Sensitivity Analysis of Radiative Heat Loading to Tube Coil with Geometric Imperfections

Abstract

The tube coil in real fired heater after some use deviates from the ideal designed geometry. The tubes slightly bend and depending on the quality of the hooks on which they are suspended, they may also shift from their design positions. Such behaviour is not accounted for in the design procedures and it is therefore important to assess the impact of the geometry imperfections on heat loads to the tubes. It has been recently shown in (Jegla et al., 2015) that geometry imperfections may contribute to increased heat flux nonuniformity, but a systematic treatment of the impact of tube position deviations has not been reported so far. The modelling methodology adopted in the present work is based on idealized flame and refractory wall behaviour, which allows to investigate the radiative heat loading of the tube coil surface. The model conditions are in essence the same as in the landmark work of (Hottel and Sarofim, 1967). Historically the approach to solve the radiative heat transfer equation was to idealise geometries and then apply zonal method. Results were obtained by analytic solution of the heat exchange factor integrals. The only difference here is that we apply modern numerical methods that make it possible to analyse more complex geometries. The geometries analysed are 2-D cuts of a row of tubes. One of the tubes is always displaced to simulate tube coil deformations. The main aim of the study is to cover scenarios with one deformed tube in a row of ideally placed ones. The results cover an array of geometric configurations that follow from the typical tube coil arrangements used in fired heaters. Namely, the geometry of tube bends (U-turns) has two basic designs, denoted as “short- radius” and “long-radius”. These two design options define the two baseline configurations. Cylindrical furnace geometry is considered.