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• A high-fidelity model of CO 2 booster refrigeration systems is proposed. • Critical but normally unavailable in practice variables are inferred. • Model has a minimum requirement on real measurements as inputs. • Onsite data from three UK supermarkets are used for demonstration. • Data integrity and thermodynamic laws are secured in the model. Supermarket refrigeration systems adopting traditional refrigerants with high global warming potential (GWP) have impacts on global warming for indirect and direct greenhouse gases (GHG) emissions. CO 2 is a popular low-GWP alternative. The transcritical operation of CO 2 systems worsens their energy performance, but provides recoverable heat as a heat source to reduce gas consumption. To evaluate operation performance, data-driven models, trained by historical data, are weak in implementation with datasets outside the scope of training data; in contrast, theoretical models have better extrapolation ability to calculate all operation conditions of CO 2 systems at supermarket. Existing theoretical modeling approaches often lack validation against the limited public-access data, which reduces model reliability for further applications, and adopt oversimplified inference methods for unmeasured variables, which increases the risks of breaking thermodynamic laws and lowering model accuracy. This study therefore develops a steady-state theoretical model for CO 2 booster refrigeration systems validated against field measurements from three UK supermarkets. The available measurements are utilized to the best level to ensure model accuracy and physical interpretability. Proposed methods to infer missing variables in CO 2 systems include condenser outlet temperature, evaporating temperature, compressor isentropic efficiency and compressor mass flow rate. Results show that proposed inference methods enhance the abilities of the proposed modeling approach to ensure data integrity, avoid breaking thermodynamic laws, and improve model accuracy by reflecting real-time actual values of unmeasured variables rather than rough assumptions. The proposed modeling approach provides satisfactory accuracy validated using high-resolution measurements across the whole year from three real supermarkets. [ABSTRACT FROM AUTHOR]

• A two-stage gas-coupled Stirling/pulse tube refrigerator with a second-stage active phase shifter is developed. • The effect of the active phase shifter on the acoustic power and phase distribution is investigated. • The regulation of the inter-stage refrigeration capacity shift by the active phase shifter phase and amplitude is analyzed. • Experiment results are carried out to verify the theoretical and simulated analyses. The Stirling/pulse tube cryocooler (SPC) is one of the most promising cryocoolers for space applications due to its advantages like high efficiency and long lifetime. The second pulse tube stage is coaxial pneumatically coupled in series with the first Stirling stage. The SPC possesses a distinctive capability to dynamically adjust the inter-stage refrigeration capacity by actively controlling the Stirling displacer in the first stage. This enables the SPC to effectively cater to varying heat loads over time. Nevertheless, the investigation into the regulation mechanism of the second-stage phase shifter on inter-stage refrigeration capacity shift is hindered by the presence of the second-stage passive phase shifter. This manuscript proposes an SPC with a second-stage active phase shifter (APS), which can actively control the phase difference between the pressure wave and mass flow at the second-stage hot end of the pulse tube in real time. The effect of the APS phase and amplitude on the inter-stage refrigeration capacity shift is analyzed using the theoretical and numerical model proven by the experiment. The first experimentally reported SPC with a second-stage APS demonstrates a refrigeration capacity of 0.22 W at 20 K plus 3.11 W at 70 K, requiring a compressor electrical power of 220 W. The SPC achieves a no-load minimum temperature of 13.5 K. [ABSTRACT FROM AUTHOR]

The variable-geometry ejector (VGE) is feasible for unstable heat-source utilization; the ejector can be adjusted to its design point to obtain high efficiency. Moreover, as the adjustable nozzle in the VGE significantly affects the performance of the ejector, a theoretical model is necessary to evaluate VGE performance. In this study, a two-dimensional theoretical model was proposed based on an adjustable-nozzle theory. Method of characteristics was employed to accurately predict the driving-flow development in the mixing section. In addition, the suction-flow velocity distribution on the effective area was considered. The proposed model was validated by employing the data from literature and additional experimental data obtained from a VGE test setup using R134a. The validation result shows that the proposed model predicts the ejector performance accurately; moreover, the model is more adaptive while the nozzle configuration changes. The theoretical model, proposed herein, is practical for the design and application of the VGE. [ABSTRACT FROM AUTHOR]