Michał Palacz
Mathematical modelling of transcritical fluid flow
inside a two-phase ejector for refrigeration systems
Ph.D. Thesis
Faculty of Energy and Environmental Engineering
Silesian University of Technology
Abstract
Due to the F-gas regulation, the phase-out of the synthetic refrigerants is the matter of fact. The limitation of the application of the high global warming potential refrigerants (GWP) is the main reason of the revival of the natural working fluids. Carbon dioxide (R744) is considered as one of the most promising alternative for the synthetic refrigerants. The GWP of the carbon dioxide is equal to 1 by definition. The thermodynamic properties of CO2
are perfect for the refrigeration systems. Nevertheless, the critical temperature of the CO2
is relatively low. Therefore, the carbon dioxide refrigeration systems installed in the warm climate zone operate in transcritical mode. Consequently, the throttling losses of the system significantly affect the COP of the system. To limit the throttling losses, and in consequence increase the COP of the system, the two-phase ejectors were introduced into the refrigera-tion system. According to the recent studies, that modificarefrigera-tion of the refrigerarefrigera-tion system improves COP by up to 30%. However, the improvement is possible only with the properly designed ejector. Hence, the computational tools for the ejector analysis are highly desirable. The formulation of such computational tool was the main scope of this thesis. Therefore, to formulate the computational approach that can be robust and effective for the ejector sim-ulation, four partial goals were defined for this thesis.
In order to automatise the computational process, the author of this thesis developed the efficient computational platform named ejectorPL. The application of the ejectorPL for the simulation of the fluid flow inside ejector guaranteed the consistent and repeating compu-tational results for various operating regimes and ejector geometries. Then, the fidelity of the HEM applied for the two-phase flow simulation was analysed. That model accuracy was evaluated by comparison of the measured motive nozzle mass flow rates with the computed ones. The measured mass flow rates were captured during the experimental investigation of the CO2ejectors, performed at SINTEF Energy Research laboratory. The range of the
operat-ing conditions used for the HEM accuracy evaluation included supercritical and subcritical motive nozzle operating regimes. Hence, the performed analysis showed the application range of HEM for the simulation of the two-phase flow ejectors for the supermarket refrig-eration units. The results of that investigation were published in the International Journal of Refrigeration.
Next, the ejectorPL software was combined with the optimisation algorithms, i.e. genetic algorithm (GA) and evolutionary algorithm (EA). That combination was used for the ejector mixing shape optimisation. The goal of the optimisation was to maximise the ejector effi-ciency. Thus, the suitable objective function (OF) was defined. In addition, the various OF setups were employed for the optimisation. First, the OF was formulated to take into ac-count two operating regimes, i.e. on- and off-design. Then, the efficiency of the optimised ejectors was verified for the different set up of the operating conditions that were not covered in OF. The results of the optimisation showed the negligible ejector efficiency improvements. Nevertheless, the presented methodology was considered as the effective approach for the ejector shape design. The more detailed description of the methodology and the optimisa-tion results was published in the Applied Thermal Engineering.
The previously proposed methodology was also employed for the full ejector shape opti-misation. Analogically to the mixing section shape optimisation, the OF was formulated to maximise the ejector performance. During the full ejector shape optimisation, the number of the optimised parameters was two times higher than for the mixing section shape optimi-sation. In this case, the mixing section shape was optimised simultaneously with the motive and suction nozzles. As a result of that optimisation, the ejector efficiency was significantly improved. The efficiency of the optimised ejectors was higher than 30% for the operating conditions used in the objective function, as well as for the operating regimes used for the verification performance. The full outcome of that study were published in the International Journal of Refrigeration.
The range of the operating regimes that were used for the optimisation was limited by the application range the HEM used for the two-phase flow simulations. To overcome those limitations, more advanced homogeneous relaxation model (HRM) was implemented into the ejectorPL. In that model, the nonequilibrium phase change is taken into account by the introduction of the relaxation time. Therefore, the metastable behaviour of the expanding fluid was included in that model. Similar to the HEM application range analysis, the HRM model accuracy was assessed for the range of the motive nozzle operating conditions typical for the modern refrigeration system. Analogically, to HEM accuracy assessment, the HRM fidelity was evaluated by comparison of the computed and measured motive nozzle mass flow rates. The comparison of the HEM and HRM performance showed that the accuracy of the HRM is higher for the subcritical regimes. Moreover, the HRM fidelity can be further improved by adaptation of the relaxation time definition. The results of the HEM and HRM accuracy analysis were published in the Applied Thermal Engineering.
