Numerical simulation of a collapsing bubble subject to gravity

© 2016 AIP Publishing LLC. The present paper focuses on the simulation of the expansion and aspherical collapse of a laser-generated bubble subjected to an acceleration field and comparison of the results with instances from high-speed videos. The interaction of the liquid and gas is handled with the volume of fluid method. Compressibility effects have been included for each phase to predict the propagation of pressure waves. Initial conditions were estimated through the Rayleigh Plesset equation, based on the maximum bubble size and collapse time. The simulation predictions indicate that during the expansion the bubble shape is very close to spherical. On the other hand, during the collapse the bubble point closest to the bottom of the container develops a slightly higher collapse velocity than the rest of the bubble surface. Over time, this causes momentum focusing and leads to a positive feedback mechanism that amplifies the collapse locally. At the latest collapse stages, a jet is formed at the axis of symmetry, with opposite direction to the acceleration vector, reaching velocities of even 300 m/s. The simulation results agree with the observed bubble evolution and pattern from the experiments, obtained using high speed imaging, showing the collapse mechanism in great detail and clarity

Simulation of bubble expansion and collapse in the vicinity of a free surface

The present paper focuses on the numerical simulation of the interaction of laser-generated bubbles with a free surface, including comparison of the results with instances from high-speed videos of the experiment. The Volume Of Fluid method was employed for tracking liquid and gas phases while compressibility effects were introduced with appropriate equations of state for each phase. Initial conditions of the bubble pressure were estimated through the traditional Rayleigh Plesset equation. The simulated bubble expands in a non-spherically symmetric way due to the interference of the free surface, obtaining an oval shape at the maximum size. During collapse, a jet with mushroom cap is formed at the axis of symmetry with the same direction as the gravity vector, which splits the initial bubble to an agglomeration of toroidal structures. Overall, the simulation results are in agreement with the experimental images, both quantitatively and qualitatively, while pressure waves are predicted both during the expansion and the collapse of the bubble. Minor discrepancies in the jet velocity and collapse rate are found and are attributed to the thermodynamic closure of the gas inside the bubble

High-speed imaging of high pressures produced by cavitation bubbles

Cavitation bubbles, when correctly tuned, may provide interesting mechanical and chemical effects to their surroundings owing to their violent collapse. Such an event may produce high-speed liquid jetting, extreme heating, as well as pressures of thousands of atmospheres. These phenomena are responsible for the severe erosion harming hydraulic machinery, but they also present interesting traits to harness in cleaning, sonochemistry, biomedical applications, among others. Here, we present experimental observations on the high pressures produced by spherically collapsing cavitation bubbles. Filming at 10 million frames/s allows for the disclosure of details on the high pressures (kbar-level) in the liquid near the bubble in its final collapse stages that precede the shock wave emission, confirming the century-old prediction of Lord Rayleigh

Cavitation bubble dynamics in a shear-thickening fluid

Cavitation has been extensively studied in Newtonian fluids and to a lesser yet significant degree in shear-thinning fluids. However, cavitation has not been previously investigated in shear-thickening fluids, of which a water-cornstarch suspension is perhaps the best-known example. An interesting property of such fluids is that, when subjected to an increase in strain rate, their viscosity increases until they exhibit solidlike behavior and can even fracture. As cavitation bubbles are capable of generating extreme strain rates, they could be affected by shear-thickening fluid behavior. As visual access is limited by opaque or non-index-matched particles present in such fluids, an experimental study of nominally cylindrical spark-induced cavitation bubbles is conducted in a 2 mm gap between two parallel flat and transparent plates, which allows visualization of the bubbles as they contact the boundary. They are theoretically studied through the cylindrical Keller-Miksis equation adapted to a shear-thickening fluid using a Cross model. For volume fractions starting from φ=0.44, the limit between continuous and discontinuous shear-thickening regime, cavitation bubbles deform increasingly until they are replaced by cavitation-induced fracture between φ=0.46 and φ=0.52. Fracture propagation speeds were found to be in the same range as fracture speeds previously reported for pressure-driven cavity expansion, albeit for estimated initial pressures that are now orders of magnitude higher

Attractiveness of demand response in the Nordic electricity market:Present state and future prospects

During the past few years demand response (DR) has appeared in the spotlight in a new way. This is due to general technological advancement, development of electricity infrastructure, especially roll-out of smart meters, and rapidly increasing amount of renewable intermittent energy sources. This paper analyzes the attractiveness of DR in the Nordic electricity market. The results show that in many market places the attractiveness of DR is improving in the long term, although variations between different years exist. Two case studies presented in the papers show that DR has economic potential for some of the customers, especially for medium to large actors, but in a large scope, number of obstacles still hinder a wide scale deployment of DR solutions.acceptedVersionPeer reviewe