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Radiative heat transfer calculations using full spectrum k-distribution method for benchmark test cases

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Abstract

In the present work, the full spectrum k-distribution method (FSK) has been adopted to calculate the radiative transfer in the presence of participating gaseous medium within an enclosure. The radiative properties of the medium is obtained from the HITEMP-2010 database. Further, the radiative properties have been assembled into a monotonically increasing function using the FSK. Moreover, a look-up table has been developed for these properties at different thermodynamic states and a multi-dimensional linear interpolation technique for unavailable thermodynamic states of gases. Furthermore, the FSK method is extended for mixture of gases using different mixing models such as superposition, multiplication and hybrid models. The radiation transfer equation (RTE) is solved by finite angle method to calculate the wall heat fluxes and the divergence of radiative heat flux for various test cases in the categories of homogeneous and non-homogeneous medium having different conditions of temperature and mole-fraction. The multiplication mixing model produces most accurate results among the mixture models used here. The results obtained from FSK has been validated against benchmark solution of line by line method (LBL). The FSK method has been also successfully applied to non-homogeneous gaseous medium for single gas or mixture of gases with almost LBL accuracy at extremely less computational cost.

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Abbreviations

G :

Irradiation

\(I_\eta \) :

Spectral intensity

\(I_{b\eta }\) :

Planck function

N :

Number density of species

\(N_g\) :

Number of participating gases

Q :

Partition function

\(S_{if}\) :

Line intensity

\(T_{ref}\) :

Reference temperature

a :

Stretching function

f :

Fractional Planck function

g :

cumulative k-distribution

k :

re-ordered absorption coefficient

\(k_{if}\) :

Absorption crossection

p :

Number of quadrature points

\(p_{self}\) :

Self pressure of gas

q :

Radiative heat flux

s :

Direction vector

w :

weight for quadrature integration

\(\beta _\eta \) :

Spectral extinction coefficient

\(\delta \) :

Line shift

\(\epsilon _{w\eta }\) :

Spectral emissivity of the wall

\(\eta \) :

Wavenumber

\(\gamma \) :

Half width at half maximum

\(\gamma _{air}\) :

Air broadened half width

\(\gamma _{self}\) :

Self broadened half width

\(\kappa _\eta \) :

Spectral absorption coefficient

\(\nabla \cdot q\) :

Divergence of radiative heat flux

\(\nu _{if}\) :

Vacuum wavenumber

\(\Omega \) :

Solid angle

\(\Phi _\eta \) :

Spectral scattering phase function

\(\sigma _{s\eta }\) :

Spectral scattering coefficient

\(\eta \) :

Wavenumber

g :

gas

if :

transition from upper state f to lower state i

ref :

reference

w :

wall

air:

air

self:

self

\(P_N\) :

Spherical harmonics method

ADF:

Absorption distribution function

CDSD:

Carbon-dioxide spectroscopic database

DOM:

Discrete ordinate method

DTM:

Discrete transfer model

FSK:

Full spectrum k-distribution method

FVM:

Finite volume method

HITEMP:

High temperature spectroscopic absorption parameter

HITRAN:

High resolution transmission spectroscopic molecular absorption database

HMM:

Hybrid mixing model

HWHM:

Half width at half maximum

LBL:

Line-by-line

MMM:

Multiplication mixing model

RTE:

Radiation transfer equation

SAM:

Spectral addition method

SLW:

Spectral line weighted sum-of-gray gases model

SMM:

Superposition mixing model

WSGG:

Weighted sum-of-gray gas model

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Authors and Affiliations

  1. Numerical Experiment Laboratory (Radiation and Fluid Flow Physics), School of Mechanical and Materials Engineering, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, 175075, India

    Kamal Khemani, Shreesh Parvatikar & Pradeep Kumar

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  1. Kamal Khemani
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  2. Shreesh Parvatikar
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  3. Pradeep Kumar
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Correspondence to Pradeep Kumar.

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Khemani, K., Parvatikar, S. & Kumar, P. Radiative heat transfer calculations using full spectrum k-distribution method for benchmark test cases. Sādhanā 48, 3 (2023). https://doi.org/10.1007/s12046-022-02059-y

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