Deflection and stresses in absorber tube of solar parabolic trough due to circumferential and axial flux variations on absorber tube supported at multiple points

In a parabolic trough system, the portion of the absorber tube facing the sun receives incident rays directly, whereas the other side receives concentrated rays resulting in circumferential non-uniform flux distribution. Near the sun facing end of the absorber tube, the flux also varies along the length depending upon the rim angle of trough and angle of incidence of sun rays. This circumferential and axial distribution of the solar flux and variation in the fluid temperature result in non-uniform temperature of the absorber tube. The temperature gradient, thus produced, can lead to bending of the tube which may pose the risk of glass cover damage. The absorber tube considered in this work is equidistantly supported at hinges. An analytical expression for deflection in the central axis of the absorber tube (from the focal line of the trough) is derived using circumferential and axial distribution of solar flux incorporating Gaussian sun shape and optical errors. Expressions for radial, circumferential and axial distributions of normal stress and strain induced in the absorber tube are also derived. Effects of angle of incidence of sun rays, optical errors, rim angle of trough, desired rise in fluid temperature and types of supports on deflection and stresses have been studied keeping solar radiation, ambient conditions, fluid, material of absorber tube, receiver's dimensions, aperture width and distance between the consecutive supports fixed. For a desired rise of 0.1 °C/m (averaged over the receiver's length) in the fluid temperature, maximum deflections of −0.57 mm and −1.51 mm have been found out for two types of supports which elevate to −2.71 mm and −7.14 mm respectively when the fluid temperature-rise increases to 1 °C/m (positive and negative signs indicate deflections away and towards the vertex line of the trough respectively). Maximum compressive (negative) stresses increase from 19.29 MPa to 66.61 MPa and tensile (positive) stresses increase from 10.14 MPa to 49.67 MPa as fluid temperature-rise increases from 0.1 °C/m to 1 °C/m. It is found that axial variation in solar flux near the sun facing end of absorber tube plays an important role in deflection.