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

Area of Science:

• Thermodynamics and Refrigeration Engineering
• Chemical Engineering

Background:

• Transcritical cycles are widely used in refrigeration, necessitating optimization for efficiency.
• Current empirical correlations for optimization have limitations in scope and applicability.
• Maximizing the coefficient of performance (COP) and determining optimal operating pressures are critical.

Purpose of the Study:

• To develop a general and rigorous framework for characterizing transcritical refrigeration cycles.
• To present an accurate, approximation-free mathematical expression for the COP.
• To derive a simple control function for these cycles.

Main Methods:

• Developed a general mathematical framework for COP calculation.
• The framework is independent of specific equations of state (EOS) and utilizes Helmholtz variables.
• Combined the derived expression with the Span-Wagner EOS for practical application.

Main Results:

• Presented an accurate mathematical expression for COP, dependent on compressor efficiency and fluid properties.
• The expression is universally applicable to any Helmholtz-dependent model and any EOS.
• Demonstrated application using CO2 and N2O as working fluids with the Span-Wagner EOS.

Conclusions:

• The proposed framework offers a rigorous and general method for analyzing transcritical cycles.
• The derived COP expression facilitates simplified control function development.
• This approach enhances the design, control, and operation of transcritical refrigeration systems.