Numerical Modelling of a Pulsed Waterjet Using the Discontinuous-Galerkin-Hancock Method

Abstract

A high-pressure pulsed waterjet actuated by a high-frequency oscillating probe is studied numerically. A compressible hyperbolic flow model is derived from the Saurel model for the numerical simulation of multiphase flows with phase transition and uses the discontinuous-Galerkin-Hancock method. The model uses the mixture Euler equations and the Noble-Abel stiffened-gas equation of state as a thermodynamic closure. The phase change is driven by a difference in Gibbs free energies in the phases, leading to a stiff relaxation term representing the cavitation rate. Each phase is compressible and evolves, sharing a single pressure, velocity, and temperature. Numerical studies were carried out to analyse cavitating flows in venturi geometries, which agree with experimental data to illustrate the flow model's applicability. This thesis presents a comprehensive study of the pulsed waterjet with and without the oscillating probe. In the first scenario, the pulsed waterjet is without the oscillating probe. The nozzle produces a jet of water with a maximum velocity of 440 m/s. When the jet collides with the wall, a pronounced water hammer effect produces a peak pressure of 82.6 MPa. The jet exhibits improved performance in the second scenario with the oscillating probe. The flow of the jet of water changes physically, producing mushroom-like packets due to alternating high and low-pressure waves induced by the probe. The maximum velocity is also faster at 470 m/s. When the jet collides with the wall, the effect of the water hammer produces a maximum pressure of 110.0 MPa, which is 23% higher than the standard jet. The minimum pressure produced is 60.0 MPa. The numerical simulations found no cavitation produced by the water jet outside the nozzle. These predicted results offer insight into the complex behaviours of the pulsed waterjet.