Full-spectrum K-distribution Model Research Articles

A wavenumber subinterval grouping strategy compatible with non-gray metal wall boundaries used in multi-scale multi-group full spectrum k-distribution gas radiation model

In the present work, strategies for the grouping of wavenumber subintervals were extended to deal with the compatibility of multi-scale multi-group full-spectrum k-distribution model with non-gray wall boundaries. The main idea is to enhance the correlated-k characteristics of absorption spectra of H2O-CO2 mixtures and emission spectra of non-gray wall within each divided group. The improvements in the calculation accuracies of radiative heat flux on the wall resulting from the new grouping strategy were evaluated using a series of 1D cases, in which combustion gases with strong inhomogeneities of temperature, pressure and molar ratio of water vapor to carbon dioxide were bounded by non-gray walls. The non-gray walls are assumed to be different metal materials with various surface states and temperatures. Finally, evaluation of the wavenumber subinterval grouping strategy was presented based on calculation of thermal imaging for directional radiation transfer from hot supersonic exhaust plume to a metal plate.

A full spectrum k-distribution based non-gray radiative property model for unburnt char

By using the concept of weighted sum of four gray particles and spectrum k-distribution (WSGP-SK), a non-gray radiative property model for unburnt char particles is developed. Based on the carbon burnout kinetic model for structure during oxidation, and the linear mixed approximation theory for complex index of refraction, spectral radiative properties of unburnt char particles are first calculated as function of the burnout ratio by Mie theory. Referring to the full spectrum k-distribution model, k-distribution is applied to reorder absorption and scattering efficiencies of particles. Then, weighting factors and efficiency factors of the non-gray radiative property model are directly obtained from Gaussian integral points of k-distribution. The model is validated against the benchmark solutions of line-by-line (LBL) model. Maximum relative errors of this model are 3% and 15% for radiative heat fluxes and source terms in non-isothermal inhomogeneous particulate media, respectively. The assumption of linearly varying radiative properties with burnout ratio (Lockwood et al. 1986) will result in a predicted deviation of 53% for radiative source terms. Results also show that this non-gray model is remarkably better than the Planck mean method. Moreover, a satisfactory comparison with LBL solutions is achieved in the gas and particle mixture by combining the non-gray WSGG-SK model (Guo et al. 2015). As a radiation sub-model, this non-gray radiative property model can significantly improve prediction accuracy of radiative heat transfer in oxy-fuel combustion.

High fidelity radiative heat transfer models for high-pressure laminar hydrogen–air diffusion flames

Radiative heat transfer is studied numerically for high-pressure laminar H2–air jet diffusion flames, with pressure ranging from 1 to 30 bar. Water vapour is assumed to be the only radiatively participating species. Two different radiation models are employed, the first being the full spectrum k-distribution model together with conventional Radiative Transfer Equation (RTE) solvers. Narrowband k-distributions of water vapour are calculated and databased from the HITEMP 2010 database, which claims to retain accuracy up to 4000 K. The full-spectrum k-distributions are assembled from their narrowband counterparts to yield high accuracy with little additional computational cost. The RTE is solved using various spherical harmonics methods, such as P1, simplified P3 (SP3) and simplified P5 (SP5). The resulting partial differential equations as well as other transport equations in the laminar diffusion flames are discretized with the finite-volume method in OpenFOAM®. The second radiation model is a Photon Monte Carlo (PMC) method coupled with a line-by-line spectral model. The PMC absorption coefficient database is derived from the same spectroscopy database as the k-distribution methods. A time blending scheme is used to reduce PMC calculations at each time step. Differential diffusion effects, which are important in laminar hydrogen flames, are also included in the scalar transport equations. It was found that the optically thin approximation overpredicts radiative heat loss at elevated pressures. Peak flame temperature is less affected by radiation because of faster chemical reactions at high pressures. Significant cooling effects are observed at downstream locations. As pressure increases, the performance of RTE models starts to deviate due to increased optical thickness. SPN models perform only marginally better than P1 because P1 is adequate except at very high pressure.

Full-Spectrum k-Distribution Model for Radiation in Gas Based on Multi-Group Methods

The k-distribution method applied in narrow band and wide band is extended to the full spectrum based on spectroscopic datebase HITEMP, educing the full-spectrum k-distribution model. Absorption coefficents in this model are reordered into a smooth,monotonically increasing function such that the intensity calculations are performed only once for each absorption coefficent value and the resulting computations are immensely more efficent.Accuracy of this model is examined for cases ranging from homogeneous one-dimensional carbon dioxide to inhomogeneous ones with simultaneous variations in temperature. Comparision with line-by-line calculations (LBL) and narrow-band k-distribution (NBK) method as well as wide-band k-distribution (WBK) method shows that the full-spectrum k-distribution model is exact for homogeneous media, although the errors are greater than the other two models. After dividing the absorption coefficients into several groups according to their temperature dependence, the full-spectrum k-distribution model achieves line-by-line accuracy for gases inhomogeneous in temperature, accompanied by lower computational expense as compared to NBK model or WBK model. It is worth noting that a new grouping scheme is provided in this paper.

Relationship between the spectral line based weighted-sum-of-gray-gases model and the full spectrum k-distribution model

The relationship between the spectral line based weighted-sum-of-gray-gases (SLW) model and the full-spectrum k-distribution (FSK) model in isothermal and homogeneous media is investigated in this paper. The SLW transfer equation can be derived from the FSK transfer equation expressed in the k-distribution function without approximation. It confirms that the SLW model is equivalent to the FSK model in the k-distribution function form. The numerical implementation of the SLW relies on a somewhat arbitrary discretization of the absorption cross section whereas the FSK model finds the spectrally integrated intensity by integration over the smoothly varying cumulative-k distribution function using a Gaussian quadrature scheme. The latter is therefore in general more efficient as a fewer number of gray gases is required to achieve a prescribed accuracy. Sample numerical calculations were conducted to demonstrate the different efficiency of these two methods. The FSK model is found more accurate than the SLW model in radiation transfer in H2O; however, the SLW model is more accurate in media containing CO2 as the only radiating gas due to its explicit treatment of ‘clear gas.’

Thermal radiation heat transfer in one- and two-dimensional enclosures using the spectral collocation method with full spectrum k-distribution model

Thermal radiation transfer in one-dimensional parallel plates and two-dimensional rectangle enclosures filled with non-gray gases, namely CO2, H2O, or their mixtures, is calculated using the spectral collocation method with full spectrum k-distribution model (SCM–FSK). The k-distribution model is a promising model for treating the spectral properties of an absorbing–emitting medium, representing an alternative to line-by-line calculations which reduces the number of radiative transfer equation (RTE) evaluations from the order of a million to the order of ten without any significant loss of accuracy. Moreover, the full spectrum k-distribution model, as a global model, can be easily combined with other numerical methods to solve the RTE. The spectral collocation method (SCM) which is used to solve partial differential equations is combined with FSK for the present problems. In order to test the accuracy and efficiency of SCM–FSK, several gas radiation transfer problems involving isothermal/non-isothermal and homogeneous/inhomogeneous non-gray gases are examined. The results obtained by SCM–FSK are assessed by comparing the predictions with line by line results. These comparisons indicate that SCM–FSK is sufficiently accurate and convenient for engineering calculations.

A Narrow Band-Based Multiscale Multigroup Full-Spectrum k-Distribution Method for Radiative Transfer in Nonhomogeneous Gas-Soot Mixtures

The full-spectrum k-distribution (FSK) approach has become a promising method for radiative heat transfer calculations in strongly nongray participating media, due to its ability to achieve high accuracy at a tiny fraction of the line-by-line (LBL) computational cost. However, inhomogeneities in temperature, total pressure, and component mole fractions severely challenge the accuracy of the FSK approach. The objective of this paper is to develop a narrow band-based hybrid FSK model that is accurate for radiation calculations in combustion systems containing both molecular gases and nongray particles such as soot with strong temperature and mole fraction inhomogeneities. This method combines the advantages of the multigroup FSK method for temperature inhomogeneities in a single species, and the modified multiscale FSK method for concentration inhomogeneities in gas-soot mixtures. In this new method, each species is considered as one scale; the absorption coefficients within each narrow band of every gas scale are divided into M exclusive spectral groups, depending on their temperature dependence. Accurate and compact narrow band multigroup databases are constructed for combustion gases such as CO2 and H2O. Sample calculations are performed for a 1D medium and also for a 2D axisymmetric combustion flame. The narrow band-based hybrid method is observed to accurately predict heat transfer from extremely inhomogeneous gas-soot mixtures with/without wall emission, yielding close-to-LBL accuracy.