Influence of Circumferential Spans of Heat Flux Distributions on Secondary Flow, Heat Transfer and Friction Factors for a Linear Focusing Solar Collector Type Absorber Tube

Abstract

Solar collector absorber tubes play a critical role in converting incident solar heat flux into absorbed thermal energy and transferring it to a heat transfer fluid. In this study a single horizontally orientated absorber tube was investigated numerically in terms of the influence of different circumferential spans of symmetrical and asymmetrical heat flux distributions on buoyancy-driven secondary flow, internal heat transfer and friction factor characteristics. Three types of circumferential heat flux boundaries were considered, namely fully uniform, partial uniform and sinusoidal non-uniform heat flux distributions. Both gravitational symmetry and asymmetry for non-uniform heat flux distributions were investigated to cover symmetry angles in terms of the gravitational field (g) of 0° (symmetrical case), 20°, 30°, 40° and 60°. Different sized stainless steel absorber tubes having a length of 10 m, and inner diameters of 62.7 mm, 52.5 mm, 40.9 mm and 35.1 mm were considered. Three dimensional steady-state simulations were performed for water as working fluid, covering laminar flow Reynolds numbers ranging from 130 to 2200, as well as for turbulent flow Reynolds numbers ranging from 3030 to 202 600. Buoyancy effects, temperature dependent fluid thermal properties, tube-wall heat conduction and the external wall heat losses by convection and radiation were taken into consideration. Average internal heat transfer coefficients, local internal heat transfer coefficients, Richardson numbers and overall friction factors were obtained for different angular spans of incident heat flux, inlet fluid temperatures, heat flux intensities and outer wall thermal conditions Laminar flow results indicated that the angular span, angular position, and intensity of the applied external heat flux all have significant influences on the buoyancy induced mixed convection inside the tube. This resulted in significant variations in the internal heat transfer coefficients and the friction factor which are not well described by classical empirical correlations. Buoyancy induced secondary flow significantly enhanced the internal heat transfer coefficient and significantly increased the friction factor compared to forced convection cases. Higher heat transfer coefficients and friction factors were obtained for non-uniform heat flux distributions compared to uniform heat flux distributions and were found to be dependent on the angle span and position of the heat flux. Higher inlet temperatures resulted in increased Nusselt numbers and lower friction factors, while higher external heat loss resulted in lower Nusselts numbers and lower friction factors. An increase in the asymmetry of the heat flux distribution resulted in a reduction of the Nusselt number and friction factor. Even though turbulent flow cases with a Reynolds number range of approximately 3000 to 9000 were also influenced by buoyancy driven secondary flow, and followed the same parameter trends, it occurred to a lesser extent compared to the laminar flow cases. Turbulent flow cases with Reynolds numbers higher than 9100, exhibited little dependence on secondary flow effects and indicates the suitability of classical fully uniform heat flux heat transfer and friction factor correlations for highly turbulent flow irrespective of the distribution or intensity of the heat flux.