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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 37 records · Page 2

Measurement of Thermal Conductivity in a Supercooled Hydrogel-Salt Complex Near Its Phase Transition

Solid-liquid phase transitions, i.e. solidification processes, have applications in data storage, development of novel thermoelectric materials, cooling of microelectronic substrates and air conditioning condensers. Standard analyses of solidification (Stefan problem) assume constant thermal properties of the solid and liquid sides. It is not known how these properties change across the spatial transition interface, though most studies report a discontinuity in the solid and liquid properties through the transition temperature [1]. When the phase transition releases enthalpy, recent research has shown if the phonon or electron transport time is of the same order of magnitude as the time scale of the atomic transformation, this increases the heat capacity of the solid material at temperatures near the phase transition temperature [2]. A fundamental understanding of the phase transition may help shed light on the molecular origins of supercooling and spontaneous nucleation, which will help with applications involving them. We report studies of supercooling and nucleation of sodium sulfate decahydrate, a salt hydrate which is of recent interest in thermal storage, and of a hydrogel-sodium sulfate complex which shows limited supercooling. We will also report the measurement of their thermal properties during the phase transition process. This will be done with a hot-wire setup which produces small temperature changes of the order of ~1 C.

crystallization, phase transformation, thermal con↗

Solidification of a binary mixture

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

Antar, B. N.↗

Thermochemical erosion

A quasi-steady multidimensional Stefan problem is treated by means of similarity, asymptotic methods, and numerical analysis. The continuous wearing away of a solid 'erodee' is effected by gradual consumption of a solid 'eroder'. In the process under study, the erodee melts and the (liquid) melt diffuses to the eroder, where an exothermic, indefinitely rapid, diffusion-controlled surface reaction occurs. The products of reaction convey some of the chemically-generated heat to the surface of the erodee, so that further melting may occur, and the process may proceed. The analysis seeks to estimate the quasi-steady rates of consumption of the erodee and eroder, for the (convenient) self-similar case of confocal parabolas defining the boundaries of the melt layer. The analysis is simplified by observing that the flow is of lubrication-theory type: creeping, primarily unidirectional motion owing to the thinness of the melt layer between the erodee and eroder, with diffusion of heat and mass predominantly perpendicular to the principal motion. The analysis is completed by consideration of the force balance on the eroder.

Butler, Gerald↗

Efficient numerical simulation of an electrothermal de-icer pad

In this paper, a new approach to calculate the transient thermal behavior of an iced electrothermal de-icer pad was developed. The method of splines was used to obtain the temperature distribution within the layered pad. Splines were used in order to create a tridiagonal system of equations that could be directly solved by Gauss elimination. The Stefan problem was solved using the enthalpy method along with a recent implicit technique. Only one to three iterations were needed to locate the melt front during any time step. Computational times were shown to be greatly reduced over those of an existing one dimensional procedure without any reduction in accuracy; the curent technique was more than 10 times faster.

Roelke, R. J.↗

Boundary layer description of directional polymer crystallisation

Nearly fifty years ago Lovinger and Gryte suggested that the directional crystallization of a polymer was analogous to the quiescent isothermal crystallization experiment but at a supercooling where the crystal growth velocity was equal to the velocity of the moving front. Our experiments showed that this equivalence holds in a detailed manner at low directional velocities. To understand the underlying physics of these situations, we modeled the motion of a crystallization front in a liquid where the left side boundary is suddenly lowered below the melting point (Stefan's problem) but with the modification that the crystallization kinetics follow a version of the Avrami model. Our numerical results surprisingly showed that the results of the polymer analog track with the Stefan results which were derived for a simple liquid that crystallizes completely at its melting point; in particular, the position of the crystal growth-front evolved with time exactly as in the Stefan problem. The numerical solution also showed that the temperature in the immediate vicinity of the growth-front decreased with increasing front velocity, which is in line with Lovinger and Gryte's ansatz. To provide a clear theoretical understanding of these numerical results we derive a boundary layer solution to the governing coupled differential equations of the polymer problem. The analytical results are in agreement with our observations from experiments and numerical computations but show that this equivalence between the small molecule and polymer analog only holds in the limit where the crystallization enthalpy is much larger than the rate at which heat is conducted away in the polymer. In particular, in the context of the temperature profile, the enthalpy generated by the crystallisation process which is spread out over a narrow spatial region can be approximated as a point source whose location and temperature correspond to the Lovinger–Gryte ansatz.

36 MATERIALS SCIENCE↗

On Boundary-Value Problems for RANS Equations and Two-Equation Turbulence Models

Currently, in engineering computations for high Reynolds number turbulent flows, turbulence modeling continues to be the most frequently used approach to represent the effects of turbulence. Such models generally rely on solving either one or two transport equations along with the Reynolds-Averaged Navier–Stokes (RANS) equations. The solution of the boundary-value problem of any system of partial differential equations requires the complete delineation of the equations and the boundary conditions, including any special restrictions and conditions. In the literature, such a description is often incomplete, neglecting important details related to the boundary conditions and possible restrictive conditions, such as how to ensure satisfying prescribed values of the dependent variables of the transport equations in the far field of a finite domain. In this article, we discuss the possible influence of boundary values, as well as near-field and far-field behavior, on the solution of the RANS equations coupled with transport equations for turbulence modeling. In so doing, we defne the concept of a welldefined boundary-value problem. Additionally, a three-dimensional, rather than a simpler one-dimensional analysis is performed to analyze the near-wall and far-field behavior of the turbulence model variables. This allows an assessment of the decay rate of these variables required to realize the boundary conditions in the far field. This paper also addresses the impact of various transformations of two-equation models (e.g., the model of Wilcox) to remove the singular behavior of the dissipation rate (ω) at the surface boundary. Finally, the issue of well-posedness regarding the governing equations is considered. A compelling argument (although not a proof) for ill-posedness is made for both direct and inverse problems.

Navier–Stokes equations↗

Vapor Transport Within the Thermal Diffusion Cloud Chamber

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

Ferguson, Frank T.↗

An implicit, sharp numerical treatment of viscous terms at arbitrarily shaped liquid-gas interfaces in evaporative flows

We report a novel methodology for accurate treatment of viscous terms in evaporation problems. The proposed scheme is an extension of the sharp viscous treatment of Kang et al. (2000) [7] to 3D phase change problems. To ensure accuracy and grid converging solutions, a new implicit approach to computing viscous fluxes across the phase interfaces is proposed, which was previously unavailable in fixed grid numerical schemes. Analytical relations were derived for the jump in velocity gradients across the 2D and 3D phase interfaces, an important constituent of the proposed scheme. The relations show a non-vanishing jump in the tangential gradients across the phase interface that are associated with evaporative flux and interfacial curvature. The proposed methodology demonstrated first order accuracy in canonical test cases. It is general and applicable to arbitrarily oriented interfaces, and can be readily implemented in existing evaporation flow solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Amplified charge and discharge rates in phase change materials for energy storage using spatially-enhanced thermal conductivity

Composites made with high thermal conductivity meshes embedded in phase change materials (PCMs) increase charge/discharge rates of latent heat energy storage systems. Here we study the benefits of spatially-dependent enhancements to thermal conductivity on the charge/discharge rates of PCMs in both one-dimensional Cartesian and one-dimensional cylindrical coordinates. Our nondimensionalized quasi-steady (Stefan number ≲ 0.1) solution indicates that the average charge (discharge) rate in a spatially-enhanced PCM outperforms the uniformly-enhanced case by maximizing the enhancement near the heat source and therein reducing the time averaged thermal resistance to melting (solidifying). Relative to a uniformly-enhanced thermal conductivity, the optimal charge/discharge rate enhancement is a modest 12% in one-dimensional Cartesian coordinates but as high as 140% in one-dimensional cylindrical coordinates. Our analytical solutions are a design guide for graded mesh structures that can be realized by advanced fabrication techniques such as additive manufacturing and applied in applications ranging from telecommunications to buildings, where PCMs are employed to harness rapidly varying energy sources.

25 ENERGY STORAGE↗

Pyroclast cooling and saturation in water

In the submarine setting pyroclast cooling and saturation, by controlling the buoyancy of individual clasts and surrounding fluid, exert fundamental controls on the dispersal and fate of volcanic material. Here, we use laboratory experiments to understand and quantify how hot and air-filled pyroclasts cool and saturate in liquid water. By measuring internal temperature and clast submerged weight in over thirty experiments, we find that pumice cools and saturates in two stages. We observe that the first stage is marked by much higher rates of cooling and saturation than the second stage and that the transition between stages is sharp. We propose conceptual and quantitative models for each stage of pyroclast cooling and saturation. Specifically we argue that the first stage is defined by the presence of internal steam. That is, hot pyroclasts ingest liquid water and generate steam. Once a clast's internal pore space is filled with steam, heat loss to the surroundings causes condensation of internal vapor and clast saturation. Stage 1 ends when all internal steam has condensed. We test this idea with a Stefan Model with advection and conclude that heat loss, rather than permeability, controls the saturation of pyroclasts above the boiling temperature. We find that permeability matters for air-filled clasts with initial temperatures below the boiling point. Stage 2 begins after all internal vapor has condensed and we propose that stage 2 cooling and saturation are controlled by heat conduction and thermal contraction of trapped gas, respectively. From our understanding of the processes that govern the stage 1 to 2 transition, we derive an empirical average pyroclast cooling rate of q = 7.5 ± 0.5 W cm -2 . Finally, we develop quantitative models for cooling-controlled porous clast saturation and for buoyant clast rise to the ocean surface. We find that meter size clasts stay buoyant for more than 10 min - long enough to reach the surface from a depth of 1000 m. Lastly, the models developed here test our understanding of clast-scale processes and demonstrate that - in hot and porous clasts - the details of internal texture do not matter because clast saturation, and thus buoyancy and fate in the water column, are governed by heat transfer.

58 GEOSCIENCES↗

Analytical Modeling of Metal Foam Composite Phase Change Materials (PCM) in Thermal Energy Storage Using Asymptotic Analysis

The use of phase change materials (PCMs) for thermal energy storage can release or absorb a significant amount of latent heat during the freezing or melting process, offering a higher energy storage density. One of the main drawbacks of PCMs is their low thermal conductivity, resulting in poor thermal performance. Recent research has attempted to enhance heat transfer and increase the thermal conductivity of PCMs, including the use of metal foams. However, modeling the metal foam composite PCM using conventional methods is computationally expensive. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder, capable of predicting the freeze-melt cycle of the metal foam composite PCM. Specifically, three temporal regimes and four spatial layers are considered in the asymptotic analysis for each phase change process. The thermal conductivity is calculated by a theoretical three-dimensional tetrakaidecahedron model, while other thermophysical properties are obtained using the method of volume averaging. The results are verified with numerical data and validated against experimental data in the literature. The presented analytical modeling framework could have the potential to be applied to other types of composite PCMs with considerably lower computational costs compared with conventional methods.

analytical model↗

A level-set immersed boundary method for reactive transport in complex topologies with moving interfaces

A simulation framework based on the level-set and the immersed boundary methods (LS-IBM) has been developed for reactive transport problems in porous media involving a moving solid-fluid interface. The interface movement due to surface reactions is tracked by the level-set method, while the immersed boundary method captures the momentum and mass transport at the interface. The proposed method is capable of accurately modeling transport near evolving boundaries in Cartesian grids. The framework formulation guarantees second order accuracy in space. Since the interface velocity is only defined at the moving boundary, an interface velocity propagation method is also proposed. The method can be applied to other moving interface problems of the “Stefan” type. Here, we validate the proposed LS-IBM both for flow and transport close to an immersed object with reactive boundaries as well as for crystal growth. Lastly, the proposed method provides a powerful tool to model more realistic problems involving moving reactive interfaces in complex domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Gravity and conduction driven melting in a sphere

In the Stefan and Neumann problems fundamentally characterizing melting, unmolten portions of a solid undergoing phase changes within spherical containers are assumed to remain stationary. An approach to these issues that is related to the theories of lubrication and film condensation is presently employed in conjunction with an approximate, closed-form solution of melting within spheres. It is shown that a group of dimensionless parameters containing Prandtl, Archimides and Stefan numbers can describe the melting process. Also given are the results of fundamental heat transfer experiments performed on the melting of a phase-change medium in a spherical shell.

Bahrami, P. A.↗

Density matrix renormalization group with efficient dynamical electron correlation through range separation

We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhancements to the TOUGH2 Simulator as Implemented in iTOUGH2

iTOUGH2 is a program for parameter estimation, sensitivity analysis, and uncertainty propagation analysis. It is based on the TOUGH2 simulator for non-isothermal multiphase, multicomponent flow and transport in fractured and porous media [Pruess, 1987, 1991, 2005, 2011; Falta et al., 1995; Pruess et al., 1999, 2002, 2012; Doughty, 2013]. The core of iTOUGH2 contains slightly modified versions of TOUGH2 modules. Most code modifications are editorial and do not affect the simulation results. As a result, standard TOUGH2 input files can be used in iTOUGH2, and identical results are obtained if iTOUGH2 is run in forward mode. However, a number of modifications have been made as described in this report. They enhance the functionality, flexibilitu, and eas-of-use of the forward simulator. This report complements the reports iTOUGH2 User's Guide, iTOUGH2 Command Referecne, and the collection of tutorial examples in iTOUGH2 Sample Problems.

54 ENVIRONMENTAL SCIENCES↗

The p-version of the finite element method in incremental elasto-plastic analysis

Whereas the higher-order versions of the finite elements method (the p- and hp-version) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. Aspects of incremental elasto-plastic finite element analysis which are particularly amenable to improvements by the p-version is discussed. These theoretical considerations are supported by several numerical experiments. First, an example for which an analytical solution is available is studied. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared to the traditional h-version but also in respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-worked lug - is presented which demonstrates how the modeling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.

Holzer, Stefan M.↗

Derivative-free robust optimization by outer approximations

We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We demonstrate the practical benefits of the algorithm on a new class of test problems.

59 BASIC BIOLOGICAL SCIENCES↗

Schwarz Methods: To Symmetrize or not to Symmetrize

A preconditioning theory for Schwarz methods is presented. The theory establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and multigrid. This paper illustrates why symmetrizing may be a bad idea for linear methods. Numerical examples are presented for a test problem.

Holst, Michael↗