Development of unsteady reduced-order methods for multi-row turbomachinery flow simulation based on the computational fluids laboratory three-dimensional solver

Rotor–stator interaction (RSI) is an inherent phenomenon in multi-row turbomachinery. Unsteady reduced-order methods, such as the harmonic balance (HB) method and the space-time gradient (STG) method, have been proposed to capture RSI with fewer computational resources compared to fully unsteady simulation. In this study, the steady mixing-plane method, the HB method, and the STG method are implemented into the open-source external computational fluid laboratory three-dimensional (CFL3D) flow solver to gain the ability to predict turbomachinery flows based on solving Reynolds-averaged Navier–Stokes equations. Additionally, a rotation interpolation approach for adjacent blades is implemented for the unsteady multi-row turbomachinery simulation. For the HB method, the phase-lag periodic conditions and the temporal interpolation approach between two adjacent blade rows are integrated into CFL3D. Then, the steady mixing-plane method, the HB method, the STG method, and the fully unsteady simulation method are conducted on a quasi-three-dimensional radial slice and a three-dimensional geometry of the National Aeronautics and Space Administration Stage-35 compressor. Both the transient and time-averaged flowfield predicted by the reduced-order methods are compared with the unsteady simulations. Results indicate that the STG method and the HB method can accurately simulate the unsteady flow with better predictions of RSI impact. For the HB method, accurate prediction of transient unsteady flow requires a minimum of seven harmonics, whereas the time-averaged flow requires only five harmonics. Additionally, a quantitative assessment of computational speed is conducted, revealing that the HB method with seven harmonics achieved a speed 28 times faster than the fully unsteady simulation.