Non-Dimensional Parameter Development For Transcritical Cycles

Increased commercial interest with regard to carbon dioxide’s use in transcritical cycles has led to numerous modifications to the basic vapor compression cycle. The transcritical refrigeration cycle is characterized by the fact that supercritical high-side pressure is an optimization variable. Most cycle adaptations have been conceived with the intent of facilitating optimal high side pressure control. Depending upon operating range, improper highside pressure definition may lead to power penalties in excess of 10%. A critical element in system design and optimization involves the mechanism for dynamic computation of the optimal high side pressure. Common approaches to this problem involve heuristics and empirical correlation. Unfortunately, such approaches are not phenomena-based. Application of such techniques limits the flexibility afforded to the control system. The approach introduced relies upon fundamental thermodynamic considerations. Optimal high side pressure is analyzed through consideration of real gas properties. These evaluations have resulted in the identification of key non-dimensional parameters that drive high-side pressure optimization. A combination of non-dimensional parameters and selected system observations form an effective computational mechanism suitable for process control. A database of thermodynamic properties for CO2 confirms the subject model’s integrity and utility. Accuracy comparable to empirical models is achievable with far less complexity. The fundamental nature of the model allows for a common optimization means independent of operating specification and working fluid. NOMENCLATURE a: compressor performance correlation coefficient(s) A: Ratio of compressor performance coefficients b: Adiabatic compression power constant C: Mass Heat Capacity COP: Coefficient of Performance f: 1/COP h: Enthalpy k: Heat Capacity Ratio, Cp/Cv m: Mass Flow P: Pressure Q: Energy Flow R: Ideal Gas Constant T: Temperature x: Mass Fraction Liquid y: Non-dimensional, Pr Z: Compressibility Greek Symbols β: Compressor energy-flow parameter γ: Adiabatic compression power, (k-1)/k ∆Hlv: Latent heat of vaporization η: Adiabatic compressor efficiency Θ: Non-dimensional parameter, Φ+Ψ Φ: Non-dimensional parameter Ψ: Non-dimensional parameter Subscripts h: high-pressure side l: low-pressure side p: constant pressure r: ratio v: constant volume evap: evaporator comp: compressor gc: gas cooler Subscripts consistent with Figure 1 1: Compressor Outlet 2: Gas Cooler Outlet 3: High Pressure SLHX outlet 4: JT Valve Outlet 5: Evaporator Outlet 6: Low Pressure SLHX outlet Superscripts ig: Ideal gas r: Residual property INTRODUCTION Growing concern over hydrofluorocarbon contributions to global warming has led to consideration of alternative, natural refrigerants. Among natural working fluids, CO2 represents a fluid of particular interest because of low toxicity, cost, availability and thermophysical properties. CO2 applications of particular commercial significance include automotive air conditioning, residential water heat pumps and cascade refrigeration systems. By definition, a transcritical cycle possesses a gas cooler and evaporator operating above and below the critical pressure, respectively. Effective gas cooler operation at supercritical pressures results in a control problem foreign to common vapor compression cycles. Compressor discharge pressure is no longer defined by conditions of saturation within the condenser. In contrast, the transcritical cycle should be optimized with respect to compressor discharge pressure. As a consequence, the minimization of cycle power requires a control strategy incorporating dynamic optimization. Many physical modifications to the transcritical vapor compression cycle have been proposed with the intent of facilitating optimal high side pressure control. Previous approaches to this problem have centered upon empirical correlation and/or control heuristics. Past thermodynamic considerations have suffered from a failure to tie system observations to the characteristics associated with optimal high side pressure. The primary deficiencies associated with previous effort are a result of model inflexibility. The nature of this inflexibility stems from numerical complexity and a lack of connectivity to the underlying thermodynamic phenomena. The subject model defines critical non-dimensional parameters, which will enable transcritical systems to continuously operate at minimum power consumption. A further objective of this work is to establish a computational framework for online control and optimization that is adaptable to any design, working fluid or operating criteria. System Description and Problem Definition JT Valve Suction Line Heat Exchanger Evaporator Compressor