Assessment of discrete ordinates method for radiative transfer in cylindrical furnaces

The solution accuracy of S-n or Discrete Ordinates Method (DOM) was assessed by comparing its predictions with exact solutions reported earlier on a cylindrical enclosure problem with steep temperature gradients. The enclosure has interior black walls and an absorbing-emitting medium of constant properties. Predictive accuracy was investigated for two angular quadrature schemes: 1) the S-n discrete ordinates approximation (S-2 and S-4) and 2) the modified piecewise constant angular (PCA) approximation. Comparative testing shows that all predictions agree well with the exact solutions and that S-n approximations produce slightly better accuracy than the modified PCA approximation in radiative heat nux densities. The sensitivity of the predictions of the DOM to radiative properties was also examined by performing calculations for various absorption coefficients. Comparative testing shows that the discrepancies between the predictions increase with the coefficient and hence the accuracy of a radiation model should be tested in isolation from radiative property estimation.