Explicit Analytical Expression for Solar Flux Distribution on an Undeflected Absorber Tube of Parabolic Trough Concentrator Considering Sun-Shape and Optical Errors

The absorber tube of the parabolic trough receives the concentrated sun-rays only on the portion facing the reflector. It leads to nonuniformity in the temperature of absorber tube. Thus, the material of tube expands differentially and the tube experiences compression and tension in its different parts. It leads to bending of the tube and the glass cover can be broken. The bending can be reduced by (i) reducing the circumferential nonuniformity in absorber's temperature (using material of high thermal conductivity) and (ii) reducing the nonuniformity in solar flux distribution (using appropriate rim angle of trough). In most of the available studies, Monte Carlo Ray Tracing software has been used to calculate the distribution of solar flux and few studies have used analytical approach. In the present work, an explicit analytical expression is derived for finding the distribution of solar flux accounting for the sun-shape and optical errors. Using it, the design calculations can be carried out in significantly lesser time and lesser computational effort. The explicit expression is also useful in validating the results computed by softwares. The methodology has been verified with the already reported results. The effects of optical errors, rim angle, and aperture width of trough on the solar flux distribution and total flux availability for absorber tube have also been studied. From the calculations, it is found that for Schott 2008 PTR70 receiver (absorber tube with 70 mm outer diameter), 126 deg, 135 deg, and 139 deg, respectively, are the appropriate rim angles corresponding to minimum circumferential nonuniformity in solar flux distribution for 3 m, 6 m, and 9 m aperture width of trough. However, 72 deg, 100 deg, and 112 deg, respectively, are the appropriate rim angles corresponding to the maximum solar flux at absorber tube for 3 m, 6 m, and 9 m aperture width of trough. Considering both the circumferential nonuniformity and the total solar flux availability, 100 deg, 120 deg, and 130 deg, respectively, are the best rim angles.