This paper aimed to improve the volute’s efficiency at both design point and off-design conditions by a robust shape optimization of the volute cross section. The objective function was to maximize the minimal value among volute static pressure coefficient at 90 percent, 100 percent and 110 percent of design flow rate respectively. The design parameters included the cross-section shape of volute and the radial position of volute cross-section. The optimization problem was solved by constrained optimization using response surfaces (CORS) method. During the process of optimization, three dimensional flow fields were analyzed using Navier-Stokes equations with SST model. The comparative results showed that the optimal volute had higher efficiency, higher static pressure recovery coefficient and lower total pressure loss coefficient and achieved an increase of 7 percent of efficiency at both design point and off-design conditions. The characteristic curves of the optimal volute changed more smoothly than those of the original one. The compressor’s overall efficiency also had an increase of 0.4 percent for the optimal volute.

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