Application of the Pseudo-Spectral Time Marching Method to Blade Response Under Upstream Perturbations

Harmonic Balance (HB) or Time Spectral (TS) methods are commonly used as an alternative to conventional implicit approaches to reduce the computational cost in time-periodic flows, such as turbomachinery analyses. HB/TS approaches are based on a system of coupled equations for all the time instants. This coupling results in significant modifications in code structure to implement the HB/TS approach in conventional implicit CFD solvers. Alternatively, the Pseudo Spectral Time Marching method (PSpTM) proposes a decoupled time-marching definition of the spectral time derivative, requiring minor changes in the CFD solver structure. In this work, the PSpTM method is applied for the first time to evaluate a fan stage's aerodynamic and aeromechanic response under complex upstream distortion. The PSpTM method was implemented into an existing unstructured edge-based, second-order, compressible RANS solver. The well-established implicit second-order backward difference (BDF2) scheme is used as a benchmark. A 60-degree sector distortion screen was used to define the upstream perturbation of an isolated fan rotor. Based on the different requirements of aerodynamic and aeroelastic fan analyses, quasi-3D and 3D rotor models were used to determine the accuracy and computational cost reduction achieved with the PSpTM model. For aerodynamic analyses, a speed-up factor of up to 8 was obtained concerning the BDF2 method. Depending on the accuracy required, speed-up factors of around 2-6 can be achieved for unsteady aeroelastic and aeroacoustic analyses.