Inverse Design of Thermal Systems with Predominant Radiation

当存在多种传热模式(辐射、对流和/或传导)时，高温热过程设备的设计非常复杂。当模式存在并耦合时，描述能量传递的方程是非常非线性的，并且在形式上可以是积分-微分形式。已经开发了非常复杂的程序来模拟这样的系统。这些程序运行成本很高，并且需要很大的内存和存储容量。它们基于正向设计；即，指定几何图形和边界条件，并计算得到的温度和传热率。如果这些都不能令人满意，则改变几何图形或其他条件，并重新运行程序。重复这一过程，直到达到预期的结果，然后固定设计。逆设计方法指定期望的结果，并直接找到在没有迭代的情况下实现该结果所需的条件。然而，逆技术的数学不如正问题的数学发达，因为描述逆设计的方程是不正常的(近乎奇异的)。基于我们以前应用于辐射系统逆设计的成功方法，我们建议将逆设计技术扩展到包括燃烧源在内的具有显著辐射换热的多模式换热的更复杂的情况，其中的数学不仅是逆的，而且是非线性的。如果结果成功，将导致更有效的高温设备的实用设计，如涡轮发动机和工业/公用炉膛和锅炉。

Design of equipment for high-temperature thermal processes is very complex when multiple modes of heat transfer (radiation, convection and/or conduction) are present. When the modes are present and coupled, the equations describing energy transfer are very nonlinear, and may be integro-differential in form. Very sophisticated programs have been developed to model such systems. These programs are expensive to run and require large memory and storage capacity . They are based on forward design; that is, the geometry and boundary conditions are specified, and the resulting temperatures and rates of heat transfer are computed. If these are unsatisfactory, then the geometry or other conditions are altered, and the program is rerun. This process is repeated until the desired outcome is reached and the design is then fixed. An inverse design method specifies the desired outcome, and directly finds the conditions necessary to achieve this outcome without iteration. However, the mathematics of inverse techniques is less developed than is the case for forward problems, because the equations describing inverse design are ill-behaved (near-singular). Based on successful methods we have previously applied to inverse design of radiating systems, we propose to extend inverse design techniques to the much more complex case of multimode heat transfer with significant radiative transfer including combustion sources, where the mathematics becomes not only inverse, but non-linear. The results, if successful, will lead to much more efficient practical design of high-temperature equipment such as turbine engines and industrial/utility furnaces and boilers.