The effect of pressure gradient on the collapse of cavitation bubbles in normal and reduced gravity

When water flows through hydraulic turbomachines, the local pressure can become low enough to vaporize the water and create vapor cavities. This phenomenon is called cavitation. When the cavities collapse, shock waves and liquid jets traveling through the inclusions can erode nearby solid surfaces. The collapse of cavitation bubbles has been extensively investigated in the case of a single bubble in a liquid at rest. However, in the case of hydraulic machines, the bubbles collapse in a flowing liquid subject to strong pressure gradients. The objective of this thesis is thus to investigate the effect of the pressure gradient on the collapse of a spherical cavitation bubble. We have performed a preliminary investigation of bubble dynamics in a flowing liquid with a pressure gradient. To this end, we have placed a Naca0009 hydrofoil in the test section of EPFL High Speed Cavitation Tunnel and used a high energy pulsed laser focusing technique to generate a single vapor bubble close to the hydrofoil’s leading edge. We have observed a significant influence of the pressure gradient on the bubble dynamics. Particularly, if the collapse phase occurs near the minimum pressure point, the microjet is no more directed towards the solid surface but towards the lower pressure zone in the stream wise direction. We have also observed a peculiar feature of a cluster of bubble dynamics, which behaves almost similar to a single bubble, exhibiting a microjet during its collapse. These unprecedented re- sults are of major importance for a better understanding of the cavitation erosion mechanism in hydraulic systems. The qualitative results obtained in the cavitation tunnel led to the investigation of the effect of a constant pressure gradient on the collapse of the bubble. An experimental setup is built to observe the dynamics of the bubble in water, subject to the gravity induced hydrostatic pressure gradient, and to measure the pressure fluctuation due to the shock waves. The bubbles are generated with a high energy pulsed laser and recorded with a high speed camera. The experimental setup is taken onboard parabolic flights. The parabolic manoeuvres allow the gravity level to be varied in the plane, which modulates the intensity of the pressure gradient in the liquid. The high speed movies taken during the flights reveal that vapor jets appear with the rebound bubble. An empirical law for the prediction of the volume of the jet is deducted from the experimental results. The volume of the jet, normalized with the volume of the rebound bubble, is found to be proportional to a non dimensional parameter ζ0=|∇p|Rmax/Δp, where ∇p is the pressure gradient, Rmax is the maximal bubble radius and Δp is the driving pressure. This dependance is enforced by a theoretical development based on the concept of the Kelvin impulse. Moreover, we identify a threshold for the apparition of the vapor jet: ζ > 4 · 10 − 4 . A new approach for the study of the bubble collapse is proposed: we look at how the energy in the initial cavitation bubble is partitioned between the collapse channels, namely the rebound, the shock wave, the jet, and the luminescence. The microgravity phases of the parabolic flights prevent the apparition of the jet. The collapse of the bubble, in this case, is perfectly spherically symmetric. Moreover, the energy dissipated through luminescence is negligible. Therefore, the study reduces to the energy partition between rebound and shock wave. The measurements uncover a systematic pressure dependence of the energy partition between rebound and shock. We demonstrate that these observations agree with a physical model relying on a first-order approximation of the liquid compressibility and an adiabatic treatment of the non-condensable gas inside the bubble. Using this model, we find that the energy partition between rebound and shock is dictated by a single non-dimensional parameter ξ=Δp(γ^6)/(pg0^1γ)/(ρc^2)^(1−1/γ), where γ is the adiabatic index of the non-condensable gas, pg0 is the pressure of the non-condensable gas at the maximal bubble radius, ρ is the liquid density, and c is the speed of sound in the liquid.