Level set method for numerical simulation of a cavitation bubble,its growth,collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier–Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving interface is captured by the level set function, and the interface velocity is resolved by “one-side” velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the “shock wave”-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating. The project supported by the National Natural Science Foundation of China (10272032 and 10672043). The English text was polished by Keren Wang.     

Numerical simulation of vortex ring formation in the presence of background flow with implications for squid propulsion

Numerical simulations are used to study laminar vortex ring formation under the influence of background flow. The numerical setup includes a round-headed axisymmetric body with an opening at the posterior end from which a column of fluid is pushed out by a piston. The piston motion is explicitly included into the simulations by using a deforming mesh. A well-developed wake flow behind the body together with a finite-thickness boundary layer outside the opening is taken as the initial flow condition. As the jet is initiated, different vortex evolution behavior is observed depending on the combination of background flow velocity to mean piston velocity () ratio and piston stroke to opening diameter () ratio. For low background flow () with a short jet (), a leading vortex ring pinches off from the generating jet, with an increased formation number. For intermediate background flow () with a short jet (), a leading vortex ring also pinches off but with a reduced formation number. For intermediate background flow () with a long jet (), no vortex ring pinch-off is observed. For high background flow () with both a short () and a long () jet, the leading vortex structure is highly deformed with no single central axis of fluid rotation (when viewed in cross-section) as would be expected for a roll-up vortex ring. For , the vortex structure becomes isolated as the trailing jet is destroyed by the opposite-signed vorticity of the background flow. For , the vortex structure never pinches off from the trailing jet. The underlying mechanism is the interaction between the vorticity layer of the jet and the opposite-signed vorticity layer from the initial wake. This interaction depends on both and . A comparison is also made between the thrust generated by long, continuous jets and jet events constructed from a periodic series of short pulses having the same total mass flux. Force calculations suggest that long, continuous jets maximize thrust generation for a given amount of energy expended in creating the jet flow. The implications of the numerical results are discussed as they pertain to adult squid propulsion, which have been observed to generate long jets without a prominent leading vortex ring. PACS 02.60.Cb, 47.32.cf, 47.32.cb, 47.20.Ft, 47.63.M-     

On the formation of vortex rings and pairs

The axisymmetric vortex sheet model developed by Nitsche & Krasny (1994) has been extended to study the formation of vortex rings (pairs) at the edge of circular (2D) tube and opening. Computations based on this model are in good agreement with the experiments (Didden (1979) for circular tube and Auerbach (1987) for 2D tube and opening). Using this new model, evidences are provided to show that the main failure of the similarity theory (the false prediction of axial trajectory of vortex ring) is due to its ignorance of the self-induced ring velocity (mutual induction for vortex pair). We further reason why the similarity theory succeeds in its prediction of radial movement of vortex ring. The effects of various parameters such as turning angle α and piston speedU _p (t) on the formation of vortex ring are investigated. Numerical result shows that turning angle α has no effect on circulation shed τ. We also discuss Glezer (1988)'s summary on the influence ofU _p upon the shedding circulation, and finally give the variation of core distribution of vortex ring with α andU _p (t). The project is supported by National Natural Science Foundation of China and Doctoral Program of Institution of Higher Education     

Dynamics of a cavitation bubble near a solid surface and the induced damage

Numerical and experimental studies of the dynamics of a cavitating bubble near a resilient metal surface were performed. To augment the experimental flow visualizations of a collapsing bubble, numerical simulations were conducted to more thoroughly identify the collapse dynamics and analyze the flow. A bubble collapse was captured using a high-speed camera and back illumination. The metal sample was made of pure aluminum placed near a collapsing cavitation bubble at various distances from the metal surface. Width, depth, and volume of the induced material deformations were measured using an optical microscope and a three-dimensional profilometer and then compared against existing experimental data from the literature. The cavitating bubble’s dynamics and the related flow were simulated numerically using the open source finite volume based flow solver CavitatingFOAM. This code solved the Navier–Stokes equations for compressible two-phase flows using an Euler–Euler approach, including the barotropic equations of state. Bubble shapes, collapse times, and obtained damage parameters were compared to experimental observations. Impact velocities, pressures, shear rates, and various flow phenomena were discussed, providing broad insight into bubble dynamics and the induced damage.     

Modes of vortex formation and transition to three-dimensionality in the wake of a freely vibrating cylinder

The present work is aimed to give some insight into the relation between vortex shedding modes and transition to three-dimensionality in the wake of a freely vibrating cylinder by establishing a numerical model and analyzing the relevant results of two- and three-dimensional simulations. The compressible flow past an elastically-mounted cylinder is solved by using the immersed boundary method (IB method). The cylinder is free to vibrate in the transverse direction with zero structure damping. The response of displacement amplitude is studied with the variation of reduced velocity. Whether P+S mode exists in three-dimensional flow and the occurrence of 2P mode is caused by flow transition from two-dimensional to three-dimensional are problems of concern. Both 2P and P+S wake modes are observed in two- and three-dimensional simulations. The numerical results indicate that the flow transition from two-dimensional to three-dimensional is coupled with the cylinder vibration in the synchronization/lock-in regime. The wake formation given by three-dimensional simulations suggests that the P+S mode might exist in reality when the flow is reverted to two-dimensional by vortex induced vibration (VIV) at Re=300–350. When Reynolds number increases to 425, the wake formation undergoes transition to three-dimensionality and 2P mode is observed. The effect of mass ratio on the flow transition to three-dimensionality is studied. The relationship between wake modes and aerodynamic forces is discussed.     

Numerical and experimental study on the motion characteristics of single bubble in a complex channel

This paper is an extended study from previous work. In this study, the focus is paid to the dynamics of bubble rising and deformation in a complex channel, while the previous work is in straight channel. For this purpose, a three-dimensional lattice Boltzmann method (LBM) is employed to simulate the dynamics behaviour of a bubble rising in a complex channel consisting of three half-round throats. To validate the numerical method, a visual experiment was carried out by means of a high-speed digital camera and computer image processing technology. The behaviour of the rising bubble through glycerine solution in a complex channel was recorded. Some physical parameters such as rising velocities, trajectory and shapes of the bubble were calculated and processed based on the experimental data. In the same conditions, the trajectory, shapes and rising velocities of the bubble were simulated during its rising process by the proposed LBM. The numerical results are in good agreement with the experimental results. It demonstrates that LBM used in this work is feasible for simulating two-phase flow in such a complex channel.     

Complex equations of flexible circular ring shells overall-bending in a meridian plane and general solution for the slender ring shells

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Dynamic Contact Behavior of a Golf Ball during Oblique Impact: Effect of Friction between the Ball and Target

The oblique impact between a golf ball and a polymethyl methacrylate (PMMA) target with smooth transparent surfaces was studied using a high-speed video camera. Video images of the impact were recorded from the backside of the target and were used to determine the contact time, contact area, and the displacement and rotation of the ball along the target. The average tangential and angular velocities were determined as functions of the inbound ball velocity. As the inbound ball velocity increased, the contact area and average tangential and angular velocities also increased while the contact time decreased. An oiled PMMA target was used to study the effect of reduced friction between the ball and target. The results were compared with earlier data for a steel target with relatively rough surfaces. The contact area and time were unaffected by friction, but the average tangential velocity increased while the average angular velocity decreased as the friction decreased.