A numerical study of radiation effects in gas turbine combustion chambers

Abstract

The finite volume, FV, method for solving the radiative transfer equation for gray gases in axisymmetric geometries was implemented to study the effect of radiation in gas turbine combustion chambers. Both a first order and a higher order interpolation scheme for determining the intensity at the cell face from the values at the cell centers were implemented. Two cases for the radiative transfer within a cylinder that have exact solutions were calculated. Solutions obtained with the FV method for the radiative intensity within the interior of the cylinder and the heat flux along the cylinder wall were compared with the calculated exact solution. Solutions with the higher order interpolation scheme were generally more accurate, but not significantly more accurate than those obtained with the first order interpolation scheme. The radiative heat flux in a cylindrical furnace was calculated and compared to measured data. The magnitude of the calculated heat flux was observed to be strongly dependent on the assumed value for the absorption coefficient. Calculations of the coupled radiation field and flow field for a premixed combustor configuration were performed. An angular resolution of 16 discrete angles was found to provide sufficient accuracy. With an assumed absorption coefficient of 0.5m, radiation was found to alter the temperature field by up to 100K and to contribute up to 16.5 % of the total wall heat flux. Background Radiation emanating from hot combustion gases in gas turbine engines contributes a significant percentage of the overall heat transfer to the wall liners of combustion chambers. In addition, the local temperature within 'Research Scientist, Chair of Heat and Power Technology; currently Research Scientist Taitech, Inc. Senior Member AIAA. t Graduate Student, Chair of Heat and Power Technology. •t-Professor, Chair of Heat and Power Technology. Copyright © 1998 American Institute of Aeronautics and Astronautics, Inc. All rights reserved. the flame zone is influenced by the amount of radiant energy it exchanges with neighboring regions and the liner wall. Emissions of pollutants, especially NOx, are a strong function of the local temperature. Hence, accurate predictions of pollutant emissions may also require consideration of transfer of thermal radiation. Modern methods for evaluating multidimensional radiative heat transfer are based on solving the radiative transfer equation (RTE). The equation is the statement of conservation of energy applied to a monochromatic pencil (bundle) of radiation propagating in an emitting, absorbing and scattering medium. The discrete ordinates method^ M* and the finite volume method^l'ffi.Io] are two popular methods for solving the RTE. The objectives of this study are to implement the finite volume method of Chui, Raithby and HughesPl>[4] for solving the RTE for gray gases in axisymmetric geometries and to investigate the effect of radiation on the surface heat flux of combustion chambers. The numerical solution technique is first reviewed including: 1) the underlying theory with special attention paid to cylindrical coordinate systems, 2) the simplifications allowed for axisymmetric conditions, 3) the first order and higher order interpolation schemes that were used to obtain values for the radiative intensity at the cell face from the values at the surrounding cell centers and 4) the boundary conditions employed. Results from the calculations of the radiative heat transfer of four cases are then presented. Two cases have an exact solution and were used to compare the performance of the two interpolation schemes. The third case has experimental data for comparison and the last case considers the coupled flow and radiation fields for a combustor configuration. Finite Volume Method The primitive variable for the analysis is the radiative intensity, I (R,sj, that represents the flow of energy from radiation per unit time, per unit area normal to the rays, per unit solid angle and per unit wavelength. The radiative intensity is a function of its spatial position, its direction and its wavelength. Direction is typically discretized using a spherical coordinate system so that the direction vector (s) is defined in terms of a polar angle (0 < 6 < -K] and an azimuthal angle (0 < tp < 2?r) that are measured with respect to a set of orthogonal base vectors. The solid angle, fi, of a surface seen from a particular point is defined as the ratio of the projected surface area normal to the direction vector between the point and surface to the distance squared between the point and surface. The solid angle is equal to the projected area when the surface is projected onto the unit sphere. The direction vector (s) illustrated in Fig. 1 is associated with the infinitesimal solid angle