Computational and reduced-order modelling of elastic wave-driven impulse enhancement in pulsed jets through passively flexible nozzles

Abstract

Elastic wave propagation and energy exchange in passively deforming cylindrical nozzles are investigated through three-dimensional, two-way fluid-structure interaction simulations. Flexible nozzles with varying stiffness (Eh = 75 to 500 N/m, E is Young's modulus, h is thickness) are subjected to pulsatile jet inflow at low Reynolds number (Re ~ 4400). Increased flexibility reduces deformation-wave speed following MoensKorteweg scaling, prolonging the expansion phase. This delayed expansion enhances jet entrainment and elastic energy storage while suppressing early shear-layer roll-up and vortex formation. During contraction, released elastic energy increases jet acceleration and vortex formation. For the most flexible nozzle, primary vortex-ring circulation increases by 52%, vortex convection distance by 9%, and peak outlet kinetic energy flux 4.6-fold versus a rigid nozzle, resulting in a 62% increase in total hydrodynamic impulse. A reduced-order model represents the coupled response as a lumped store-and-release oscillator, derived as a single-mode projection of the inviscid one-dimensional wave equation and closed at the exit by two terms: (i) an inertial end correction that adds the external fluid column of length Le = R accelerating with the jet, and (ii) a vortex-radiation damping term, active only during ejection, determined by the discharged-jet momentum theorem. This damping reproduces the post-overshoot velocity decay undamped closures fail to capture. The model predicts the simulated resonance frequency within 6% and momentum impulse within 4% across Eh = 75 to 500 N/m, and recovers energy histories. Outlet kinetic energy flux is predicted within 6% for the three stiffer nozzles and 14% for the most compliant.