Characteristics of Differential Entropy Generation in a Transonic Rotor and Its Applications to Casing Treatment Designs

Casing treatments improve compressor stability but often at the expense of compressor efficiency. In this study, the differential entropy generation rate (DEGR) was applied to both efficiency evaluation and stall margin estimation. Rotor 67 was used as the compressor in this study and the simulation results were analyzed to correlate the distribution of the DEGR with the flow structures in the rotor at three rotating speeds. The characteristics of the DEGR at each speed were analyzed, exhibiting the characteristics of the flow structures at peak efficiency (PE) and near stall (NS) flow conditions. Loss analysis was conducted on the peak efficiency operating condition, particularly at 100% rotating speed. The critical state of the DEGR was investigated to identify stall occurrences on the near-stall condition. It was thus concluded that the DEGR can be a unified measure of both efficiency and stall margin. This theoretical exploration was subsequently applied to the design of casing treatments with two objectives: enhancing peak efficiency at 100% rotating speed and improving stability margins at all speeds. Two casing treatments were designed, with two circumferential grooves positioned axially at different locations. Their mechanisms for reducing the high DEGR area in the peak efficiency condition of 100% speed and suppressing an increase in DEGR during approaching stall were investigated, respectively. The results indicated that the presence of a groove near the leading edge of the blade tip can effectively suppress stall at all speeds. In order to achieve peak efficiency at high speeds, the extent of casing treatment coverage above the shock wave plays a crucial role in minimizing losses.