A new control volume analysis is developed in this paper aiming at assessing the circumferential grooves effectiveness on stability improvement. The underlying mechanism for this approach is based on the hypothesis that the spike stall precursors can be triggered by the forward spillage of the rotor tip leakage flow and the onset condition of such a spillage is determined by the axial momentum balance within the rotor tip region. Control volumes are defined to quantify the axial momentum balance of the whole region where the grooves influence the flow at the rotor tip. The distribution curve of the cumulative axial momentum along the axial chord indicates that the grooves change the rotor tip loading and increase the stability, which is useful to assess the different grooved casings. As an example, multiple-groove configurations for a transonic rotor are analyzed. The results verified the cumulative axial momentum distribution for different grooved casings are in accordance with the stall margin extension variations. Another example is to prescreen the best double-groove configurations for a low speed compressor. By using this current approach, a double-groove configuration was selected and validated by experiments. These examples demonstrate the current approach has great potential in helping pre-screen circumferential grooves. As an important issue, peak efficiency changed by the grooves is discussed in the last section. Entropy production is quantitatively compared with and without grooves.

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