Investigation of Blade Tip Interaction With Casing Treatment in a Transonic Compressor—Part II: Numerical Results

A single stage transonic axial compressor was equipped with a casing treatment consisting of 3.5 axial slots per rotor pitch in order to investigate its influence on stall margin characteristics, as well as on the rotor near tip flow field, both numerically and experimentally. Contrary to most other studies, a generic casing treatment (CT) was designed to provide optimal optical access in the immediate vicinity of the CT, rather than for maximum benefit in terms of stall margin extension. The second part of this two-part paper deals with the numerical developments and their validation, carried out in order to efficiently perform time-accurate casing treatment simulations. The numerical developments focus on the extension of an existing coupling algorithm in order to carry out unsteady calculations with any exterior geometry coupled to the main flow passage (in this case a single slot), having an arbitrary pitch. This extension is done by incorporating frequency domain, phase-lagged boundary conditions into this coupling procedure. Whereas the phase lag approach itself is well established and validated for standard rotor-stator calculations, its application to casing treatment simulations is new. Its capabilities and validation will be demonstrated on the given compressor configuration, making extensive use of the detailed particle image velocimetry flow field measurements near the rotor tip. Instantaneous data at all measurement planes will be compared for different rotor positions with respect to the stationary slots in order to evaluate the time-dependent interaction between the rotor and the casing treatment.