Session T13: Cavitation, Nucleation, Collapse, Coalescence I

A Comprehensive Model for Cavitation Nuclei: Homogeneous and Heterogeneous Analysis using Gibbs Free Energy

A general Gibbs free energy approach is proposed to model cavitation inception for homogeneous and heterogeneous nucleation. The effect of gas content is explored using the ideal gas law. Analytic solutions of the critical radius for incipient and desinent cases are obtained as functions of gas content. Hysteresis between the incipient and desinent cases is explored. The initial diameter as a function of critical pressure is also expressed as an analytic solution, a relationship that is widely used in CSM experiments. The presence of impurities, modeled as idealized rough geometry is analyzed. The effect of roughness and gas content is found to reduce the barriers to nucleation and stabilize the bubble nuclei. A model is proposed for the rate of the cumulative nuclei histogram with respect to bubble diameter which recovers the $-4$ power law observed experimentally.   

Laser-induced cavitation in normal, critical and supercritical Helium

Laser-induced cavitation dynamics have been thoroughly studied in many liquids under saturation conditions, while in some applications, such as supercritical fluid, cavitation can occur at supercritical conditions.  Supercritical fluids offer two significant features in studying cavitation, surface tension vanishes and the buoyancy force becomes negligible due to the convergence of liquid and gas densities.  Herein, we experimentally investigate laser-induced cavitation dynamics in Helium-4 at temperatures below and higher than critical temperature, these temperatures are sufficiently low to ensure liquid purity and absence of dissolved air.  Our optical-access cryogenic device is described in Speirs et al. [1].  The device uses four windows, with two used for illumination and ultra-high-speed image capturing, with frame rates up to 7 million frames per second.  A different window is used to transmit a pulsed Nd:YAG laser beam, focused by a parabolic mirror, to generate the cavitation bubble.   We measure shock speeds and show cavitation generated by reflected shocks.   The collapse dynamics are compared to the prevailing models, showing significant deviations.   We also show myriad of microbubbles generated in the spinodal regime.   

Tip vortex cavitation at incipient conditions of a confined elliptic hydrofoil

LES of a confined elliptic hydrofoil is performed at Re=900000 under incipient conditions. A polydisperse model is used to track the concentration of bubbles of different sizes, and to investigate the effects of water quality on inception. It was found that inception is strongly dependent on the amounts of nuclei in the freestream. When the flow is deplete of nuclei, inception is an intermittent event confined to a position very close to the hydrofoil's tip. However, when the flow is rich in nuclei, a larger portion of the tip vortex cavitates, as well as part of the suction side very close to the leading edge of the hydrofoil. Probability density functions revealed that cavitation occurs in any region experiencing a pressure field lower than vapor pressure when the flow is rich in nuclei, while extremely low values of pressure (usually kPa of tension) are required to make a flow deplete of nuclei cavitate.   

Supersonic jetting from cavitation bubble pair interaction

Cavitation bubbles in a heterogeneous environment are known to develop jets that penetrate through the bubble. Jets with supersonic velocities with respect to the bubble content have been found for bubbles collapsing very close to elastic and rigid boundaries. Here, we demonstrate that two bubbles that are identical in volume but are created out of phase at a proper distance can accelerate a jet to supersonic velocities. Compared to a rigid boundary, the high-speed jet formed by bubble pairs does not atomize while penetrating the body of the bubble. The fluid dynamics leading to this ultrafast needle-shaped jet are studied with high-speed imaging at two million frames per second. We present evidence that this ultrafast needle jet is induced by a singularity created by the concave collapse of the elongated neck of the second bubble that is further amplified through shock wave emission. Compressible viscous flow simulations reveal a favorable comparison with the experiments and explain the narrow parameter range where the supersonic jetting is found.   

Bubble bursting jets are driven by the purely inertial collapse of gas cavities

The analysis of numerical simulations describing the collapse of capillary cavities reveals that the jets originated from the bursting of bubbles are driven by the condition that the dimensionless liquid flow rate per unit length directed towards the axis of symmetry, q_∞, remains nearly constant in time. This observation, which is justified in physical terms because liquid inertia and mass conservation prevents appreciable changes in q_∞ during the short time scale characterizing the jet ejection process, together with the fact that bubble bursting jets are produced from the bottom of a conical cavity, justify the purely inertial scalings for the jet width and velocity found here, r_jet∝(q_∞τ)^1/2 and v_jet∝(q_∞/τ)^1/2, with τ indicating the dimensionless time after the jet is ejected, a result which notably differs from the common belief that the jet width and velocity follow the inertio-capillary scaling r_jet∝τ^2/3 and v_jet∝τ^-1/3 . Our description, which differs from previous results on the subject, reproduces the time evolution of the jet width and velocity for over three decades in time, obtaining good agreement with numerical simulations from the instant of jet inception until the jet width is comparable to that of the initial bubble.   

Numerical validation of two cavitating hydrofoil profiles using the VOF homogeneous mixture approach

The Volume of Fluid homogeneous mixture approach coupled with a cavitation model is used in this work to perform numerical simulations on hydrofoils. A comparison between the complete and the asymptotic cavitation models is first made. The various cavitation models offered in Star-CCM+ and Fluent are then compared and validated using two experimental cases where attached cavitation was reported. The first case focuses on a static rectangular foil made with a modified NACA-0009 section at various cavitation numbers. The vapor bubble length, the pressure distribution and the hydrodynamic forces are compared to the experimental data with satisfactory agreement. The second case simulates an oscillating NACA 16-012 foil in cavitating conditions where the pitch about mid-chord is varied around 5° ± 5° in a sinusoidal manner. The unsteady hydrodynamics of this second case adds challenges to the numerical simulations. The cyclic lift coefficient is compared with the experimental results. A specific case of vapor bubble collapse with a significant impact on lift is investigated in this work. The presentation concludes with some numerical recommendations for proper spatial and temporal discretizations for cavitation simulations and discusses the impact of the models' growth and collapse scaling factors.   

Impact of Homogeneous Pressure Perturbation on the Dynamics of Bubble Collapse and Coalescence in a Single and Multi-Bubble Systems

The objective of this study is investigation of the influence of homogeneous pressure perturbation on rising bubble morphology by analyzing shear stress and strain effects at the bubble-liquid interface. A numerical model is developed using the finite volume method with a Dirichlet pressure-inlet boundary and side walls, capturing bubble dynamics qualitatively and quantitatively, and validated with RMSE <1% against experimental data containing optical diagnostics and quantitative measurements, ensuring accurate representation of key parameters like the morphology of the rising bubble and its local velocity during ascent. The numerical model uses approximately 10⁵ elements with a mesh size 0.0025 times the domain dimension, employs volume of fluid scheme for multiphase physics, and achieves stability through relaxation factors of 0.3 for pressure and 0.4 for momentum, along with a geometric reconstruction scheme for volume fraction discretization to capture sharp interfaces between the two phases. The study observed critical bubble behaviors, including deformation, breakup (re-entrant jet), and coalescence. Analysis of non-dimensional numbers (Atwood), compressibility, pressure perturbation strength, perturbation type (planar and radial), and bubble location reveals their individual and collective effects on bubble dynamics. The study offers valuable insights into the interplay between pressure perturbation and rising bubbles with a robust CFD model for multiphase physics.