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Results for “Two-dimensional phase field equation”

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
NASA NTRS1990

A numerical method for phase-change problems

A highly accurate and efficient finite-difference method for phase-change problems with multiple moving boundaries of irregular shape is developed by employing a coordinate transformation that immobilizes moving boundaries and preserves the conservative forms of the original governing equations. The numerical method is first presented for one-dimensional phase-change problems (involving large density variation between phases, heat generation, and multiple moving boundaries) and then extended to solve two-dimensional problems (without change of densities between phases). Numerical solutions are obtained non-iteratively using an explicit treatment of the interfacial mass and energy balances and an implicit treatment of the temperature field equations. The accuracy and flexibility of the present numerical method are verified by solving some phase-change problems and comparing the results with existing analytical, semi-analytical and numerical solutions. Results indicate that one- and two-dimensional phase-change problems can be handled easily with excellent accuracies.

Kim, Charn-Jung↗
DOE OSTI2024

Wave-packet manipulation of He Rydberg states by a seeded free-electron laser

We report a two-dimensional pump-control-probe spectroscopic study of the dynamics of singly excited He Rydberg-state wave packets with a seeded extreme ultraviolet (XUV) free-electron laser (FEL) source. A pair of coherent XUV pulses, defined by their coarse time separation and relative phase, created and manipulated the wave packets. The He atoms were postionized by infrared (IR) pulses, and the ion yield was measured as a function of XUV phase and IR arrival time. We tagged and sorted the relative phase of the XUV pulse pair on a single-shot basis by fitting each FEL spectrum with a suitable function that accounts for nonidealities of the XUV pulse pairs, associated with the seeding process; more generally, the fit returns the time-dependent electric field of the FEL spectra. The experimental two-dimensional maps of ion yields, measured as a function of IR (probe) delay and of XUV (pump-control) phase, were compared with the solution of the first-order time-dependent Schrödinger equation for this field. Despite the fact that the experimental conditions imply strong excitation, beyond the approximations of first-order perturbation theory, the simulated map satisfactorily reproduces the experimental one for temporally well-separated pulses. We show that by selecting data at appropriate values of pump-control phase, we enhance or suppress the amplitude of chosen wave-packet components consisting of two or more Rydberg states. When the temporal overlap of the pulse pair cannot be neglected, the phase reconstruction is underdetermined, and we provide a simplified comparison between data and simulations. Published by the American Physical Society 2024

Dumergue, Mathieu (ORCID:0000000236984406)↗
NASA NTRS1993

Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

Walker, Kevin P.↗
NASA NTRS1985

Waveform synthesis of surface waves in a laterally heterogeneous earth by the Gaussian beam method

The present investigation is concerned with an application of the Gaussian beam method to surface waves in the laterally heterogeneous earth. The employed method has been developed for ray tracing and synthesizing seismograms of surface waves in cases involving the laterally heterogeneous earth. The procedure is based on formulations derived by Yomogida (1985). Vertical structure of the wave field is represented by the eigenfunctions of normal mode theory, while lateral variation is expressed by the parabolic equation as in two-dimensional acoustic waves or elastic body waves. It is demonstrated that a large-amplitude change can result from a slight perturbation in the phase velocity model.

Yomogida, K.↗
NASA NTRS1991

A finite element model of conduction, convection, and phase change near a solid/melt interface

Detailed understanding of heat transfer and fluid flow is required for many aerospace thermal systems. These systems often include phase change and operate over a range of accelerations or effective gravitational fields. An approach to analyzing such systems is presented which requires the simultaneous solution of the conservation laws of energy, momentum, and mass, as well as an equation of state. The variable property form of the governing equations are developed in two-dimensional Cartesian coordinates for a Newtonian fluid. A numerical procedure for solving the governing equations is presented and implemented in a computer program. The Galerkin form of the finite element method is used to solve the spatial variation of the field variables, along with the implicit Crank-Nicolson time marching algorithm. Quadratic Langrangian elements are used for the internal energy and the two components of velocity. Linear Lagrangian elements are used for the pressure. The location of the solid/liquid interface as well as the temperatures are determined form the calculated internal energy and pressure. This approach is quite general in that it can describe heat transfer without phase change, phase change with a sharp interface, and phase change without an interface. Analytical results from this model are compared to those of other researchers studying transient conduction, convection, and phase change and are found to be in good agreement. The numerical procedure presented requires significant computer resources, but this is not unusual when compared to similar studies by other researchers. Several methods are suggested to reduce the computational times.

Viterna, Larry A.↗
NASA NTRS1989

Numerical analysis of flow through oscillating cascade sections

The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and nonzero interblade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the periodic boundary conditions. Approximate nonreflecting boundary conditions were coded for the inlet and exit boundary conditions. Sample unsteady solutions were performed for an oscillating cascade and compared to experimental data. Also, test cases were run for a flat plate cascade to compare with the unsteady, small-perturbation, subsonic analyis. The predictions for oscillating cascades with nonzero interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. The zero degree interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus nonreflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distributions for certain flow conditions.

Huff, Dennis L.↗
NASA NTRS1989

Numerical analysis of flow through oscillating cascade sections

The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and nonzero interblade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the perioidic boundary conditions. Approximate nonreflecting boundary conditons were coded for the inlet and exit boundary conditions. Sample unsteady solutions were performed for an oscillating cascade and compared to experimental data. Also, test cases were run for a flat plate cascade to compare with the unsteady, small-perturbation, subsonic analysis. The predictions for oscillating cascades with nonzero interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. The zero degree interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus nonreflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distribution for certain flow conditions.

Huff, Dennis L.↗
NASA NTRS1989

Numerical analysis of flow through oscillating cascade sections

The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and non-zero inter-blade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the periodic boundary conditions. Approximate nonreflecting boundary conditions have been coded for the inlet and exit boundary conditions. Sample unsteady solutions have been performed for an oscillating cascade and compared to experimental data. Also, test cases were fun for a flat plate cascade to compare with an unsteady, small-perturbation, subsonic analysis. The predictions for oscillating cascades with non-zero inter-blade phase angles are in good agreement with experimental data and small-perturbation theory. The zero degree inter-blade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus non-reflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distributions for certain flow conditions. This code is expected to be used as a tool for reviewing simpler models that do not include the full nonlinear aerodynamics or as a final check for designs against flutter in turbomachinery.

Huff, Dennis L.↗
NASA NTRS1989

The stability of a compressible stratified shear layer

The stability of a shear layer under the effect of gravity is investigated using the compressible magnetohydrodynamic (MHD) equations, including an effective gravity term to represent the curvature effects of the flow and magnetic field line geometry. A general eigenmode equation is derived for a two-dimensional MHD fluid, and an energy-principle analysis to explain the effect of compressibility on the critical Richardson number is presented. For the case of a hyperbolic tangent shear flow and exponential density profile, it was found that, in the Boussinesq approximation, the compressibility raises the critical Richardson number from 1/4 to as much as 1/2, with the exact value depending on the value of the magnetic field at infinity. Under approximation of a strong asymptotic magnetic field, without invoking the Boussinesq approximation, it is shown both analytically and numerically that the density gradient terms cause the shear instability to be dispersive. The long-wavelength stability boundary for the Richardson number J = 0 is characterized by a normalized phase velocity c =

Wang, Z.↗
DOE OSTI2025

Squeezing quantum states in three-dimensional twisted crystals

Bloch's theorem provides a conventional starting point for describing wave propagation in periodic media, but in ordered materials where competing spatial periods coexist it is rendered ineffective, often with dramatic consequences. Here we develop an alternate approach that uses coherent free-particle vortex states to study quantum states in supertwisted crystals: three-dimensional stacks of atomically thin two-dimensional layers. Here, this formalism leads naturally to the representation of the spectrum using squeezed coherent states, and it reveals the crucial role of a Coriolis coupling in the equations of motion. This identifies an underlying noncommutative geometry and novel edge state structure in a family of complex ordered structures.

36 MATERIALS SCIENCE↗
DOE OSTI2026

The high explosives & affected targets (HEAT) dataset

Artificial Intelligence (AI) surrogate models offer a computationally efficient alternative to full-physics simulations, yet no existing datasets are publicly available for training, testing, and validation of machine learning models of the dynamics of high-explosive driven shocks through multiple materials. Shock propagation through materials is a computationally challenging problem because simulations must include material-specific equations of state (EOS) along with descriptions of other physical processes such as plastic deformation, phase change, damage processes, fluid instabilities, and multi-material interactions. Shocks are typically initiated by high-velocity impacts or explosive loading. The latter case necessitates the addition of models of reactive materials to represent high-explosive (HE) detonation. Here, to address the lack of an expansive dataset for multi-material shock propagation in the AI/ML community, we present the High-Explosives and Affected Targets (HEAT) Dataset. HEAT is a physics-rich collection of two-dimensional, cylindrically symmetric, simulations generated using an Eulerian, multi-material, shock-propagation code developed at Los Alamos National Laboratory. The dataset includes two partitions: (1) the expanding shock-cylinder (CYL) simulations, Figs. 1, and (2) the Perturbed Layered Interface (PLI) simulations, Fig. 2. Entries in both partitions consist of time series of arrays of thermodynamic fields (pressure, density, and temperature), kinematic fields (position and velocity), and additional fields that depend on thermodynamic and/or kinematic fields (e.g., material stress). Materials in the CYL partition include solids (aluminium, copper, depleted uranium, stainless steel, tantalum, and a generic polymer), a liquid (water), gases (air, nitrogen), and a generic detonating material (high explosive, HE). The PLI partition spans a highly varying geometry but consists of fixed materials across entries: Copper, aluminium, stainless steel, generic polymer, and generic HE. HEAT captures critical phenomena such as momentum transfer, shock propagation, plastic deformation, and thermal effects, making HEAT a valuable benchmark for development of AI/ML emulation of multi-material shock propagation.

36 MATERIALS SCIENCE↗
NASA NTRS1976

Non-equilibrium radiation from viscous chemically reacting two-phase exhaust plumes

A knowledge of the structure of the rocket exhaust plumes is necessary to solve problems involving plume signatures, base heating, plume/surface interactions, etc. An algorithm is presented which treats the viscous flow of multiphase chemically reacting fluids in a two-dimensional or axisymmetric supersonic flow field. The gas-particle flow solution is fully coupled with the chemical kinetics calculated using an implicit scheme to calculate chemical production rates. Viscous effects include chemical species diffusion with the viscosity coefficient calculated using a two-equation turbulent kinetic energy model.

Penny, M. M.↗
NASA NTRS1976

High-beta turbulence in two-dimensional magnetohydrodynamics

Equations of ideal magnetohydrodynamics are used to study incompressible turbulent flows in a specified geometry where all the field quantities vary with only two spatial dimensions. The procedures adopted are basically those of Kraichnan (1967), in which classical equilibrium ensembles are built around constants of the motion identified from the Fourier-transformed equations of motion. Once the constants of the motion are identified, the statistical formulation of the problem is presented in a phase space whose coordinates are the real and imaginary parts of the Fourier coefficients. Canonical ensembles are constructed in this phase space by classical arguments. The theory developed permits isolation of some qualitatively new gross physical effects which have so far not been calculated. One of the more novel physical effects is the appearance of macroscopic structures involving long-wavelength, self-generated, magnetic fields for a wide range of initial parameters.

Fyfe, D.↗
NASA NTRS1976

Influence of drag coefficient equations on particle motion calculations

An important phase of laser velocimetry investigations in gas flow fields is an analysis of the particle motion in the gas. The present paper examines three important aspects of particle motion calculations. A comparison of various drag coefficient equations with available experimental sphere drag data is made to determine the relative accuracy of the various empirical expressions available. Then, the most accurate drag coefficient equation is used to determine the limitations of Stokes drag equation for calculating relaxation lengths behind normal shocks, and percent velocity lags in one-dimensional constant velocity gradient regions. Finally, a two-dimensional constant velocity gradient gas flow field is examined to determine the importance of the coupling between the governing equations for the components of particle velocity.

Walsh, M. J.↗
NASA NTRS1981

Heat transfer of phase-change materials in two-dimensional cylindrical coordinates

Two-dimensional phase-change problem is numerically solved in cylindrical coordinates (r and z) by utilizing two Taylor series expansions for the temperature distributions in the neighborhood of the interface location. These two expansions form two polynomials in r and z directions. For the regions sufficiently away from the interface the temperature field equations are numerically solved in the usual way and the results are coupled with the polynomials. The main advantages of this efficient approach include ability to accept arbitrarily time dependent boundary conditions of all types and arbitrarily specified initial temperature distributions. A modified approach using a single Taylor series expansion in two variables is also suggested.

Labdon, M. B.↗
NASA NTRS1985

Defect-phase-dynamics approach to statistical domain-growth problem of clock models

The growth of statistical domains in quenched Ising-like p-state clock models with p = 3 or more is investigated theoretically, reformulating the analysis of Ohta et al. (1982) in terms of a phase variable and studying the dynamics of defects introduced into the phase field when the phase variable becomes multivalued. The resulting defect/phase domain-growth equation is applied to the interpretation of Monte Carlo simulations in two dimensions (Kaski and Gunton, 1983; Grest and Srolovitz, 1984), and problems encountered in the analysis of related Potts models are discussed. In the two-dimensional case, the problem is essentially that of a purely dissipative Coulomb gas, with a sq rt t growth law complicated by vertex-pinning effects at small t.

Kawasaki, K.↗
NASA NTRS1987

Numerical simulation of the flow field and fuel sprays in an IC engine

A two-dimensional model for axisymmetric piston-cylinder configurations is developed to study the flow field in two-stroke direct-injection Diesel engines under motored conditions. The model accounts for turbulence by a two-equation model for the turbulence kinetic energy and its rate of dissipation. A discrete droplet model is used to simulate the fuel spray, and the effects of the gas phase turbulence on the droplets is considered. It is shown that a fluctuating velocity can be added to the mean droplet velocity every time step if the step is small enough. Good agreement with experimental data is found for a range of ambient pressures in Diesel engine-type microenvironments. The effects of the intake swirl angle in the spray penetration, vaporization, and mixing in a uniflow-scavenged two-stroke Diesel engine are analyzed. It is found that the swirl increases the gas phase turbulence levels and the rates of vaporization.

Nguyen, H. L.↗
NASA NTRS1992

Intermodulation in the oscillatory magnetoresistance of a two-dimensional electron gas

The oscillatory magnetoresistance wave form of a 2-D electron gas shows multiple structures when two subbands are populated. In addition to high-field oscillations at a frequency equal to the sum of the two frequencies corresponding to the concentrations of the subbands, and to a superposition at intermediate fields, we observed oscillations at the difference frequency at low fields and higher temperatures. The field range at which the frequency difference is observed increases with increasing temperature. The crossover from superposition to frequency difference is accompanied by a beat. Similar beats, whose field location shows identical temperature dependence, can be observed in data obtained by other groups on different structures. The various components of the wave form can be attributed to different phase relations between the diagonal and off-diagonal elements of the conductivity tensor. It is shown how the intermodulation term, when inserted into the extended oscillatory equation, can give rise to all three structures.

Schacham, S. E.↗