SBIR Phase I: Development of an Accurate and Efficient Radiative Transfer Model in a Body-Fitted Coordinate System

*** 9661586刘本小企业创新研究第一阶段项目将开发一种适用于任何复杂几何形状的贴体坐标（BFC）系统的准确高效的辐射传递模型。在锅炉、炉膛、火箭发动机等高温燃烧系统中，辐射传热是主要的传热方式。由于数学特性的不同，对于复杂的问题，辐射传递方程与流体输运控制方程的完全耦合和同时求解一直是非常困难的。本文将采用RTE的偶宇称公式（EPF）结合离散坐标法（DOM）来模拟辐射传热。与传统的RTE不同，DOM的EPF是一个二阶微分方程。将利用中心差分格式和迎风格式对离散坐标方程进行空间离散化，并对这两种格式的性能进行研究。为了研究该辐射模型在BFC系统中的准确性，将考虑几个不规则几何的基准问题，并将该模型的解与其他可用解进行比较。由于EPF和描述流体动力学的控制方程之间具有相同的数学结构，因此本辐射模型对于复杂几何问题具有很高的精度和效率。待建立的辐射传递模型将具有与流体输运方程相同的数学结构，两者在数值上完全兼容。这将有助于同时求解燃烧系统中的RTE和其他控制方程。如果目前的模型在第一阶段成功验证，它将在第二阶段扩展到3D。此外，由于其巨大的优势，它将被实现到商业计算流体动力学（CFD）代码中

*** 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 .***