Liangyu Wang

Narrow-Band Based Multiscale Full-Spectrum k-Distribution Method for Radiative Transfer in Inhomogeneous Gas Mixtures

The full-spectrum k-distribution (FSK) method has become the most promising model for radiative transfer in participating media since its introduction a few years ago. It achieves line-by-line (LBL) accuracy for homogeneous media with only a tiny fraction of LBL’s computational cost. Among the variants of the FSK method for dealing with inhomogeneous media, the multiscale FSK (MSFSK) method not only provides a strategy to treat the inhomogeneity problem by introducing an overlap coefficient, it also accommodates a solution to the so-called mixing problem (mixing of k-distributions for different gas species). The evaluation of MSFSK parameters, however, is tedious and excludes the MSFSK method from practical applications. In this paper a new scheme of evaluating k-distributions and overlap coefficients from a database of narrow-band k-distributions is formulated, treating each gas specie as a single scale. The new scheme makes the MSFSK method efficient and convenient for practical applications, and ready to accommodate nongray absorbing particles (such as soot) in the medium. The method virtually eliminates errors caused by uncorrelatedness due to independently varying species concentrations. It was also found that, in addition, breaking up a gas mixture into gas scales reduces the error caused by temperature inhomogeneities. The mathematical development of the new scheme is described and validated; the concept and the implication of the overlap coefficient are discussed. Sample calculations for inhomogeneous media with step changes in species mole fraction and temperature are performed to demonstrate the accuracy of the new scheme by comparison with LBL calculations.

Hybrid Full-Spectrum Correlated k-Distribution Method for Radiative Transfer in Nonhomogeneous Gas Mixtures

The full-spectrum k-distribution (FSK) approach is a promising model for radiative transfer calculations in participating media. FSK achieves line-by-line (LBL) accuracy for homogeneous media at a tiny fraction of LBL’s high computational cost. However, inhomogeneities in gas temperature, total pressure, and component-gas mole fractions change the spectral distribution of the absorption coefficient and can cause inaccuracies in the FSK approach. In this paper, a new hybrid FSK method is proposed that combines the advantages of the multigroup FSK (MGFSK) method for temperature inhomogeneities in a single gas species and the multiscale FSK (MSFSCK) method for concentration inhomogeneities in gas mixtures. In this new hybrid method, the absorption coefficients of each gas species in the mixture are divided into M spectral groups depending on their temperature dependence. Accurate MGFSK databases are constructed for combustion gases, such as CO2 and H2O. This paper includes a detailed mathematical development of the new method, method of database construction, and sample heat transfer calculations for 1D inhomogeneous gas mixtures with step changes in temperature and species mole fractions. Performance and accuracy are compared to LBL and plain FSK calculations. The new method achieves high accuracy in radiative heat transfer calculations in participating media containing extreme inhomogeneities in both temperature and mole fractions using as few as M 2 spectral groups for each gas species, accompanied by several orders of magnitude lower computational expense as compared to LBL solutions. DOI: 10.1115/1.2909612

Modeling nongray gas-phase and soot radiation in luminous turbulent nonpremixed jet flames

Much progress has been made in radiative heat transfer modeling with respect to treatment of nongray radiation from both gas-phase species and soot particles, while radiation modeling in turbulent flame simulations is still in its infancy. Aiming at reducing this gap, this paper introduces state-of-the-art models of gas-phase and soot radiation to turbulent flame simulations. The full-spectrum k-distribution method (Modest, M.F., 2003, Journal of Quantitative Spectroscopy & Radiative Transfer, 76, 69–83) is implemented into a three-dimensional unstructured CFD code for nongray radiation modeling. The mixture full-spectrum k-distributions including nongray absorbing soot particles are constructed from a narrow-band k-distribution database created for individual gas-phase species, and an efficient scheme is employed for their construction in CFD simulations. A detailed reaction mechanism including NO x and soot kinetics is used to predict flame structure, and a detailed soot model using a method of moments is employed to determine soot particle size distributions. A spherical-harmonic P1 approximation is invoked to solve the radiative transfer equation. An oxygen-enriched, turbulent, nonpremixed jet flame is simulated, which features large concentrations of gas-phase radiating species and soot particles. Nongray soot modeling is shown to be of greater importance than nongray gas modeling in sooty flame simulations, with gray soot models producing large errors. The nongray treatment of soot strongly influences flame temperatures in the upstream and the flame-tip region and is essential for accurate predictions of NO. The nongray treatment of gases, however, weakly influences upstream flame temperatures and, therefore, has only a small effect on NO predictions. The effect of nongray soot radiation on flame temperature is also substantial in downstream regions where the soot concentration is small. Limitations of the P1 approximation are discussed for the jet flame configuration; the P1 approximation yields large errors in the spatial distribution of the computed radiative heat flux for highly anisotropic radiation fields such as those in flames with localized, near-opaque soot regions.

Treatment of Wall Emission in the Narrow-Band Based Multiscale Full-Spectrum k-Distribution Method

The multiscale full-spectrum k-distribution (MSFSK) method has become a promising method for radiative heat transfer in inhomogeneous media. In this paper a new scheme is proposed to extend the MSFSK’s ability in dealing with boundary wall emission by distributing this emission across the different gas scales. This scheme pursues the overlap concept of the MSFSK method and requires no changes in the original MSFSK formulation. A boundary emission distribution function is introduced and two approaches of evaluating the function are outlined. The first approach involves line-by-line integration of the spectral absorption coefficients and is, therefore, impractical. The second approach employs a narrow-band k-distribution database to calculate all parameters as in the original narrow-banded based MSFSK formulation and is, therefore, efficient. This distribution scheme of wall emission is evaluated and the two approaches are compared by conducting sample calculations for radiative heat transfer in strongly inhomogeneous media using both the MSFSK method and the line-by-line method. DOI: 10.1115/1.2717936

A Hybrid Multi-Scale Full-Spectrum k-Distribution Method for Radiative Transfer in Inhomogeneous Gas Mixtures

A new full-spectrum k-distribution (FSK) method has been developed, which integrates the advantage of the multi-group FSK method in dealing with temperature inhomogeneities for single-species media with the advantages of the multi-scale FSK method in dealing with partial pressure inhomogeneities for gas mixtures. The new method can achieve great accuracy for radiative heat tranfer calculations in participating media with inhomogeneities in both temperature and gas concentrations. The mathematical development of the new method is described, and several sample calculations are performed to demonstrate the accuracy the new method by comparison with line-by-line calculations.

A PDF/Photon Monte Carlo Method for Radiative Heat Transfer in Turbulent Flames

Thermal radiation plays a dominant role in heat transfer for most combustion systems. Accurate predictions of radiative heat transfer are essential for the correct determination of flame temperature, flame structure, and pollutant emissions in combustion simulations. In turbulent flames, transported probability density function (PDF) methods provide a reliable treatment of nonlinear processes such as chemical reactions and radiative emission. Here a second statistical approach, a photon Monte Carlo (PMC) method, is employed to solve the radiative transfer equation (RTE). And a state-of-the-art model for spectral radiative properties, the full-spectrum k-distribution (FSK) method, is employed. The FSK method provides an efficient and accurate approach for spectral integration in radiation calculations. The resulting model is applied to simulate radiation and turbulence/radiation interactions in nonluminous turbulent non-premixed jet flames. The initial results reported here emphasize sensitivities of computed results to variations in the physical and numerical models. Results with versus without radiation, results obtained using two different RTE solvers, and results with a gray-gas approximation versus a spectral FSK method are compared.Copyright

Multi-Scale Full-Spectrum k-Distribution Method for Radiative Transfer in Inhomogeneous Gas Mixtures With Wall Emission

The multi-scale full-spectrum k-distribution (MSFSK) method has become a promising method for radiative heat transfer in inhomogeneous media. In this paper an original distribution scheme is proposed to extend the MSFSK’s ability in dealing with boundary wall emission. This scheme pursues the overlap concept of the MSFSK method and requires no changes in the original MSFSK formulation. A boundary emission overlap coefficient is introduced and two approaches of evaluating the coefficient are outlined. The distribution scheme is evaluated and the two approaches are compared by conducting sample calculations for radiative heat transfer in strongly inhomogeneous media using both the MSFSK method and the line-by-line method.Copyright