Reduced-dimensional prediction method for the axial aerodynamic forces in the off-design operation of near-critical CO₂ centrifugal compressors

In the high-load centrifugal compressor of near-critical CO₂ (NcCO₂) power-generation cycle, the overload of axial aerodynamic force causes significant harms to the structural safety and operational stability of turbomachinery components. Based on a transcritical CO₂ compressor of a MWt-class simple recuperated cycle, we numerically studied the aero-thermodynamic characteristics of back-cavity leakage, and discussed the physical model of the axial aerodynamic forces in off-design operation of NcCO₂ compressors. Finally, reduced-dimensional prediction method for the axial aerodynamic forces in the near-critical CO₂ compressor was developed. Wherein, the Japikse's method was used to estimate the primary aerodynamic loads of centrifugal impeller, and a 1-D radial equilibrium equation with angular velocity ratio was derived to predict the thrust force acting on the impeller back disk. Furtherly, based on the near-wall distribution pattern of angular velocities and physical property of Rankine vortex, a semi-empirical model of angular velocity ratio was introduced and completed the model of back-disk force. In validation, the reduced-dimensional prediction method exhibited satisfactory accuracy with perfectly acceptable errors compared to the refined CFD simulations. Thereby, a reduced-dimensional prediction method for the axial aerodynamic forces was developed for the economical and agile analysis of NcCO₂ compressors in engineering practices.