In modern engineering, compressors play a vital role across numerous industries by enabling the delivery of fluids at elevated pressures for a variety of applications, including HVAC systems, aircraft engines, and process industries. The performance of centrifugal compressors is characterized by parameters such as flowrate, efficiency, and pressure rise. Traditional methods of evaluating compressor performance, such as physical testing, are often time-consuming and costly, making them less practical for iterative design or optimization. Advancements in Computational Fluid Dynamics (CFD) have provided a faster and more cost-effective means of assessing compressor behavior. This study presents a comprehensive CFD-based analysis of a two-stage centrifugal compressor utilized in HVAC applications aimed at predicting its performance, that is, flow factor vs head factor and flow factor vs efficiency for given rotational speeds and inlet guide vane (IGV) angle positions. Focus is on predicting surge flow points, choke flow points, mapping the compressor performance curve and mapping surge line for IGV partial opening cases at various rotational speeds of the impeller. Simulations were conducted using the ANSYS CFX software. The results illustrate the effectiveness of CFD in accurately predicting critical performance metrics and operational limits for centrifugal compressors. Additionally, the study can potentially explore the impact of different geometric modifications on compressor stability and surge margin, providing valuable insights for future design improvements.