*** 9661586 Liu This Small Business Innovation Research Phase I project will develop an accurate and efficient radiative transfer model suitable for any complicated geometry in a body-fitted coordinate (BFC) system. Radiative heat transfer is the dominant heat transfer mode in boilers, furnaces, rocket engines, and other high-temperature combustion systems. Due to different mathematical characteristics, entirely coupled and simultaneous solution of the radiative transfer equation (RTE) and the governing equations for fluid transport has been very difficult for complicated problems. In this proposal, radiative heat transfer will be simulated by the even parity formulation (EPF) of RTE in combination with the discrete ordinates method (DOM). Unlike the conventional RTE, the EPF of the DOM is a second-order differential equation. A central difference scheme and a upwind scheme will be utilized to discretize the discrete ordinates equations spatially and performance from these two schemes will be studied. To investigate the accuracy of the present radiation model in a BFC system, several benchmark problems with irregular geometries will be considered and the solutions from the present model will be compared with other available solutions. Due to the same mathematical structure between the EPF and the governing equations for describing the fluid dynamics, the present radiation model is expected to be very accurate and efficient for problems with complicated geometries. The radiative transfer model to be developed will have the same mathematical structure as the fluid transport equations and they are entirely compatible with each other numerically. This will facilitate simultaneous solution of the RTE and other governing equations in a combustion system. If the present model is successfully proven in Phase I, it will be extended to a 3D in Phase II. Furthermore, it will be implemented into a commercial computational fluid dynamics (CFD) code due to its tremendous advantages .***
