Comparison of dynamic PTC thermal models using semi‐analytical and finite volume methods

Abstract

Resource potential estimation of concentrating solar power (CSP) applications with parabolic through collectors (PTC) needs to address time‐dependent heat transfer fluid (HTF) temperature at collector field's outlet. HTF temperature distribution depends on several time‐dependent variables; i.e., HTF temperature at PTC inlet, direct beam radiation, HTF flow rate and its properties, and PTC parameters, i.e., overall heat transfer coefficient. The present paper develops a time‐dependent one‐dimensional thermal model for PTCs using the analytical solution of governing partial differential equation assuming time‐invariant material properties, inlet temperature, and incident irradiation. Time‐dependency component is then integrated into the analytical solution using a time advancing numerical scheme. The results are presented in a generalized non‐dimensional form, which features familiar parameters, i.e., normalNnormalTnormalU. It is shown that in contrast to the developed semi‐analytical method, mesh‐based methods suffer from an additional error source due to smoothening around normalt∗=1. As a result, it is also showed that the developed method can use time steps 10 to 25 times larger than mesh‐based methods that achieve similar accuracy levels. In addition, developed method's each time‐step is found to be about 13 times faster. The combined speed‐up is identified as 130–325 for PTC simulations that have high variations in inlet temperature. © 2017 American Institute of Chemical Engineers Environ Prog, 37: 1191–1200, 2018