Optimizing Jet Impulse by Tuning the Wave Propagation in Bio-Inspired Flexible Nozzles

Cephalopods, such as squids and jellyfish, achieve high propulsive efficiency through pulsed jets expelled from their flexible, deformable funnels. The wave propagation along the flexible funnel influences the strength and convection speed of the jet vortex rings and the associated jet impulse. Inspired by this biological mechanism, we design passive flexible nozzles for underwater propulsion and analyze their propulsive performance using three-dimensional strongly coupled partitioned fluid-structure interaction simulations based on the Arbitrary Lagrangian-Eulerian framework. We investigate how nozzle flexibility and shape influence impulse generation, as well as nonlinear deformations governed by wave propagation and vortex ring formation. To optimize performance, we parameterize nozzle geometries using spline curves defined by control points and apply a multi-fidelity Bayesian optimization (BO) with spline control points and wall thickness as design variables. For the multi-fidelity BO, we do an initial design space exploration using our simulation framework and evaluate optimal solutions for subsequent nozzle generations using experimental load cell measurements. The resulting optimized nozzle exhibits enhanced impulse performance compared to both a baseline flexible cylindrical nozzle and rigid counterparts. We observe that the optimized jet impulse is strongly correlated with the tuned wave propagation speed through the nozzle. Interestingly, the optimised nozzle geometry also mirrors key morphological features observed in natural cephalopod funnels.