Application of the harmonic balance method in simulating almost periodic turbomachinery flows

The time-domain harmonic balance method is now popular in simulating unsteady turbomachinery flows. The essence of this method is that the time marching of a periodic or almost-periodic flow problem is substituted by several coupled steady computations at different time instants in the period of interest. The state-of-the-art non-uniform time sampling algorithm is adopted in our time-domain harmonic balance flow solver to simulate multistage turbomachinery unsteady flows. For a specific blade row in a multi-rows configuration, only the interactions from the adjacent blade rows are considered. A typical highly loaded 1.5 stage fan is studied as validation test case. The results showed that the nonuniform time sampling method is robust regardless of the frequencies considered. In this IGV-Rotor-Stator configuration, the interactions between the upstream-traveling rotor shock and IGV blades and the interactions between the rotor wakes and stator blades are all well captured. Thus, the timeaveraged performance map obtained by the harmonic balance method with five resolved frequencies matches well with the reference time-accurate computations. The computational time of this five-frequency harmonic balance simulation is affordable, which ensures the code can be used in performing fast unsteady analysis in the design phase. Besides, the single passage unsteady calculation with the shape-correction phase shift method applied is also performed for comparison purpose. A simple interpolation technique is proposed to update the Fourier coefficients of each disturbance as frequently as possible, thus the convergence speed is enhanced. Similar results can be obtained by this shape-correction phase shift method, making it an alternative unsteady calculation module in an in-house CFD package.