Approximation for radiant energy transport in nongray, nonscattering gases
Approximation for radiant energy transfer in nongray, nonscattering gases, using mean absorption coefficient in gray-gas transport equation
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Approximation for radiant energy transfer in nongray, nonscattering gases, using mean absorption coefficient in gray-gas transport equation
Source function solution for radiative heat transfer through nonisothermal absorbing and emitting gray gas
Zoning techniques applied to gray gas and black body radiation transport models including view effects and nonisothermal emission
Results are presented from the Navier-Stokes and viscous shock-layer (VSL) calculations with nonequilibrium and equilibrium chemistry, respectively. These calculations contain coupling to the Aerotherm radiation code RAD. A simplified form of the electron energy equation is used to obtain an electron temperature in the Navier-Stokes calculations. The radiation in the flowfield is calculated using this temperature. The Navier-Stokes code is used at high altitude only, whereas the VSL code is employed for the entire entry period to make estimates of the radiative and convective heating to the Fire II vehicle. Results from the Navier-Stokes code have also been compared with the predictions of Lee and Kawamura, who used gray-gas radiation model and thin-layer Navier-Stokes equations. Quite good agreement is obtained between the measured and computed values of radiative and convective heating from the VSL code in th medium-to-low altitude flight regime of the Fire II vehicle. At high altitudes, the Navier-Stokes calculations considerably overpredict the Fire II flight data for radiative intensity. This is attributed to the deficiencies in the Aerotherm radiation model when used for low-density flight conditions. This model contains the thermal equilibrium assumption and precludes accounting for the collision-limiting phenomenon at high altitudes. Present Navier-Stokes calculations highlight the effect of these assumptions on radiative heating calculations for such conditions.
The influence of radiative energy transfer on the entrance region flow is investigated under supersonic and subsonic flow conditions in a channel. Two-dimensional compressible Navier-Stokes equations are solved numerically in conjunction with the radiative flux equations. The channel walls are assumed to be black. Nongray as well as pseudo gray gas models are used to represent the absorption-emission characteristic of the medium. The participating species considered are different amounts of water vapor in water vapor-air mixtures. Results obtained for different flow conditions indicate that the radiative interaction can moderately influence the overall energy transfer, but the flowfield is not changed significantly.
Basic formulations, analyses, and numerical procedures are presented to investigate radiative heat interactions in diatomic and polyatomic gases under local and nonlocal thermodynamic equilibrium conditions. Essential governing equations are presented for both gray and nongray gases. Information is provided on absorption models, relaxation times, and transfer equations. Radiative flux equations are developed which are applicable under local and nonlocal thermodynamic equilibrium conditions. The problem is solved for fully developed laminar incompressible flows between two parallel plates under the boundary condition of a uniform surface heat flux. For specific applications, three diatomic and three polyatomic gases are considered. The results are obtained numerically by employing the method of variation of parameters. The results are compared under local and nonlocal thermodynamic equilibrium conditions at different temperature and pressure conditions. Both gray and nongray studies are conducted extensively for all molecular gases considered. The particular gases selected for this investigation are CO, NO, OH, CO2, H2O, and CH4. The temperature and pressure range considered are 300-2000 K and 0.1-10 atmosphere, respectively. In general, results demonstrate that the gray gas approximation overestimates the effect of radiative interaction for all conditions. The conditions of NLTE, however, result in underestimation of radiative interactions. The method developed for this study can be extended to solve complex problems of radiative heat transfer involving nonequilibrium phenomena.
A second-order differential Reynolds Stress turbulence model has been applied to the Favre-averaged Navier-Stokes equations for the study of supersonic flows with finite-rate chemistry and radiation. An assumed Beta Probability Density Function is applied to account for the chemical source terms and the radiative flux terms in the conservation equations. A seven-species, seven-reaction finite rate chemistry mechanism is used to simulate the combustion process. The tangent slab approximation is used in radiative flux formulation. A pseudo-gray gas model is used to represent the absorption-emission characteristics of the participating species. The turbulence/radiation interaction is achieved via a new formulation. The resulting formulation is validated by comparison with experimental data on reacting supersonic axisymmetric jets. Results obtained for specific conditions indicate that the effect of chemical reaction on the turbulence is significant. Also, the radiative heat transfer is enhanced by the turbulence.
Convective and radiant heat transfer for flow of a transparent gas in a tube with a gray wall
Thermal radiation from gas not in thermodynamic equilibrium
Gas local thermodynamic equilibrium effect on calculated thermal radiation emission
Iterative solution for source function in gray atmosphere in radiation equilibrium
Radiative transfer inside gray atmosphere in strict equilibrium shows similarity transformation exists
Hopf analytical solution for greenhouse parameter in gray planetary atmosphere
Unattainability of detailed balancing in thermodynamic equilibrium of gray atmosphere
Entropy defect and source function in gray atmosphere thermodynamics
Excerpts from a paper describing the numerical examination of concurrent-flow flame spread over a thin solid in purely forced flow with gas-phase radiation are presented. The computational model solves the two-dimensional, elliptic, steady, and laminar conservation equations for mass, momentum, energy, and chemical species. Gas-phase combustion is modeled via a one-step, second order finite rate Arrhenius reaction. Gas-phase radiation considering gray non-scattering medium is solved by a S-N discrete ordinates method. A simplified solid phase treatment assumes a zeroth order pyrolysis relation and includes radiative interaction between the surface and the gas phase.
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Coupled radiative and convective heat transfer is investigated for an absorbing gas flowing in a finite length channel and heated by blackbody radiation directed along the flow axis. The problem is formulated in one dimension and numerical solutions are obtained for the temperature profile of the gas and for the radiation escaping the channel entrance, assuming both gray and nongray absorption spectra. Due to radiation trapping, the flowing gas is found to have substantially smaller radiation losses for a given peak gas temperature than a solid surface that is radiatively heated to this temperature. A greenhouse effect is also evident whereby radiation losses are minimized for a gas having stronger absorption at long wavelengths.