Abstarct: The growing issue of global warming and its resulting environmental threats is the primary concern of this study. Therefore, centrifugal compressor chillers are examined in this research as an influential system in terms of electrical energy consumption and the use of refrigerants with high Global Warming Potential (GWP). Centrifugal chiller compressors perform the compression process using centrifugal force. Previous studies have analyzed the thermodynamic performance of single-stage and two-stage centrifugal chiller cycles. However, due to the sensitivity of centrifugal compressors to the mass flow rate, in this study, besides the thermodynamic analysis of the chiller cycle, the centrifugal compressor is also examined theoretically and through Computational Fluid Dynamics (CFD). Thermodynamic modeling in this study was performed using the EES software, and the results were validated through MATLAB and other research findings. In this research, single-stage and two-stage refrigeration cycles with different refrigerants were studied. The EES modeling results indicated that, with the same mass flow rate and pressure ratio, in the cycle with R134a refrigerant, the coefficient of performance (COP) of the two-stage cycle increased by 8% compared to the single-stage, and for R744 refrigerant, the increase was 23%. Furthermore, the intermediate pressure in two-stage cycles was investigated, and it was determined that the highest COP under similar conditions occurs when the intermediate pressure is 1.7 times the evaporator pressure. Various refrigerants were examined, and among them, R134a had the highest COP, while R744 had the lowest. This study also evaluated the effects of subcooling and superheating. Subcooling the refrigerant exiting the condenser by 8°C increased the COP by approximately 3%. The economic analysis showed that for a given capacity, centrifugal chillers require twice the investment compared to reciprocating chillers, while operating and maintenance costs are 30% lower, leading to a 50% reduction in CO₂ emissions. Contrary to thermodynamic modeling, where compressor efficiency remains constant with increasing mass flow rate and pressure ratio, this study investigated changes in the COP with variations in isentropic efficiency. Under ideal conditions, a 50% increase in cooling capacity results in a 5% drop in isentropic efficiency, and consequently, the COP of both single-stage and two-stage systems decreases by 6.5%. Compressor performance maps were provided according to cycle conditions, and numerical analysis was used to investigate Mach number values in the impeller under varying mass flow rates.