Efficient Routines for Obtaining Radiation View-Factor for Non-Uniform Horizons

Tariq Muneer,Stoyanka Ivanova

doi:10.3390/en13102551

Tariq Muneer, Stoyanka Ivanova

Open Access

https://doi.org/10.3390/en13102551

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Abstract

There are a large number of engineering applications wherein estimation of radiation exchange between surfaces is required. One important part of the latter procedure is to obtain the so-called ‘view factor’ of the emitter–receiver combination. The principal aim of this article is to present finite-element based procedures to obtain view factor with good time efficiency. As such routines presented here compute the view factor between a non-uniform emitter field and the receiving surface. An example of this is ground-reflected solar radiation to thermal or photovoltaic collectors, the foreground itself being composed of surfaces that have wide-ranging reflectivities. Four routines have been presented here: one based on a uniform grid for emitting and receiving surfaces using a brute force approach (Uniform Populous Grid (UPG)), and another that used non-uniform grid for the receiving surface, where cells’ sizes increased in arithmetic progression as one withdraws from the common edge (Non Uniform Grid Populous (NUGP)). The last two routines used combinations of the first two approaches with Monte-Carlo approach (Uniform Grid Monte-Carlo (UGMC) and Non Uniform Grid Monte-Carlo (NUGMC)). It was found that the NUGP algorithm was the most efficient to reduce the calculation error for the same number of computations, it was about 450 times (430 for non-uniform reflectivity) more accurate than UPG, 160 (125) times more than UGMC and 70 (60) times more than NUGMC. Finally a comparison of advantages and disadvantages of all four considered routines was added, using the following criteria: ease of programming, computational execution time, accuracy of results obtained, and predictability of the errors.

Highlights

A number of engineering applications require estimation of radiation exchange between surfaces which in turn leads to computation of ‘view factor’
We have developed a hybrid version of Monte Carlo method within the present work and shall be explained
Speaking two types of geometries were considered—surfaces that were perpendicular to each other, and those that were at an obtuse angle

Summary

Introduction

A number of engineering applications require estimation of radiation exchange between surfaces which in turn leads to computation of ‘view factor’. View factor (VF), Fi-j may be defined as the fraction of the radiation leaving surface i that is intercepted by surface j [1]. The view factor (VF) is known in engineering literature as geometry-, angle-, shape- or configuration factor. This article will be based on obtaining numerical solution for view factor using four procedures. The procedures range from the simplest routine that uses a uniform grid (brute force approach) to a procedure that efficiently combines the Monte-Carlo technique with generation of a non-uniform grid that increases the cell size as one draws away from the emitter–receiver common edge. The manner in which the non-uniform grid is generated has been refined after trialling very many procedures

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