Validation of the non-linear harmonic approach for quasi-unsteady simulations in turbomachinery

Unsteady simulations, which are necessary to resolve the time-dependent flow between stationary and rotating parts in axial compressors, require an appropriate rotor-stator interface. For this interface, usually the so called domain-scaling or sliding mesh approach is used. This method requires the pitch of the simulated blades to be equal, to allow the usage of periodic boundary conditions and to cut down the number of represented blade passages in order to save computational time. This is based on the assumption that the flow is identical inside all blade passages. When it comes to the simulation of modern multi-stage compressors, it becomes almost impossible to conduct unsteady simulations with this approach, as blade numbers of different rows usually don't have common multiples. In order to overcome that problem, a new method called the nonlinear harmonic approach has been introduced. The main idea of the method is, that the different calculated flow variables are divided into a time-averaged part and another part based on a Fourier decomposition, which represents the oscillating influence of the perturbations caused by the adjacent rows. Superimposing these two parts leads to a quasi-unsteady solution. For this simulation method, the pitches of the different blade rows don't have to be changed, so that it also becomes possible to simulate multistage machines with discretizing only one passage per blade row. For this paper, a full-annulus unsteady simulation with about 40 million gridpoints was performed and the results are compared to a NLH simulation with only 1 simulated blade passage per row with 1.38 million gridpoints. Additionally, a NLH simulation with a much finer mesh with 7 million gridpoints is also included.