Leonid A. Dombrovsky

Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements

A modified two-flux approximation is suggested for calculating the hemispherical transmittance and reflectance of a refracting, absorbing, and scattering medium in the case of collimated irradiation of the sample along the normal to the interface. The Fresnel reflection is taken into account in this approach. It is shown that the new approximation is rather accurate for the model transport scattering function. For an arbitrary scattering medium, the error of the modified two-flux approximation is estimated by comparison with the exact numerical calculations for the Henyey-Greenstein scattering function in a wide range of albedos and optical thicknesses. Possible applications of the derived analytical solution to identification problems are discussed.

Thermal radiation from nonisothermal spherical particles of a semitransparent material

Abstract The applicability of radiation transfer theory for calculations of the thermal radiation emitted by spherical particle of a semitransparent material, and in particular the determination of radial heat generation profiles, is analyzed. For homogeneous isothermal particles, a comparison with the exact solution based on the Mie theory shows that the radiation transfer calculations are sufficiently accurate for diffraction parameter of the particle of x ≥ 20. Numerical examples for large particles illustrate the transition from conditions of dominant radiation of the central region of the particle to conditions of the surface layer emission. A new differential approximation for radiation transfer in a refracting particle is proposed. This approximation called MDP 0 (modified DP 0 ) is much simpler than the radiation transfer equation. Using MDP 0 , we have a chance to consider radiation–conduction interaction in nonisothermal particles without great computational efforts.

Heating and evaporation of semi-transparent diesel fuel droplets in the presence of thermal radiation

Absorption and scattering spectral efficiency factors for spherical semi-transparent fuel droplets are approximated by simple analytical expressions as functions of imaginary and real parts of the complex index of refraction and the diffraction parameters of droplets. These expressions are applied to the modelling of thermal radiation transfer in Diesel engines. On the basis of the P-1 approximation, which is applicable due to the large optical thickness of combustion products, various ways of spectral averaging for absorption and scattering coefficients are suggested. Assuming that the concentration of fuel droplets is small, the scattering effects are ignored and the analysis is focused on approximations for the absorption coefficient. The average absorption coefficient of droplets is shown to be proportional to ard2+b, where rd is the droplet radii, and a and b are quadratic functions of gas temperature. Explicit expressions for a and b are derived for diesel fuel droplets in the range 5–50 μm and gas temperatures in the range 1000–3000 K. The expression for the average absorption coefficient of droplets is implemented into the research version of VECTIS CFD code of Ricardo Consulting Engineers. The effect of thermal radiation on heating and evaporation of semi-transparent diesel fuel droplets is shown to be considerably smaller when compared with the case of black opaque droplets.

Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles

An improved method used to determine the absorption and scattering characteristics of a weakly absorbing substance containing bubbles is suggested. The identification procedure is based on a combination of directional-hemispherical measurements and predictions of Mie-scattering theory including approximate relations for a medium with polydisperse bubbles. A modified two-flux approximation is suggested for the calculation of directional-hemispherical transmittance and reflectance of a refracting and scattering medium. The complete identification procedure gives not only the spectral radiative properties but also the volume fraction of bubbles and the characteristics of possible impurity of the medium. This procedure is used to obtain new data on near-infrared properties of fused-quartz samples containing bubbles.

Absorption of thermal radiation in a semi-transparent spherical droplet: a simplified model

The boundary-value problem for calculation of differential absorption of thermal radiation is formulated based on the modified DP0 approximation. The solution of this problem is supplemented by simple analytical approximations for the normalised absorbed radiation power. The latter is used together with the analytical approximation for the efficiency factor of absorption, suggested earlier. The resulting simplified model is applied to the specific problem of absorption of thermal radiation by a diesel fuel droplet. Two types of diesel fuel have been considered. It is pointed out that the radial distribution of absorbed thermal radiation power is non-monotonic. The power absorbed in the droplet core is shown to be rather large and almost homogeneous. Also, the absorbed power is large in the vicinity of the droplet surface, but is minimal in the intermediate region. It is pointed out that the variations of the refractive index of diesel fuel with wavelengths can smooth the predicted radial dependence of the thermal radiation power, absorbed in diesel fuel droplets.

A simplified non-isothermal model for droplet heating and evaporation

A simple model for heating and evaporation of non-isothermal droplets is suggested. This model is based on the parabolic approximation of the temperature profiles inside droplets. The d-squared law of droplet evaporation is modified to take into account droplet heating. Comparison with numerical solutions of the transient problem for moving droplets shows the applicability of this approximation to modelling the heating and evaporation processes of fuel droplets in diesel engines. The simplicity of the model makes it particularly convenient for implementation into multidimensional CFD codes to replace the widely used model of isothermal droplets.

Spectral properties of diesel fuel droplets

Absorption spectra of several types of diesel fuel are studied experimentally. Index of refraction of these fuels is calculated using subtractive Kramers - Kronig analysis. The ageing process of fuels is simulated by prolonged boiling. Radiative properties of diesel fuel droplets are calculated using the Mie theory and a simplified approach, based on approximations of absorption and scattering efficiency factors. It is pointed out that the accuracy of the simplified approach is sufficient for practical applications in the visible and infrared ranges, for various types of diesel fuel, and for droplet radii in the range from 5 to 50 mm. The monodisperse approximation is shown to be applicable for the analysis of infrared radiative properties of realistic polydisperse diesel fuel sprays. q 2002 Elsevier Science Ltd. All rights reserved.

A parabolic temperature profile model for heating of droplets

A model for convective heating of droplets, which takes into account their finite thermal conductivity, is suggested. This model is based on the assumption of the parabolic temperature profile in the droplets. A rigorous numerical solution, without restrictions on temperature profiles inside droplets, is compared with predictions of the parabolic temperature profile and isothermal models

A modified differential approximation for thermal radiation of semitransparent nonisothermal particles: application to optical diagnostics of plasma spraying

Abstract A modified differential approximation proposed recently by the author is formulated for nonisothermal particles. This approximation called MDP0 (modified DP0) is much simpler than the radiation transfer equation (RTE). Comparison with the RTE solution confirms an acceptable accuracy of MDP0. An improved model of particle heating in plasma spraying is proposed. This model, which includes MDP0 equations, takes into account the radiation–conduction interaction inside the particle. Calculations for metal oxide particles in a typical plasma jet show that the particle color temperature, which is usually determined in monitoring the plasma spraying, is very sensitive to the absorption index of the particle substance. This effect should be taken into account in experimental evaluations of the bulk temperature of particles.

Heat transfer by radiation from a hot particle to ambient water through the vapor layer

Abstract Heat transfer by thermal radiation from a hot spherical particle to ambient water through the concentric vapor shell is analyzed by the use of different theoretical models. In the case of the vapor layer thickness Δ comparable with the radiation wavelength, the wave effects are taken into account. For greater values of Δ, the problem solution is derived by combination of the Mie theory for the particle emissivity, the Fresnel’s equations for radiation reflection/refraction on the vapor–water interface, and the radiation transfer equation for calculation of heat absorption profiles in water. A justified approximate description of the radiation heat transfer between corium melt particles and boiling water, as applied to vapor explosion analysis in the case of nuclear reactor severe accident, is proposed. Numerical examples illustrate effects of the particle size and the vapor shell thickness.