Unsteady Flow Modeling Across the Rotor/Stator Interface Using the Nonlinear Harmonic Method

Abstract

The paper presents results of the incorporation of the harmonic nonlinear method into an existing turbomachinery Navier-Stokes code. This approach, introduced by He and Ning in 1998, can be considered as a bridge between classical steady state and full unsteady calculations, providing an approximate unsteady solution at affordable calculation costs. The unsteady flow perturbation is Fourier decomposed in time, and by a casting in the frequency domain transport equations are obtained for each time frequency. The user controls the accuracy of the unsteady solution through the order of the Fourier series. Alongside the solving of the time-averaged flow steady-state equations, each frequency requires the solving of two additional sets of conservation equations (for the real and imaginary parts of each harmonic). The method is made nonlinear by the injection of the so-called deterministic stresses, resulting from all the solved frequencies, into the time-averaged flow solver. Because of the transposition to the frequency domain, only one blade channel is required like a steady flow simulation. The presented method also features a new improved treatment that enhances the flow continuity across the rotor/stator interface by a reconstruction of the harmonics and the time-averaged flow on both sides of the interface. A non-reflective treatment is applied as well at each interface. Validation for analytical and turbomachinery test cases are presented. In particular, results are compared between the harmonic method, steady-state mixing plane and full unsteady calculations. The comparison with the reference full unsteady calculation provides a quantitative indication of the accuracy of the approach, as well as the significant gain in CPU time, whereas the comparison with classical quasi-steady state solutions indicates the gain of accuracy. A multistage compressor flow is also presented to show the capabilities of the method.