Performance enhancement of a vented quarter-circular solar thermal collector using proportional, proportional-integral, and proportional-integral-derivative controllers

Abstract

The present study investigates the performance of three continuous controllers (proportional, proportional-integral, proportional-integral-derivative) in a solar thermal collector with a quarter-circular configuration and an arc-shaped collector plate. The main goal is to analyze and compare the system’s performance under steady-state and transient conditions. The chamber has an adiabatic horizontal surface and a cold vertical surface. A temperature probe is positioned at the outlet port, a key difference from similar past studies, to monitor and provide feedback to the flow controller. Air entering through the inlet port dynamically adapts its speed according to the controller feedback and finally exits through the outlet port at the atmospheric condition. The numerical setup focuses on controlling convective heat transfer within the collector chamber using flow controllers to ensure the desired air temperature for process applications outside the collector chamber. This approach differs from previous literature efforts, which analyzed controller behavior in the internal thermal cooling of vented enclosures. The current study uses the finite element technique to resolve Navier-Stokes and energy equations. The probe response is assessed by applying different configurations of proportional, integral, and derivative controllers, each featuring a controlled gain. The findings reveal that only the proportional controller shows steady-state error (maximum 45.75 %) by allowing air to drive the least heat away from the collector plate. Nevertheless, it responds quickly (within 0.96 s) among the three controllers. On the other hand, both proportional-integral and proportional-integral-derivative controllers eliminate steady-state error at the expense of exhibiting a slower response (at least 4.89 s). However, they ensure the maximum thermal transference from the solar thermal collector. The present study offers a better understanding of the role of the three controllers in suitably controlling the temperature of air flowing out of a vented quarter-circular solar thermal collector. Moreover, this study suggests using the proportional controller on the solar thermal collector when faster thermal stability is required for the output process while recommending the proportional-integral or proportional-integral-derivative controller for achieving more precise heating operations. The results indicate that using the proportional controller leads to more thermal waste due to lower convective transport (Nu_avg = 5.63). Although the proportional-integral and proportional-integral-derivative controllers achieve optimal thermal transfer (Nu_avg = 11.18), the proportional-integral controller does so with minimum complexity.