An analysis of the symmetry issue in the ℓ-distribution method of gas radiation in non-uniform gaseous media

- ℓ-distribution/ICE scheme model is considered.
- It suffers from symmetry issues when applied in highly non-isothermal media.
- A criterion is proposed to handle the symmetry issue.
- The criterion is general and theoretically justified.
- It can be simplified within the ℓ-distribution framework.
- Its application improves the ℓ-distribution method.
- It can be applied together with a large number of gas radiation models.

The recently proposed ℓ-distribution/ICE (Iterative Copula Evaluation) method of gas radiation suffers from symmetry issues when applied in highly non-isothermal and non-homogeneous gaseous media. This problem is studied in a detailed theoretical way. The objective of the present paper is: 1/to provide a mathematical analysis of this problem of symmetry and, 2/to suggest a decisive factor, defined in terms of the ratio between the narrow band Planck and Rosseland mean absorption coefficients, to handle this issue. Comparisons of model predictions with reference LBL calculations show that the proposed criterion improves the accuracy of the intuitive ICE method for applications in highly non-uniform gases at high temperatures.