Explicit expressions for temperature distribution and deflection in absorber tube of solar parabolic trough concentrator

The portion of absorber tube of parabolic trough, facing the reflector, receives concentrated rays and the portion facing the sun receives direct incident rays resulting in circumferential non-uniform flux distribution. It leads to circumferential non-uniformity in the temperature of absorber tube. Thus, the absorber tube experiences differential expansion that results in tension and compression in its different parts leading to bending of the tube. Using the distribution of solar flux on the absorber tube incorporating the effects of Gaussian sun shape and optical errors, explicit expressions for finding the absorber's temperature distribution and corresponding deflection in the central axis of absorber tube (from the focal line of trough) are derived in the current work. Deflection due to the weight of the absorber tube is also accounted. The absorber tube is considered to be supported at its ends. To allow the absorber tube to elongate freely, supports are chosen such that they can move axially. Two types of conditions are considered: (i) the ends of absorber tube are allowed to rotate in the planes passing through focal line of the trough and (ii) rotation is not allowed. Keeping solar radiation, ambient conditions, receiver's dimensions, trough's aperture width, fluid and material's properties of absorber tube fixed, calculations have been carried out to study the effects of desired rise in fluid temperature, optical errors and rim angle of trough on absorber's temperature distribution and deflection in the absorber tube. For the chosen system dimensions, fluid's properties and absorber's material, as fluid's temperature rise increases from 0.1 °C/m (averaged over the receiver's length) to 0.5 °C/m, the maximum circumferential difference in absorber's temperature increases from 9 °C to 23 °C and the maximum deflection increases from −5.9 mm to −13.7 mm (positive and negative signs indicate deflections away and towards the vertex line of the trough respectively). As optical errors increase from 0 mrad to 20 mrad, the maximum circumferential difference in absorber's temperature decreases from 14 °C to 11 °C and the maximum deflection decreases from −8.8 mm to −7.2 mm. As rim angle increases from 60° to 140°, the maximum circumferential difference in absorber's temperature decreases from 16 °C to 7 °C and the maximum deflection decreases from −9.0 mm to −1.7 mm.