Application of a Novel Pseudo-Spectral Time-Marching Method to Turbomachinery

A novel efficient method to evaluate time-periodic flows is applied to turbomachinery configurations in this paper (PSpTM). The technique reduces the overall computational cost of unsteady CFD calculations relative to conventional implicit approaches. The method is based on a pseudo-spectral definition of the time derivative rearranged in a time-marching fashion. The key advantage of this novel formulation compared with classical harmonic methods is that it requires minor modifications in the CFD solver structure. The method was implemented into an existing unstructured edge-based, second-order, compressible RANS solver. To benchmark the method, a well-established implicit time scheme based on a second-order backward implicit approach (BDF2) is used. Sample unsteady turbomachinery configurations are used to determine the accuracy and efficiency of the method. The accuracy of the solution is highly linked to the number of harmonics prescribed for the solution. An adequate level of accuracy was obtained while retaining a reduced number of harmonics, with approximately twice the number of harmonics of the unsteady perturbation. Notable savings in computational cost were observed when the PSpTM method was used with speed-up factors of between 2 and 10 with respect to the BDF2, depending on the case. However, the PSpTM method exhibits a poor periodic convergence rate, leaving room for further improvements in efficiency. However, even in its current form and with the current understanding, the method has a remarkable performance.