Design and multi-objective optimization of a dual layer recirculation casing treatment for a transonic centrifugal compressor

To enhance the stability and aerodynamic performance of a transonic centrifugal compressor, a dual layer recirculation casing treatment (dual-RCT) was numerically developed in this study using steady simulations. Compared with a conventional single-RCT, the dual-RCT mitigated downstream blockage, increased the recirculation flow, and reduced the inducer tip loading, resulting in a modest expansion of the mass flow range and a marginal improvement in peak pressure ratio, while maintaining a comparable peak efficiency. A multi-objective optimization framework was constructed using OLHS sampling, a Kriging surrogate model, and the NSGA-II algorithm, with mass flow range, peak efficiency, and peak pressure ratio defined as the objective functions. Through linear regression, the three-objective problem was reduced to a two-objective formulation. The optimized results indicated that the maximum achievable mass flow range reached 229% of that of the smooth-wall (SW) compressor. Further analysis showed that the first recirculation slot achieved optimal performance when located upstream of the shock and leakage vortex interaction, whereas the second slot was most effective when positioned downstream of the shock impingement on the suction surface. Flow field analysis revealed that the dual-RCT deflected both the shock wave and the leakage vortex, delayed the formation of low Mach number regions, and suppressed wall vortex development, thereby improving the inducer flow characteristics. However, the large low Mach number region was shifted farther downstream of the second slot and developed more rapidly, while mixing losses and other dissipative effects also contributed to increased entropy generation, resulting in an overall efficiency reduction of approximately 0.56-2.8%.