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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Eight-moment approximation solar wind models

Heat conduction from the corona is important in the solar wind energy budget. Until now all hydrodynamic solar wind models have been using the collisionally dominated gas approximation for the heat conductive flux. Observations of the solar wind show particle distribution functions which deviate significantly from a Maxwellian, and it is clear that the solar wind plasma is far from collisionally dominated. We have developed a numerical model for the solar wind which solves the full equation for the heat conductive flux together with the conservation equations for mass, momentum, and energy. The equations are obtained by taking moments of the Boltzmann equation, using an 8-moment approximation for the distribution function. For low-density solar winds the 8-moment approximation models give results which differ significantly from the results obtained in models assuming the gas to be collisionally dominated. The two models give more or less the same results in high density solar winds.

Olsen, Espen Lyngdal↗
NASA NTRS2003

Modified Laser Flash Method for Thermal Properties Measurements and the Influence of Heat Convection

The study examined the effect of natural convection in applying the modified laser flash method to measure thermal properties of semiconductor melts. Common laser flash method uses a laser pulse to heat one side of a thin circular sample and measures the temperature response of the other side. Thermal diffusivity can be calculations based on a heat conduction analysis. For semiconductor melt, the sample is contained in a specially designed quartz cell with optical windows on both sides. When laser heats the vertical melt surface, the resulting natural convection can introduce errors in calculation based on heat conduction model alone. The effect of natural convection was studied by CFD simulations with experimental verification by temperature measurement. The CFD results indicated that natural convection would decrease the time needed for the rear side to reach its peak temperature, and also decrease the peak temperature slightly in our experimental configuration. Using the experimental data, the calculation using only heat conduction model resulted in a thermal diffusivity value is about 7.7% lower than that from the model with natural convection. Specific heat capacity was about the same, and the difference is within 1.6%, regardless of heat transfer models.

Lin, Bochuan↗
NASA NTRS1991

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Tamma, Kumar K.↗
NASA NTRS2010

Investigation of a Gallium MPD Thruster with an Ablating Cathode

Arc impedance, exhaust velocity, and plasma probe measurements are presented. The thruster is driven by a 50 microsecond pulse from a 6.2 milliohm pulse forming network, and gallium is supplied to the discharge by evaporation of the cathode. The arc voltage is found to vary linearly with the discharge current with an arc impedance of 6.5 milliohms. Electrostatic probes yield an exhaust velocity that is invariant with the discharge current and has a peak value of 20 kilometers per second, which is in reasonable agreement with the value (16 plus or minus 1 kilometer per second) calculated from the mass bit and discharge current data. Triple probe measurements yield on axis electron temperatures in the range of 0.8-3.8 eV, electron densities in the range of 1.6 x 10(exp 21) to 2.1 x 10(exp 22) per cubic meter, and a divergence half angle of 16 degrees. Measurements within the interelectrode region yield a peak magnetic field of 0.8 T, and the observed radial trends are consistent with an azimuthally symmetric current distribution. A cathode power balance model is coupled with an ablative heat conduction model predicting mass bit values that are within 20% of the experimental values.

Thomas, Robert E.↗
NASA NTRS1980

Finite-element analysis of nonlinear conduction problems subject to moving fields

Through the use of a space-time warp, specialized moving finite elements are developed that can be employed to generate a nonlinear heat conduction model for situations involving traveling boundary and heat generation fields superposed on an initial state. To facilitate the solution of the resulting nonlinear finite-element formulation, a multilevel heuristic iterative solution strategy is developed. In order to demonstrate the versatility and accuracy of the moving elements and their associated nonlinear solution strategy, the results of several numerical experiments are presented.

Padovan, J.↗
NASA NTRS1996

An Investigation of the Compatibility of Radiation and Convection Heat Flux Measurements

A method for determining time-resolved absorbed surface heat flux and surface temperature in radiation and convection environments is described. The method is useful for verification of aerodynamic, heat transfer and durability models. A practical heat flux gage fabrication procedure and a simple one-dimensional inverse heat conduction model and calculation procedure are incorporated in this method. The model provides an estimate of the temperature and heat flux gradient in the direction of heat transfer through the gage. This paper discusses several successful time-resolved tests of this method in hostile convective heating and cooling environments.

Liebert, Curt H.↗
NASA NTRS2010

Adaptive Numerical Algorithms in Space Weather Modeling

Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics based space weather modeling and even forecasting.

Toth, Gabor↗
NASA NTRS1989

Variable thermal properties and thermal relaxation time in hyperbolic heat conduction

Numerical solutions were obtained for a finite slab with an applied surface heat flux at one boundary using both the hyperbolic (MacCormack's method) and parabolic (Crank-Nicolson method) heat conduction equations. The effects on the temperature distributions of varying density, specific heat, and thermal relaxation time were calculated. Each of these properties had an effect on the thermal front velocity (in the hyperbolic solution) as well as the temperatures in the medium. In the hyperbolic solutions, as the density or specific heat decreased with temperature, both the temperatures within the medium and the thermal front velocity increased. The value taken for the thermal relaxation time was found to determine the 'hyperbolicity' of the heat conduction model. The use of a time dependent relaxation time allowed for solutions where the thermal energy propagated as a high temperature wave initially, but approached a diffusion process more rapidly than was possible with a constant large relaxation time.

Glass, David E.↗
NASA NTRS1991

Parallelized solvers for heat conduction formulations

Based on multilevel partitioning, this paper develops a structural parallelizable solution methodology that enables a significant reduction in computational effort and memory requirements for very large scale linear and nonlinear steady and transient thermal (heat conduction) models. Due to the generality of the formulation of the scheme, both finite element and finite difference simulations can be treated. Diverse model topologies can thus be handled, including both simply and multiply connected (branched/perforated) geometries. To verify the methodology, analytical and numerical benchmark trends are verified in both sequential and parallel computer environments.

Padovan, Joe↗
NASA NTRS1992

Miniature high temperature plug-type heat flux gauges

The objective is to describe continuing efforts to develop methods for measuring surface heat flux, gauge active surface temperature, and heat transfer coefficient quantities. The methodology involves inventing a procedure for fabricating improved plug-type heat flux gauges and also for formulating inverse heat conduction models and calculation procedures. These models and procedures are required for making indirect measurements of these quantities from direct temperature measurements at gauge interior locations. Measurements of these quantities were made in a turbine blade thermal cycling tester (TBT) located at MSFC. The TBT partially simulates the turbopump turbine environment in the Space Shuttle Main Engine. After the TBT test, experiments were performed in an arc lamp to analyze gauge quality.

Liebert, Curt H.↗
NASA NTRS1992

Miniature high temperature plug-type heat flux gauges

The objective is to describe continuing efforts to develop methods for measuring surface heat flux, gauge active surface temperature, and heat transfer coefficient quantities. The methodology involves inventing a procedure for fabricating improved plug-type heat flux gauges and also for formulating inverse heat conduction models and calculation procedures. These models and procedures are required for making indirect measurements of these quantities from direct temperature measurements at gauge interior locations. Measurements of these quantities were made in a turbine blade thermal cycling tester (TBT) located at MSFC. The TBT partially simulates the turbopump turbine environment in the Space Shuttle Main Engine. After the TBT test, experiments were performed in an arc lamp to analyze gauge quality.

Liebert, Curt H.↗
NASA NTRS1999

Microwave Radiometric Signatures of Different Surface Types in Deserts

In arid environments, specific microwave signatures have been observed with the Special Sensor Microwave/Imager (SSM/I). For a given diurnal change in surface skin temperature, the corresponding change in the microwave brightness temperature is smaller than expected. With the help of a 1D, time-dependent heat conduction model, this behavior is explained by microwave radiation coming from different depths in the soil, depending on the soil type and on the microwave radiation frequency. Using the eight-times daily estimates of the surface skin temperature by the International Satellite Cloud Climatology Project (ISCCP) and a simple Fresnel model, collocated month-long time series of the SSM/I brightness temperatures and the surface skin temperatures give a consistent estimate of the effective microwave emissivity and penetration depth parameters. Results are presented and analyzed for the Sahara and the Arabian Peninsula, for July and November 1992. The case of the Australian desert is also briefly mentioned. Assuming a reasonable thermal diffusivity for the soil in desert areas, the microwave radiation is estimated to come from soil layers down to depths of at least five wavelengths in some locations. Regions where the microwave radiation comes from deeper soil layers also have large microwave emissivity polarization differences and large visible reflectances, suggesting that these areas correspond to sand dune fields.

Prigent, Catherine↗
NASA NTRS1984

Stability Test for Transient-Temperature Calculations

Graphical test helps assure numerical stability of calculations of transient temperature or diffusion in composite medium. Rectangular grid forms basis of two-dimensional finite-difference model for heat conduction or other diffusion like phenomena. Model enables calculation of transient heat transfer among up to four different materials that meet at grid point.

Campbell, W.↗
NASA NTRS2009

A Model of Thermal Conductivity for Planetary Soils: 1. Theory for Unconsolidated Soils

We present a model of heat conduction for mono-sized spherical particulate media under stagnant gases based on the kinetic theory of gases, numerical modeling of Fourier s law of heat conduction, theoretical constraints on the gas thermal conductivity at various Knudsen regimes, and laboratory measurements. Incorporating the effect of the temperature allows for the derivation of the pore-filling gas conductivity and bulk thermal conductivity of samples using additional parameters (pressure, gas composition, grain size, and porosity). The radiative and solid-to-solid conductivities are also accounted for. Our thermal model reproduces the well-established bulk thermal conductivity dependency of a sample with the grain size and pressure and also confirms laboratory measurements finding that higher porosities generally lead to lower conductivities. It predicts the existence of the plateau conductivity at high pressure, where the bulk conductivity does not depend on the grain size. The good agreement between the model predictions and published laboratory measurements under a variety of pressures, temperatures, gas compositions, and grain sizes provides additional confidence in our results. On Venus, Earth, and Titan, the pressure and temperature combinations are too high to observe a soil thermal conductivity dependency on the grain size, but each planet has a unique thermal inertia due to their different surface temperatures. On Mars, the temperature and pressure combination is ideal to observe the soil thermal conductivity dependency on the average grain size. Thermal conductivity models that do not take the temperature and the pore-filling gas composition into account may yield significant errors.

Piqueux, S.↗
NASA NTRS2012

Heat Transfer Modeling for Rigid High-Temperature Fibrous Insulation

Combined radiation and conduction heat transfer through a high-temperature, high-porosity, rigid multiple-fiber fibrous insulation was modeled using a thermal model previously used to model heat transfer in flexible single-fiber fibrous insulation. The rigid insulation studied was alumina enhanced thermal barrier (AETB) at densities between 130 and 260 kilograms per cubic meter. The model consists of using the diffusion approximation for radiation heat transfer, a semi-empirical solid conduction model, and a standard gas conduction model. The relevant parameters needed for the heat transfer model were estimated from steady-state thermal measurements in nitrogen gas at various temperatures and environmental pressures. The heat transfer modeling methodology was evaluated by comparison with standard thermal conductivity measurements, and steady-state thermal measurements in helium and carbon dioxide gases. The heat transfer model is applicable over the temperature range of 300 to 1360 K, pressure range of 0.133 to 101.3 x 10(exp 3) Pa, and over the insulation density range of 130 to 260 kilograms per cubic meter in various gaseous environments.

Daryabeigi, Kamran↗
NASA NTRS2007

Iapetus' Geophysics: Rotation Rate, Shape, and Equatorial Ridge

Iapetus has preserved evidence that constrains the modeling of its geophysical history from the time of its accretion until now. The evidence is (a) its present 79.33-day rotation or spin rate, (b) its shape that corresponds to the equilibrium figure for a hydrostatic body rotating with a period of approximately 16 h, and (c) its high, equatorial ridge, which is unique in the Solar System. This paper reports the results of an investigation into the coupling between Iapetus' thermal and orbital evolution for a wide range of conditions including the spatial distributions with time of composition, porosity, short-lived radioactive isotopes (SLRI), and temperature. The thermal model uses conductive heat transfer with temperature-dependent conductivity. Only models with a thick lithosphere and an interior viscosity in the range of about the water ice melting point can explain the observed shape. Short-lived radioactive isotopes provide the heat needed to decrease porosity in Iapetus? early history. This increases thermal conductivity and allows the development of the strong lithosphere that is required to preserve the 16-h rotational shape and the high vertical relief of the topography. Long-lived radioactive isotopes and SLRI raise internal temperatures high enough that significant tidal dissipation can start, and despin Iapetus to synchronous rotation. This occurred several hundred million years after Iapetus formed. The models also constrain the time when Iapetus formed because the successful models are critically dependent upon having just the right amount of heat added by SLRI decay in this early period. The amount of heat available from short-lived radioactivity is not a free parameter but is fixed by the time when Iapetus accreted, by the canonical concentration of Al-26, and, to a lesser extent, by the concentration of Fe-60. The needed amount of heat is available only if Iapetus accreted between 2.5 and 5.0Myr after the formation of the calcium aluminum inclusions as found in meteorites. Models with these features allow us to explain Iapetus? present synchronous rotation, its fossil 16-h shape, and the context within which the equatorial ridge arose.

geophysics↗