Mathematical model of an innovative double U-tube sun-tracked PTC and its experimental verification

The paper describes in detail an in-house mathematical model, allowing to simulate the operation of an innovative double U-tube sun-tracked Parabolic Trough Collector (PTC). The analysed solar collector is characterized by a modular structure and is designed for low-temperature applications. A double U-tube pipe is used inside the evacuated collector tube, which is the study's main novelty. The energy balance equations are derived for a single U-tube, assuming the uniform flow of the Heat Transfer Fluid (HTF) through all collector U-tubes. The resulting differential equations are solved by approximating the derivatives with appropriate differential schemes. The proposed one-dimensional model with distributed parameters makes it possible to simulate the collector operation under transient conditions. A test stand with the analysed PTC is built to verify the obtained results accuracy and perform an extensive experimental verification. The measured and computed temperature courses of the HTF at the collector outlet are compared for different operation conditions. For all analysed cases, a fully satisfactory agreement between measurement and computational results is obtained. Estimating the accuracy of the developed model results with the measurements, the Root Mean Squared Errors (RMSE) are calculated for three measurement series (for selected days). The obtained RMSE values are 0.375 °C, 0.349 °C, and 0.632 °C for the selected day of January, May, and August, respectively. It proves the high efficiency of the proposed model. The proposed PTC model's main advantage is its simplicity and low computational cost, allowing for its online application.