Obstructed View Factor Calculations in Closed Cavities Using Radiation Heat Transfer

Because of relaxed requirements on laser-beam uniformity and reduced sensitivity to hydrodynamic instabilities, the ICF Program has concentrated the most of its effort, on the X-ray or indirect drive approach to ICF since 1976. In indirect drive ICF, the driver energy, from laser beams or ion beams, is first absorbed in a high-Z closed cavity which surrounds the capsule, called “hohlraum”. The material heated by the driver emits X-rays, which ultimately drive the capsule implosion. For optimally designed targets, almost 70%–80% of the driver energy can be converted to X-rays. Our main focus is on the view factor calculations for hohlraum geometry of the laser driven indirect ICF approach. This analysis is very important to symmetrically irradiate the ICF capsule. View factor calculations has different radiation heat transfer applications, especially, for indirect drive ICF. In the present work, the obstructed view factor calculations for a square geometry are performed using crossed strings method. For view factor evaluation of the radiation heat transport calculations, different methods are being used. The crossed strings method is much more reliable for simple geometries among the available view factor evaluation techniques. Different cases have been studied for the view factor calculations. These cases include the view factor calculations; if radiations are emitted either from horizontal or vertical axis and a special case for the obstructed view factor calculations. When a third surface is involved in the two already existing surfaces the view factor is said to be the obstructed one rather than the unobstructed ones. Shadow effect method is used for the obstructed view factor calculations. On the other hand, obstructed view factors are computed by subtracting the view factors to the shadows of the obstruction polygons from the unobstructed view factor. The multiple overlaps could become quite complicated while calculating obstructed view factors. Two distinct computer programmes are developed and improved using FORTRAN-90 to evaluate obstructed and unobstructed view factors, for a square geometry. Radiation emission, from both horizontal and vertical surfaces, is considered for calculation of obstructed and unobstructed view factors. The programmes are liabile of calculation for the view factors of variable length of the square square geometry in both horizontal and vertical directions, respectively. In the case of obstructed view factors calculations, certain degree of error was expected. Bench mark of the developed programmes is performed using “Summation Rule”. For the error estimation the unobstructed and obstructed view factors are compared for the similar geometry and found in good agreement, showing the accuracy and reliability of the programmes.