Non-gray Gas Research Articles

Radiation transfer computation in cylindrical arc columns using a Monte Carlo method

A one-dimensional, axisymmetric, Monte Carlo radiative transfer method has been developed to calculate the energy transfer and temperature profiles of moderate to high pressure cylindrical electric arc columns. The model includes the energy transfer due to the emission and absorption of a non-gray gas and thermal conduction but neglects convection. The thermal and electrical conductivities and the wavelength dependent spectral absorptivities are calculated based on assumption of local thermodynamical equilibrium (LTE). To verify the method, calculations were performed for the case of an electric arc in air at 30 atm pressure. The results were compared to those obtained from an earlier calculation which used the diffusion approximation for the radiative transfer. This case is representative of conditions that are typical of constrictors in arc heaters. The method was then applied to an arc in NH 3 at 1 atm for conditions that are typical of the constrictor in arcjet thrusters. The geometrical part of the method was then extended to enable a fully two-dimensional, axisymmetric simulation of radiative transfer for generic geometrical shapes.

COMBINED CONVECTION AND RADIATION IN SIMULTANEOUSLY DEVELOPING FLOW AND HEAT TRANSFER WITH NONGRAY GAS MIXTURES

Abstract Combined convection and radiation in simultaneously developing laminar flow and heat transfer in a smooth tube is numerically considered with the P-I approximation and the exponential wideband model. The fluid is a mixture of carbon dioxide, water vapor, and nitrogen, The bulk mean temperature variation, temperature profiles, and Nusselt numbers are shown for a uniform inlet temperature and several constant wall temperatures. Nusselt numbers for simultaneously developing flow are compared with those for thermally developing flow. The effects of the mole fraction of the nongray gases and the wall emissivity on convective and radiative Nusselt numbers are explored.

Investigation of Radiative Transfer in Nongray Gases Using a Narrow Band Model and Monte Carlo Simulation

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship that only provides the noncorrelated results for nongray analysis. Two features of the MCM that are different from other nongray numerical methods are discussed. The simplicity of the MCM is demonstrated by considering the case of radiative transfer between two reflecting walls. The results for the radiative dissipation distributions and the net radiative wall heat fluxes are obtained for uniform, parabolic, and boundary layer type temperature profiles, as well as for a parabolic concentration profile. They are compared with available results of other methods. Good agreements are found for all the cases considered.

Discrete Ordinates Solutions of Nongray Radiative Transfer With Diffusely Reflecting Walls

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting walls. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wall heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wall reflections without any closure approximation applied.

Parallelization of 3-D Radiative Heat Transfer Analysis in Non-gray Gas.

A parallel computational method is developed for the Monte Carlo analysis of radiative heat transfer in three-dimensional nongray gas enclosed by gray walls. The highly parallel computer AP1000 is used for the analysis. For the nongray gas, a mixture of water vapor and carbon dioxide is chosen as the absorbing-emitting medium. Three types of parallelization are studied: type (1), event parallelization; type (2), combination of event parallelization and algorithm parallelization, and type (3), memory-saving algorithm of type (2). When 512 cells are used, values of the speed-up ratios of 395, 430, and 370 are obtained for types (1), (2), and (3), respectively. The maximum number of elements which can be treated is increased from 1200 for type (1) to 140000 for type (3).

Radiative Characteristics of Nongray Gas Containing Anisotropic Scattering Particles.

The Monte Carlo method is applied to study the effects of nongray gas and anisotropic scattering on the temperature profiles of particle-gas mixture between parallel black cold walls. The gas is nongray combustion gas and the particle is assumed to have gray surface and behaves as an absorber, emitter and anisotropic scatterer of radiative energy. The analysis is based on radiative transfer in a medium which is internally heated uniformly. For comparison, analyses with gray gas and with isotropic scattering particles are also carried out. The results obtained show that within the particle number density region where radiation-heat-transfer enhancement is expected, the gray gas assumption presents a flatter temperature profi1e than that of the nongray gas. When the particle density is increased, the layer temperature at the center first decreases and then, for greater particle density, it increases. But the temperature of the mixture adjacent to the wall, after being decreased, approaches a certain value when the particle density is increased. In the higher particle density region, the anisotropic scattering effect causes layer temperature higher than that of isotropic scattering.

Nongray Radiative Gas Analyses Using the S-N Discrete Ordinates Method

The S-N discrete ordinates method is applied to analyze radiative heat transfer in nongray gases. Spectral correlation between the terms in the equation of transfer is considered for black or nearly nonreflecting walls. Formulations to apply the S-N method using a narrow-band or the exponential wide-band model are presented. The net radiative wall heat fluxes and the radiative source distributions are obtained for uniform, parabolic, and boundary layer type temperature profiles, as well as for a parabolic concentration profile. The narrow- and wide-band nongray solutions are compared with gray-band approximations using the same band models. The computational speed of the gray-band approximation is obtained at the expense of accuracy in the internal fluxes and radiative source distributions. The wall radiative flux predictions by the gray-band approximation are satisfactory.

Radiation due to CO2 or H2O and particles in cylindrical media

This study considers nongray, absorbing, emitting, anisotropically scattering, one-dimensional, radiative transfer in cylindrical media. The radiation transfer is due to a gas composed of either CCh or H2O, soot and particles. The temperature of these constituents is equal and uniform throughout the medium. The nongray effects are due to the spectrally discontinuous absorption/emission behavior of the gas and the spectrally continuous absorption/emission behavior of the soot. The absorption coefficient of the nongray gas is modeled according to Edwards' exponential wide-band models. The absorption coefficient of the soot is inversely proportional to wavelength. The scattering phase function of the gray particles is represented as the sum of an isotropic component and a delta-function. An accurate solution to this problem is obtained by using the Pi-approximation coupled with the integral form of the equation of transfer. The bandwidths are determined by utilizing the wide-band models, and the spectral integration is performed over all wavelengths according to a two-point quadrature for each band. Comprehensive parameter surveys are performed in order to establish a detailed understanding of the complex interaction between radiatively participating particles and molecular gases.

A Computational and Experimental Study of Natural Convection and Surface/Gas Radiation Interactions in a Square Cavity

Interactions of natural convection and surface/gas radiation in a nongray gas filled square cavity are investigated in the present paper, both computationally and experimentally. A schematic of the cross sectional view of the cavity is depicted. The cavity is heated from the isothermal side wall located at x = H, which is maintained at a temperature of T{sub H}, and cooled from the opposing side wall with a temperature of {Tc} located at x = 0. All the interior surfaces are assumed to be nonslip and radiatively black for the computations. Various thermal boundary conditions are specified for the horizontal walls. Carbon dioxide gas is considered as the medium. The overheat ratio {delta} (defined as T{sub H} {minus} {Tc})/T{sub o}, where T{sub o} is the reference film temperature, ({Tc} + T{sub H})/2 has been limited to small values ({delta} < 0.2) in the experimental study of natural convection-radiation interactions in the past (Kurosaki et al., 1982). In the present investigation, significantly higher values of {delta} are used in the computations and experiments.

Transient energy transfer by conduction and radiation in nongray gases

A general formulation is presented to investigate the transient radiative interaction in nongray absorbing-emitting species between two parallel plates. Depending on the desired sophistication and accuracy, any nongray absorption model from the line-by-line models to the wide-band model correlations can be employed in the formulation to investigate the radiative interaction. Special attention is directed to investigate the radiative interaction in a system initially at a uniform reference temperature when the temperature of the bottom plate is reduced suddenly to a lower but constant temperature. The interaction is considered for the case of radiative equilibrium as well as for combined radiation and conduction. General as weU as limiting forms of the governing equations are presented, and solutions are obtained numerically by employing the method of variation of parameters. Specific results are obtained for CO, CO2, H2O, and OH. The information on species H2O and OH is of special interest for the proposed scramjet engine application. The results demonstrate the relative ability of different species for radiative interactions.

Combined conduction and radiation heat transfer in concentric cylindrical media

The exact radiative transfer expressions for gray and nongray gases which are absorbing, emitting and nonscattering, contained between infinitely long concentric cylinders with black surfaces, are given in local thermodynamic equilibrium. Resulting energy equations due to the combination of conduction and radiation modes of heat transfer, under steady state conditions for gray and nongray media, are solved numerically using the undetermined parameters method. A single 4.3-micron band of CO2 is considered for the nongray problems. The present solutions for gray and nongray gases obtained in the plane-parallel limit (radius ratio approaches to one) are compared with the plane-parallel results reported in the literature.

Enhancement of radiative heat transfer in the laminar channel flow of non-gray gases

The enhancement of radiative heat transfer based on the multi-band feature of radiative gas is analyzed theoretically for the system of laminar channel flow of high-temperature CO 2 and combustion gases between two parallel heat-absorbing surfaces. An integrodinerential equation of energy conservation, which takes into account the multi-band feature of the radiative gas, is solved numerically, and the enhancement effect by installing a solid plate in the radiative gas is calculated. From the results, it is shown that enhancements of local heat flux of up to 80% for CO 2 and 36% for combustion gas are attainable.

Combined Radiation and Convection in Absorbing, Emitting, Nongray Gas-Particulate Tube Flow

The interaction of thermal radiation with conduction and convection in thermally developing absorbing, emitting, nongray gas–particulate turbulent suspension flow through a circular tube is investigated. The contribution of thermal radiation is obtained through evaluation of the total hemispherical emittance of the particulate cloud and through evaluation of single band absorptances for molecular gases, modified to account for the interaction with the particles. The governing differential equation is derived as a (nonlinear) energy equation, coupled with integral equations to find the thermal radiation contributions. The energy equation is solved numerically by an implicit finite difference method with an iterative procedure. Qualitative results for Nusselt numbers are shown for a variety and range of parameters, such as optical thickness of particulates and single molecular gas bands, relative gas band position and band width, and temperature ratios (heated as well as cooled suspension flows).

Heat transfer analysis of non-gray gas in a flow system. 2nd Report. The case of large temperature difference between gas and a heat absorbing surface.

This study aims at establishing a heat transfer analysis of a laminar channel flow of non-gray gas in the case of a large temperature difference between the gas and a heat absorbing surface. An energy conservation equation which includes the multi-band feature of radiative gas, and the temperature dependence of thermal and radiative properties is established. The temperature dependence of radiative properties are taken into account by using a scaling method proposed by Edwards. From a comparison between the constant property non-scaling results and the variable property scaling ones, it is made clear that specific heat at constant pressure plays an important role in the energy conservation equation. It is also made clear that the constant property non-scaling analysis under-estimates the radiation shield effect by the low temperature region near the heat absorbing surface. For practical engineering purpose, variable property non-scaling analysis is recommended from the view point of CPU time.

Heat transfer analysis of non-gray gas in a flow system. 1st Report. The case of small temperature difference between gas and a heat absorbing surface.

This study aims at establishing a heat transfer analysis of non-gray gas in a flow system. An integro-differential equation of energy conservation is established for the laminar channel flow of non-gray gas, which includes the multi-band feature of radiative gas. The numerical analysis was conducted and the results are compared with the results obtained from the analysis based on the conventional gray gas assumption. From the comparison of these results, it is made clear that the radiative heat flux qr obtained from the gray analysis is greater than that of the non-gray analysis, and convective heat flux qc is vice versa. By comparing the divergence of radiative heat flux and temperature profile, it is made clear that the gray gas analysis estimates excessively small absorption of radiation in the cold region near the heat absorbing surfaces. This results in the large qr and small qc compared with the non-gray analysis.

Theoretical Investigation of the Effects of Aerosol Characteristics on the Radiative Heat Transfer in the Atmospheric Boundary Layer

An analysis is carried out on the radiative heat transfer in a nonisothermal, nonhomogeneous atmospheric boundary layer. Nongray gases and atmospheric aerosols are considered to emit, absorb and anisotropically scatter radiation energy. The effect of size, optical constants and concentration of aerosols on heating rate are studied. Various conditions of the atmospheric layer are considered. The maximum effect of the aerosol diameter is found in the case of the diameter being nearly equal to the wavelength of the visible light. The effect of the imaginary part of the complex refractive index of aerosol on the heating rate is very large. A complex, large dependence of the heating rate on the humidity is recognized. When the urban atmosphere is treated, the influence of the aerosol on the radiative heat transfer is strong, and an inversion layer may be produced by the aerosol.

Radiative heat transfer in rotary kilns

Radiative heat transfer between a nongray freeboard gas and the interior surfaces of a rotary kiln has been studied by evaluating the fundamental radiative exchange integrals using numerical methods. Direct gas-to-surface exchange, reflection of the gas radiation by the kiln wall, and kiln wall-to-solids exchange have been considered. Graphical representations of the results have been developed which facilitate the determination of the gas mean beamlength and the total heat flux to the wall and to the solids. These charts can be used to account for both kiln size and solids fill ratio as well as composition and temperature of the gas. Calculations using these charts and an equimolar CO2−H2O mixture at 1110 K indicate that gas-to-surface exchange is a very localized phenomenon. Radiation to a surface element from gas more than half a kiln diameter away is quite small and, as a result, even large axial gas temperature gradients have a negligible effect on total heat flux. Results are also presented which show that the radiant energy either reflected or emitted by a surface element is limited to regions less than 0.75 kiln diameters away. The radiative exchange integrals have been used, together with a modified reflection method, to develop a model for the net heat flux to the solids and to the kiln wall from a nongray gas. This model is compared to a simple resistive network/gray-gas model and it is shown that substantial errors may be incurred by the use of the simple models.

Laminar, Mixed-Convection, Boundary-Layer, Nongray-Radiative, Diffusion Flames

The two-dimensional, laminar, mixed-mode convection (free and forced), boundary-layer, radiative, diffusion flame has been analytically investigated with special attention directed toward the nongray nature of the combustion products. The solution procedures include Shvab-Zeldovich approximation and von Mises transformation for the physical transport equations and the finite difference method for the computation of the transformed equations. The local radiative fluxes for nongray, gray and radiatively-ideal gases are prescribed in detail. Twelve parameters that govern the flame characteristics have been identified. Setting appropriate parameters to zero yields several limiting solutions which are compared with the reported results. In addition to extensive results of distributions in the field variables and fluxes, the ratio of the radiation loss to the combustion energy evolved was computed and a radiatively-ideal gas having behaviors similar to the nongray gases was identified.

Coaxial radiative and convective heat transfer in gray and nongray gases

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.

A Simple Differential Approximation for Radiative Transfer in Non-Gray Gases

A Simple Differential Approximation for Radiative Transfer in Non-Gray Gases