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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Specially tailored transfinite-element formulations for hyperbolic heat conduction involving non-Fourier effects

The phenomenon of hyperbolic heat conduction in contrast to the classical (parabolic) form of Fourier heat conduction involves thermal energy transport that propagates only at finite speeds, as opposed to an infinite speed of thermal energy transport. To accommodate the finite speed of thermal wave propagation, a more precise form of heat flux law is involved, thereby modifying the heat flux originally postulated in the classical theory of heat conduction. As a consequence, for hyperbolic heat conduction problems, the thermal energy propagates with very sharp discontinuities at the wave front. Accurate solutions are found for a class of one-dimensional hyperbolic heat conduction problems involving non-Fourier effects that can be used effectively for representative benchmark tests and for validating alternate schemes. Modeling/analysis formulations via specially tailored hybrid computations are provided for accurately modeling the sharp discontinuities of the propagating thermal wave front. Comparative numerical test models are presented for various hyperbolic heat conduction models involving non-Fourier effects to demonstrate the present formulations.

Tamma, Kumar K.↗
NASA NTRS1994

User's manual for the NASA Lewis ice accretion/heat transfer prediction code with electrothermal deicer input

A version of LEWICE has been developed that incorporates a recently developed electrothermal deicer code, developed at the University of Toledo by William B. Wright. This was accomplished, in essence, by replacing a subroutine in LEWICE, called EBAL, which balanced the energies at the ice surface, with a subroutine called UTICE. UTICE performs this same energy balance, as well as handles all the time-timperature transients below the ice surface, for all of the layers of a composite blade as well as the ice layer itself. This new addition is set up in such a fashion that a user may specify any number of heaters, any heater chordwise length, and any heater gap desired. The heaters may be fired in unison, or they may be cycled with periods independent of each other. The heater intensity may also be varied. In addition, the user may specify any number of layers and thicknesses depthwise into the blade. Thus, the new addition has maximum flexibility in modeling virtually any electrothermal deicer installed into any airfoil. It should be noted that the model simulates both shedding and runback. With the runback capability, it can simulate the anti-icing mode of heater performance, as well as detect icing downstream of the heaters due to runback in unprotected portions of the airfoil. This version of LEWICE can be run in three modes. In mode 1, no conduction heat transfer is modeled (which would be equivalent to the original version of LEWICE). In mode 2, all heat transfer is considered due to conduction but no heaters are firing. In mode 3, conduction heat transfer where the heaters are engaged is modeled, with subsequent ice shedding. When run in the first mode, there is virtually identical agreement with the original version of LEWICE in the prediction of accreted ice shapes. The code may be run in the second mode to determine the effects of conduction on the ice accretion process.

Masiulaniec, Konstanty C.↗
NASA NTRS1989

Analysis of coordinated observations of a giant stellar flare

Multi-wavelength observations of a giant flare on the star AD Leo were obtained with the 2.1 m and 0.9 m telescopes at McDonald Observatory and the International Ultraviolet Explorer satellite. The quality, spectral coverage, and time resolution of the data represented a major improvement over any published stellar flare data. Two theoretical, quantitative flare models were developed. Combining the models, the chromospheric emission model predictions in the hydrogen Balmer lines, Da II K, Mg II h + k and the optical continuum were compared to the observations, with the result that much of the gradual phase flare emission could be produced by the x ray and conductive heated atmospheres. The models lend insight into the impulsive phase flare emission, but do not reproduce it. Soft x ray and conductive heating of the chromosphere is a natural consequence of the coronal temperatures that have been observed during the gradual phase of flares on the sun and on M dwarf stars. The improved flare observations and quantitative flare models presented here show that these heating mechanisms can produce atmospheres whose emission matches many of the observed stellar flare features.

Lambert, David L.↗
NASA NTRS1992

Computer Program For Variable-Conductance Heat Pipes

VCHPDA provides accurate mathematical models of transient as well as steady-state performance of variable-conductance heat pipes over wide range of operating conditions. Applies to heat pipes with either cold, wicked or hot, nonwicked gas reservoirs and uses ideal-gas law and "flat-front" (negligible vapor diffusion) gas theory. Calculates length of gas-blocked region and temperature of vapor in active portion of heat pipe by solving set of nonlinear equations for conservation of energy and mass. Written in FORTRAN 77.

Antoniuk, D.↗
NASA NTRS1976

Oscillations and stability of numerical solutions of the heat conduction equation

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Kozdoba, L. A.↗
NASA NTRS2006

Beam Heating of Samples: Modeling and Verification

Energy absorbed from the X-ray beam by the sample requires cooling by forced convection (i.e. cryostream) to minimize temperature increase and the damage caused to the sample by the X-ray heating. In this presentation we will first review the current theoretical models and recent studies in the literature, which predict the sample temperature rise for a given set of beam parameters. It should be noted that a common weakness of these previous studies is that none of them provide actual experimental confirmation. This situation is now remedied in our investigation where the problem of x-ray sample heating is taken up once more. We have theoretically investigated, and at the same time, in addition to the numerical computations, performed experiments to validate the predictions. We have modeled, analyzed and experimentally tested the temperature rise of a 1 mm diameter glass sphere (sample surrogate) exposed to an intense synchrotron X-ray beam, while it is being cooled in a uniform flow of nitrogen gas. The heat transfer, including external convection and internal heat conduction was theoretically modeled using CFD to predict the temperature variation in the sphere during cooling and while it was subjected to an undulator (ID sector 19) X-ray beam at the APS. The surface temperature of the sphere during the X-ray beam heating was measured using the infrared camera measurement technique described in a previous talk. The temperatures from the numerical predictions and experimental measurements are compared and discussed. Additional results are reported for the two different sphere sizes and for two different supporting pin orientations.

Kazmierczak, Michael↗
NASA NTRS2002

A Modified Wall Matching Treatment to Account for Local Solid to Fluid Thermal Coupling

The wall-matching methodology of Wilcox is modified to include a solid-wall, thermal-conduction model. This coupled fluid-thermal-structure model is derived assuming that the wall thermal-structure behavior is locally one-dimensional and that structural deformations, due to thermally induced stresses, are not significant. The one-dimensional coupled fluid-thermal-structure model is derived such that the wall temperature is removed as an independent boundary condition variable. The one-dimensional coupled fluid-thermal-structure model is also derived for the general case of an arbitrary mixture of thermally prefect gases and a wall of arbitrary thickness and conductivity by using a compressible, streamwise-pressure-gradient-corrected, wall-matching function and Fourier's law of heat conduction. The resulting model was implemented in the VULCAN CFD code as a new boundary condition type. VULCAN was then used to simulate a two-dimensional Mach 6 wind tunnel facility nozzle flow to demonstrate/validate the one-dimensional coupled fluid-thermal-structure model. The nozzle internal-wall surface temperature and heat transfer distributions computed using the one-dimensional coupled fluid-thermal-structure model are compared to wall temperature and heat transfer distributions from an iterative multi-dimensional analysis obtained by coupling the VULCAN CFD code and the MSC/NASTRAN-thermal code. The one-dimensional coupled fluid-thermal-structure model analysis is shown to be very robust and in excellent agreement with the multi-dimensional iteratively coupled analysis. It is also shown that the one-dimensional analysis can be used as an initial guess for the multi-dimensional iteratively coupled analysis.

White, Jeffery A.↗
NASA NTRS2002

A Modified Wall Matching Treatment to Account for Local Solid to Fluid Thermal Coupling

The wall-matching methodology of Wilcox is modified to include a solid-wall, thermal-conduction model. This coupled fluid-thermal-structure model is derived assuming that the wall thermal-structure behavior is locally one-dimensional and that structural deformations, due to thermally induced stresses, are not significant. The one-dimensional coupled fluid-thermal-structure model is derived such that the wall temperature is removed as an independent boundary condition variable. The one-dimensional coupled fluid-thermal-structure model is also derived for the general case of an arbitrary mixture of thermally prefect gases and a wall of arbitrary thickness and conductivity by using a compressible, streamwise-pressure-gradient-corrected, wall-matching function and Fourier's law of heat conduction. The resulting model was implemented in the VULCAN CFD code as a new boundary condition type. VULCAN was then used to simulate a two-dimensional Mach 6 wind tunnel facility nozzle flow to demonstrate/validate the one-dimensional coupled fluid-thermal-structure model. The nozzle internal-wall surface temperature and heat transfer distributions computed using the one-dimensional coupled fluid-thermal-structure model are compared to wall temperature and heat transfer distributions from an iterative multi-dimensional analysis obtained by coupling the VULCAN CFD code and the MSC/NASTRAN-thermal code. The one-dimensional coupled fluid-thermal-structure model analysis is shown to be very robust and in excellent agreement with the multi-dimensional iteratively coupled analysis. It is also shown that the one-dimensional analysis can be used as an initial guess for the multi-dimensional iteratively coupled analysis.

White, Jeffery A.↗
NASA NTRS2002

Optimal Design of Functionally Graded Metallic Foam Insulations

The focus of our work has been on developing an insight into the physics that govern the optimum design of thermal insulation for use in thermal protection systems of launch vehicle. Of particular interest was to obtain optimality criteria for designing foam insulations that have density (or porosity) distributions through the thickness for optimum thermal performance. We investigate the optimum design of functionally graded thermal insulation for steady state heat transfer through the foam. We showed that the heat transfer in the foam has competing modes, of radiation and conduction. The problem assumed a fixed inside temperature of 400 K and varied the aerodynamic surface heating on the outside surface from 0.2 to 1.0 MW/sq m. The thermal insulation develops a high temperature gradient through the thickness. Investigation of the model developed for heat conduction in foams showed that at high temperatures (as on outside wall) intracellular radiation dominates the heat transfer in the foam. Minimizing radiation requires reducing the pore size, which increases the density of the foam. At low temperatures (as on the inside wall), intracellular conduction (of the metal and air) dominates the heat transfer. Minimizing conduction requires increasing the pore size. This indicated that for every temperature there was an optimum value of density that minimized the heat transfer coefficient. Two optimization studies were performed. One was to minimize the heat transmitted though a fixed thickness insulation by varying density profiles. The second was to obtain the minimum mass insulation for specified thickness. Analytical optimality criteria were derived for the cases considered. The optimality condition for minimum heat transfer required that at each temperature we find the density that minimizes the heat transfer coefficient. Once a relationship between the optimum heat transfer coefficient and the temperature was found, the design problem reduced to the solution of a simple nonlinear differential equation. Preliminary results of this work were presented at the American Society of Composites meeting, and the final version was submitted for publication in the AIAA Journal. In addition to minimizing the transmitted heat, we investigated the optimum design for minimum weight given an acceptable level of heat transmission through the insulation. The optimality criterion developed was different from that obtained for minimizing beat transfer coefficient. For minimum mass design, we had to find for a given temperature the optimum density, which minimized the logarithmic derivative of the insulation thermal conductivity with respect to its density. The logarithmic derivative is defined as the ratio of relative change in the dependent response (thermal conductivity) to the relative change in the independent variable (density). The results have been documented as a conference paper that will be presented at the upcoming AIAA.

Haftka, Raphael T.↗
NASA NTRS2000

Effect of Elevated Pressure on the Heat Transfer and Power Requirements During Bridgman Growth of PMN-PT Crystals

Performance of the furnace during Bridgman growth of the lead magnesium niobate-lead titanate crystal (PMN-PT) is analyzed. PMN-PT is electrostrictive ceramic that has near ideal strain-voltage function. Furthermore piezoelectric (2000 to 2300 pC/N) and coupling (92 to 95%) constants are exceptionally good. Due to these properties PMN-PT has wide range of applications - from sonars to transducers in a high precision optical systems. In this research first attempt to crystallize PMN-PT in a Mellen type vertical Bridgman furnace was not successful, as melting temperature of precursor materials was not achieved. At this point choice was between building a new more powerful facility or finding ways to enhance performance of the existing furnace. Besides adjusting power supply to the individual heating elements, redesigning ampoule holding cartridge and improving furnace insulation one more radical improvement was proposed. The entire furnace was placed into the high pressure chamber. Further experiments confirmed that temperature inside the furnace was increased sufficiently to melt precursor materials to obtain PMN-PT. Numerical modeling is undertaken to find limitations of this technique and to predict temperature distribution inside the ampoule. It is of interest also to account for main factors contributing to a higher temperatures achieved in the furnace under the higher pressure (up to 10 atm.). Numerical model of the furnace is based on general purpose finite - element code FIDAP and on previous efforts to model Bridgman type furnace with multiply heaters. In order to account for all heat transfer mechanism involved - conduction, convection and radiation - different parts of the furnace are modeled in accordance with expected dominant mode of heat transfer - conduction in the solid parts, conduction and radiation in the ampoule, gas convection and conduction in the furnace openings complemented with wall-to-wall radiation. Because of these complicating factors, dimensional rather than non-dimensional modeling is performed using steady-state 2-D and 3-D models. Particular attention is paid to the modeling of radiation in a semitransparent material of ampoule 7 sapphire. The radiation model is validated by solving realistic test problem - conduction and radiation heat transfer in the fused quartz. Results are in agreement with both experimental and analytical data.

Bune, Andris↗
NASA NTRS1991

Energy Models for One-Carrier Transport in Semiconductor Devices

Moment models of carrier transport, derived from the Boltzmann equation, made possible the simulation of certain key effects through such realistic assumptions as energy dependent mobility functions. This type of global dependence permits the observation of velocity overshoot in the vicinity of device junctions, not discerned via classical drift-diffusion models, which are primarily local in nature. It was found that a critical role is played in the hydrodynamic model by the heat conduction term. When ignored, the overshoot is inappropriately damped. When the standard choice of the Wiedemann-Franz law is made for the conductivity, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime required empirical modification of this law, or nonstandard choices. Simulations of the hydrodynamic model in one and two dimensions, as well as simulations of a newly developed energy model, the RT model, are presented. The RT model, intermediate between the hydrodynamic and drift-diffusion model, was developed to eliminate the parabolic energy band and Maxwellian distribution assumptions, and to reduce the spurious overshoot with physically consistent assumptions. The algorithms employed for both models are the essentially non-oscillatory shock capturing algorithms. Some mathematical results are presented and contrasted with the highly developed state of the drift-diffusion model.

Jerome, Joseph W.↗
NASA NTRS1988

Comparison of vibration dissociation coupling and radiative heat transfer models for AOTV/AFE flowfields

A series of detailed studies comparing various vibration dissociation coupling models, reaction systems and rates, and radiative heating models has been conducted for the nonequilibrium stagnation region of an AFE/AOTV vehicle. Atomic and molecular nonequilibrium radiation correction factors have been developed and applied to various absorption coefficient step models, and a modified vibration dissociation coupling model has been shown to yield good vibration/electronic temperature and concentration profiles. While results indicate sensitivity to the choice of vibration dissociation coupling model and to the nitrogen electron impact ionization rate, by proper combinations accurate flowfield and radiative heating results can be obtained. These results indicate that nonequilibrium effects significantly affect the flowfield and the radiative heat transfer. However, additional work is needed in ionization chemistry and absorption coefficient modeling.

Carlson, Leland A.↗
NASA NTRS1972

The effect of gravity induced free convection upon the melting phenomena of a finite paraffin slab for thermal control

Two theoretical models were developed to predict the thermal response of the phase change material to a given hot plate temperature. A two-dimensional pure conduction model was developed to predict the melting of the phase change material when heat transfer was a function of conduction. A combined conduction-convection model, also two-dimensional, was developed to predict the phase change phenomena when heat transfer was a function of conduction and gravity-induced free convection. Both models were solved using explicit finite difference approximations on a digital computer. The experimental equipment consisted of a rectangular cell utilizing a heat chamber, an expansion chamber, and a test chamber; a sixteen channel multipoint recorder, and a fluid flow system. The recorder monitered hot and cold plate temperatures and interior node temperatures at two second intervals. A comparison of theoretical temperature profiles and experimental temperature profiles is presented for six runs at various angles of inclination of the test cell with respect to the horizontal direction. A detailed discussion of results is presented.

Bain, R. L.↗
NASA NTRS2003

Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

The use of multi-dimensional finite volume numerical techniques with finite thickness models for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the one-dimensional semi -infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody were investigated. An array of streamwise orientated heating striations were generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients due to the striation patterns two-dimensional heat transfer techniques were necessary to obtain accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates because it did not account for lateral heat conduction in the model.

Daryabeigi, Kamran↗
NASA NTRS1974

Transient analysis of a thermal storage unit involving a phase change material

The transient response of a single cell of a typical phase change material type thermal capacitor has been modeled using numerical conductive heat transfer techniques. The cell consists of a base plate, an insulated top, and two vertical walls (fins) forming a two-dimensional cavity filled with a phase change material. Both explicit and implicit numerical formulations are outlined. A mixed explicit-implicit scheme which treats the fin implicity while treating the phase change material explicitly is discussed. A band algorithmic scheme is used to reduce computer storage requirements for the implicit approach while retaining a relatively fine grid. All formulations are presented in dimensionless form thereby enabling application to geometrically similar problems. Typical parametric results are graphically presented for the case of melting with constant heat input to the base of the cell.

Griggs, E. I.↗
NASA NTRS1985

Models of the upper atmosphere

Several computer models of the thermosphere are discussed. J70MM, the Jacchia 1970 model with matrix and matrix mean output, and J703X, the Jacchia 1970, 1971, and 1977 models, are of primary interest. The subroutines in these programs were studied in detail, and several mistakes were found and corrected. It is proposed that a weighted average of the three-hour geomagnetic index be used in the models rather than a single index value. The densities (for a given date and time) generated by the J703X program (all three models), using both a single value of the index and weighted averages for three different lag times, are tabulated and discussed. Most of the equations used in the models are the results of empirical curve fits. An attempt was made to generate a theoretical prediction of the thermospheric temperature profile based on a simple physical model of atmospheric heat conduction in a spherically-symmetric shell. The exponential heating theory and the temperature dependence of k are discussed.

Davis, T. M.↗