Numerical analysis of radiative transfer of a non-gray flame using statistical narrow band method

Radiative heat transfer plays a significant role where high temperature participating gases exists, such as in boilers, jet engines and internal combustion engines. Analysis of such devices should include accurate radiative heat transfer calculations. In this work, radiative heat transfer in a flame is numerically analyzed using correlated-k statistical narrow band method. In order to achieve high order accuracy, current model utilizes k-distributions which are obtained from high temperature databases, namely HITEMP. Flame model is developed on a commercial software suit -- Ansys FLUENT -- on which all energy, fluid mechanics and chemistry equations are solved simultaneously. Radiative calculations are on another platform -- MATLAB. Communications between these two software are established using TUI command of cfd software via MSDOS command. Radiative transfer equation is expressed numerically using discrete ordinates method in which 196 angular directions and 20x20 meshing are applied. In k-distributions, absorption coefficients - k values for each narrow band are presented with 7 point Gauss quadrature scheme. k-distributions are calculated for every species considered. CO$_2$ radiative properties are presented with 3 line parameters for 96 narrow bands of 25 cm$^{-1}$ bandwidth, while 367 bands are used for H$_2$O of same bandwidth. Six verification cases are tested and compared with benchmark results to show that current model is at line-by-line accuracy. A turbulent hydrocarbon flame is modeled and non-gray solution is compared with gray solution. The results indicate that coupled cfd and accurate radiative heat transfer calculations using correlated-k narrowband model is feasible and gray model overestimates the emissions from the flame when compared to non-gray model.