitude E-field penetration of the surface plasmas. The current loss in the convolute region does increase with contaminant inventory. The loss assuming 4 ML is 12% larger than for 2 ML, with 4 ML being the better match to experiment.

Arrhenius equation↗

DOE OSTI2021

Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

In this study, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.

3D–1D coupled blood flow models↗

DOE OSTI2021

Simultaneous velocity and density measurements of fully developed Rayleigh-Taylor mixing

Here, the dynamics of molecular mixing and the energy transfer process in the Rayleigh-Taylor instability (RTI) are studied through the collection of simultaneous density-velocity measurements. These experiments provide simultaneous density-velocity field measurements, in contrast to previous point measurements. Statistically stationary experiments are performed in a “convective-type” gas tunnel facility, with density contrast achieved through the injection of helium into the bottom stream. Three experiments at Atwood number ≈ 0.1 are captured at three outer scale Reynolds numbers Re = 520, 2260, and 4050. Particle image velocimetry and laser induced fluorescence are employed simultaneously. Statistics of the density and velocity show self-similar collapse of RTI profiles at large Reynolds number Re >2000. Flat velocity profiles indicate homogeneous turbulence characteristics in the core of the mixing region. Significant anisotropy develops in the flow, with horizontal velocity fluctuations being only 60% of the vertical velocity fluctuations. The turbulent mass flux is found to be asymmetric about the centerline, with increased peak towards the spike. Measurements of the molecular mixing show that mixing is maximized at the core of the flow and increases with increased Reynolds number. The transport equation of density-specific-volume correlation b shows that it is mostly produced in the core of the mixing region, and that the spatial evolution of its profile is the result of transport by bulk motion of the bubble and spike. Energy transfer from gravitational potential energy to turbulent kinetic energy and viscous dissipation is observed to occur in the experiment with a ratio of dissipated energy to potential energy released of 38%. The analysis of the turbulent kinetic energy transport equation budget reveals that production is the primary mechanism towards the growth of turbulent kinetic energy in the core of the flow, and is asymmetrically slightly skewed towards the spike. However, it is through the transport that the strong advection at the edges of the mixing region is maintained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Influence of Equation-of-States on Supercritical CO2 Combustion Mixtures

Abstract Fossil fuel based direct-fired supercritical CO2 (sCO2) cycles are gaining the attention of industry, academia, and government due to their remarkable efficiency and carbon capture at high-source temperatures. Modeling plays an important role in the development of sCO2 combustors because experiments are very expensive at the designed operating conditions of these direct-fired cycles. Inaccurate density estimates are detrimental to the simulation output. Hence, this work focuses on comprehensive evaluation of the influence and applicability of various equation-of-states (EOS) which are being used in the supercritical combustion modeling literature. A state-of-the-art supercritical combustion modeling methodology is used to simulate counter-flow supercritical CO2 flames by using various equation-of-states. The results show that using the corresponding state principle to evaluate compressibility factor is not accurate. Also, van der Waal type EOSs predictions can be as accurate as complex Benedict–Webb–Rubin EOSs; hence van der Waal EOSs are more suitable to simulate sCO2 combustor simulations. Non-ideal effects are significant under the operating conditions considered in this work. The choice of EOS significantly influences the flame structure and heat release rate. Also, assuming the binary interaction parameter as zero is reasonable in sCO2 combustion simulations.

Energy & Fuels↗

DOE OSTI2022

Wedge-Shaped Hopper Design for Milled Woody Biomass Flow

The bioenergy industry has been challenged by unstable flow and transport of milled biomass in material handling operations. Handling issues such as hopper clogging and auger jamming are attributed to knowledge gaps between existing handling units designed for bulk solids and their suitability for milled biomass with high compressibility. This work investigates various flow behaviors of granular woody biomass in wedge-shaped hoppers. Herein, hopper flow physical experiments and numerical simulations are conducted to study the influence of the critical material attributes and critical processing parameters on the flow pattern, arching, and throughput. The results show that (1) the preferred flow pattern, mass flow, can be achieved by controlling the material’s internal friction angle, hopper inclination, and hopper wall friction; (2) hopper arching, governed by the competing gravity-driven force against flow resistance from material internal friction and material–wall friction, can be controlled by the hopper wall friction angle and the inclination angle; and (3) flow throughput can be accurately estimated from our empirical equation with inputs of hopper outlet geometry and particle-scale to bulk-scale material attributes. This study elucidates woody biomass flow physics and provides guidance for industrial equipment design.

09 BIOMASS FUELS↗

DOE OSTI2020

Benchmark of interfacial area concentration approaches for the two-fluid model in gas-dispersed condensing flow

Accurate predictions of interfacial area concentration (IAC) are required for closure of the condensation phase change term. The interfacial area transport equation (IATE) can dynamically predict interfacial area concentration and is increasingly being used in the benchmarking of phase change flows over static based correlations which require a flow regime map. For higher flow regimes, the two-group two-fluid IATE model can separately model the transport of spherical bubbles and cap/slug bubbles. Recently, a modified formulation of the one-group and two-group two-fluid model with interfacial area transport equation was proposed for gas-dispersed condensing flows. Three datasets have been used for validation consisting of condensing two-phase flow data in the unheated section of a vertical annulus with conditions spanning a range of pressures, inlet subcoolings and mass fluxes for benchmarking the various IAC approaches. For bubbly flows, the coupled void transport - IATE simulation results in good agreement in the predictions of the void fraction and the interfacial area concentration under nearly all sixty conditions. Considering the proposed two-group two-fluid IATE model formulation, the group-2 Nusselt number correlation is investigated to account for the appropriate heat transfer length scale for group-2 bubbles. Validation of the proposed two-group two-fluid model against the new dataset shows good agreement with experimental data with significant improvement over the one-group IATE model for conditions with substantial group-2 void fraction throughout the simulation domain.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Statistical Treatment of Inverse Problems Constrained by Differential Equations-based Models with Stochastic Terms

This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is to formulate the inverse problem, in particular the objective function, to find the closest forward distribution (i.e., the output of the stochastic forward problem) that best explains the distribution of the observations in a certain metric. We use proper scoring rules, a concept employed in statistical forecast verification, namely energy, variogram, and hybrid (i.e., combination of the two) scores. We study the performance of the proposed formulation in the context of two applications: a coefficient field inversion for subsurface flow governed by an elliptic partial differential equation with a stochastic source and a parameter inversion for power grid governed by differential-algebraic equations. In both cases we show that the variogram and the hybrid scores produce better parameter inversion results than does the energy score, whereas the energy score leads to better probabilistic predictions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Universal scaling laws and density slopes for dark matter haloes

Smalls scale challenges suggest some missing pieces in our current understanding of dark matter. In this work, a cascade theory for dark matter is proposed to provide extra insights, similar to the cascade phenomenon in hydrodynamic turbulence. The kinetic energy is cascaded in dark matter from small to large scales involves a constant rate $ε_u$ (≈–4.6×10 –7 m 2 / s 3 ). Confirmed by N-body simulations, the energy cascade leads to a two-thirds law for kinetic energy $v^2_r$ on scale $\textit{r}$ such that $v^2_r∝(ε_ur)^{2/3}$. Equivalently, a four-thirds law can be established for mean halo density $ρ_s$ enclosed in the scale radius $r_s$ such that $ρ_s ∝ε^{2/3}_uG^{–1}r^{–4/3}_s$, which was confirmed by galaxy rotation curves. Critical properties of dark matter might be obtained by identifying key constants on relevant scales. First, the largest halo scale $r_l$ can be determined by $–u^3_0/ε_u$, where u0 is the velocity dispersion. Second, the smallest scale rη is dependent on the nature of dark matter. For collisionless dark matter, $r_η∝(–Gℏ/ε_u)^{1/3}$ ≈ 10 –13 m , where ℏ is the Planck constant. An uncertainty principle for momentum and acceleration fluctuations is also postulated. For self-interacting dark matter, $r_η∝ε^2_uG^{–3}(σ/m)^3$, where σ/m is the cross-section of interaction. On halo scale, the energy cascade leads to an asymptotic density slope γ = –4/3 for fully virialized haloes with a vanishing radial flow, which might explain the nearly universal halo density. Based on the continuity equation, halo density is analytically shown to be closely dependent on the radial flow and mass accretion, such that simulated haloes can have different limiting slopes. A modified Einasto density profile is proposed accordingly.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Wetlands Geoprocessor (v 1.0)

Wetlands have often been described as the “Earth’s kidneys” because wetlands have the ability filter pollutants and purify water. Based upon wetland storage capacity, average daily flow, and inflow nutrient loading this model estimates potential load reductions of nitrate and orthophosphate) from a constructed surface flow wetland (CW). The model relies upon equations, coefficients, and models provided by Cheng et al. 2020 and Cheng & Basu 2017. Nitrogen (N) and phosphorus are important nutrients to ecosystems, but high concentrations can lead to water quality issues. Major sources of these nutrients come from agricultural areas where fertilizer is applied in large quantitates and/or animal waste is present. Excess nitrate and phosphorus may result in overgrowth of algae, which can decrease the dissolved oxygen in water, thereby harming and killing fish and other aquatic species. This model evaluates water purification results and estimates cost to install a surface flow constructed wetlands.

Davis, Cleve↗

DOE OSTI2020

Probing interfacial momentum closures in two-phase bubbly flow with machine learning-aided methods

Computational fluid dynamics (CFD) approach has already reached a high level of maturity for single-phase flows, however the development of closure models for two-phase flow requires additional attention. Multiphase CFD (M-CFD) methods resolve the conservation equations for mass, momentum and energy while differing in the approaches and strategies adopted in the physical closure models. The most widely adopted framework for M-CFD is the Eulerian-Eulerian two-fluid approach which assumes that all phases are co-existing inside each computational cell. For each fluid, the full set of conservation equations is solved; therefore, each fluid has a different velocity field. For adiabatic two-phase flow, the mechanisms of the interfacial momentum transfer are modeled by the interfacial forces representing different physical mechanisms. One of the crucial issues in the development and application of two-fluid model is the understanding of the interfacial momentum closures which determines the bubble distribution and migration behaviors. Dedicated experiments are performed to support the physical understanding and drive the closures’ development. However, limitations exist due to the uncertainties in the experimental measurement and the simplified analytical assumptions which have difficulties on representing the complex non-linear flow fields. In this paper, a data-driven approach, Feature Similarity Measurement (FSM), is developed and proposed to resolve the challenges of modeling the interfacial forces closures. Case study is performed with two-phase flow scenarios where the high-fidelity experimental data is available. Within the Eulerian-Eulerian two-fluid framework, only momentum equations for gas and liquid phases are solved and reduced-order interfacial momentum closures are aided with FSM. Predictions of void fraction and velocity fields are analyzed and demonstrate the potential of machine learning-driven interfacial forces closures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

An eigenvalue-based method for computing the relaxed pressure in compressible multiphase flow with N phases

The modeling of compressible multiphase flows is a decades-old area of study with many applications across various fields. Many of these application areas use stiff pressure relaxation. This process involves the solution of a nonlinear system with N + 1 equations and N + 1 unknowns, where N is the number of phases. The resolution of this system with general equations of state (EOSs) is difficult. Furthermore, nonlinear systems can admit multiple solutions, and current solution methods do not address this possibility. Very recently, a thermodynamic relaxation method was introduced, which effectively maps a relatively simple predictor equation of state onto a more complex target equation of state. In this context, the target EOSs are the chosen EOSs for the thermodynamic model. Furthermore, this thermodynamic relaxation has the benefit of simplifying the stiff pressure relaxation system of equations. In this article, we show this system reduces to a polynomial of degree N, which can be recast as an eigenvalue problem through the use of the associated companion matrix. We show that although this eigenvalue method is generally less efficient than Newton–Raphson iteration, it does not suffer from convergence issues and finds all N roots of the polynomial. Hence, the method provides a fail-safe for root-finding iterative methods and a way to address the issue of multiple solutions to the nonlinear system of equations in stiff pressure relaxation.

Eigenvalue algorithm↗

DOE OSTI2021

Coupling Finite Element and Finite Volume Simulation Within MOOSE

This work focuses on adding capability to couple finite element (FE) variables into finite volume (FV) physics within INL’s Multiphysics Object-Oriented Simulation Environment (MOOSE). This coupling can allow for improvement of multiphysics simulations where one set of physics is best suited for an FE discretization, while another set is best suited for an FV discretization. Electrohydrodynamics, which govern liquid metal reactor concepts and plasma dynamics, is a fitting example where the electromagnetic field equations are solved with FE and the fluid flow is solved with FV. The new FE to FV coupling method can be summarized as taking the element or face average of the FE variable value or gradient and applying that quantity directly in the FV equation objects.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

CFL Optimized Forward–Backward Runge–Kutta Schemes for the Shallow-Water Equations

Abstract We present the formulation and optimization of a Runge–Kutta-type time-stepping scheme for solving the shallow-water equations, aimed at substantially increasing the effective allowable time step over that of comparable methods. This scheme, called FB-RK(3,2), uses weighted forward–backward averaging of thickness data to advance the momentum equation. The weights for this averaging are chosen with an optimization process that employs a von Neumann–type analysis, ensuring that the weights maximize the admittable Courant number. Through a simplified local truncation error analysis and numerical experiments, we show that the method is at least second-order in time for any choice of weights and exhibits low dispersion and dissipation errors for well-resolved waves. Further, we show that an optimized FB-RK(3,2) can take time steps up to 2.8 times as large as a popular three-stage, third-order strong stability-preserving Runge–Kutta method in a quasi-linear test case. In fully nonlinear shallow-water test cases relevant to oceanic and atmospheric flows, FB-RK(3,2) outperforms SSPRK3 in admittable time step by factors roughly between 1.6 and 2.2, making the scheme approximately twice as computationally efficient with little to no effect on solution quality. Significance Statement The purpose of this work is to develop and optimize time-stepping schemes for models relevant to oceanic and atmospheric flows. Specifically, for the shallow-water equations we optimize for schemes that can take time steps as large as possible while retaining solution quality. We find that our optimized schemes can take time steps between 1.6 and 2.2 times larger than schemes that cost the same number of floating point operations, translating directly to a corresponding speedup. Our ultimate goal is to use these schemes in climate-scale simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Science & Technology - Other Topics↗

DOE OSTI2020

Probabilistic neural networks for fluid flow surrogate modeling and data recovery

We consider the use of probabilistic neural networks for fluid flow surrogate modeling and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (i) the shallow-water equations, (ii) a two-dimensional cylinder flow, (iii) the wake of a NACA0012 airfoil with a Gurney flap, and (iv) the NOAA sea surface temperature data set. Furthermore, the present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow surrogate model but also systematically quantifies the uncertainty therein to assist with model interpretability.

42 ENGINEERING↗

DOE OSTI2022

Fluid structure interaction of a subaqueous pendulum: Analyzing the effect of wake correction via large eddy simulations

The dynamic behavior of a subaqueous cylindrical pendulum and corresponding flow dynamics are investigated. The objectives were twofold: (i) to examine whether the two-dimensional model equations sufficiently capture the three-dimensional dynamics and (ii) to investigate the emerging three-dimensional vortical flow structures. Large eddy simulations with two-way coupling fluid structure interaction were carried out using the immersed boundary method to simulate the motion of the pendulum and its interactions with the initially stagnant water. The resulting pendulum motion is compared against measured data obtained in a series of experimental tests to validate the simulation results and the model equations with and without wake corrections. An analysis of the flow vorticity revealed the development of a vortex ring during the first swing and the formation of tip vortices. The evolution of the vortex rings emerging from the motion of the subaqueous cylindrical pendulum was visualized using Q-criteria showing a reasonable agreement with vortical structures observed in the experiment using particle imaging velocimetry. The hydrodynamic moments acting on the simulated pendulum and the moments calculated from the model equations are analyzed. Using the insights from these numerical simulations, a modification of the wake correction is proposed to enhance the accuracy of the rate of decay and period. The transient effect of coherent flow on pendulum dynamics, especially the added mass effect, is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗