Improvement of full-spectrum k-distribution method using quadrature transformation

Abstract

The full-spectrum k-distribution (FSK) method can provide great accuracy combined with outstanding numerical efficiency for the evaluation of radiative transfer in nonhomogeneous nongray media. However, k-distributions cover several orders of magnitude, making their efficient numerical integration difficult. Different quadrature schemes give different levels of accuracy as compared to exact values unless a large number of quadrature points is employed. To improve efficient implementation of the FSK method, an integration method with quadrature transformation is investigated in this work. Several radiative heat transfer calculations were carried out to test the effects of quadrature transformation on accuracy at different thermodynamic states. Results show that for most thermodynamic states employing the transformation for the integration of k-values can greatly reduce the number of required quadrature points while maintaining good accuracy. Based on this, the FSK look-up table previously developed by the authors was updated to include k-values corresponding to the new quadrature points with transformation. Two scaled flames are used to verify both the accuracy and efficiency of the updated table.