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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2010

INTEGRATION OF THE ROTATION OF AN EARTH-LIKE BODY AS A PERTURBED SPHERICAL ROTOR

For rigid bodies close to a sphere, we propose an analytical solution that is free from elliptic integrals and functions, and can be fundamental for application to perturbed problems. After reordering the Hamiltonian as a perturbed spherical rotor, the Lie-series solution is generated up to an arbitrary order. Using the inertia parameters of different solar system bodies, the comparison of the approximate series solution with the exact analytical one shows that the precision reached with relatively low orders is at the same level of the observational accuracy for the Earth and Mars. Thus, for instance, the periodic errors of the mathematical solution are confined to the microarcsecond level with a simple second-order truncation for the Earth. On the contrary, higher orders are required for the mathematical solution to reach a precision at the expected level of accuracy of proposed new theories for the rotational dynamics of the Moon.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

The magnetic particle in a box: Analytic and micromagnetic analysis of probe-localized spin wave modes

The dipole field from a probe magnet can be used to localize a discrete spectrum of standing spin wave modes in a continuous ferromagnetic thin film without lithographic modification to the film. Obtaining the resonance field for a localized mode is not trivial due to the effect of the confined and inhomogeneous magnetization precession. We compare the results of micromagnetic and analytic methods to find the resonance field of localized modes in a ferromagnetic thin film, and investigate the accuracy of these methods by comparing with a numerical minimization technique that assumes Bessel function modes with pinned boundary conditions. We find that the micromagnetic technique, while computationally more intensive, reveals that the true magnetization profiles of localized modes are similar to Bessel functions with gradually decaying dynamic magnetization at the mode edges. We also find that an analytic solution, which is simple to implement and computationally much faster than other methods, accurately describes the resonance field of localized modes when exchange fields are negligible, and demonstrating the accessibility of localized mode analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Stochastic weighted particle methods for population balance equations

Highlights: {yields} Weight transfer functions for Monte Carlo simulation of coagulation. {yields} Efficient support for single-particle growth processes. {yields} Comparisons to analytic solutions and soot formation problems. {yields} Better numerical accuracy for less common particles. - Abstract: A class of coagulation weight transfer functions is constructed, each member of which leads to a stochastic particle algorithm for the numerical treatment of population balance equations. These algorithms are based on systems of weighted computational particles and the weight transfer functions are constructed such that the number of computational particles does not change during coagulation events. The algorithms also facilitate the simulation of physical processes that change single particles, such as growth, or other surface reactions. Four members of the algorithm family have been numerically validated by comparison to analytic solutions to simple problems. Numerical experiments have been performed for complex laminar premixed flame systems in which members of the class of stochastic weighted particle methods were compared to each other and to a direct simulation algorithm. Two of the weighted algorithms have been shown to offer performance advantages over the direct simulation algorithm in situations where interest is focused on the larger particles in a system. The extent of this advantage depends on the particular system and on the quantities of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A fast reduced model for a shell-and-tube based latent heat thermal energy storage heat exchanger and its application for cost optimal design by nonlinear programming

Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlinear solidification/melting process of phase change materials (PCMs) leads to a large-scale complex dynamics system, where the system behavior depends on a set of parameters. In a design setting, repeated model evaluations are required over the set of parameters results in significant computational burden. In this paper, an explicit analytic solution was built for the propagation of the solidification front in a cylindrical coordinate. The analytic solution approach is further employed to develop a low computational reduced model (RM) as a module for a shell-and-tube based LHTES heat exchanger. The levelized Cost of Energy (LCOE) is used as a design metric and the RM model is used to apply system-level constraints in the nonlinear programming formulation that facilitates efficient global optimal design of the PCM properties, flow conditions and tube geometries. The use of LCOE as the design metric prevents over design of the heat transfer rate and also establishes a fair ground for evaluation of different thermal storage technologies and their integrated applications with other systems. Optimal results showed that a higher effectiveness results in a higher LCOE; the velocity of the HTF and the length of the channel are highly correlated with each other; both larger PCM latent energy and conductivity result in lower LCOE.

25 ENERGY STORAGE↗
DOE OSTI2012

Radiation Hydrodynamics Test Problems with Linear Velocity Profiles

As an extension of the works of Coggeshall and Ramsey, a class of analytic solutions to the radiation hydrodynamics equations is derived for code verification purposes. These solutions are valid under assumptions including diffusive radiation transport, a polytropic gas equation of state, constant conductivity, separable flow velocity proportional to the curvilinear radial coordinate, and divergence-free heat flux. In accordance with these assumptions, the derived solution class is mathematically invariant with respect to the presence of radiative heat conduction, and thus represents a solution to the compressible flow (Euler) equations with or without conduction terms included. With this solution class, a quantitative code verification study (using spatial convergence rates) is performed for the cell-centered, finite volume, Eulerian compressible flow code xRAGE developed at Los Alamos National Laboratory. Simulation results show near second order spatial convergence in all physical variables when using the hydrodynamics solver only, consistent with that solver's underlying order of accuracy. However, contrary to the mathematical properties of the solution class, when heat conduction algorithms are enabled the calculation does not converge to the analytic solution.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

A simple analytic model for the evolution of captured galactic disks

The general analytic solution developed by Steinman-Cameron and Durisen and published in 1988 for the evolution of dissipative nonplanar disks is applied to captured galactic disks in model galaxies with nonspherical, scale-free, logarithmic gravitational potentials. Such potentials produce flat rotation curves, similar to those seen in real galaxies. In this case, the analytic solution yields a self-similar structure for the warps and twists that develop while the disks is settling. Being scale-free in a simple, analytic form, this solution is completely defined by only a few dimensionless fitting parameters. As a result, it can be utilized as a mathematical tool to fit settling disks in real galaxies. The minimum time it takes for a disk to settle into a steady state orientation is also a scale-free quantity when expressed in units of the precession period or the orbit period. For realistic parameters, settling times are on the order of one-half to two periods. The use of the time-dependent structure of settling disks as a probe of the three-dimensional mass distribution of the host galaxies, including dark halos, is discussed.

Steiman-Cameron, Thomas Y.↗
DOE OSTI2016

Single-Bubble Flow Boiling Phenomena - Interface Tracking Simulation

Boiling, as one of the most efficient heat transfer mechanisms, is widely used in various engineering systems. Better understanding and modeling of this process remains a major challenge in multiphase flow research. The distribution of vapor in boiling system affects the heat transfer rate and may cause unfavorable conditions, such as heater burn-out. A number of flow regimes have been observed experimentally. In general, there are three regimes under boiling conditions: nucleate boiling, transition boiling, and film boiling. The nucleate boiling regime is categorized into partial boiling regime and fully developed nucleate boiling, according to behavior of bubble dynamics and heat transfer characteristics. In the first region, as the wall temperature increases, the fraction of the wall surface subject to nucleate boiling increases until bubble formation occupies the entire heated surface. Heat transfer in this region is a complex mixture of single-phase forced convection and nucleate boiling. As bubble density increases, bubbles turn to coalesce and form insulating vapor patches, which impedes liquid flow back to the surface. The heat transfer rate under this condition reduces dramatically. This point is called Critical Heat Flux (CHF), which leads to boiling crisis. The behavior of boiling crisis is dependent on local fluid conditions due to bubble growth and departure. Experiments are the ultimate tool for boiling model development and verification, but they still lack some capabilities needed for better understanding of the local mechanism of this phenomena. It's difficult to capture many important details at the pressure/temperature conditions of interest using experimental techniques, such as full three dimensional measurements of velocity and temperature distribution and estimates of heat flux partitioning during the boiling process. The interface tracking simulation (ITS) is one of the promising approaches to describe heat transfer of boiling phenomena and their underlying mechanisms. The advances of high performance computing (HPC) in recent years made it possible to apply DNS to a wide variety of adiabatic flows. Some work has been done to implement evaporation / condensation models as well. Lee and Nydahl performed a numerical simulation of bubble growth and departure assuming that the bubble has the shape of a truncated sphere and a micro-layer exists during bubble growth. A 2-D cylindrical bubbles simulation has been done by Son with a simplified model to predict the heat flux in a thin liquid micro-layer. A direct simulation of 2D film boiling is conducted by Juric and Tryggvason. The film boiling, below critical pressure with a modified Level Set Method, is studied by Son and Dhir. Ose and Kunugi have developed a boiling and condensation model on subcooled boiling phenomena. Fuchs performed numerical simulations of bubble growth and departure considering wall conduction effects. Fully transient heat and fluid flow is modeled with a free surface of a rising bubble and a periodic calculation of the whole cycling of a growing, detaching, and rising bubble. Mukherjee and Kandikar have done a numerical simulation of an evaporating meniscus on a moving heated surface with level set method. The heat transfer associated with the advancing and receding contact angle has been studied. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate single-bubble growth scenarios. For a single bubble simulation in infinite liquid, the analytical solution exists and can be compared with the numerical results for verification purposes. The presented capabilities will be utilized in the large scale DNS of boiling flows in the future. The finite-element based code, PHASTA is used for the simulation. It is a parallel, hierarchic, higher-order accurate, adaptive, stabilized, transient analysis flow solver, which has been shown to be an effective tool for a wide range of single and two-phase flow problems. It has been shown to be highly scalable on top supercomputers ({approx}85% scaling on up to 3 million mesh partitions using a 92 billion element mesh . PHASTA has been shown to reliably predict the details of adiabatic bubbly flows as well as single-phase flows with heat transfer. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate a single-bubble growth scenario. For a single bubble growth in superheated water, the analytical solution exists and can be compared with the numerical results for verification purposes. The second-order accurate spatial and time discretization is used for the flow solver in the presented work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics

We present a new multidimensional high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method that supports hypoelastic and hyperelastic strength models for simulating solid dynamics with higher-order elements. We also present new one-dimensional test problems that have an analytic solution corresponding to a hyperelastic–plastic wave. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated high-order Taylor series polynomials. The stress fields are represented using nodal quantities. The constitutive models used to calculate the deviatoric stress are either a hypoelastic–plastic, infinitesimal strain hyperelastic–plastic, or finite strain hyperelastic–plastic model. These constitutive models require new methods for calculating high-order polynomials for the velocity gradient and deformation gradient in an element. The plasticity associated with the strength model is determined using a radial return method to with a J 2 yield criterion and perfect plasticity. The temporal evolution of the governing equations is achieved with the total variation diminishing Runge–Kutta (TVD RK) time integration method. A diverse suite of 1D and 2D test problems are calculated. Here, the new 1D piston test problems, which have analytic solutions for each elastic–plastic model, are presented and calculated to demonstrate the stability and formal accuracy of the various models with the new Lagrangian DG method. 2D test problems are calculated to demonstrate the stability and robustness of the new Lagrangian DG method on multidimensional problems with high-order elements, which have faces that can bend.

42 ENGINEERING↗
DOE OSTI2014

On the interaction between turbulence and a planar rarefaction

The modeling of turbulence, whether it be numerical or analytical, is a difficult challenge. Turbulence is amenable to analysis with linear theory if it is subject to rapid distortions, i.e., motions occurring on a timescale that is short compared to the timescale for nonlinear interactions. Such an approach (referred to as rapid distortion theory) could prove useful for understanding aspects of astrophysical turbulence, which is often subject to rapid distortions, such as supernova explosions or the free-fall associated with gravitational instability. As a proof of principle, a particularly simple problem is considered here: the evolution of vorticity due to a planar rarefaction in an ideal gas. Analytical solutions are obtained for incompressive modes having a wave vector perpendicular to the distortion; as in the case of gradient-driven instabilities, these are the modes that couple most strongly to the mean flow. Vorticity can either grow or decay in the wake of a rarefaction front, and there are two competing effects that determine which outcome occurs: entropy fluctuations couple to the mean pressure gradient to produce vorticity via baroclinic effects, whereas vorticity is damped due to the conservation of angular momentum as the fluid expands. Whether vorticity grows or decays depends upon the ratio of entropic to vortical fluctuations at the location of the front; growth occurs if this ratio is of order unity or larger. In the limit of purely entropic fluctuations in the ambient fluid, a strong rarefaction generates vorticity with a turbulent Mach number on the order of the rms of the ambient entropy fluctuations. The analytical results are shown to compare well with results from two- and three-dimensional numerical simulations. Analytical solutions are also derived in the linear regime of Reynolds-averaged turbulence models. This highlights an inconsistency in standard turbulence models that prevents them from accurately capturing the physics of rarefaction-turbulence interaction. In addition to providing physical insight, the solutions derived here can be used to verify algorithms of both the Reynolds-averaged and direct numerical simulation variety. Finally, dimensional analysis of the equations indicates that rapid distortion of turbulence can give rise to two distinct regimes in the turbulent spectrum: a distortion range at large scales where linear distortion effects dominate, and an inertial range at small scales where nonlinear effects dominate.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

DOC-WMF - A Generic Model for Assessment of Waste Disposal Facilities - 19278

Numerical models and computer codes play an important role in the safety assessment of nuclear waste disposal facilities, as well as in the regulatory review of proponents' safety assessments. An important part of a safety assessment is the radiation dose calculation. This paper presents a computer code called DOC-WMF for calculating radiation dose from nuclear waste disposal facilities. DOC-WMF is a generic code that could be used for dose calculations for deep geological or near surface disposal facilities of nuclear wastes. DOC-WMF is much faster than complicated 3-D numerical models in terms of computational speed since the model uses the commercial code GoldSim as the computation engine which is based on analytical solutions for contaminant transport. As a result, it enables a user to quickly assess the dose consequences of multiple options or scenarios for a nuclear waste disposal facility. DOC-WMF was adapted from, and an improvement to, the Scoping of Options and Analyzing Risk (SOAR) model developed by the United States Nuclear Regulatory Commission (US NRC). A key improvement over the SOAR model is that DOC-WMF allows the calculation of dose contributions from other pathways such as food ingestion and air inhalation in addition to the drinking water pathway which is the sole dose contribution considered in the SOAR model. DOC-WMF also allows for: the consideration of 55 radionuclides with option to add more if required; the choice of source release method; various pathways to the biosphere; and dose calculations including an extended array of exposure pathways. In addition, DOC-WMF can simulate more complex hydrogeological settings and waste forms than SOAR does. DOC-WMF was compared against known analytical solutions for verification. It was then applied to two test cases and the results were compared. The first was a hypothetical deep geological disposal repository. The second test case was a near-surface nuclear waste disposal facility. DOC-WMF independently modeled these two test cases and achieved similar results as the more complicated numerical models did. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1978

Unsteady flow in a supersonic cascade with subsonic leading-edge locus

Linearized theory is used to predict the unsteady flow in a supersonic cascade with subsonic axial flow velocity. A closed-form analytical solution is obtained by using a double application of the Wiener-Hopf technique. Although numerical and semianalytical solutions of this problem have already appeared in the literature, this paper contains the first completely analytical solution. It has been stated in the literature that the blade source should vanish at the infinite duct resonance condition. The present analysis shows that this does not occur. This apparent discrepancy is explained in the paper.

Adamczyk, J. J.↗
NASA NTRS1990

A two-step iterative method for evolving nonlinear acoustic systems to a steady-state

A new approach for evolving two-dimensional nonlinear acoustic systems with flow to a steady state is presented. The approach is a two-step iterative method which is tested on a benchmark acoustic problem for which an exact analytical solution is available. Results are also calculated for a nonlinear acoustic problem for which an exact analytical solution is not known. Results indicate that the two-step method represents a powerful, efficient, and stable method for evolving two-dimensional acoustic systems to a steady state, and that the method is applicable to any number of spatial dimensions and to other hyperbolic systems. It is noted that for the benchmark problem only a single iteration on the method is required when the transient and steady-state field are of the same order of magnitude; however, four iterations are required when the steady-state field is several orders of magnitude smaller than the transient field. This method requires six iterations before achieving a steady state for the nonlinear test problem.

Watson, Willie R.↗
DOE OSTI2015

Flow regimes for fluid injection into a confined porous medium

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governing equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.

58 GEOSCIENCES↗
NASA NTRS1992

Uniform GTD solution for the diffraction by metallic tapes on panelled compact-range reflectors

Metallic tape is commonly used to cover the interpanel gaps which occur in paneled compact-range reflectors. It is therefore of interest to study the effect of the scattering by the tape on the field in the target zone of the range. An analytical solution is presented for the target zone fields scattered by 2D metallic tapes. It is formulated by the generalized scattering matrix technique in conjunction with the Wiener-Hopf procedure. An extension to treat 3D tapes can be accomplished using the 2D solution via the equivalent current concept. The analytical solution is compared with a reference moment method solution to confirm the accuracy of the former.

Somers, G. A.↗
DOE OSTI2016

ELECTRON ACCELERATION AT A CORONAL SHOCK PROPAGATING THROUGH A LARGE-SCALE STREAMER-LIKE MAGNETIC FIELD

Using a test-particle simulation, we investigate the effect of large-scale coronal magnetic fields on electron acceleration at an outward-propagating coronal shock with a circular front. The coronal field is approximated by an analytical solution with a streamer-like magnetic field featuring a partially open magnetic field and a current sheet at the equator atop the closed region. We show that the large-scale shock-field configuration, especially the relative curvature of the shock and the magnetic field line across which the shock is sweeping, plays an important role in the efficiency of electron acceleration. At low shock altitudes, when the shock curvature is larger than that of the magnetic field lines, the electrons are mainly accelerated at the shock flanks; at higher altitudes, when the shock curvature is smaller, the electrons are mainly accelerated at the shock nose around the top of closed field lines. The above process reveals the shift of the efficient electron acceleration region along the shock front during its propagation. We also find that, in general, the electron acceleration at the shock flank is not as efficient as that at the top of the closed field because a collapsing magnetic trap can be formed at the top. In addition, we find that the energy spectra of electrons are power-law-like, first hardening then softening with the spectral index varying in a range of −3 to −6. Physical interpretations of the results and implications for the study of solar radio bursts are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

Physics of heat pipe rewetting

Although several studies have been made to determine the rewetting characteristics of liquid films on heated rods, tubes, and flat plates, no solutions are yet available to describe the rewetting process of a hot plate subjected to a uniform heating. A model is presented to analyze the rewetting process of such plates with and without grooves. Approximate analytical solutions are presented for the prediction of the rewetting velocity and the transient temperature profiles of the plates. It is shown that the present rewetting velocity solution reduces correctly to the existing solution for the rewetting of an initially hot isothermal plate without heating from beneath the plate. Numerical solutions have also been obtained to validate the analytical solutions.

Chan, S. H.↗
DOE OSTI2016

Viscous effects on the Rayleigh-Taylor instability with background temperature gradient

Here we studied the growth rate of the compressible Rayleigh-Taylor instability in the presence of a background temperature gradient, Θ, using a normal mode analysis. The effect of Θ variation is examined for three interface types corresponding to the combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous, and viscous-inviscid) at different Atwood numbers, At, and when at least one of the fluids' viscosity is non-zero, as a function of the Grashof number. For the general case, the resulting ordinary differential equations are solved numerically; however, dispersion relations for the growth rate are presented for several limiting cases. An analytical solution is found for the inviscid-inviscid interface and the corresponding dispersion equation for the growth rate is obtained in the limit of large Θ. For the viscous-inviscid case, a dispersion relation is derived in the incompressible limit and Θ=0. Compared to Θ=0 case, the role of Θ<0 (hotter light fluid) is destabilizing and becomes stabilizing when Θ>0 (colder light fluid). The most pronounced effect of Θ ≠ 0 is found at low At and/or at large perturbation wavelengths relative to the domain size for all interface types. On the other hand, at small perturbation wavelengths relative to the domain size, the growth rate for the Θ<0 case exceeds the infinite domain incompressible constant density result. The results are applied to two practical examples, using sets of parameters relevant to Inertial Confinement Fusion coasting stage and solar corona plumes. The role of viscosity on the growth rate reduction is discussed together with highlighting the range of wavenumbers most affected by viscosity. The viscous effects further increase in the presence of background temperature gradient, when the viscosity is temperature dependent.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗