Multifrequential Harmonic Balance Computations for a Multistage Compressor

Abstract

To reduce the cost of unsteady flow simulations, a pseudo-spectral method (the so-called Time Spectral Method – TSM) has been proposed in the literature, which takes into account the flow time periodicity. Thanks to Fourier spectral analysis, the unsteady Navier-Stokes equations can be read as 2N+1 steady equations coupled by a source term. This approach has been implemented in the structured multiblock flow solver elsA .It efficiently computes unsteady flows and shows major improvements regarding the computational time (to a factor up to ten). However this method is only able to compute a flow field composed of one frequency and its harmonics in each blade row. The present work extends this method to a more general case in which the frequencies are not necessarily multiples of a base frequency. A multistage compressor is computed using increasing levels of complexity regarding the unsteady rows interactions. In the first step, two rows (a rotor and a stator) are modeled with an injection boundary condition accounting for the inlet guide vane wakes. Therefore, two fundamental frequencies are seen by the rotor. The influence of the frequency content in the rotor (i.e. number of harmonics of the blade passing frequencies and their combinations) is analyzed. The validation of the results is done against results obtained with classical time-marching URANS computations. Then the method is applied to the three-stage compressor CREATE.