A flow capacity function approach for centrifugal impeller inlet design

A useful strategy for reducing loss and improving efficiency during the preliminary design of centrifugal compressors involves reducing the relative Mach number at the tip of the impeller inlet (M_w1t). However, existing flow capacity functions (FCFs) usually produce local M_w1t solutions owing to the difficulty in providing appropriate mathematical settings for the constraint parameter, including the inlet flow blockage and nonuniformity. This study defines and validates a new FCF approach for solving the minimum M_w1t and key geometric parameters at centrifugal impeller inlets using first-principles based modeling and three-dimensional computational fluid dynamics (CFD) simulations. The new FCF is developed based on the inlet hub radius as opposed to the inlet shape factor, and it incorporates the boundary layer thickness, blade taper, and inlet meridional end-wall curvatures to account for inlet blockage and flow nonuniformity. The utility and capability of the newly developed FCF method were demonstrated by a one-dimensional analysis and rigorous three-dimensional CFD calculations over a range of flow coefficients. The numerical results reveal that the newly developed FCF (1) yields a smaller inlet relative Mach number across the entire span than the previous FCFs, (2) achieves a 3.96% improvement in isentropic efficiency and 5.86% increase in the total pressure ratio at a flow coefficient of 0.0363 relative to the previous FCFs, and (3) has high-fidelity design accuracy and is competitive with the two-dimensional throughflow approach.