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Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗
DOE OSTI2022

Computational Methodology to Simulate Pyrometallurgical Processes in a Secondary Lead Furnace

Pyrometallurgical recovery of nonferrous metals involves a combination of thermally intensive transformations during exothermic gas-phase reactions, endothermic decomposition of solid charge, and melting of simpler solids. In the recovery of secondary lead, simultaneous thermal effects in a reverberatory-style furnace cause a melt pool to accumulate at the bottom, with lighter solids (slag) floating above and gaseous products from decomposition of the charge diffusing through the gas–slag interface. Species from oxy-fuel combustion of natural gas, species profiles from smelting reactions, and the formation of a melt pool consisting primarily of lead are simulated via a time-averaged formulation. Predictions of outflow are compared with preset inflow profiles to ensure conservation of mass. Thermal profiles for solid, liquid, and gas phases are presented by species. A novel method is implemented to model the latent heat of fusion using a heterogeneous chemical reaction. The simulation is conducted in Simcenter STAR-CCM+ v. 16.02.009-R8.

Rao, Vivek↗
DOE OSTI2023

Multirate partitioned Runge–Kutta methods for coupled Navier–Stokes equations

Earth system models are complex integrated models of atmosphere, ocean, sea ice, and land surface. Coupling the components can be a significant challenge due to the difference in physics, temporal, and spatial scales. Further, this study explores multirate partitioned Runge-Kutta methods for the fluid-fluid interaction problem and demonstrates its parallel performance by using the PETSc library. We consider compressible Navier-Stokes equations with gravity coupled through a rigid-lid interface. Our large-scale numerical experiments reveal that multirate partitioned Runge-Kutta coupling schemes (1) can conserve total mass; (2) have second-order accuracy in time; and (3) provide favorable strong- and weak-scaling performance on modern computing architectures. We also show that the speedup factors of multirate partitioned Runge-Kutta methods match theoretical expectations over their base (single-rate) method.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A numerical method for simulating variable density flows in membrane desalination systems

Here, we present a novel method for simulating unsteady, variable density, fluid flows in membrane desalination systems. By assuming the density varies only with concentration and temperature, the scheme decouples the solution of the governing equations into two sequential blocks. The first solves the governing equations for the temperature and concentration fields, which are used to compute all thermophysical properties. The second block solves the conservation of mass and momentum equations for the velocity and pressure. We show that this is computationally more efficient than schemes that iterate over the full coupled equations in one block. We verify that the method achieves second-order spatial-temporal accuracy, and we use the method to investigate buoyancy-driven convection in a desalination process called vacuum membrane distillation. Specifically, we show that with gravity properly oriented, variations in temperature and concentration can trigger a double-diffusive instability that enhances mixing and improves water recovery. We also show that the instability can be strengthened by providing external heating.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

One-dimensional, transient modeling of a fixed-bed regenerator as a replacement for recuperators in supercritical CO 2 power cycles

Fixed-bed regenerators may be a low cost alternative to recuperators for supercritical CO 2 power cycles. However, the transient nature of regenerators operating in sCO 2 power cycles has not been previously characterized. This study details a one-dimensional, transient model of a fixed-bed regenerator that captures phenomena such as local fluid properties and heat transfer coefficients, entrained fluid heat capacity, and the effects of conservation of mass during process switching. The model is validated with experimental results of a 10 kWth regenerator. This comparison shows that the model predicts temperature as a function of both time and space exceptionally well. The model predicts effectiveness, heat transfer, and discharge temperatures within 5%, and predicts pressure drop and fluid carryover within 10%. This model could be used in future studies to simulate regenerators within a supercritical CO 2 power cycle.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2022

Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency

Here, we consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are defined by a variational procedure. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function, mimicking the Lagrange functional that appears in the theoretical derivation. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method, and illustrate its usefulness and effectiveness with numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Digital bead modeling for wire-arc directed energy deposition

Prediction of 2D cross-section and full 3D geometry for stacked weld beads is critical for the outcome of wire-arc directed energy deposition (DED) parts; however, most additive path planning software packages model beads as extrusions of a rectangle. Weld beads are not rectangular, and the resulting shape is dependent upon physics effects at the moment of deposition. Physics phenomena such as the geometry of the underlying surface, the heat input of the welding mode, and the direction of gravity contribute to bead shape. Here, this paper presents a novel implicit modeling method that discretizes a 2D area or 3D volume of space into pixels or voxels and constructs fields based on these physics phenomena. The fields are combined using a weighting scheme trained on 3D scan measurements of welds and wire-arc DED prints. Pixels or voxels are added until the known amount of deposited volume has been achieved. Thereby, a strong conservation of mass principle is applied to the process. Utilizing machine learning techniques, the present model can be trained on a database of scans allowing for the representation of a wide variety of prints. Results show that this method can produce predictions with realistic bead morphology and sub-millimeter form error.

Bead geometry modeling↗
DOE OSTI2020

Analyzing Wildland Fire Smoke Emissions Data Using Compositional Data Techniques

By conservation of mass, the mass of wildland fuel that is pyrolyzed and combusted must equal the mass of smoke emissions, residual char and ash. For a given set of conditions, these amounts are fixed. This places a constraint on smoke emissions data which violates statistical assumptions for many of the methods currently used to analyze these data such as linear regression, analysis of variance, and t-tests. These data are inherently multivariate and non-negative parts of a whole. This paper introduces the field of compositional data analysis to the emissions community and provides examples of appropriate statistical treatment of emissions data. It is shown that modified combustion efficiency should not be used as a predictor variable for other smoke emissions because it is not an independent variable. An alternative method based on compositional linear trends to estimate trace gas composition using CO and CO2 is presented. The data used in this paper resulted from projects the DOD/DOE/EPA Strategic 586 Environmental Research and Development Program projects RC-1648 and 1649. The senior 587 author appreciates the guidance and R scripts provided by Prof. Girty at San Diego State 588 University to estimate linear trends by perturbation. J. P.-A. was supported by the Spanish 589 Ministry of Science, Innovation and Universities under the project CODAMET (RTI2018-590 095518-B-C21, 2019-2021). The data used in this study have been previously published and are 591 available in the original publications. DRW conceived the initial manuscript (70 percent) and 592 performed the bulk of the data analysis. JPA provided statistical guidance and compositional data 593 expertise and contributed 20 percent of the manuscript. TJJ and HJ were extensively involved in 594 the study that provided the data. TJJ provide smoke emissions expertise and HJ provided 595 combustion expertise. The authors declare that they have no conflict of interest. The use of trade 596 or firm names in this publication is for reader information and does not imply endorsement by 597 the U.S. Department of Agriculture of any product or service.

simplex, compositional data analysis, balance, log↗
DOE OSTI2021

nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling

Time- and rate-dependent material functions in non-Newtonian fluids in response to different deformation fields pose a challenge in integrating different constitutive models into conventional computational fluid dynamic platforms. Considering their relevance in many industrial and natural settings alike, robust data-driven frameworks that enable accurate modeling of these complex fluids are of great interest. The main goal is to solve the coupled Partial Differential Equations (PDEs) consisting of the constitutive equations that relate the shear stress to the deformation and fully capture the behavior of the fluid under various flow protocols with different boundary conditions. Here, in this work, we present non-Newtonian physics-informed neural networks (nn-PINNs) for solving systems of coupled PDEs adopted for complex fluid flow modeling. The proposed nn-PINN method is employed to solve the constitutive models in conjunction with conservation of mass and momentum by benefiting from Automatic Differentiation (AD) in neural networks, hence avoiding the mesh generation step. nn-PINNs are tested for a number of different complex fluids with different constitutive models and for several flow protocols. These include a range of Generalized Newtonian Fluid (GNF) empirical constitutive models, as well as some phenomenological models with memory effects and thixotropic timescales. nn-PINNs are found to obtain the correct solution of complex fluids in spatiotemporal domains with good accuracy compared to the ground truth solution. We also present applications of nn-PINNs for complex fluid modeling problems with unknown boundary conditions on the surface, and show that our approach can successfully recover the velocity and stress fields across the domain, including the boundaries, given some sparse velocity measurements.

42 ENGINEERING↗
DOE OSTI2024

Empirical correlations between the function of entropy ( Z S ) and net artificial viscous work in a shock physics hydrocode

Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. Here, in this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy Z S , and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Time-dependent relaxed magnetohydrodynamics: Inclusion of cross helicity constraint using phase-space action

In this work, a phase-space version of the ideal magnetohydrodynamic (MHD) Lagrangian is derived from first principles and shown to give a relabeling transformation when a cross-helicity constraint is added in Hamilton's Action Principle. A new formulation of time-dependent “relaxed” magnetohydrodynamics is derived using microscopic conservation of mass and macroscopic constraints on total magnetic helicity, cross helicity, and entropy under variations of density, pressure, fluid velocity, and magnetic vector potential. This gives Euler–Lagrange equations consistent with previous work on both ideal and relaxed MHD equilibria with flow, but generalizes the relaxation concept from statics to dynamics. The application of the new dynamical formalism is illustrated for short-wavelength linear waves, and the interface connection conditions for Multiregion Relaxed MHD (MRxMHD) are derived. The issue of whether E+u×B=0 should be a constraint is discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Considerations for the modeling of the laser ablation region of ICF targets with Lagrangian simulations

Recently, much effort has been dedicated to the improvement of models and modeling choices utilized in radiation hydrodynamic simulations of direct drive inertial confinement fusion experiments in an effort to improve their predictive capability. In this paper, we consider the choice in mesh for the simulation of the laser ablation of a direct-drive-like target and compare Lagrangian simulations with various mesh zoning choices with Eulerian simulations with fixed resolution in the laser energy deposition region. Using these simulations, we demonstrate how errors in ablation pressure, laser deposition rate, shock speed, and density profile arise from insufficient zoning following from the conservation of mass of Lagrangian zones. These considerations place stringent requirements on the initial t = 0 zoning in the solid density shell for simulations aiming at resolving the ablation and laser absorption region. However, with sufficiently fine zoning in the t = 0 shell, agreement with Eulerian simulations and analytic scaling laws can be recovered.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry↗
DOE OSTI2026

Axisymmetric hydrodynamics in numerical relativity: treating coordinate singularity, artificial heating and modeling MHD instabilities

Two-dimensional axisymmetric simulations of binary neutron star (BNS) merger remnant are a cheap alternative to 3D simulations. To maintain realism for secular timescales, simulations must avoid accumulated errors from drifts in conserved quantities and artificial heating, and they must model turbulent transport in a way that remains plausible throughout the evolution. It is also crucial to avoid numerical artifacts due to the polar coordinate axis singularity. Methods that behave well near the axis often break flux-conservative form of the hydrodynamic equations, resulting in significant drifts in conserved quantities. We present a flux-conservative scheme that maintains smoothness near the axis without sacrificing conservative formulation of the equations or incurring drifts in conserved global quantities. We compare the numerical performance of different treatments of the hydrodynamic equations when evolving a hypermassive neutron star resembling the remnant of a BNS merger. These simulations demonstrate that the new scheme combines the axis smoothness of non-conservative methods with the mass and angular momentum conservation of other conservative methods on $\sim 10^2$ ms timescales of viscous and neutrino-driven evolution. Because fluid profiles remain smooth in the remnant interior, it is possible to remove artificial heating by evolving the entropy density. We show how physical heating and cooling terms can be easily calculated from source terms of the conservative evolution variables and demonstrate our implementation. Finally, we discuss and implement improvements to the effective viscosity scheme to better model the effect of magnetohydrodynamic instabilities as the remnant evolves.

axisymmetry↗
DOE OSTI2023

Data-driven prediction of the output composition of an atmospheric pressure plasma jet

Cold atmospheric plasma (CAP) in open air hosts numerous chemical species engaged in thousands of chemical reactions. Comprehensive diagnosis of its chemical composition is important across various fields from medicine, where reactive oxygen and nitrogen play key roles, to surface modification. In applications, a centimeter-scale helium–air jet operates for minutes, featuring micrometer-sized streamers and an atmospheric pressure-induced collision frequency in the hundreds of GHz range. To address this intricate multi-scale issue, we introduce a machine learning approach: using a physics-informed neural network (PINN) to tackle the multi-scale complexities inherent in predicting the complete list of species concentrations, gas temperature, and electron temperature of a CAP jet supplied with a mixture of helium and air. Experimental measurements of O 3 , N 2 O, and NO 2 concentrations downstream of the plasma jet, combined with fundamental physics laws, the conservation of mass and charge, constrain the PINN, enabling it to predict the concentrations of all species that are not available from the experiment, along with gas and electron temperatures. The results, therefore, obey all the physical laws we provided and can have a chemical balance with the measured concentrations. In conclusion, this methodology holds promise for describing and potentially regulating complex systems with limited experimental datasets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence

In recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of partial differential equations is enforcing physical constraints and boundary conditions. In this work, we propose a general framework to directly embed the notion of an incompressible fluid into convolutional neural networks, and apply this to coarse-graining of turbulent flow. These physics-embedded neural networks leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. Here, we demonstrate results on three-dimensional fully developed turbulence, showing that this technique drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Estimating Scaled Cloud Height in Pulse Jet Mixed Vessels

To suspend and mix radioactive slurries without pumps or impellers, the performance of pulsed jet mixed vessels has been investigated. The slurry in the pulse tubes is expelled impinging upon the vessel floor and lifting solids to a “cloud height” in a cyclic process. Experiments measuring cloud height for a variety of waste simulants have been conducted for vessel configurations that varied vessel diameter, fill height and pulse tube number, volume, and nozzle diameter. The elevation to which suspended particles rise is termed the cloud height and derives from a balance between the fluid forces of the jet and the gravitational forces acting on the particle ensemble. Here we use scaling to estimate the cloud height based on conservation of mass and momentum and jet similarity. We find that the cloud height varies with the nozzle exit velocity to the 2/3 power in agreement with observations.

cloud height, effective cleaning radius, effective↗
DOE OSTI2025

Openpronghorn

OpenPronghorn is a simulation tool specifically tailored for modeling thermal-hydraulic phenomena in advanced nuclear reactors. It is built on the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source platform that facilitates the development of high-performance scientific computing applications. OpenPronghorn solves the Navier-Stokes equations, which describe the conservation of mass, momentum, and energy in fluid flows, using the finite volume numerical method. The code supports a wide range of fluid flow conditions that are applicable to nuclear reactors, including incompressible and weakly compressible flows, as well as single-phase and multiphase flows. It is capable of modeling diverse flow regimes, including laminar and turbulent flows, using various turbulence models such as the standard k-epsilon models, the v2f model, and the mixing length model. For multiphase flows, OpenPronghorn employs a mixture a Eulerian modeling approach with mixture, drift-flux, and full Eulerian models, and includes open-sourced interfacial transfer correlations for drag, exchange, and heat transfer coming from the scientific literature. OpenPronghorn's modular design allows it to handle multiscale simulations, ranging from detailed Reynolds-Averaged Navier Stokes (RANS) simulations to coarse-mesh and lumped parameter models. This flexibility enables users to perform high-fidelity simulations of specific reactor components as well as system-level analyses of entire reactor circuits. The code can be coupled with other MOOSE-based tools using the MultiApp system, allowing for the transfer of coupling quantities such as mass flow rates, heat fluxes, and boundary conditions between different simulation scales. One of the main features of OpenPronghorn is the it includes built-in validation cases from the open-source scientific literature and supports the implementation of user-defined models and correlations through MOOSE's FunctorMaterial system. OpenPronghorn is designed to be computationally efficient, leveraging the SIMPLE projection method for large-scale problems, and can be run on high-performance computing systems to handle the extensive computational demands of detailed reactor simulations. Overall, OpenPronghorn is a versatile and robust tool that provides critical insights into the thermal-hydraulic behavior of advanced nuclear reactors, supporting the design, safety, and optimization of next-generation nuclear energy systems.

Retamales, Mauricio Eduardo Tano [Idaho National L↗