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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Comparing the MELCOR Aerosol Deposition Model with Exact Analytical Solutions

Exact analytical solutions are presented for the evolution of the aerosol particle mass density function in a control volume for particle deposition due to gravitational settling, thermophoresis, and diffusion. The solutions are for arbitrary initial mass density functions and are applied for an initial lognormal density function. Integration of these solutions provides the suspended mass in the control volume as a function of time. These solutions serve as an exact benchmark to assess the accuracy of numerical methods. For the numerical algorithm used in MELCOR, excellent agreement is obtained for gravitational settling, diffusive deposition, and thermophoretic deposition for the suspended aerosol mass. In all cases, the default number of discrete particle size bins of 10 is shown to converge, with hardly any advantage to using 20 size bins.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Analytical solutions of the Arrhenius-Semenov problem for constant volume burn

Analytical solutions to the Semenov thermal ignition problem for constant volume burn governed by Arrhenius reaction kinetics are derived. Specifically, an approximate analytical solution technique for the Arrhenius-Semenov differential equation is derived for reaction orders n ϵ R> 0 and exact solutions are also constructed for reaction orders n ϵ N : n ≤ 3. The approximation technique relies on expansion of the respective nondominant terms in the differential equation at the lower and upper bounds of the reaction progress variable in order to create a pair of integrable series. The two integrated series are then connected to create a single continuous analytical solution. Excellent agreement is observed between the analytical approximation and solutions obtained numerically. The presented approximation constitutes a simple and robust strategy for solving the Arrhenius-Semenov problem analytically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Semi-analytic solutions to the Noh problem with a black box EoS

The objective of this paper is to derive a method of constructing semi-analytic solutions to the Noh problem when the equation of state is a black box. Such solutions can be used for verification tests of hydrodynamics codes. We present the underlying theory, the method for finding solutions, and several examples of derived semi-analytic solutions. We end by performing a classic verification convergence test comparing numerical results from a hydrodynamics code against a non-trivial semi-analytic solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

ExactPack: A python library of exact analytic solutions

Verification of multi-physics simulation software against problems with known analytic or semi-analytic solutions is an important aspect of research into a wide variety of fields involving the motion of fluids, shock physics and other dynamic material properties. Previous work comparing simulation results against analytic solutions has been ad-hoc, with developers frequently writing their own analytic solvers. This has resulted in a large amount of duplicated effort. The python library ExactPack has been developed as a collection of analytic and semi-analytic solvers to a variety of multi-physics problems, providing a consistent API to a set of well-tested solver implementations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Analytical solution and parameter estimation for heat of wetting and vapor adsorption during spontaneous imbibition in tuff

An analytical expression is derived for the thermal response observed during spontaneous imbibition of water into a dry core of zeolitic tuff. Sample tortuosity, thermal conductivity, and thermal source strength are estimated from fitting an analytical solution to temperature observations during a single laboratory test. Here, the closed-form analytical solution is derived using Green's functions for heat conduction in the limit of “slow” water movement; that is, when advection of thermal energy with the wetting front is negligible. The solution has four free fitting parameters and is efficient for parameter estimation. Laboratory imbibition data used to constrain the model include a time series of the mass of water imbibed, visual location of the wetting front through time, and temperature time series at six locations. The thermal front reached the end of the core hours before the visible wetting front. Thus, the predominant form of heating during imbibition in this zeolitic tuff is due to vapor adsorption in dry zeolitic rock ahead of the wetting front. The separation of the wetting front and thermal front in this zeolitic tuff is significant, compared to wetting front behavior of most materials reported in the literature. This work is the first interpretation of a thermal imbibition response to estimate transport (tortuosity) and thermal properties (including thermal conductivity) from a single laboratory test.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An Analytical Solution for the Initiation and Early Progression of Fretting Wear in Spherical Contacts

Abstract This article derives analytical solutions to calculate the wear volume at the initiation of fretting motion and its early progression over the first few oscillation cycles. The Archard-based model considers a deformable hemisphere that is contact with a deformable flat block. The material pairs investigated are special alloys, the Inconel 617/Incoloy 800H, and Inconel 617/Inconel 617. The analytical study begins with a unidirectional frictional sliding contact, where the local interfacial sliding distance and the nominal sliding distance at the initiation of gross slip are derived. The obtained analytical expressions for unidirectional sliding are then used to derive the corresponding wear volume for the initiation and early progression of gross slip and the wear volume for a general fretting cycle under elastic conditions. These analytical derivations are all verified by the finite element analysis (FEA). The FEA method and the analytical solutions render virtually identical results for both similar and dissimilar material pairs. The effects of plasticity on the wear volume under elastic–plastic conditions are also investigated. It is found that the fretting wear volumes obtained from the FEA simulations, which include plasticity, are close to those obtained from the analytical expressions for purely elastic regimes. All the results are presented in normalized forms, which can be easily generalized and applied to three-dimensional fretting wear of other material pairs.

Engineering↗
DOE OSTI2025

Code associated with Publication “Analytic Solutions and Field-Scale Application for Verification of Coupled Thermo-Hydro-Mechanical Processes in Subsurface Fractured Media”

As part of a submitted paper, which is collection of previously published analytical solutions to coupled thermo-hydro-mechanical problems in subsurface flow and transport, we have prepared a collection of python scripts to compute and plot those analytic solutions. All code to be released implements existing methods; there are no novel algorithms nor any major innovations to existing software.

Hyman, Jeffrey↗
DOE OSTI2020

Analytical Solutions for Seismic Fluid-Structure Interaction of Head-Supported Cylindrical Tanks

Fluid-structure interaction (FSI) of earthquake shaking is a design consideration in the civil, nuclear, chemical, and mechanical industries. Preliminary sizing of structures and components in these industries will often use analytical solutions because there is insufficient information to warrant the analysis of numerical models. Here, this study extends prior analytical work on seismic FSI of base-supported tanks in the 1980s to accommodate head-supported tanks with geometries similar to those proposed for new-build, liquid (fluid)-filled, advanced reactors. Analytical solutions are derived for flexible, head-supported, cylindrical tanks subjected to small-amplitude, unidirectional, horizontal seismic motion, and address frequencies of lateral motions of the tank, hydrodynamic pressures, frequencies of waves, wave heights, and reactions at the head support. Solutions are presented for a range of tank dimensions and could be used for a) preliminary design of head-supported cylindrical tanks and their supporting structures with idealized seismic input, and b) verification of numerical models to be used for final seismic analysis, design, and probabilistic risk assessment.

42 ENGINEERING↗
DOE OSTI2024

Analytic solutions of the DGLAP evolution and theoretical uncertainties

The energy dependence for the singlet sector of Parton Distributions Functions (PDFs) is described by an entangled pair of ordinary linear differential equations. Although there are no exact analytic solutions, it is possible to provide approximated results depending on the assumptions and the methodology adopted. These results differ in their sub-leading, neglected terms and ultimately they are associated with different treatments of the theoretical uncertainties. In this work, a novel analytic approach in Mellin space is presented and a new methodology for obtaining closed and exponentiated analytic solutions is devised. Different results for the DGLAP evolution at Next-Leading-Order are compared, discussing advantages and disadvantages for each solution. The generalizations to higher orders are addressed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. Furthermore, the simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation

With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. Here, the selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

3D Exact Analytical Solutions of Two-fluid Plasma, Magnetohydrodynamics, and Neutral Fluid Equations for the Creation of Ordered Structures as well as Jet-like Flows

The 3D exact analytical solutions of ideal two-fluid plasma, single-fluid plasma, and neutral fluid equations have been found using physically justifiable assumptions. Surprisingly these solutions satisfy all nonlinearities in the systems. It is pointed out that these solutions explain the fundamental mechanism behind the creation of a vast variety of ordered structures in plasmas and fluids. In the limiting case of 2D dependence of fields, the theoretical model for plasma is applied to explain the formation of spicules in the solar chromosphere. It is pointed out that the main contribution of electron (ion) baroclinic vectors is to produce vorticity in the plasma, and that magnetic field generation is coupled with the flow of both electrons and ions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Black Box Equations of State: Creating Semi-analytic Solutions to the Noh Problem and Verifying Equation of State Interfaces

The objective of this report is threefold. First, it details a method for deriving a semi-analytic solution to the Noh Problem when using a “black-box” equation of state. Such capability allows us to perform verification on complicated, more realistic equations of state. Examples include Steinberg equations of state for materials and tabulated equations of state. The second objective is to apply the methodology to verify the singularity-eos equation of state library. We do so by solving the Rankine-Hugoinot jump conditions for the Noh Problem, ensuring singularity derives the correct solution and comparing the error to an exact implementation of the equation of state. The third objective is to perform verification of the xRAGE Eulerian hydrodynamics code when interfaced with singularity. We provide the theory, analysis, documentation for a python implementation of the proposed solver, and verification results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Predictive process mapping for laser powder bed fusion: A review of existing analytical solutions

One of the main challenges in the laser powder bed fusion (LPBF) process is making dense and defect-free components. These porosity defects are dependent upon the melt pool geometry and the processing conditions. Power-velocity (PV) processing maps can aid in visualizing the effects of LPBF processing variables and mapping different defect regimes such as lack-of-fusion, under-melting, balling, and keyholing. This work presents an assessment of existing analytical equations and models that provide an estimate of the melt pool geometry as a function of material properties. The melt pool equations are then combined with defect criteria to provide a quick approximation of the PV processing maps for a variety of materials. Finally, the predictions of these processing maps are compared with experimental data from the literature. Here, the predictive processing maps can be computed quickly and can be coupled with dimensionless numbers and high-throughput (HT) experiments for validation. The present work provides a boundary framework for designing the optimal processing parameters for new metals and alloys based on existing analytical solutions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Benchmarking magnetised three-wave coupling for laser backscattering: analytic solutions and kinetic simulations

Understanding magnetised laser–plasma interactions is important for controlling magneto-inertial fusion experiments and developing magnetically assisted radiation and particle sources. For nanosecond pulses at non-relativistic intensities, interactions are dominated by coherent three-wave interactions, whose nonlinear coupling coefficients became known only recently when waves propagate at oblique angles with the magnetic field. In this paper, backscattering coupling coefficients predicted by warm-fluid theory are benchmarked using particle-in-cell simulations in one spatial dimension, and excellent agreements are found for a wide range of plasma temperatures, magnetic field strengths and laser propagation angles, when the interactions are mediated by electron-dominant hybrid waves. Systematic comparisons between theory and simulations are made possible by a rigorous protocol. On the theory side, the initial boundary value problem of linearised three-wave equations is solved, and the transient-time solutions allow the effects of growth and damping to be distinguished. On the simulation side, parameters are carefully chosen and calibration runs are performed to ensure that comparisons are well controlled. Fitting simulation data to analytical solutions yields numerical growth rates that match theory predictions within error bars. Although warm-fluid theory is found to be valid for a wide parameter range, genuine kinetic effects have also been observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

Abstract Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, H I . Here, we point to the existence of an analytical solution for such a problem for an arbitrary H I beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotonic power-law suppression of nonadiabatic excitations with time T of QA, without any signature of a transition to a glass phase, which is usually characterized by a logarithmic energy relaxation. This behavior suggests that the energy relaxation can differ in classical and quantum spin glasses strongly, when it is assisted by external time-dependent fields. In specific cases of H I , the solution also shows a considerable quantum speedup in computations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Integrating Analytical Solutions and U-Net Model for Predicting Groundwater Contaminant Plumes in Pump-and-Treat Systems

Pump-and-treat (P&T) is a common technique for groundwater remediation involving the extraction and treatment of contaminated water above ground. Optimizing the design and operation of the P&T well network is essential for maximizing the system’s effectiveness and efficiency. However, this optimization often necessitates many model evaluations, leading to computationally demanding tasks. This study introduces a novel approach that integrates analytical solutions for groundwater dynamics with the U-Net (Ronneberger et al., 2015) deep learning framework to predict groundwater contaminant plume migration under dynamic pumping conditions. By incorporating the Thiem equation (Thiem, 1906) into the input preprocessing, the U-Net model transforms sparse well data into a continuous spatial field that captures the hydraulic impacts of pumping activities. This integration enables the model to leverage both deep learning capabilities and classical physics-based groundwater theories, enhancing prediction accuracy and computational efficiency. These advancements can facilitate rapid, large-scale evaluations of P&T optimization simulations, allowing for timely and effective decision-making in well placement and system management. We demonstrate the model's robust performance across both simplified transient 2D models and a more complex 3D heterogeneous site model at the 200 West P&T facility at the Hanford Site. The U-Net-based model offers substantial computational advantages, reducing simulation times significantly compared to full physics-based models and providing a powerful tool for rapid site evaluation and P&T system optimization, such as evaluating alternative P&T well network designs. Our findings highlight the potential of advanced machine learning models to significantly enhance the efficiency and sustainability of groundwater remediation efforts, offering a novel application of U-Net architecture in environmental science.

Pump-and-treat↗