Radiative Heat Transfer Calculations using Full Spectrum k-Distribution Method for Benchmark Test Cases

TL;DR

This paper presents an efficient full spectrum k-distribution method for calculating radiative heat transfer in gaseous media, validated against line-by-line data, and applicable to complex, non-homogeneous conditions with high accuracy.

Contribution

The study develops an extended FSK method with a look-up table and interpolation for various thermodynamic states, and compares different gas mixture models, achieving near line-by-line accuracy at reduced computational cost.

Findings

FSK method matches line-by-line accuracy for radiative transfer.

Multiplication mixing model yields the most accurate results for gas mixtures.

The method efficiently handles non-homogeneous, non-isothermal, non-isobaric media.

Abstract

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