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NASA NTRS1984

Finite difference solutions of heat conduction problems in multi-layered bodies with complex geometries

A numerical procedure is presented for analyzing a wide variety of heat conduction problems in multilayered bodies having complex geometry. The method is based on a finite difference solution of the heat conduction equation using a body fitted coordinate system transformation. Solution techniques are described for steady and transient problems with and without internal energy generation. Results are found to compare favorably with several well known solutions.

Masiulaniec, K. C.↗

NASA NTRS1986

SSME thrust chamber modeling with Navier Stokes equations

The capability of predicting two-dimensional, compressible and reacting flow in the combustion chamber and nozzle of the Space Shuttle Main Engine (SSME) is demonstrated. A nonorthogonal body fitted coordinate system has been used to represent the combustor and nozzle geometry. The Navier-Stokes equations are solved for the entire thrust chamber with the k-epsilon turbulence model accounting for compressibility and large pressure gradients effects. Results of the computational test cases reveal all expected features of the transonic nozzle flows including location of sonic line, internal shock and boundary layer build-up. Calculated performance parameters such as thrust, flow rate, and specific impulse are also in reasonble agreement with available data. The results show promising potential of solving full Navier-Stokes equations with heat transfer and two-phase combustion in truly comprehensive modeling of rocket engines.

Przekwas, A. J.↗

NASA NTRS1986

Lower mass limit of an evolving interstellar cloud and chemistry in an evolving oscillatory cloud

Simultaneous solution of the equation of motion, equation of state and energy equation including heating and cooling processes for interstellar medium gives for a collapsing cloud a lower mass limit which is significantly smaller than the Jeans mass for the same initial density. The clouds with higher mass than this limiting mass collapse whereas clouds with smaller than critical mass pass through a maximum central density giving apparently similar clouds (i.e., same Av, size and central density) at two different phases of its evolution (i.e., with different life time). Preliminary results of chemistry in such an evolving oscillatory cloud show significant difference in abundances of some of the molecules in two physically similar clouds with different life times. The problems of depletion and short life time of evolving clouds appear to be less severe in such an oscillatory cloud.

Tarafdar, S. P.↗

NASA NTRS1987

A two-fluid model for solar wind fluid with higher order moments

A spherically symmetric two-fluid model for the solar wind with higher-order moments is presented. In this model, continuity, momentum, temperature and heat flux equations for two components (electrons and protrons) in steady solar wind states are simultaneously solved by using a time-dependent method. This work is used to compare solutions of the steady-state solar wind with and without higher order moments, and to study the effects of thermal conduction. The coupling between electrons and protrons is also given special attention. The numerical solutions of the steady-state solar wind in both subsonic and supersonic regions between the Sun and 1 AU are obtained and graphically illustrated.

Wang, Jingfang↗

NASA NTRS1988

A numerical simulation of the full two-dimensional electrothermal de-icer pad

The ability to predict the time-temperature history of electrothermal de-icer pads is important in the subsequent design of improved and more efficient versions. These de-icer pads are installed near the surface of aircraft components, for the specific purpose of removing accreted ice. The proposed numerical model can incorporate the full 2-D geometry through a section of a region (i.e., section of an airfoil), that current 1-D numerical codes are unable to do. Thus, the effects of irregular layers, curvature, etc., can now be accounted for in the thermal transients. Each layer in the actual geometry is mapped via a body-fitted coordinate transformation into uniform, rectangular computational grids. The relevant heat transfer equations are transformed and discretized. To model the phase change that might occur in any accreted ice, in an enthalpy formulation the phase change equations are likewise transformed and discretized. The code developed was tested against numerous classical numerical solutions, as well as against experimental de-icing data on a UH1H rotor blade obtained from the NASA Lewis Research Center. The excellent comparisons obtained show that this code can be a useful tool in predicting the performance of current de-icer models, as well as in the designing of future models.

Masiulaniec, Konstanty C.↗

NASA NTRS1987

A low-Reynolds-number two-equation turbulence model for predicting heat transfer on turbine blades

A modified form of the Lam-Bremhorst low-Reynolds number kappa-epsilon turbulence model was developed for predicting transitional boundary layer flows under conditions characteristic of gas turbine blades. The application of the model to flows with pressure gradients is described. Tests against a number of turbine blade cascade data sets are included. Some additional refinements of the model that were made in recent months are explained.

Patankar, Suhas V.↗

NASA NTRS1988

Meteorological Sensor Calibration Facility

The meteorological sensor calibration facility is designed to test and assess radiosonde measurement quality through actual flights in the atmosphere. United States radiosonde temperature measurements are deficient in that they require correction for errors introduced by long- and short-wave radiation. The effect of not applying corrections results in a large bias between day time and night time measurements. This day/night bias has serious implications for users of radiosonde data, of which NASA is one. The derivation of corrections for the U.S. radiosonde is quite important. Determination of corrections depends on solving the heat transfer equation of the thermistor using laboratory measurements of the emissivity and absorptivity of the thermistor coating. The U.S. radiosonde observations from the World Meteorological Organization International Radiosonde Intercomparison were used as the data base to test whether the day/night height bias can be removed. Twenty-five noon time and 26 night time observations were used. Corrected temperatures were used to calculate new geopotentials. Day/night bias in the geopotentials decreased significantly when corrections were introduced. Some testing of thermal lag attendant with the standard carbon hygristor took place. Two radiosondes with small bead thermistors imbedded in the hygristor were flown. Detailed analysis was not accomplished; however, cursory examination of the data showed that the hygristor is at a higher temperature than the external thermistor indicates.

Schmidlin, F. J.↗

NASA NTRS1989

Development of free-piston Stirling engine performance and optimization codes based on Martini simulation technique

A FORTRAN computer code is described that could be used to design and optimize a free-displacer, free-piston Stirling engine similar to the RE-1000 engine made by Sunpower. The code contains options for specifying displacer and power piston motion or for allowing these motions to be calculated by a force balance. The engine load may be a dashpot, inertial compressor, hydraulic pump or linear alternator. Cycle analysis may be done by isothermal analysis or adiabatic analysis. Adiabatic analysis may be done using the Martini moving gas node analysis or the Rios second-order Runge-Kutta analysis. Flow loss and heat loss equations are included. Graphical display of engine motions and pressures and temperatures are included. Programming for optimizing up to 15 independent dimensions is included. Sample performance results are shown for both specified and unconstrained piston motions; these results are shown as generated by each of the two Martini analyses. Two sample optimization searches are shown using specified piston motion isothermal analysis. One is for three adjustable input and one is for four. Also, two optimization searches for calculated piston motion are presented for three and for four adjustable inputs. The effect of leakage is evaluated. Suggestions for further work are given.

Martini, William R.↗

NASA NTRS1988

Gas-jet and tangent-slot film cooling tests of a 12.5 deg cone at Mach number of 6.7

Tests were conducted in the Langley 8-Foot High Temperature Tunnel to determine the aerothermal effects of gaseous nitrogen-coolant ejection on a 3-ft base-diameter, 12.5 degree half-angle cone. Free-stream Mach number, total temperature, and unit Reynolds number per foot were 6.7, 3300 deg R, and 1.4 million, respectively. Two coolant ejection noses were tested, an ogive frustum with a forward-facing 0.8-in radius gas-jet tip, and a 3-in radius hemisphere with a 0.243-in high rearward-facing tangent slot. Data include surface pressures and heating rates, shock shapes, and shock-layer profiles; results are compared with no-cooling data obtained with 1-in and 3-in radius solid noses. Surface pressures were reduced with gas-jet ejection but were affected little by tangent-slot ejection. For both gas-jet and tangent-slot ejection, high coolant flow rates reduced heating even far downstream from the region of ejection; however, low coolant rates caused transition to turbulence and increased heating. Shock-layer profiles of pitot pressure, Mach number, and total temperature were reduced for both gas-jet and tangent-slot ejection. Insight into the gas-jet heat-flux mechanisms was obtained by using shock-layer rake data and established, no-cooling, heat-transfer equations.

Nowak, Robert J.↗

NASA NTRS1989

Analysis of the low gravity tolerance of Bridgman-Stockbarger crystal growth. I - Steady and impulse accelerations

The effects of steady and impulse-type residual accelerations on dopant distributions during directional solidification in 2D and 3D 'generic' models of the Bridgman-Stockbarger technique are investigated using numerical methods. The calculations are based on the thermophysical properties of molten germanium doped with a low concentration of gallium. A Chebyshev collocation pseudospectral method is used for the solution of the governing momentum-, mass-, species-, and heat-transfer equations. Only convection caused by temperature gradients is considered. It is found that lateral nonuniformity in composition is very sensitive to the orientation of the steady component of the residual gravity vector and to the particular operating conditions under consideration. It is also found that laterally or radially averaged composition profiles are alone insufficient to describe the extent of residual convection in a spacecraft environment. The effects of impulse-type disturbances can be severe and can extend for times on the order of 1000 sec after the termination of the impulse.

Alexander, J. Iwan D.↗

NASA NTRS1990

Effect of a crystal-melt interface on Taylor-vortex flow

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal-melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two-phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two-phase system is given by the classical results for a rigid-walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow-gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two-phase system becomes less stable as the finite gap tends to the narrow-gap limit. The two-phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n = 1; the stability of these n = 1 modes is sensitive to the latent heat of fusion.

Mcfadden, G. B.↗

NASA NTRS1990

Radiobrightness of diurnally heated, freezing soil

Freezing and thawing soils exhibit unique radiometric characteristics. To examine these characteristics, diurnal insolation is modeled as one-dimensional heating of a moist soil half-space during a typical fall at a northern Great Plains site. The one-dimensional heat flow equation is nonlinear because both the enthalpy (the change in internal energy with temperature at constant pressure) and the thermal conductivity of freezing soils are nonlinear functions of temperature. The problem is particularly difficult because phase boundaries propagate in time, and because soils, particularly clay-rich soils, freeze over a range of temperatures rather than at 0 C. Diurnal radiobrightness curves at 10.7, 18.0, and 37.0-GHz were computed for each month. The 37.0-GHz radiobrightness best tracks soil surface temperature; the 10.7-37.0-GHz spectral gradient of thawed soils is strongly positive; the spectral gradient of frozen soils is slightly negative; and the midnight-to-noon spectral gradient is shifted by approximately +0.1 K/GHz by diurnal changes in the surface temperature and the thermal gradient. These observations support the use of the scanning multichannel microwave radiometer 37.0-GHz radiobrightness and its 10.7-37.0-GHz spectral gradient as discriminants in a frozen soil classifier for high-latitude prairie.

England, Anthony W.↗

NASA NTRS1992

Modeling the seasonal cycle of CO2 on Mars: A fit to the Viking lander pressure curves

We have constructed a more accurate Mars thermal model, similar to the one used by Leighton and Murray in 1966, which solves radiative, conductive, and latent heat balance at the surface as well as the one-dimensional heat conduction equation for 40 layers to a depth of 15 meters every 1/36 of a Martian day. The planet is divided into 42 latitude bands with a resolution of two degrees near the poles and five degrees at lower latitudes, with elevations relative to the 6.1 mbar reference areoid. This estimate of the Martian zonally averaged topography was derived primarily from radio occultations. We show that a realistic one-dimensional thermal model is able to reproduce the VL1 pressure curve reasonably well without having to invoke complicated atmospheric effects such as dust storms and polar hoods. Although these factors may cause our deduced values for each model parameter to differ from its true value, we believe that this simple model can be used as a platform to study many aspects of the Martian CO2 cycle over seasonal, interannual, and long-term climate timescales.

Wood, S. E.↗

NASA NTRS1992

Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)

Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.

Fan, Mark S.↗

NASA NTRS1992

A comparison of superconductor and manganin technology for electronic links used in space mission applications

The electronic link connecting cryogenically cooled radiation detectors to data acquisition and signal processing electronics at higher temperatures contributes significantly to the total heat load on spacecraft cooling systems that use combined mechanical and cryogenic liquid cooling. Using high transition temperature superconductors for this link has been proposed to increase the lifetime of space missions. Herein, several YBCO (YBa2Cu3O7) superconductor-substrate combinations were examined and total heat loads were compared to manganin wire technology in current use. Using numerical solutions to the heat-flow equations, it is shown that replacing manganin technology with YBCO thick film technology can extend a 7-year mission by up to 1 year.

Caton, R.↗

NASA NTRS1992

Forced precession of the cometary nucleus with randomly placed active regions

The cometary nucleus is assumed to be triaxial or axisymmetric spheroid rotating about its axis of maximum moment of inertia and is forced to precess due to jets of ejected material. Randomly placed regions of exposed ice on the surface of the nucleus are assumed to produce gas and dust. The solution of the heat conduction equation for each active region is used to find the gas sublimation rate and the jet acceleration. Precession of the comet nucleus is followed numerically using a phase-averaged system of equations. The gas production curves and the variation of the spin axis during the orbital motion of the comet are presented.

Szutowicz, Slawomira↗

NASA NTRS1993

Recent refinements and increased capabilities in balloon vertical performance analysis

The NASA Thermal Trajectory analysis model for predicting the vertical performance of balloons is described in terms of two critical refinements and recent results. The model employs heat-balance equations and a vertical equation of motion, and revised methods are employed to predict maximum balloon volume, balloon shape, and the continuous computation of gas loss. Also incorporated are modeling techniques for assessing the solar radiation input that can affect the load tapes, and autoballast control algorithms are employed. The model permits the evaluation of the presence of cap layers as well as the effects of small leaks and programmed venting. The revised model is shown to give good predictions of balloon performance during flight in terms of altitude changes, descent rates, gas-mass flow, and leak potential. The model is found to be more versatile due to autoballasting and leak analysis, and good prediction are possible for the float phase and descent of current balloon shapes.

Conrad, G. R.↗

NASA NTRS1992

The stability functions in the bulk similarity formulation for the unstable boundary layer

An update is presented for the function C in the heat transfer equation and for the function Bw in the momentum transfer equation of the bulk similarity approach for the atmospheric boundary layer (ABL). Motives for this update are recent developments in the formulation of Monin-Obukhov functions for the surface layer, and the availability of the new data set of FIFE-89, the 1989 phase of the First ISLSCP Field Experiment, which took place over the same hilly prairie terrain in northeastern Kansas as the 1987 phase, i.e., FIFE-87. Functional forms developed in earlier studies are considered. In addition, a new form is derived based on a simple dual structure of the ABL. The functions are calibrated with the data set obtained during FIFE-87; the results are then verified with the independent data set acquired during FIFE-89.

Sugita, Michiaki↗