Design and optimization of multi-stage centrifugal compressor with uncertainty quantification of off-design performances

The use of multi-stage centrifugal compressors carries out a leading role in oil and gas process applications. Green operation and market competitiveness require the use of low-cost reliable compression units with high efficiencies and wide operating range. The preliminary design of these machines is a fundamental step towards the achievements of such performance goals. A methodology is presented for the design optimization of multi-stage centrifugal compressors with prediction of the compressor map and estimation of the uncertainty limits. A one-dimensional (1D) design tool has been developed: it automatically generates a multi-stage radial compressor that satisfies the target machine requirements based on a few input parameters: the suction quantities and the fluid properties. The design procedure allows for a customizable compressor design, where critical parameters such as the stage number, shaft number, stage pressure ratio and impeller outlet angle are either user-defined or automatically calculated by the software via design algorithms. The compressor geometry is calculated at the nominal design point. The compressor performance map is then assessed using the method proposed by Casey-Robinson (2013), and the approach developed by Al-Busaidi-Pilidis (2016) to evaluate the global compressor performance for an arbitrary multi-stage configuration. The off-design performance method relies on empirical correlations calibrated on the performance maps of a large number of single-stage centrifugal compressors. These coefficients present a large uncertainty due to the scatter of the original experimental dataset from which they were obtained. An uncertainty quantification study was conducted using two different uncertainty propagation techniques: Monte Carlo method (MCM) and generalized Polynomial Chaos Expansion (gPCE). In this way, the predicted performance maps are bounded by error bars representing 95% confidence intervals. This information represents an essential tool for the designer during the preliminary design of multi-stage multi-shaft centrifugal compressors. Finally, the 1D design procedure has been coupled to an in-house optimizer based on evolutionary algorithms and specifically designed for the enhancement of turbomachinery components. The complete design procedure has been applied to a multi-stage industrial compressor test case. A multi-objective optimization that targets maximum compressor efficiency and flow range has been performed. The results of the optimization show the existence of optimum compressor architectures and how the Pareto fronts evolve depending on the number of stages and shafts.