Casing treatments (CTs) have been proved to beneficially affect the behavior of tip clearance flow and compressor stability. This paper presents the design of casing treatment for a mixed-flow compressor with a very small tip gap of 0.1mm. In the first part, the potential of applying two traditional types of casing treatments, i.e. circumferential grooves and axial slots, to enhance the stability of a mixed-flow compressor is investigated. The flow details in the reference compressor with smooth casing are examined first. It is found that a separating vortex is formed due to the reversed flow on the blade suction side near the rotor trailing edge at the near-stall point. It is supposed to be responsible for the decrease in total pressure ratio when the compressor approaches to stall. The numerical stall, i.e. the breakdown of the simulation, is initiated from the spillage of tip leakage flow over the rotor blade leading edge. The effect of circumferential grooves on the compressor performances is not remarkable. The implement of axial slots ameliorates the total pressure ratio and extend the flow range substantially, but with higher efficiency penalty than the circumferential grooves. The recirculation formed in the axial skewed slots eliminates the separation vortex near the trailing edge and suppresses the spillage of the tip leakage flow forward the rotor leading edge simultaneously. The axial skewed slots are further designed and optimized numerically by DoE (Design of Experiments). As DoE factors the axial length, the height, the open area ratio, and the number per blade passage of the slots are varied. Their effects on the two target values stall margin and polytropic efficiency are investigated. The plot of stall margin improvement (SMI) with a function of the peak efficiency improvement (PEI) indicates that the SMI changes reversely with the PE. There are two trends in the correlation curves of SMI with PE. For the configurations with the open area ratio of 20%, the SMI is changed from 9% to 23% with 1% decrease in PE by varying other three factors. For the CTs with the open area ratio of 60% the augment in SMI from 17.8% to 26.3% produces extra efficiency loss of 4.2%.
