Abstract: The supercritical carbon dioxide (SCO₂) Brayton cycle power generation system is highly promising due to its high energy conversion efficiency and environmental benefits. The sealing performance of rotating machinery, such as centrifugal compressors within the system, directly impacts the power generation efficiency and service life, making the development of high-performance seals crucial for this application. The rotating machinery in the SCO₂ Brayton cycle power generation system typically operates under complex conditions characterized by high speed, high pressure, and high vibration, often near the critical point of carbon dioxide. Under these conditions, carbon dioxide exhibits significant variations in its physical properties, such as high density and low viscosity. The abrupt changes in pressure and physical properties can lead to severe disturbances in film thickness, making gas film face seals with rigid surfaces prone to failure modes, such as face contact and seal ring fragmentation. To address these issues and further enhance the shock resistance and adaptability of seals, this study focused on a novel flexible dam compliant foil face gas seal. Based on the theories of gas lubrication and elasticity mechanics, and considering the real gas effect and turbulence effect, a gas-elastic coupling lubrication model for an SCO₂ flexible dam compliant foil face gas seal was established. This model was used to investigate the coupling relationship between the film pressure on the sealing face and the deformation of the foil, revealing the coordinated operating mechanism of seal deformation. A comparative analysis of the performance differences among four different seal dam models was conducted, and further studies were carried out on the impact of operating parameters and foil structure parameters on sealing performance. The results showed that the novel flexible dam compliant foil face gas seal, with its fully flexible sealing face structure, significantly enhanced shock resistance and adaptability compared to rigid dam foil face gas seals. The fluid dynamic pressure effect generated in the gaps between the foils of the flexible dam, as well as the secondary dynamic pressure effect caused by the wave deformation of the foil face under dynamic pressure, effectively improved the seal's opening force and gas film stiffness. While the presence of gaps between the foils in the dam might slightly increase the leakage rate, this increase was significantly reduced under high rotational speeds. In contrast, the opening force, gas film stiffness and stiffness-leakage ratio were markedly enhanced, highlighting the advantages of the SCO₂ flexible dam compliant foil face gas seal under high rotational speed conditions. Through the rational design of the foil face structure, the overall sealing performance could be effectively improved.