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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Extending a scaling equation of state to QCD

Whether quantum chromodynamics (QCD) exhibits a phase transition at finite temperature and density is an open question. It is important for hydrodynamic modeling of heavy ion collisions and neutron-star mergers. Lattice QCD simulations have definitively shown that the transition from hadrons to quarks and gluons is a crossover when the baryon chemical potential is zero or small. Here, we combine the parametric scaling equation of state, usually associated with the three-dimensional Ising model, with a background equation of state based on a smooth crossover from hadrons to quarks and gluons. Comparison to experimental data from the Beam Energy Scan II at the Relativistic Heavy Ion Collider or in heavy ion experiments at other accelerators may allow the critical exponents and amplitudes in the scaling equation of state to be determined for QCD if a critical point exists.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Sensitivity of Au + Au collisions to the symmetric nuclear matter equation of state at 2–5 nuclear saturation densities

We demonstrate that proton and pion flow measurements in heavy-ion collisions at incident energies ranging from 1 to 20 GeV per nucleon in the fixed target frame can be used for an accurate determination of the symmetric nuclear matter equation of state at baryon densities equal 2–4 times nuclear saturation density n 0 . We simulate Au + Au collisions at these energies using a hadronic transport model with an adjustable vector mean-field potential dependent on baryon density n B . Here, we show that the mean field can be parametrized to reproduce a given density dependence of the speed of sound at zero temperature $c$$^{2}_{s}$ (n B , T = 0), which we vary independently in multiple density intervals to probe the differential sensitivity of heavy-ion observables to the equation of state at these specific densities. Recent flow data from the STAR experiment at the center-of-mass energies √ s NN = {3.0, 4.5} GeV can be described by our model, and a Bayesian analysis of these data indicates a hard equation of state at n B ϵ (2, 3)n 0 and a possible phase transition at n B ϵ (3, 4)n 0 . More data at √ s NN = 2–5 GeV, as well as a more thorough analysis of the model systematic uncertainties will be necessary for a more precise conclusion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Dual Representations and H ∞ -Optimal Control of Partial Differential Equations

We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.

42 ENGINEERING↗
DOE OSTI2022

Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas

Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for a broad class of non-ideal pressure-density relations that satisfy a monotonicity property. Further, we develop a Newton-Raphson algorithm for numerical solution of the steady-state problem, which is made possible by a systematic non-dimensionalization of the equations. The developed algorithm has been extensively tested on benchmark instances and shown to converge robustly to a generalized solution. Previous results [1]-[4], indicate that the steady-state network flow equations for an ideal gas are difficult to solve by the Newton-Raphson method because of its extreme sensitivity to the initial guess. In contrast, we find that non-dimensionalization of the steady-state problem is key to robust convergence of the Newton-Raphson method. We identify criteria based on the uniqueness of solutions under which the existence of a non-physical generalized solution found by a non-linear solver implies non-existence of a physical solution, i.e., infeasibility of the problem. Finally, we compare pressure and flow solutions based on ideal and non-ideal equations of state to demonstrate the need to apply the latter in practice. The solver developed in this article is open-source and is made available for both the academic and research communities as well as the industry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Ambient-Frequency-Data Based System-Level Inertia Estimation Using Physical Equation and its Practice on Hawaii Islands

Here, in this paper, a practical ambient-frequency-data-based inertia estimation method using a physical equation is proposed and validated by real measurement data from Hawaii island grids. With high renewable penetration, accurate inertia estimation is important and urgent. Ambient frequency oscillation always exists in power grids, so the proposed method has advantages of real-time inertia estimation and no need for additional disturbances. This paper first developed the physical equation for inertia estimation to offer a clear mechanism for easy implementation in practice. To apply the proposed method in actual grids, a practical method to extract the ambient frequency oscillation from frequency measurement is further proposed. The inertia estimation using the physical equation is validated by KIUC simulation data and HECO field data, in which error rates are around 2% and 8%, respectively. Practical inertia estimation is challenging due to the large amounts of resources contributing to the power grid's effective inertia, but the method provided in this paper can offer a novel way for practical inertia estimation, which can help renewable penetration to boost carbon-free grid.

14 SOLAR ENERGY↗
DOE OSTI2023

Direct Numerical Simulation of Partial Fuel Stratification Assisted Lean Premixed Combustion for Assessment of Hybrid G-Equation/Well-Stirred Reactor Model

Partial fuel stratification (PFS) is a promising fuel injection strategy to stabilize lean premixed combustion in spark-ignition (SI) engines. PFS creates a locally stratified mixture by injecting a fraction of the fuel, just before spark timing, into the engine cylinder containing homogeneous lean fuel/air mixture. Further, this locally stratified mixture, when ignited, results in complex flame structure and propagation modes similar to partially premixed flames and allows for faster and more stable flame propagation than a homogeneous lean mixture. This study focuses on understanding the detailed flame structures associated with PFS-assisted lean premixed combustion. First, a two-dimensional direct numerical simulation (DNS) is performed using detailed fuel chemistry, experimental pressure trace, and realistic initial conditions mapped from a prior engine large-eddy simulation (LES), replicating practical lean SI operating conditions. DNS results suggest that the conventional triple flame structure is prevalent during the initial stage of flame kernel growth. Both premixed and nonpremixed combustion modes are present with the premixed mode contributing dominantly to the total heat release. Detailed analysis further reveals the effects of flame stretch and fuel pyrolysis on flame displacement speed. Based on the DNS findings, the accuracy of a hybrid G-equation/well-stirred reactor (WSR) combustion model is assessed for the PFS-assisted lean operation in the LES context. It is found that the G-equation model qualitatively captures the premixed branches of the triple flame, while the WSR model predicts the nonpremixed branch of the triple flame. Finally, potential needs for improvements to the hybrid G-equation/WSR modeling approach are discussed.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control

Herein, we present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional sub-spaces whose basis functions are realizations of a sequence of neural networks. Here, the finite-dimensional subspaces are then used to define a standard Galerkin approximation of the variational equation. This approach enjoys a number of advantages, including: the sequential nature of the algorithm offers a systematic approach to enhancing the accuracy of a given approximation; the sequential enhancements provide a useful indicator for the error that can be used as a criterion for terminating the sequential updates; the basic approach is largely oblivious to the nature of the partial differential equation under consideration; and, some basic theoretical results are presented regarding the convergence (or otherwise) of the method which are used to formulate basic guidelines for applying the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

QCD equation of state at finite chemical potentials for relativistic nuclear collisions

In this work, we review the equation of state of QCD matter at finite densities. We discuss the construction of the equation of state with net baryon number, electric charge, and strangeness using the results of lattice QCD simulations and hadron resonance gas models. Its application to the hydrodynamic analyses of relativistic nuclear collisions suggests that the interplay of multiple conserved charges is important in the quantitative understanding of the dense nuclear matter created at lower beam energies. Several different models of the QCD equation of state are discussed for comparison.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Superposed hyperbolic kink and pulse solutions of coupled $φ$ 4 , NLS and mKdV equations

Here, in this paper, we obtain novel solutions of a coupled $φ$ 4 , a coupled nonlinear Schrödinger equation and a coupled modified Korteweg de Vries equation which can be re-expressed as a linear superposition of either the sum or the difference of two hyperbolic pulse solutions or the sum of either a two-kink or a kink and an antikink solution. These results demonstrate that the notion of superposed solutions extends to coupled nonlinear equations as well.

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 OSTI2020

Nemchinov-Dyson Solutions of the Two-Dimensional Axisymmetric Inviscid Compressible Flow Equations [Review]

We investigate the two-dimensional (2D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the 2D velocity field is space-time separable and linearly variable in each corresponding spatial coordinate, we proceed to derive an in nite family of elliptic or hyperbolic, uniformly expanding or contracting \gas cloud" solutions. Construction of specific example solutions belonging to this family is dependent on the solution of a system of nonlinear, coupled, second-order ordinary differential equations, and the prescription of an additional physical process of interest (e.g., uniform temperature or uniform entropy flow). The physical and computational implications of these solutions as pertaining to quantitative code verification or model qualification studies are discussed in some detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ordinary differential equations, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder-decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs with important benchmark problems from computational physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Equation of State Optimization and Uncertainty Quantization: Implementation in the LANL EOS Production Code OpenSesame

We detail the approaches of particle swarm optimization and Bayesian inference through Markov chain Monte Carlo for equation of state development. This work includes formulation of the modeling for the equation of state, numeric optimization of the parametric models via particle swarm optimization, and generation of probability distributions of equations of state from Markov chain Monte Carlo.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

The absence of ray-effects in the discrete ordinate solution to the transport equation in spherical coordinates in multi-dimensions

The streaming operator of the transport equation is derived for spherical coordinates by starting from Newton’s second law for a free particle expressed in spherical coordinates. We shall show that the partial derivatives with respect to the velocity variables of the particle, which are absent in the Cartesian coordinate formulation of the transport equation, arise in the spherical coordinate formulation of the transport equation in response to the centrifugal force which prevents a free particle from ‘falling into the origin’ of the coordinate system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Analysis of an Elasto-Hydrodynamic Seal by Using the Reynolds Equation

This paper reports numerical studies of an Elasto-Hydrodynamic (EHD) seal, which is being developed for supercritical CO2 (sCO2) turbomachinery applications. Current sCO2 turbomachinery suffers from high leakage rates, which is creating a major roadblock to the full realization of sCO2 power technology. The high leakage rates not only penalize the efficiencies but also create environmental concerns due to greenhouse effects caused by the increased CO2 discharge to the atmosphere. The proposed EHD seal needs to work at elevated pressures (10–35 MPa) and temperatures (350–700 °C) with low leakage and minimal wear. The unique mechanism of the EHD seal provides a self-regulated constriction effect to restrict the flow without substantial material contact, thereby minimizing leakage and wear. This work utilizes a physics-based modeling approach. The flow through the gradually narrowing seal clearance is modeled by the well-known Reynolds equation in EHD lubrication theory, while the deformation of the seal is modeled by using the governing equations of three-dimensional solid mechanics. As for the solution methodology, COMSOL’s Thin-Film Flow and Solid Mechanics modules were employed with their powerful capabilities. The numerical results were presented and discussed. It was observed that the Reynolds equation fully coupled with the surface deformation was able to successfully capture the constriction effect. The maximum and minimum leakages were calculated to be 2.25 g/s and 0.1 g/s at P = 5.5 MPa and P = 11 MPa for the design seal, respectively. It was interesting to observe that the seal leakage followed a quadratic trend with increasing pressure differential, which can become advantageous for high-pressure applications such as sCO2 power generation technology.

42 ENGINEERING↗
DOE OSTI2021

P–V–T Equation of State of Iridium Up to 80 GPa and 3100 K

In the present study, the high-pressure high-temperature equation of the state of iridium has been determined through a combination of in situ synchrotron X-ray diffraction experiments using laser-heating diamond-anvil cells (up to 48 GPa and 3100 K) and density-functional theory calculations (up to 80 GPa and 3000 K). The melting temperature of iridium at 40 GPa was also determined experimentally as being 4260 (200) K. The results obtained with the two different methods are fully consistent and agree with previous thermal expansion studies performed at ambient pressure. The resulting thermal equation of state can be described using a third-order Birch–Murnaghan formalism with a Berman thermal-expansion model. The present equation of the state of iridium can be used as a reliable primary pressure standard for static experiments up to 80 GPa and 3100 K. A comparison with gold, copper, platinum, niobium, rhenium, tantalum, and osmium is also presented. On top of that, the radial-distribution function of liquid iridium has been determined from experiments and calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Building an Equation of State Density Ladder

The confluence of major theoretical, experimental, and observational advances are providing a unique perspective on the equation of state of dense neutron-rich matter—particularly its symmetry energy—and its imprint on the mass-radius relation for neutron stars. In this contribution, we organize these developments in an equation of the state density ladder. Of particular relevance to this discussion are the impact of the various rungs on the equation of state and the identification of possible discrepancies among the various methods. A preliminary analysis identifies possible tension between laboratory measurements and gravitational-wave detections that could indicate the emergence of a phase transition in the stellar core.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

High-Fidelity Simulations of Supercritical CO2 Based Oxy-Combustion with Non-Ideal Equation of State

The supercritical carbon dioxide (sCO2) Allam-Fetvedt cycle employs high-temperature oxy-combustion using sCO2 as the working fluid, leading to a unique and challenging environment for materials. In this cycle, pressurized gaseous fuel is combusted in the presence of a hot oxidant flow containing a mixture of CO2 and oxygen and a hot CO2 diluent recycle stream at approximately 300 bar under lean combustion conditions. We present high-fidelity reacting simulations of this oxy-combustor environment and compare the results when performing simulations with ideal and non-ideal equations of state. By doing so, we identify if the combustor behavior at the regime of interest is sensitive enough to the equation of state to justify the added computational cost incurred with a non-ideal equation of state.

equation of state↗