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At least 739 records · Page 41

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Coupled Lattice Boltzmann Modeling Framework for Pore-Scale Fluid Flow and Reactive Transport

In this paper, we propose a modeling framework for pore-scale fluid flow and reactive transport based on a coupled lattice Boltzmann model (LBM). We develop a modeling interface to integrate the LBM modeling code parallel lattice Boltzmann solver and the PHREEQC reaction solver using multiple flow and reaction cell mapping schemes. The major advantage of the proposed workflow is the high modeling flexibility obtained by coupling the geochemical model with the LBM fluid flow model. Consequently, the model is capable of executing one or more complex reactions within desired cells while preserving the high data communication efficiency between the two codes. Meanwhile, the developed mapping mechanism enables the flow, diffusion, and reactions in complex pore-scale geometries. We validate the coupled code in a series of benchmark numerical experiments, including 2D single-phase Poiseuille flow and diffusion, 2D reactive transport with calcite dissolution, as well as surface complexation reactions. The simulation results show good agreement with analytical solutions, experimental data, and multiple other simulation codes. In addition, we design an AI-based optimization workflow and implement it on the surface complexation model to enable increased capacity of the coupled modeling framework. Compared to the manual tuning results proposed in the literature, our workflow demonstrates fast and reliable model optimization results without incorporating pre-existing domain knowledge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Semicomputational calculation of Bragg shift in stratified materials

The fiber Bragg grating (FBG) may be viewed as a one dimensional photonic band-gap crystal by virtue of the periodic spatial perturbation imposed on the fiber core dielectric material. Similar to media supporting Bloch waves, the engraved weak index modulation, presenting a periodic “potential” to an incoming guided mode photon of the fiber, yields useful spectral properties that have been the basis for sensing applications and emerging quantum squeezing and solitons. The response of an FBG sensor to arbitrary external stimuli represents a multiphysics problem without a known analytical solution despite the growing use of FBGs in classical and quantum sensing and metrology. Here, we study this problem by first presenting a solid mechanics model for the thermal and elastic states of a stratified material. Additionally, the model considers an embedded optical material domain that represents the Bragg grating, here in the form of an FBG. Using the output of this model, we then compute the optical modes and their temperature- and stress-induced behavior. The developed model is applicable to media of arbitrary shape and composition, including soft matter and materials with nonlinear elasticity and geometric nonlinearity. Finally, we employ the computed surface stress and temperature distributions along the grating to analytically calculate the Bragg shift, which is found to be in reasonable agreement with our experimental measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1990

An alternative formulation of the global sensitivity equations

To optimize the performance of any system, the sensitivity derivatives of the system's output variables with respect to its input variables must be readily available. It is also desirable that these derivatives be inexpensive to calculate as the optimization process requires many evaluations of the output variables and their derivatives. Optimization methods that have been developed for use in automated structural design programs may not be extended for use in integrated multidisciplinary design programs until adequate means of calculating accurate sensitivity derivatives of complex, internally coupled systems have been developed. Until the development of the Global Sensitivity Equations (GSE), the only method of determining the sensitivity derivatives of coupled systems has been by using finite differences. Analytical or semi-analytical derivatives do not exist as there is no analytical solution to the coupled problem. Also, difficulties arise because the finite difference method is expensive as the system has to iterate to a converged solution for each incremental input variable. The method may not be accurate, and the choice of the input variable increment may cause the difference in the output variable to be insignificant compared to computer numerical error if the choice is too small, or the process may not predict the true value of the output variable if the increment is too large. The GSE allow the system's sensitivity derivatives to be calculated as functions of the component subsystem's (local) sensitivity derivatives. These local sensitivity derivatives are calculated from specifically decoupled subsystems, whereas the GSE account for total system coupling. Since the subsystems are decoupled, it may be possible for the local derivatives to be calculated by analytical or semi-analytical methods, which generally reduce cost and improve accuracy. Several academic problems have been solved using GSE and have demonstrated encouraging results.

James, Benjamin B.↗

NASA NTRS1992

Development of a CFD code for internal flows in liquid fueled engines

To support the design efforts of engines in which liquid propellants are used, one is often required to analyze incompressible, two-dimensional or axisymmetric flows within ducts and cavities with rotating walls and complicated geometries. The steady-state solution is of interest in most cases. This code is intended to provide a tool for efficient computational fluid dynamics (CFD) analysis of such flow problems, taking advantage of the artificial compressibility concept and the Beam-Warming numerical scheme modified for second order accurate, implicit boundary conditions. These concepts ensure a stable, robust, and accurate algorithm due to the reduced speed of sound and the accuracy of the boundary conditions. The code is dedicated only to two-dimensional or axisymmetric flows with or without swirl. Three-dimensional computation is excluded to increase efficiency and speed. This paper briefly presents the theory of the code, as well as several benchmark applications with comparison to well known analytical solutions. In all these test cases, the code produced accurate results.

Dakhoul, Youssef↗

NASA NTRS1994

Coagulation algorithms with size binning

The Smoluchowski equation describes the time evolution of an aerosol particle size distribution due to aggregation or coagulation. Any algorithm for computerized solution of this equation requires a scheme for describing the continuum of aerosol particle sizes as a discrete set. One standard form of the Smoluchowski equation accomplishes this by restricting the particle sizes to integer multiples of a basic unit particle size (the monomer size). This can be inefficient when particle concentrations over a large range of particle sizes must be calculated. Two algorithms employing a geometric size binning convention are examined: the first assumes that the aerosol particle concentration as a function of size can be considered constant within each size bin; the second approximates the concentration as a linear function of particle size within each size bin. The output of each algorithm is compared to an analytical solution in a special case of the Smoluchowski equation for which an exact solution is known . The range of parameters more appropriate for each algorithm is examined.

Statton, David M.↗

NASA NTRS1977

Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.

Walden, H.↗

DOE OSTI2022

Modeling gas release from a Bingham plastic slurry and deconvoluting measured data

Physics-based models for predicting the off-gassing characteristics of agitated slurries are presented. This approach decomposes the system into two separate but coupled slurry and headspace models. The physics driving bubble transport through the slurry and gas mixing within the headspace are discussed. An analytical expression for predicting the time evolution of the headspace concentration using first principles theory is also presented. Predictions from the numerical models, as well as expectations from the analytical solution, both agree with measured off gassing data for two different experimental operating conditions. After benchmarking the numerical model predictions against experimental data, the model was used to make predictions for gas release from a full-scale vessel and to perform sensitivity analyses to examine the sensitivity of gas release to parameters such as yield stress, consistency index, slurry density, bubble size, bubble concentration, and impeller speed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1991

Advanced development of the boundary element method for elastic and inelastic thermal stress analysis

The focus of this dissertation is on advanced development of the boundary element method for elastic and inelastic thermal stress analysis. New formulations for the treatment of body forces and nonlinear effects are derived. These formulations, which are based on particular integral theory, eliminate the need for volume integrals or extra surface integrals to account for these effects. The formulations are presented for axisymmetric, two and three dimensional analysis. Also in this dissertation, two dimensional and axisymmetric formulations for elastic and inelastic, inhomogeneous stress analysis are introduced. The derivatives account for inhomogeneities due to spatially dependent material parameters, and thermally induced inhomogeneities. The nonlinear formulation of the present work are based on an incremental initial stress approach. Two inelastic solutions algorithms are implemented: an iterative; and a variable stiffness type approach. The Von Mises yield criterion with variable hardening and the associated flow rules are adopted in these algorithms. All formulations are implemented in a general purpose, multi-region computer code with the capability of local definition of boundary conditions. Quadratic, isoparametric shape functions are used to model the geometry and field variables of the boundary (and domain) of the problem. The multi-region implementation permits a body to be modeled in substructured parts, thus dramatically reducing the cost of analysis. Furthermore, it allows a body consisting of regions of different (homogeneous) material to be studied. To test the program, results obtained for simple test cases are checked against their analytic solutions. Thereafter, a range of problems of practical interest are analyzed. In addition to displacement and traction loads, problems with body forces due to self-weight, centrifugal, and thermal loads are considered.

Henry, Donald P., Jr.↗

DOE OSTI2024

Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime

This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.

Domain-based method↗

DOE OSTI2021

Micro-continuum approach for mineral precipitation

Abstract Rates and extents of mineral precipitation in porous media are difficult to predict, in part because laboratory experiments are problematic. It is similarly challenging to implement numerical methods that model this process due to the need to dynamically evolve the interface of solid material. We developed a multiphase solver that implements a micro-continuum simulation approach based on the Darcy–Brinkman–Stokes equation to study mineral precipitation. We used the volume-of-fluid technique in sharp interface implementation to capture the propagation of the solid mineral surface. Additionally, we utilize an adaptive mesh refinement method to improve the resolution of near interface simulation domain dynamically. The developed solver was validated against both analytical solution and Arbitrary Lagrangian–Eulerian approach to ensure its accuracy on simulating the propagation of the solid interface. The precipitation of barite (BaSO 4 ) was chosen as a model system to test the solver using variety of simulation parameters: different geometrical constraints, flow conditions, reaction rate and ion diffusion. The growth of a single barite crystal was simulated to demonstrate the solver’s capability to capture the crystal face specific directional growth.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1995

Active control of panel vibrations induced by a boundary layer flow

The problems of active and passive control of sound and vibration has been investigated by many researchers for a number of years. However, few of the articles are concerned with the sound and vibration with flow-structure interaction. Experimental and numerical studies on the coupling between panel vibration and acoustic radiation due to flow excitation have been done by Maestrello and his associates at NASA/Langley Research Center. Since the coupled system of nonlinear partial differential equations is formidable, an analytical solution to the full problem seems impossible. For this reason, we have to simplify the problem to that of the nonlinear panel vibration induced by a uniform flow or a boundary-layer flow with a given wall pressure distribution. Based on this simplified model, we have been able to consider the control and stabilization of the nonlinear panel vibration, which have not been treated satisfactorily by other authors. Although the sound radiation has not been included, the vibration suppression will clearly reduce the sound radiation power from the panel. The major research findings are presented in three sections. In section two we describe results on the boundary control of nonlinear panel vibration, with or without flow excitation. Sections three and four are concerned with some analytical and numerical results in the optimal control of the linear and nonlinear panel vibrations, respectively, excited by the flow pressure fluctuations. Finally, in section five, we draw some conclusions from research findings.

Chow, Pao-Liu↗

DOE OSTI2023

Exploring the working range of automated standard dilution analysis of nutrient elements in foods by inductively coupled plasma optical emission spectrometry

Inductively coupled plasma optical emission spectrometry (ICP-OES) is an important tool for measuring nutrient elements in food. ICP-OES methods typically determine analytical concentrations using external standard calibration but can be susceptible to matrix effects. The method of standard additions does not suffer from matrix effects but is time consuming and labor intensive. Automated standard dilution analysis (SDA) allows for online matrix matched calibration without preparing individual standard additions for each sample matrix. This approach may solve both time and matrix issues and has been described in the literature as an attractive alternative to standard additions. The working range of the method for nutrient elements, however, is an understudied feature of SDA that may be a potential drawback to routine analysis of foods. We evaluated automated SDA performance through the analysis of 10 reference materials and four fortified (i.e., spiked) foods spanning the AOAC food triangle. We evaluated the working range, accuracy, and precision for analyses of nutrient elements in foods. Accepted accuracy (80–120% recovery) was achieved for 10 nutrient elements, Ca, Cu, Fe, K, Mg, Mn, Na, P, S, and Zn, when the analytical solution concentration to standard concentration ratio was less than 10. This equates to a working range for each element spanning at least two orders of magnitude. Removing outliers, Z scores (n = 95) ranged from –1.8 to 0.88, and the average recovery (n = 85) from fortification experiments was 97 ± 12% (2σ). Therefore, automated SDA applied to ICP-OES may be used for nutrient elemental analyses in samples with difficult matrices such as foods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1982

Finite element analysis of the effect of a non-planar solid-liquid interface on the lateral solute segregation during unidirectional solidification

The effect of solid-liquid interface shape on lateral solute segregation during steady-state unidirectional solidification of a binary mixture is calculated under the assumption of no convection in the liquid. A finite element technique is employed to compute the concentration field in the liquid and the lateral segregation in the solid with a curved boundary between the liquid and solid phases. The computational model is constructed assuming knowledge of the solid-liquid interface shape; no attempt is made to relate this shape to the thermal field. The influence of interface curvature on the lateral compositional variation is investigated over a range of system parameters including diffusivity, growth speed, distribution coefficient, and geometric factors of the system. In the limiting case of a slightly nonplanar interface, numerical results from the finite element technique are in good agreement with the analytical solutions of Coriell and Sekerka obtained by using linear theory. For the general case of highly non-planar interface shapes, the linear theory fails and the concentration field in the liquid as well as the lateral solute segregation in the solid can be calculated by using the finite element method.

Carlson, F. M.↗

DOE OSTI2020

Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions

Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\textit{α}$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $α > \frac{1}{2}$ . A numerical implementation of the SDRG method yields a power-law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading-order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $\textit{α}$, corresponding to a critical behavior with an effective central charge $\textit{c}$ = ln(2), independent of $\textit{α}$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $\textit{α}$. For a wide range of partition size $\textit{l}$, the EE fits a critical behavior with a central charge close to $\textit{c}$ = 1, which is the same as for the clean Haldane-Shastry model with a power-law-decaying interaction with $\textit{α}$ = 2. Only for small $l \ll L$, in a range which increases with the number of spins N, we find deviations which are rather consistent with the strong disorder fixed point central charge $\textit{c}$ = ln(2). Furthermore, we find using ED that the concurrence shows power-law decay, albeit with smaller power exponents than obtained by SDRG. Finally, we also present results obtained with DMRG and find agreement with ED for sufficiently small $\textit{α}$ < 2, whereas for larger $\textit{α}$ DMRG tends to underestimate the entanglement entropy and finds a faster decaying concurrence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1989

An analytic development of orbit determination for a distant, planetary orbiter

With the advent of the Mariner '71 Mission, NASA has been sending spacecraft to orbit various distant bodies within the solar system. At present, there is still no adequate theory describing the inherent state estimation accuracy, based on two-way, coherent range-rate data. It is the purpose of this article to lay the groundwork for a general elliptic theory, and in addition to provide an analytic solution for the special case of circular orbits. It is shown that circular orbits about distant planets may suffer singularities in over-all position error estimation. These singularities are due to orbit inclination, placement of the line-of-nodes, and insignificant cross-velocity at the start and end of retrograde motion when orbiting a superior planet. Even though these conclusions appear to yield poor state estimation, one should not be unduly alarmed inasmuch as the stated conditions for singularity are not maintained for extended periods during typical mission scenarios. However, mission analysts should be aware of these potential pitfalls and realize that spuriously large results for circular orbiters can be obtained and are not the result of incorrect assumptions or faulty software. The general elliptic problem appears so involved that analytic inversion at this time is just not feasible, and in any case the resulting expression for the position error would likely be so lengthy that any understanding would be lost in the maze.

Russell, R. K.↗

NASA NTRS1974

Steady state asymmetric planetary electrical induction

An analytic solution is presented for the steady state electric and magnetic fields induced by the motional electric field of the solar wind in the atmosphere or interior of a planet that is asymmetrically surrounded by solar wind plasma. The electrically conducting ionosphere or interior must be in direct electrical contact with the solar wind over the day side of the planet. The conducting region of the planet is modeled by a sphere or a spherical shell of arbitrarily stratified electrical conductivity. A monoconducting cylindrical cavity is assumed to extend downstream on the night side of the planet. The solar wind is assumed to be highly conducting so that the induced fields are confined to the planet and cavity. Induced currents close as sheet currents at the solar wind-cavity and solar wind-planet interfaces. Numerical evaluations of the analytic formulas are carried out for a uniformly conducting spherical model.

Horning, B. L.↗

DOE OSTI2021

Solidification dynamics in metal additive manufacturing: analysis of model assumptions

Solidification characteristics in the meltpool drive the process-microstructure relationship which helps dictate the material properties of as-built parts in additive manufacturing; therefore, being able to accurately and quickly simulate the size, shape, and solidification characteristics in the melt pool is of great interest to the field. In this study, we investigate various important physical phenomena (dynamic material properties, fluid-flow, radiation and vaporization) which can either be included or neglected in a continuum finite volume model (FVM) and their effect on the solidification conditions. Additionally, since the simplest form of such a model (conduction only) has an analytic solution which is much faster, its viability is also considered. Since the inclusion of some of these physical phenomena will inherently change the net energy input as well as the amount of energy needed to achieve melting of a control volume, each set of included phenomena had an effective absorption efficiency which was calibrated to closely match the dimensions of the melt pool to that of the ground truth data. The ground truth data for this study was defined to be the output of the FVM which included all the physical phenomena (OF). This study then goes on to compare the effects on solidification conditions each of these calibrated models has. It was found that most of the change in solidification conditions comes from the inclusion of latent heat. A posterior correlation factor (PCF) is then introduced to enable an analytic model to predict similar solidification conditions to OF model.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Exact and locally implicit source term solvers for multifluid-Maxwell systems

Recently, a family of models that couple multifluid systems to the full Maxwell equations have been used in laboratory, space, and astrophysical plasma modeling. These models are more complete descriptions of the plasma than reduced models like magnetohydrodynamic (MHD) since they are derived more closely from the full kinetic Vlasov-Maxwell system, without assumptions like quasi-neutrality, negligible electron mass, etc. Thus these models naturally retain non-ideal MHD effects like electron inertia, Hall term, pressure anisotropy/nongyrotropy, displacement current, among others. One obstacle to broader application of these model is that an explicit treatment of their source terms leads to the need to resolve rapid processes like plasma oscillation and electron cyclotron motion, even when these are not important. In this paper, we suggest two ways to address this issue. First, we derive the analytic solutions to the source update equations, which can be implemented as a practical, but less generic solver. We then develop a time-centered, locally implicit algorithm to update the source terms, allowing stepping over the fast kinetic time-scales. For a plasma with S species, the locally implicit algorithm involves inverting a local (3 S + 3) × (3 S + 3) matrix only, thus is very efficient. The performance can be further increased by using the direct update formulas to skip null calculations. In this paper, we present benchmarks illustrating the exact energy-conservation of the locally implicit solver, as well as its efficiency and robustness for both small-scale, idealized problems and largescale, complex systems. The locally implicit algorithm can be also easily extended to include other local sources, like collisions and ionization, which are difficult to solve analytically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗