Showing papers in "Journal of Thermophysics and Heat Transfer in 1993"

Review of chemical-kinetic problems of future NASA missions, II: Mars entries

Abstract: A number of chemical-kinetic problems related to phenomena occurring behind a shock wave surrounding an object flying in the earth atmosphere are discussed, including the nonequilibrium thermochemical relaxation phenomena occurring behind a shock wave surrounding the flying object, problems related to aerobraking maneuver, the radiation phenomena for shock velocities of up to 12 km/sec, and the determination of rate coefficients for ionization reactions and associated electron-impact ionization reactions. Results of experiments are presented in form of graphs and tables, giving data on the reaction rate coefficients for air, the ionization distances, thermodynamic properties behind a shock wave, radiative heat flux calculations, Damkoehler numbers for the ablation-product layer, together with conclusions.

Thermoacoustic Refrigerator for Space Applications

Abstract: A new spacecraft cryocooler which uses resonant high-amplitude sound waves in inert gases to pump heat is described. The phasing of the thermoacoustic cycle is provided by thermal conduction. This "natural" phasing allows the entire refrigerator to operate with only one moving part (the loudspeaker diaphragm). A spacequalified thermoacoustic refrigerator was flown on the Space Shuttle Discovery (STS-42) in January, 1992. It was entirely autonomous, had no sliding seals, required no lubrication, used mostly low-tolerance machined parts, and contained no expensive components. Thermoacoustics is shown to be a competitive candidate for food refrigerator/freezers and commercial/residential air conditioners. The design and performance of the Space ThermoAcoustic Refrigerator (STAR) is described.

Material-dependent catalytic recombination modeling for hypersonic flows

Abstract: A new model to predict catalytic recombination rates of O and N atoms over silica re-entry thermal protection system is reported. The model follows the general approach of Halpern and Rosner, but adds estimates of some key physical mechanism parameters based on realistic surface potentials. This novel feature can therefore produce rate expressions for any surface for which structure is known. Testing the model for N over W, and N and O over SiO2 produces recombination probabilities in good agreement with published measurements at high surface temperature. In the case of N and O over SiO2, the model accounts for surface NO production due to O and N cross recombination.

Variable Refractive Index Effects on Radiation in Semitransparent Scattering Multilayered Regions

Abstract: A simple set of equations is derived for predicting the temperature distribution and radiative energy flow in a semitransparent layer consisting of an arbitrary number of laminated sublayers that absorb, emit, and scatter radiation. Each sublayer can have a different refractive index and optical thickness. The plane composite region is heated on each exterior side by a different amount of incident radiation. The results are for the limiting case where heat conduction within the layers is very small relative to radiative transfer, and is neglected. The interfaces are assumed diffuse, and all interface reflections are included in the analysis. The thermal behavior is readily calculated from the analytical expressions that are obtained. By using many sublayers, the analytical expressions provide the temperature distribution and heat flow for a diffusing medium with a continuously varying refractive index, including internal reflection effects caused by refractive index gradients. Temperature and heat flux results are given to show the effect of variations in refractive index and optical thickness through the multilayer laminate.

Thermal conductivities of quantum well structures

Abstract: This work analyzes the size and the boundary effects of a gallium arsenide- (GaAs) based quantum well (QW) structure on the thermal conductivity of the well material. Calculations show that the order of phonon mean free path (MFP) is equal to or even longer than the typical dimension of the well (-200 A or less). Holland's model is applied to match the thermal conductivity data of bulk GaAs from 2 to above 600 K. The equation of phonon radiative transfer (EPRT) developed from the Boltzmann transport equation is then introduced for the heat transport in the QW structure. Boundary conditions are built from the diffuse phonon mismatch theory, and approximate solutions are obtained for the cases of heat flow perpendicular and parallel to the well. Results show that the thermal conductivity of the quantum well can be one order-of-magnitude lower than that of its corresponding bulk form at room temperature. The size and boundary effects also cause anisotropy of the thermal conductivity, even though the unit cell of GaAs is cubic.

View factors for perpendicular and parallel rectangular plates

Abstract: Simplified expressions (in comparison to currently used expressions, such as one developed by Howell, 1982) are developed for computing the view factors for rectangular perpendicular and parallel plates in the analysis of radiant exchanges between surfaces separated by a radiatively transparent medium. It is shown that the reported expressions for rectangular perpendicular and parallel plates with varying position and size having parallel boundaries satisfy the properties of the view factors.

Electron-impact vibrational relaxation in high-temperature nitrogen

Abstract: Vibrational relaxation process of N2 molecules by electron-impact is examined for the future planetary entry environments. Multiple-quantum transitions from excited states to higher/lower states are considered for the electronic ground state of the nitrogen molecule N2(X1 S+). Vibrational excitation and de-excitation rate coefficients obtained by computational quantum chemistry are incorporated into the "diffusion model" to evaluate the time variations of Vibrational number densities of each energy state and total vibrational energy. Results show a nonBoltzmann distribution of number densities at the earlier stage of relaxation, which in turn suppresses the equilibration process, but affects little on the time variation of total vibrational energy. An approximate rate equation and a corresponding relaxation time from the excited states, compatible with the system of flow conservation equations, are derived for the first time. The relaxation time from the excited states indicates the weak dependency of the initial vibrational temperature, and is shorter than the previously obtained relaxation time in which only excitation from the ground state was considered. The empirical curve-fit formulas for the improved e-V relaxation time is obtained. The rate equation and the relaxation time, suited for the numerical simulation of the highly ionized planetary entry flowfields, are suggested.

Discrete ordinates solutions for radiatively participating media in a cylindrical enclosure

Abstract: The radiative transfer equation is solved by the S-N discrete ordinates method in the two-dimensional r-z coordinates system. The walls of the enclosure are diffuse, and the participating medium absorbs, emits, and anisotropically scatters the radiative energy. Diffuse wall incidence, isothermal medium emission, and collimated incidence problems are considered. Effects of the scattering phase functions on average incident radiation and net radiative heat fluxes are studied. In addition, the effects of scattering albedo, optical thickness, and the wall emissivity are briefly discussed.

Single Droplet Vaporization Including Thermal Radiation Absorption

Abstract: Total hemispherical absorption distributions for n-decane and water droplets irradiated by a blackbody under spherically symmetric conditions are used in the calculation of transient droplet heating and vaporization. The gas model used is based on the extended film theory. Three liquid-phase models have been extended to include thermal radiation absorption. The results show that radiation absorption can be as important as, or more important than, the choice of liquid-phase model. Based on the effective-conductivity model, two dimensionless parameters expressing the ratios of radiation absorption and gas-liquid heat transfer to liquid conductive and convective heat transfer are defined. It is shown that the first parameter determines the droplet heating regime. Over 200 numerical calculations using the effective-conductivity model and various initial and ambient conditions have been performed for water and w-decane droplets. It is shown that the ratio of the two dimensionless parameters evaluated at the initial time can be used to correlate and predict the radiation absorption influence on the droplet lifetime. All cases investigated correspond to the slow heating regime. Under the conditions analyzed, the nonuniformity of the radiation absorption has little effect on the overall droplet heating and vaporization process. CD = cp = F =

Vibrational relaxation measurements in an expanding flow using spontaneous Raman scattering

Abstract: Vibrational relaxation of nitrogen in a two-dimensional nozzle flow is studied with spontaneous Raman scattering. An electric arc-driven shock tube operating as a reflected shock tunnel produces stagnation conditions of 5600 K and 100 atm. A 248-nm KrF laser pulse is focused into the nozzle to produce spatially resolved spontaneous Raman spectra. Vibrational population distributions are derived from the spectra for the states v = 0 to v = 8. The experimental results are compared with two theoretical models: (1) the Landau-Teller relaxation model and (2) a numerical solution of the master equations using transition rates derived from Schwartz, Slawsky and Herzfeld (SSH) theory. We have measured a value for the Landau-Teller correction factor (phi) to be 1.0-1.5. 13 refs.

Comparison of kinetic models for atom recombination on high-temperature reusable surface insulation

Abstract: Five kinetic models are compared for their ability to predict recombination coefficients for oxygen and nitrogen atoms over high-temperature reusable surface insulation (HRSI). Four of the models are derived using Rideal-Eley or Langmuir-Hinshelwood catalytic mechanisms to describe the reaction sequence. The fifth model is an empirical expression that offers certain features unattainable through mechanistic description. The results showed that a four-parameter model, with temperature as the only variable, works best with data currently available. The model describes recombination coefficients for oxygen and nitrogen atoms for temperatures from 300 to 1800 K. Kinetic models, with atom concentrations, demonstrate the influence of atom concentration on recombination coefficients. These models can be used for the prediction of heating rates due to catalytic recombination during re-entry or aerobraking maneuvers. The work further demonstrates a requirement for more recombination experiments in the temperature ranges of 300-1000 K, and 1500-1850 K, with deliberate concentration variation to verify model requirements.

Flight Measurements of Low-Velocity Bow Shock Ultraviolet Radiation

Abstract: The ultraviolet spectrum, atomic oxygen 1304-nm radiation intensity, total plasma density, and electron temperature of a Mach 12 bow shock were obtained by a sounding rocket experiment launched from the Wallops Flight Facility (WFF) on April 25, 1990 at 12:32 am Eastern Standard Time (EST) A two-stage, Terrier Malamute rocket which attained an apogee of 720 km was used in this experiment Optical data in the 200400-nm wavelength range were obtained from 37 to 75 km at a vehicle velocity of 35 km/s at various locations on the 01016-m radius hemispherical dome Electron probe and VUV OI 1304-nm measurements were obtained near nose cone ejection at 37 km This article presents a discussion of the instruments used and the key data obtained

Total thermal radiation absorption by a single spherical droplet

Abstract: The total energy absorption distribution inside a liquid droplet irradiated by blackbody emission is determined by spectral and solid angle integrations of the spectral absorption distribution given by electromagnetic theory. Results are presented for 1-100-micron radius n-decane and water droplets irradiated by a blackbody at 850-2000 K, in several axisymmetric configurations. Under spherically symmetric irradiation conditions, the water absorption results are used to verify the applicability and accuracy of the geometrical-optics approximation through comparison with those results. It is verified that the trapezoidal quadrature is usually a good approximation for spectral integration. The geometrical-optical approach leads to total absorptance values with errors larger than 10 percent for droplets smaller than 25 microns. Only the two principal bands of decane, including their wings, are needed to fairly well predict total absorption distribution in decane droplets. 24 refs.

Effect of thermal radiation on transient combustion of a fuel droplet

Abstract: The effect of radiation heat transfer on transient combustion of a fuel droplet with a finite rate of chemical reaction and variable properties has been studied under the assumption of spherical symmetry. Evaporation curves, transient variation of flame location, temperature profiles, and the ratio of the flame to droplet radius were compared to previously published results without the radiation effect. It was found that the radiation reduces by at least 25% the maximum flame temperature. Furthermore, the present results were compared to the experimental data of several researchers. As a consequence, it was shown that the reason for the previous discrepancy between the theory and experiment was attributed to the radiation.

Inverse Radiation Problem for Simultaneous Estimation of Temperature Profile and Surface Reflectivity

Abstract: A method is presented for simultaneous estimation of the unknown temperature distribution and the diffuse surface reflectivity in an absorbing, emitting, and isotropically scattering medium from the knowledge of the exit radiation intensities. The inverse radiation problem is recast as an optimization problem in finite-dimensional space and the conjugate gradient method of minimization is then used for its solution. The scheme is stable, insensitive to the initial guess, and in the absence of measurement errors the estimated solution converges to the exact result. 25 refs.

Review of the thermal contact conductance of junctions with metallic coatings and films

Abstract: The reliability of standard electronic modules may be improved by decreasing overall module temperature. This may be accomplished by enhancing the thermal contact conductance at the interface between the module frame guide rib and the card rail to which the module is clamped. The surface irregularities resulting from the machining or extruding of the components cause the true contact area to be much less than the apparent contact area, increasing the contact resistance. Some metallic coatings deform easily under load and increase the contact area and associated conductance. This investigation evaluates possible coatings and determines those most suitable for enhancing contact conductance based upon predictions using existing theories for thermal contact conductance of coated junctions.

Radiation transport around axisymmetric blunt body vehicles using a modified differential approximation

Abstract: A moment method for computing 3D radiative transport in axisymmetric thermochemical nonequilibrium flows is developed. The method uses the P-1 approximation to reduce the governing system of integro-differential equations to a coupled set of partial differential equations. The numerical solution of these equations for realistic variations of the radiation properties is discussed. Representative results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.

Magnetic field effects on the computed flow over a Mars return aerobrake

Abstract: A numerical algorithm is developed to calculate the electromagnetic phenomena simultaneously with the fluid flow in the shock layer over an axisymmetric blunt body in a thermal equilibrium, chemical nonequilibrium environment. The flowfield is solved using an explicit time-marching, first-order spatially accurate scheme. The electromagnetic phenomena are coupled to the real-gas flow solver through an iterative procedure. The electromagnetic terms introduce a strong stiffness, which was overcome by using significantly smaller time steps for the electromagnetic conservation equation. The technique is applied in calculating the flow over a Mars return aerobrake vehicle entering the Earth's atmosphere. For the case where no external field is applied, the electromagnetic effects have little impact on the flowfield. With the application of an external magnetic field of 0.05 to 0.1 T, the solution indicates an increase in stagnation line shock standoff distance, wall pressure, and radiative heat transfer and a decrease in convective heat transfer.

Measurement and analysis of nitric oxide radiation in an arc-jet flow

Abstract: On the bases of the centerline enthalpy value deduced from heat transfer measurements and the NOZNT code, it is possible to predict the freestream conditions in an arcjet wind tunnel flow. The translational-rotational and vibrational temperature of NO is nearly reproducible by NOZNT. Relative to the electron and electronic temperatures, the vibrational temperature of N2 and NO are significantly lower at enthalpies of less than 45 MJ/kg. The enthalpy deduced from spectroscopic measurements is in rough agreement with that deduced from heat transfer measurements.

Inverse problem of estimating interface conductance between periodically contacting surfaces

Abstract: The conjugate gradient method of minimization with adjoint equation is used to solve the inverse problem of estimating the timewise variation of interface conductance between periodically contacting solids, under quasi-steady-state conditions. It is assumed that no prior information is available on the functional form of the interface conductance, except the magnitude of the period. The accuracy of the inverse analysis is examined by using simulated inexact temperature measurements obtained at the interior of the region. Small periods are usually the most difficult on which to perform an inverse analysis. For such cases, the present method is found to be more accurate and stable than the B-Spline approach. 19 refs.

Measurements of laminar mixed convection flow over a horizontal forward-facing step

Abstract: Measurements and predictions of buoyancy-assisting laminar mixed convection flow over a horizontal, two-dimensional forward-facing step are reported. Laser-Doppler velocimeter (LDV) and cold wire anemometer were used to simultaneously measure the velocity and the temperature distributions, respectively. Flow visualizations were conducted to determine the reattachment lengths for different inlet velocities (u(0) between 0.255 m/s and 0.50 m/s), wall freestream temperature differences (Delta-T between 0 C and 37 C), and step heights (s between 0.79 cm and 1.75 cm). The results reveal that the buoyancy force due to wall heating has a negligible effect on the velocity and temperature distributions and the reattachment lengths, as long as the flow remains stable and two-dimensional. The inlet velocity and the step height, on the other hand, significantly affect the flow and thermal fields. The local heat transfer coefficient is found to increase as the inlet velocity increases and the step height decreases. On the other hand, the length of the recirculation regions upstream and downstream of the step are found to increase as the inlet velocity and the step height increase. Correlation equations are developed to predict the reattachment lengths that appear upstream and downstream of the step. The measured results agree well withmore » numerical predictions. 10 refs.« less

Monte Carlo simulation of radiating reentry flows

Abstract: The Direct Simulation Monte Carlo (DSMC) method is applied to a radiating, hypersonic, axisymmetric flow over a blunt body in the near continuum regime. The ability of the method to predict the flowfield radiation and the radiative heating is investigated for flow over the Project Fire II configuration at 11.36 kilometers per second at an altitude of 76.42 kilometers. Two methods that differ in the manner in which they treat ionization and estimate electronic excitation are employed. The calculated results are presented and compared with both experimental data and solutions where radiation effects were not included. Differences in the results are discussed. Both methods ignore self absorption and, as a result, overpredict measured radiative heating.

Radiative transfer by the YIX method in nonhomogeneous, scattering, and nongray media

Abstract: A numerical solution of the integral equation of radiative heat transfer using the YIX method involving a mixture of highly anisotropic scattering particles and a nongray absorbing gas is presented. To validate the three-dimensional calculation, bench mark solutions are established on a model problem using a high-order accuracy method, the product integration method (PIM). Various effects, e.g., the discrete ordinates sets, first integration point of the YIX quadrature, optical thickness of the medium, grid sizes, and spectral resolution on the accuracy of the three-dimensional calculation are discussed. Results for three-dimensional calculations are presented. For all cases, the pressure variation has less significant effect on the results than those by particle density or temperature variations. The three-dimensional nonhomogeneous cases have different trends of variation in radiative flux and divergence due to their nonuniform particle density distribution and nonisothermal participating medium. The use of the YIX method with discrete ordinates for the multidimensional calculations of highly anisotropic scattering and spectrally-dependent medium is shown to be accurate and flexible.

Refractive index and scattering effects on radiative behavior of a semitransparent layer

Abstract: Heat transfer characteristics are analyzed for a plane layer of semitransparent material with refractive index not less than 1. Energy transfer in the material is by conduction, emission, absorption, and isotropic scattering. Each side of the layer is heated by radiation and convection. For a refractive index larger than unity, there is internal reflection of some of the energy within the layer. This, coupled with scattering, has a substantial effect on distributing energy across the layer and altering the temperature distribution from when the refractive index is unity. The effect of scattering is examined by comparisons with results from an earlier paper for an absorbing layer. Results are given for a gray medium with a scattering albedo up to 0.999, and for a two-band spectral variation of the albedo with one band having low absorption. Radiant energy leaving the surface as a result of emission and scattering was examined to determine if it could be used to accurately indicate the surface temperature.

Natural convection in a cavity with fins attached to both vertical walls

Abstract: Numerical calculations are presented for two-dimensional natural convection flow inside an air-filled cavity with fins/baffles—of length 0.1, 0.3, and 0.5 of the cavity width—attached along both the heated and the cooled side of the cavity. The governing equations in the stream function-vorticity formulation are solved using finite differences. The Arakawa differencing scheme is used to represent the convection terms. Flow characteristics are investigated for three baffle lengths and Grashof numbers in the range of 9.0 x 103 to 1.0 x 105. A multicellular flow structure is found to exist for a baffle length of 0.1. However, when the baffle length is equal to 0.3 or greater, the fluid flow breaks down into secondary circulations—in addition to the primary circulation— and that, in turn, results in higher heat transfer rates across the two sides of the cavity. Nomenclature Gr = Grashof number, g/3ATw3/v2 h = baffle length N = number of baffles Pr = Prandtl number, via T = temperature u' = nondimensional velocity in £ direction v' = nondimensional velocity in £ direction w = cavity width z = cavity length a = thermal diffusivity j8 = coefficient of thermal expansion d = baffle thickness £ = nondimensional spatial coordinate 0 = nondimensional temperature A = cavity aspect ratio, z/w v = kinematic viscosity £ = nondimensional spatial coordinate r = nondimensional time ^ = nondimensional stream function i// = stream function H = nondimensional vorticity co = vorticity

Longitudinal heat dispersion in porous beds with real-gas flow

Abstract: The forced convective flow of a slightly superheated vapor through a packed bed is analyzed numerically for low-to-moderate pressure range by implementing real-gas and ideal-gas models. The porous bed was taken to be composed of uniformly sized, randomly packed spherical particles. The flow of the gas through the packed bed was limited to the range of applicability of the Ergun-Forchheimer relation. The significance of longitudinal thermal dispersion was examined by alternately implementing and omitting this aspect which was incorporated in the effective thermal conductivity of the vapor phase. The use of a real-gas model at elevated pressures was found to be an important aspect for accurate results. The longitudinal thermal dispersion effects were found to have minor significance at high Reynolds numbers. The use of separate energy equations for the solid and vapor phases was observed to be justified by the studies performed. Nomenclature asr = specific surface area of the bed particles, m2/m3 cp = specific heat at constant pressure, J/kg-K dp = particle diameter, m F = geometric factor defined in Eq. (8) hsr = fluid-to-particle heat transfer coefficient, W/m2-K K = permeability, m2 k = thermal conductivity, W/m-K L = length of the packed bed, m P = pressure, N/m2 Pr = Prandtl number, jjicp/k R = gas constant for Refrigerant-11, J/kg-K Rep = particle Reynolds number, updp/im T = temperature, K t = time, s u = velocity component in x direction, m/s Z = compressibility factor e = porosity IJL = absolute viscosity, kg/m-s p = density, kg/m3 { ) = local volume average of a quantity Subscripts

Cool-down of a vertical line with liquid nitrogen

Abstract: Analytical and numerical modeling is presented for predicting the thermofluid parameters of the cool-down process of an open-to-air vertical tube carrying liquid nitrogen. A two-fluid mathematical model is employed to describe the flowfield. In this model four distinct flow regions were analyzed: 1) fully liquid, 2) inverted annular film boiling, 3) dispersed flow, and 4) fully vapor. These flow regimes were observed in an experimental investigation constructed for validating the mathematical model, and also in previous experiments by other investigators. For the single-phase regions, the one-dimensional form of mass, momentum, and energy equations were used. For the two-phase regions, the volume-averaged, phasic one-dimensional form of conservation equations were applied. The one-dimensional energy equation was formulated to determine the tube wall temperature history. The numerical procedure is based on the semi-implicit, finite-difference technique. The calculations for the inverted annular film boiling were performed implicitly. The computations for the tube wall, fully liquid, and dispersed flow regions were performed explicitly. In each region, the appropriate models for heat transfer and shear stress rates are used. Results and comparisons of the predicted numerical models with the experimental data for several constant inlet flow rates of liquid nitrogen into a vertical, insulated tube are presented. Nomenclature Aw = cross-sectional area of the flow channel, m2 cp = specific heat capacity, J/kg °C Da = area-averaged, population-mean diameter of drops, m ALix = maximum entrainable diameter of drops, m £&ax = maximum stable diameter of drops, m Dsmd = Sauter mean diameter of a droplet population, m Dv = volume averaged, population-mean diameter of drops, m d = diameter of the flow channel, m g = local acceleration of gravity, m/s2 h = enthalpy, J/kg hc = convective heat transfer coefficient, W/m2 °C hnb = heat transfer coefficient for nucleate boiling, W/m2 °C ^,sat = saturation enthalpy of either liquid or vapor, J/kg k = thermal conductivity, W/m °C Lfg = latent heat of vaporization, J/kg m'" = interfacial mass transfer rate, kg/m3s q" = heat flux per unit area, W/m2 q'" = heat transfer rate per unit volume, W/m3 <7evaP - vaporization heat flux, W/m2 #rad = wa ^ to liquid radiation, W/m2 q"% = vapor to drop radiation heat flux, W/m2 q^d = wall to drop radiation heat flux, W/m2 q'^v = wall to vapor radiation heat flux, W/m2 Pi = inner perimeter of tubular flow channel, Pr = Prandtl number, cpiji/kl p = pressure, N/m2 m

Computation of nonequilibrium hypersonic flowfields around hemisphere cylinders

Abstract: Hypersonic flows past hemisphere cylinders at zero incidence in chemical and thermal nonequilibrium are investigated for a range of Mach numbers from 10 to 18. The numerical code shows excellent comparison for surface pressure and heat transfer prediction with recent experiments conducted in a shock tunnel. The numerical code also compares well for stagnation point heat flux predictions at altitudes of 22 and 37 km with a set of earlier experiments. Numerical solutions with the vibrational equilibrium model are compared with those of multitemperature nonequilibrium. The stagnation point heat transfer is 10-23% higher for the nonequilibrium solutions in the Mach number range of 12-18. The importance of a multitemperature model for accurate prediction of stagnation properties, particularly the heat transfer, is noted. The variation in computed shockstandoff distance substantiates that the Mach number independence principle applicable to ideal gases does not hold for dissociating flows. Over the range of Mach numbers, the noticeable influence of vibrational relaxation on the temperature distributions and mass concentrations in the vicinity of shocks is shown in the present study.