Performance optimization of a three-stage cascade refrigeration system using response surface methodology

Abstract

Ultra-low-temperature refrigeration is an essential criterion for cryogenic applications, biomedical preservation, and vaccine storage. Three-stage cascade refrigeration system is a conventional solution generally preferred for applications requiring temperatures below 80 ◦ C. In this study, a detailed thermodynamic model was created using the Engineering Equation Solver (EES), and performance optimization was carried out using Response Surface Methodology (RSM) based on a Central Composite Design (CCD) that included 30 experimental runs. The evaporator and condenser temperatures at the low-, medium-, and high-temperature stages were treated as independent decision variables, whereas the coefficient of performance (COP), exergy efficiency ( η ₑₓ), total exergy destruction (˙ E ◦ dest ), and total compressor power (P comp ) served as the primary performance responses. The results indicated that the system achieved its optimal thermodynamic performance with an evaporator temperature of 90.043 C and condenser temperatures of 56.411 ◦ C, 10.941 ◦ C, and 26.077 ◦ C for the low, medium, and high-temperature cycles, respectively. Specifically, the maximum COP was recorded at 0.697, while the highest exergy efficiency reached 41.4 %. The total exergy destruction and compressor power consumption were also minimized to 5.545 kW and 11.394 kW, respectively. The main contribution of this study is employing RSM to systematically optimize the operating parameters of a conventional three-stage cascade cycle. By integrating RSM with detailed thermodynamic analysis, this study provides an optimization framework that can guide the design and operation of low-temperature cascade refrigeration systems.