Analytical Infrared Delta-Four-Stream Adding Method from Invariance Principle

Abstract The single-layer solutions using a four-stream discrete ordinates method (DOM) in infrared radiative transfer (IRT) have been obtained. Two types of thermal source assumptions—Planck function exponential and linear dependence on optical depth—are considered. To calculate the IRT in multiple layers with a vertically inhomogeneous atmosphere, an analytical adding algorithm has been developed by applying the infrared invariance principle. The derived adding algorithm of the delta-four-stream DOM (δ-4DDA) can be simplified to work for the delta-two-stream DOM (δ-2DDA). The accuracy for monochromatic emissivity is investigated for both δ-2DDA and δ-4DDA. The relative error for the downward emissivity can be as high as 15% for δ-2DDA, while the error is bounded by 2% for δ-4DDA. By incorporating δ-4DDA into a radiation model with gaseous transmission, δ-4DDA is much more accurate than δ-2DDA. Also, δ-4DDA is much more efficient, since it is an analytical method. The computing time of δ-4DDA is about one-third of the corresponding inverse matrix method.

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Analytical Delta-Four-Stream Doubling–Adding Method for Radiative Transfer Parameterizations

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-12-0122.1 ◽

2013 ◽

Vol 70 (3) ◽

pp. 794-808 ◽

Cited By ~ 28

Author(s):

Feng Zhang ◽

Zhongping Shen ◽

Jiangnan Li ◽

Xiuji Zhou ◽

Leiming Ma

Keyword(s):

Optical Properties ◽

Radiative Transfer ◽

Transfer Process ◽

Solar Spectrum ◽

Single Layer ◽

Discrete Ordinates ◽

Discrete Ordinates Method ◽

Atmospheric Profile ◽

Relative Errors ◽

Transmission And Absorption

Abstract Although single-layer solutions have been obtained for the δ-four-stream discrete ordinates method (DOM) in radiative transfer, a four-stream doubling–adding method (4DA) is lacking, which enables us to calculate the radiative transfer through a vertically inhomogeneous atmosphere with multiple layers. In this work, based on the Chandrasekhar invariance principle, an analytical method of δ-4DA is proposed. When applying δ-4DA to an idealized medium with specified optical properties, the reflection, transmission, and absorption are the same if the medium is treated as either a single layer or dividing it into multiple layers. This indicates that δ-4DA is able to solve the multilayer connection properly in a radiative transfer process. In addition, the δ-4DA method has been systematically compared with the δ-two-stream doubling–adding method (δ-2DA) in the solar spectrum. For a realistic atmospheric profile with gaseous transmission considered, it is found that the accuracy of δ-4DA is superior to that of δ-2DA in most of cases, especially for the cloudy sky. The relative errors of δ-4DA are generally less than 1% in both the heating rate and flux, while the relative errors of δ-2DA can be as high as 6%.

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Numerical Modeling of Radiative Heat Transfer in Pool Fire Simulations

Heat Transfer, Part A ◽

10.1115/imece2005-81095 ◽

2005 ◽

Cited By ~ 4

Author(s):

G. Krishnamoorthy ◽

S. Borodai ◽

R. Rawat ◽

J. Spinti ◽

P. J. Smith

Keyword(s):

Heat Transfer ◽

Radiative Heat Transfer ◽

Radiative Heat ◽

Pool Fire ◽

Computational Time ◽

Discrete Ordinates ◽

Absorption Coefficients ◽

Radiation Model ◽

Discrete Ordinates Method ◽

Property Model

Different approaches to modeling radiative heat transfer in Large Eddy Simulations (LES) of a 38 cm diameter methane pool fire are compared. The P-1 radiation model and the discrete ordinates method are spatially decomposed to solve the radiative transport equation (RTE) on parallel computers. The radiative properties are obtained in the form of mean absorption coefficients from total emissivity data or of spectral absorption coefficients extracted from a narrow band model (RADCAL). The predictions are compared with experimental data. The different approaches are able to predict total radiative heat loss fractions with only a moderate loss of accuracy. However, only the discrete ordinates method is able to qualitatively predict the distributions of the radiative heat flux vectors in regions away from the fire. Results obtained from the calculations performed with the gray property model are very close to those obtained with non-gray calculations. Employing the P-1 radiation model with the gray property model provides adequate coupling between the hydrodynamics and radiative heat transfer while decreasing computational time by about 20% compared to the discrete ordinates method in moderate size grids. The computational savings associated with the P-1 model can become significant in LES calculations that are performed on large computational grids (employing hundreds to thousands of processors) to resolve structures on the scale of the pool diameter. Such resolution is necessary to capture both the large structures on the scale of the pool fire and the smaller regions of air engulfments and visible flame structures that are pivotal to characterizing soot location and temperature.

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