Radiative Heat Flux Distribution Research Articles

Determination of Radiative Fluxes in an Absorbing, Emitting, and Scattering Vapor Formed by Laser Irradiation

A two-dimensional computer model is developed to determine the radiative heat flux distributions within the vapor formed above a metal target irradiated by a laser beam. An axisymmetric cylindrical enclosure containing a radiatively participating medium is considered. Scattering is assumed to be isotropic and allowances are made for variation of the radiative properties of the medium and boundaries. The P-1 and P-3 spherical harmonics approximations are used to solve the integro-differential radiative transfer equation. The resulting equations are then solved for the radial and axial heat fluxes using a finite-difference algorithm. The most significant factors affecting the results obtained from both the P-1 and P-3 approximations were the optical thickness of the medium and the type of laser profile incident upon the medium. Using different wall reflectivities and scattering albedos had a smaller effect. Changing the medium temperature had an insignificant effect as long as medium temperatures were below 20,000 K.

Heat transfer in gas turbine combustors

The present paper is concerned with the prediction of the local flow, heat-transfer, and combustion processes inside a three-dimensional can combustor chamber of a gas turbine. A three-dimensional numerical solution technique is used to solve the governing time-averaged partial differential equations and the physical modeling for turbulence, combustion, and thermal radiation. Heat-transfer modeling is emphasized in this paper. A method to calculate the distribution of temperature, radiative heat flux, and total heat flux of the liner is described. The implications of neglecting radiative heat transfer in gas turbine combustion chamber calculations are discussed. The influence of working pressure on radiative heat transfer is investigated, comparing the radiative heat flux and temperature distribution of the liner for three different working pressures: 5, 15, and 25 bar. Both radiative and convective fluxes increase with pressure, mainly because of the increase of inlet air temperature and gas emissivity. The ratio of the fluxes to the energy supplied to the combustor is very small. However, the accurate assessment of the flux distribution is an essential prerequisite for the prediction of the liner temperature distribution and liner life. 22 references.

Structure and spectral radiation properties of turbulent ethylene/ air diffusion flames

An experimental and theoretical study of the structure and radiation properties of round, turbulent, luminous ethylene/air diffusion flames is described. Measurements included mean and fluctuating velocities, mean concentrations of major gas species, soot volume fractions, monochromatic absorption (632.8 nm), spectral emission (1000–5500 nm), and total radiative heat flux distributions. Flame structure was predicted using a Favre-averaged k-∈-g turbulence model and the laminar flamelet approximation. Spectral radiation intensities were predicted using a narrow-band model—both ignoring (using mean properties) and considering (using a stochastic method) turbulence/radiation interactions. Total radiative heat fluxes were found by summing spectral intensities over wavelength and paths through the flame. The comparison between predicted and measured flame structure was reasonably good. Differences between mean-property and stochastic radiation emission predictions were significant (50–300 percent) suggesting strong turbulence/radiation interactions in luminous flames. However, both radiation analyses represented trends due to changes in position and burner flow rate reasonably well. This suggests that soot volume fractions may approximate universal functions of mixture fraction in turbulent flames, even though this correspondence is only crudely observed in laminar flames due to hydrodynamic complications of soot particle motion.

Radiative transfer in a gas-turbine combustor

A methodology is presented to predict radiative transfer in an axisymmetric cylindrical enclosure representing a typical gas-turbine combustor that contains radiatively participating gases and particles. Inhomogeneities of the radiative properties and temperature distribution of the medium are allowed for, and the boundaries are assumed to be diffusely emitting and reflecting. The effects of axial and radial variations of temperature and soot properties on radiative heat flux distributions at the wall are investigated. Film cooling is shown to have a marked effect on wall heat flux, especially when it quenches the soot oxidation process. Radiative flux at the wall is greater if the temperature of the medium is uniform, rather than if it has a center-peaked radial temperature profile.

Differential Approximation of Radiative Heat Transfer in a Gray Medium: Axially Symmetric Radiation Field

The differential approximation is used to analyze an axially symmetric radiation field for a gray medium within a finite, cylindrical enclosure. The medium emits, absorbs, and isotropically scatters radiant energy and is subject to a specified heat generation. Numerical solutions are obtained for the radiative heat flux and emissive power distributions. It is found that the accuracy of the differential approximation is of the same order for the axially symmetric and one-dimensional problems.

A comparison of mathematical models of the radiative behaviour of a large-scale experimental furnace

Three two-flux models, which had been developed previously for the approximate treatment of two-dimensional radiative energy transfer in industrial heaters, have been modified and applied to prediction of the thermal behaviour of a cylindrical large-scale gas-fired experimental furnace. Testing of the predictions has been carried out by utilising previously reported experimental values, and some zone method predictions. Cross-sectional average gas temperatures predicted using the zone and Roesler methods are found to be almost identical at any axial station, both slightly underestimating the measured values. The spherical harmonic (S-H) two-flux model distribution runs below and parallel to the Roesler predictions. The Schuster-Schwarzschild (S-S) type two-flux model with assumed plane parallel radiation (b=1) produces acceptable agreement in the first half of the furnace, and subsequent progressively increasing overestimation, whereas the same model with b=2 (isotropic radiation) underpredicts temperature in the first half of the furnace and leads to good agreement thereafter. Reasonable predictions are also obtained for the distributions of net heat flux density at the water-cooled sidewalls. The percentage errors in the predicted overall heat transfer to the water cooled walls are, with the exception of the S-S type with b=1, less than 3.5 for all the models. As the calculations involved in their use are relatively simple and economical, the Roesler, the isotropic S-S type, and the S-H type two-flux models should prove useful to designers for the approximate prediction of temperature and radiative heat flux distributions in axi-symmetrical furnaces in which one-dimensional flow, temperature and heat release patterns may reasonably be assumed.

The effect of solid particles on radiative transfer in a cylindrical test furnace

The influence of a solid particle suspension on the radiative heat flux distribution at the sink surface of a cylindrical test furnace was investigated by injecting alumina and magnesia particles into the fuel stream. A mathematical simulation of the furnace using the “zone method” of analysis was found to predict radiative distributions in reasonable agreement with the measured values. The radiative interchange within the system allowed for the emission, absorption and anisotropic scatter of the solid particle suspension. The results indicate that alumina and magnesia particles do not appreciably affect the radiative transfer, in the test furnace. However, the simulation predicts that particles with the complex refractive index of carbon would significantly increase the radiative transfer to the heat transfer surface at similar particle concentrations.

A chromatographic and interferometric study of the diffusion flame around a simulated fuel drop

The structure of the diffusion flame surrounding a simulated burning drop of n -hepatane was investigated. The drop was examined while burning at atmospheric pressure in a uniform air flow field at several air velocities. The composition and temperature profiles along several radial lines around the drop were determined by means of gas chromatography and optical interferometry. The composition analysis yielded concentrations of the fuel vapor as well as O 2 , CO 2 , CO, N 2 , CH 4 , C 2 H 2 , and C 2 H 4 in dried samples. The composition and temperature profiles were used to evaluate the mass and heat-flux distributions around the drop. The radiative heat-flux distributions from gas and soot were also evaluated. It was found that the flame structure varies markedly around the drop and that the air velocity has a large effect on the temperature profiles. At high air velocities, double-peaked temperature profiles were observed in the trailing half of the flame. Radiation, often ignored in the past, was found to be about 40% of the total heat transferred to the drop. Gas radiation is about 10% of the total radiation, the remainder being due to soot.

Heat-transfer measurements in a cylindricaltest furnace

An oil-cooled, gas-fired cylindrical test furnace was constructed to investigate the radiative and total heat-flux distributions at the circumferential sink wall. The furnace was instrumented such that flow patterns, gas-concentration profiles, temperature distributions, and radiative and total heat-flux distributions could be measured directly. Some typical examples of each of the above measurements are presented and discussed. The radiative heat-flux distribution at the sink wall has been calculated by dividing thefurnace enclosure into a number of uniform elements and simulating the radiative transfer by the Monte Carlo Method. The distributions calculated on the bases of measured temperatures within the furnace, or a measured flow pattern and gas-concentration patterns within the furnace, were found to agree well with the experimental data.

A mathematical simulation of radiant heat transfer in a cylindrical furnace

AbstractThe radiative heat transfer in a cylindrical furnace was investigated both experimentally and theoretically.The flow pattern within the combustion chamber was measured and found to differ from that of an identical cold model for which extensive theoretical and experimental work had been previously carried out.The Monte Carlo Method was used to solve for the radiative transfer part of the non‐linear integro‐differential equations describing the combustion and heat transfer in a cylindrical furnace.The radiative heat flux distribution obtained from the simulation agreed well with data obtained from a cylindrical test furnace.

An improved differential approximation for radiative transfer with spherical symmetry

An improved closure condition is used to construct a purely differential equation that, with associated boundary conditions, describes radiative transfer with spherical symmetry. The method is equivalent in degree of complexity to the P4 moment approximation, that is, a spherical harmonic expansion retaining four terms. The improved closing condition is especially constructed to allow both isotropic radiation and unidirectional, beamlike radiation. The method is applied to the problem of radiative equilibrium of a grey gas between two concentric black spheres maintained at different temperatures. Both radiative heat flux and temperature distribution from the present model are compared to known exact results. Predictions from the improved differential approximation in the crucial limit of a transparent gas are superior to those from both the conventional P2 and P± moment approximations, which predict qualitatively incorrect results in this limit when the inner sphere becomes small compared to outer.

Radiant heat flux distribution in a cylindrically-symmetric nonisothermal gas with temperature-dependent absorption coefficient

Equations are presented for the spectral radiant heat flux distribution in an absorbing and emitting gas of prescribed temperature distribution contained in a long cylinder whose internal surface is black. The temperature of the gas is taken to vary in the radial direction only, while the absorption coefficient of the gas is taken to vary with temperature as well as frequency of radiation. Equations are also presented for the radiant heat flux distribution in a gray gas in which the absorption coefficient is a function of temperature only. The equations, which are derived from the general equation of radiative transfer, are presented in terms of integral functions peculiar to the cylindrical geometry. Radiant heat flux distributions are calculated for several absorption coefficient and temperature distributions with the gray-gas model. The effects of absorption coefficient and temperature profiles on the heat flux distribution in a cylindrical medium are compared with equivalent effects in a plane parallel medium. The effects of absorption coefficient and temperature profiles on the heat flux distribution in the annular region between two concentric cylinders are also examined for cases in which the inner cylinder is a core of very opaque gas.

Radiant heat flux distribution in a cylindrically-symmetric nonisothermal gas with temperature-dependent absorption coefficient

Radiant heat flux distribution in a cylindrically-symmetric nonisothermal gas with temperature-dependent absorption coefficient

Analysis of the radiant heat absorption in the boundary layer surrounding an evaporating drop

AbstractAn approximate analysis is made of the effect of the absorption of thermal radiation on the temperature gradients surrounding an evaporating droplet which is suspended in a high temperature environment. The Hottel‐Cohen method for calculating the radiant heat flux distribution in an enclosure containing an absorbing medium of non‐uniform temperature, has been applied to the spherical symmetrical model of the system. Conduction and radial movement of the cold vapor from the droplet have been included.The analysis shows that, at atmospheric pressure, the absorption of radiant energy in the boundary layer is very small and hence does not affect the temperature gradient nor the rate of heat transfer at the droplet surface.This method of analysis, with the associated solution of the equations describing the reception factors, is quite general and can be applied to any spherical enclosure containing an absorbing medium whether it be one of concentric or hollow spheres.