Modelo matemático baseado em equações diferenciais para compressores centrífugos que operam com CO2 próximo ao ponto crítico

Abstract

Supercritical CO2 Brayton cycles offer a promising solution for efficient and environmentally friendly power systems. However, accurately modeling the behavior of sCO2 presents challenges that make the design of highly efficient compressors difficult. On the one hand, the nonlinear properties displayed by CO2 near its critical point require the utilization of simplified and smoothed versions of equations of state in Computational Fluid Dynamics (CFD) models to ensure convergence. On the other hand, 0-D mathematical models combined with empirical pressure loss relations, commonly used in the field, are not recommended for this case. As an alternative, we propose a differential analysis that combines thermodynamics and fluid mechanics. This alternative model considers the rotor's channel geometry, incorporates the full terms of the Helmholtz equation of state (EoS), and utilizes analytical forms for the pressure losses. Simulations were conducted to showcase the performance of various rotor's geometries. It is important to note that this model does not account the pressure gradient in the radial and tangential directions of the rotor, as it is not a 3-D CFD method. The derivation of all equations used in the mathematical model is provided in the Chapter 4. The results revealed that the blade's angle of inclination, β, and the radius of curvature of the flow channel, rc, emerge as the most influential geometric factors in the compression process. Furthermore, the influence of these factors is more pronounced when the CO2 state is near the critical point. In conclusion, we recommend incorporating this novel approach during the preliminary design phase of sCO2 centrifugal compressors.