A robust Monte Carlo based ray-tracing approach for the calculation of view factors in arbitrary three-dimensional geometries

摘要

Drawing on ideas from computer-based graphical representations, the conventional use of finite element based approaches to represent three-dimensional (3D) geometries of interest is challenged in this work by the use of a modest suite of geometric "primitives" (i.e., generic shapes such as a sphere, a cone, a flat surface) that in combination via a set of affine transformations can provide a realistic approximation to almost any conceivable 3D body. Initially, a robust C++program using the latest CPU vectorization technologies [e.g., OpenMP and streaming single instruction multiple data (SIMD) extension]) was developed and validated against a broad range (around a dozen) of known analytical view factor solutions. The impact of ray density level, random number generators, and "fast" numerical approximations for widely used trigonometric functions were all extensively examined at this stage in terms of solution accuracy and required run-time. Extensive use was made at this stage of the in-built program profiling capabilities within the XCode 4.2 IDE to identify "choke points" within the evolving computer code. The program was subsequently interfaced to the ANSYS Polyflow package to develop a fully conjugate heat transfer model of an operational furnace used to draw specialized polymer optical fibers. The Monte Carlo ray-tracing (MCRT) calculated view factors for all surfaces within the drawing furnace were found to be in excellent agreement with those calculated by numerical solution of the integral equations used to define the various view factors, while a good fit was obtained between the heat transfer model and measured experimental temperature profiles for the case of a nondeforming preform. A wide range of preform drawing cases was then examined, with rapid convergence (within 3-4 iterations) obtained between the furnace heat transfer calculations and the updating of the various view factor estimates.