Vladimir P. Solovjov

SLW modeling of radiative transfer in multicomponent gas mixtures

Abstract The methods of spectral integration for SLW modeling in the multicomponent gas mixtures are considered. The direct method and the method of convolution are extended to the multicomponent mixtures. Two new methods of spectral integration are proposed: the method of superposition and the multiplication method. A hybrid method based on desirable attributes of the latter two methods is also considered. The validation of the methods is performed by the prediction of radiative transfer in isothermal homogeneous media and in a ternary gas mixture layer with step-wise variation of temperature and species concentrations (water vapor, carbon dioxide and carbon monoxide). The HITEMP spectral database is used for evaluation of SLW spectral parameters and line-by-line benchmark solution.

An Efficient Method for Modeling Radiative Transfer in Multicomponent Gas Mixtures With Soot

An efficient approach for predicting radiative transfer in high temperature multicomponent gas mixtures with soot particles is presented. The method draws on the previously published multiplication approach for handling gas mixtures in the spectral line weighted-sum-of-gray-gases (SLW) model. In this method, the gas mixture is treated as a single gas whose absorption blackbody distribution function is calculated through the distribution functions of the individual species in the mixture. The soot is, in effect, treated as another gas in the mixture. Validation of the method is performed by comparison with line-by-line solutions for radiative transfer with mixtures of water vapor, carbon dioxide, and carbon monoxide with a range of soot loadings (volume fractions). Comparison is performed also with previously published statistical narrow band and classical weighted-sum-of-gray-gases solutions.

A local-spectrum correlated model for radiative transfer in non-uniform gas media

A new local-spectrum correlated model is developed for the solution of the radiative transfer equation (RTE) in non-uniform gas media at high temperature. The spectral integration of the RTE is performed with the help of a new gas absorption spectrum distribution function termed the cumulative wavenumber. The new approach features local-spectrum correlation, rather than the global-spectrum correlation used traditionally. A local correction factor introduced to account for spatial variations in species concentrations and gas temperature is performed independently in each spectral interval under the assumption of local-spectrum correlation. Hence, the dependence of predictions on the selection of a reference temperature is nearly eliminated. The method is shown to be capable of treating non-gray particulates and boundaries.

SLW-1 Modeling of Radiative Heat Transfer in Nonisothermal Nonhomogeneous Gas Mixtures With Soot

The spectral line weighted-sum-of-gray-gases (SLW) model consisting only of a single gray gas and of one clear gas is developed as an efficient spectral method for modeling radiation transfer in gaseous medium. The model is applied here in prediction of radiative transfer in nonisothermal and nonhomogeneous gas mixtures with nongray soot. The absorption spectrum of the gas mixture and soot particles is treated as a spectrum of a single effective gas, reducing the problem to the simplest case of the SLW model with a single gray gas and a clear gas. Good accuracy can be achieved by the optimal choice of the model’s gray gas absorption coefficient and its weight by application of the absorption-line blackbody distribution functions of individual species in the mixture calculated with a high-resolution spectral database. The SLW-1 model is validated by comparison with benchmark solutions using the line-by-line method, the SLW method with a large number of gray gases, and the SNB model.

An exact formulation of k-distribution methods in non-uniform gaseous media and its approximate treatment within the Multi-Spectral framework

The main restriction of k-distribution approaches for applications in radiative heat transfer in gaseous media arises from the use of a scaling or correlation assumption to treat non-uniform situations. It is shown that those cases can be handled exactly by using a multidimensional k-distribution that addresses the problem of spectral correlations without using any simplifying assumptions. Nevertheless, the approach cannot be suggested for engineering applications due to its computational cost. Accordingly, a more efficient method, based on the so-called Multi-Spectral Framework, is proposed to approximate the previous exact formulation. The model is assessed against reference LBL calculations and shown to outperform usual k-distribution approaches for radiative heat transfer in non-uniform media.

The Generalized SLW Model

The Generalized SLW Method is presented, formulating the SLW method with the help of both the ALBDF and the Inverse ALBDF. The result is two equivalent symmetric models: the SLW Model and the Inverse SLW Model. The advantage of the unified dual formulation and of application of the ALBDF and the Inverse ALBDF is in more efficient implementation of the model and the elimination of the solution of the implicit equations for the absorption cross-sections in the construction of the spectral model in the case of nonisothermal media. The generalized approach explores all possibilities of the SLW method under both direct and inverse formulations including its limiting cases: the minimal one clear gas-one gray gas SLW-1 model, and the case when the number of gray gases approaches infinity termed the Exact SLW model. The present work outlines the steps in a unified construction of the generalized SLW model in isothermal and non-isothermal media, and compares different forms of the modelled radiative quantities in plane parallel media: directional total radiative flux, total emissivity, Planck mean and Rosseland mean absorption coefficients.

SOLUTION OF THE RADIATIVE TRANSFER EQUATION BY THE MOMENT METHOD USING POLYNOMIALS OF SPECIAL FORM

Abstract A new version of the moment method, based on the use of Cutteridge-Devyatov polynomials, is described. The procedure is illustrated by a sample solution of the radiative transfer equation in an absorbing and isotropically-scattering medium. The reflectivity and transmissivity of an isotropically-scattering, plane-parallel slab are determined for isotropically-incident radiation. Numerical results are compared with exact solutions. Generalization to cases involving inhomogeneous, anisotropically-scattering and emitting media are discussed.

Temperature Measurement Using Infrared Spectral Band Emissions From H2O

Temperature Measurement Using Infrared Spectral Band Emissions From H2O Daniel Jared Ellis Department of Mechanical Engineering, BYU Master of Science Currently there is no known method for accurately measuring the temperature of the gas phase of combustion products within a solid fuel flame. The industry standard is a suction pyrometer and thermocouple which is intrusive, both spatially and temporally averaging, and difficult to use. In this work a new method utilizing the spectral emission from water vapor is investigated through modeling and experimental measurements. This method was demonstrated along a 0.75m line of sight, averaged over 1 minute in the products of a natural gas flame but has the potential to produce a spatial resolution on the order of 5 cm and a temporal resolution of less than 1 millisecond. The method employs the collection of infrared emission from water vapor over discrete wavelength bands and then uses the ratio of those emissions to infer temperature. A 12.5 mm lens has been positioned within a water cooled probe to focus flame product gas emission into an optical fiber where the light is transmitted to a Fourier Transform Infrared Spectrometer (FTIR). The same optical setup was also used to collect light from a black body cavity at a known temperature in order to calibrate the spectral sensitivity of the optical system and FTIR detector. Experiments were conducted in the product gas of a 150 kWth methane flame comparing the optical emission results to a suction pyrometer with type K thermocouple. The optical measurement produced gas temperatures approximately 1 4% higher than the suction pyrometer. Broadband background emission was also seen by the optical measurement and was removed assuming grey body radiation. This background emission can be used to determine particle emission temperature and intensity. Additional work will be needed to demonstrate the method under conditions with significant particle emission. Additional work is also needed to demonstrate the work over a smaller path length and shorter time scale.

STAGNATION ZONES OF IDEAL FLOWS IN LONG AND NARROW BANDS

We investigate stagnation zones of flows of ideal incompressible fluid in narrow and long bands. With the bandwidth being much less than its length, these flows are almost stationary over large subdomains, where their potential functions are almost constant. These subdomains are called s-zones. We estimate the size and the location of these s-zones.

Green’s Function Approach to Nonlinear Conduction and Surface Radiation Problems

An exact approach for solving both transient and steady state conduction and surface radiation problems is presented. The method is based on the use of Green’s function, and the temperature field is obtained by solving an integral equation. This is in contrast to the approach presented in radiative heat transfer texts in which temperature profiles are obtained from the simultaneous solution of coupled integral and differential equations. The analysis presented in this paper provides insight into the solution of this important class of problems. The method is illustrated by solving two representative problems. The first problem considered is the steady state analysis of a radiating fin. The second problem considered is the transient analysis of a radiating target, which is used to determine the temporal response of radiation thermometers. DOI: 10.1115/1.4000234