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In this work, a circumferential groove on the shroud was applied to a centrifugal compressor and optimized to improve the stability of the compressor. To reduce the number of design variables before optimization, the position of the casing groove that maximizes the stall margin of the compressor was firstly selected. The width and height of the casing groove were optimized using the RSM (Response Surface Method) and the full factorial design of experiments to increase the stall margin further. It was observed that the optimized case with the casing groove can increase the stall margin by 7.0% but the adiabatic efficiency at the design condition decreases by 0.99%, in comparison to the reference case without the groove. Finally, the flow field of both cases with and without the optimized casing groove was compared to each other to analyze effects of the casing groove on the stall margin and design efficiency. The casing groove decreases the leakage flow across the impeller tip and weakens the tip leakage vortex, consequently decreasing the blockage near the shroud and improving the stall margin. However, it was found that the spillage of the flow from the casing groove increases the mixing loss near the shroud.

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