Robust optimization and stochastic simulation of a centrifugal blood pump under uncertain conditions

The current paper aims to robustly optimize a blood pump by reducing its sensitivity to operational uncertainties. Moreover, the effects of physical and operational uncertainties on the hydrodynamic and hemocompatibility characteristics of the robust optimized centrifugal blood pump are investigated. The baseline design is a centrifugal blood pump inspired by a commercial pump used as a left ventricular assist device. The numerical analysis is performed using the SST k-omega turbulence model and a power-law model of hemolysis. The physical and operational conditions are considered to be uncertain with Beta probability distribution functions. For quantification of the uncertainties, the non-intrusive polynomial chaos method is used, and the assessment of each stochastic parameter’s influence on the quantities of interest, that is, the sensitivity analysis, the Sobol’ indices are utilized. The primary objective of the present study is to minimize the variation in the pump's efficiency and head coefficient while maintaining the pump's operating point, ensuring that the maximum hemolysis index of the robust optimum design does not exceed that of the baseline design. To this end, robust optimization is carried out via a hybrid evolutionary algorithm. The optimization results clearly show that the robust optimum design is less sensitive to the physical and operational uncertainties. Furthermore, sensitivity analysis is in accordance with theories of turbomachines. Pump efficiency and the maximum hemolysis index are primarily influenced by the variations in blood viscosity, while the head coefficient is mainly affected by rotational speed and flow rate. The pump’s velocity field is greatly affected by the mass flow rate in the diffuser regions and the rotational speed in other zones.