Accurate and Model-Free Control Function for a Single Stage Transcritical Refrigerator Cycle

Transcritical cycles are a successful and probed system in engineering practices, particularly in refrigeration. Therefore, their optimization is a critical factor in the design, control, and operation in order to maximize the coefficient of performance (COP) and to find the optimal pressure operating conditions. Often, this labor is faced using empirically based correlations, which are limited by their origin and the configuration of the cycle. In this regard, this work is devoted to the development of a rigorous and general framework in order to characterize the behavior and performance of a simple transcritical refrigeration cycle. An accurate mathematical expression for the COP depending on the compressor efficiency and the properties of the working fluid is presented. The expression proposed has no approximations and is relevant to any model depending on the Helmholtz variable group, being easy to combine with any equation of state (EOS), regardless of its complexity. From this expression, it is possible to derive a simple control function for transcritical refrigeration cycles. As an example, the expression is combined with the Span-Wagner EOS, presenting a comprehensive application for a transcritical cycle using CO₂ and N₂O as working fluids.