In this paper, we study the fluid–structure interaction of a three-dimensional (3-D) flexible membrane immersed in an unsteady separated flow at moderate Reynolds numbers. We employ a body-conforming variational fluid–structure interaction solver based on the recently developed partitioned iterative scheme for the coupling of turbulent fluid flow with nonlinear structural dynamics. Of particular interest is to understand the flow-excited instability of a 3-D flexible membrane as a function of the non-dimensional mass ratio ($m^{*}$), Reynolds number ($Re$) and aeroelastic number ($Ae$). For a wide range of parameters, we examine two distinct stability regimes of the fluid–membrane interaction: deformed steady state (DSS) and dynamic balance state (DBS). We propose stability phase diagrams to demarcate the DSS and DBS regimes for the parameter space of mass ratio versus Reynolds number ($m^{*}$-$Re$) and mass ratio versus aeroelastic number ($m^{*}$-$Ae$). With the aid of the global Fourier mode decomposition technique, the distinct dominant vibrational modes are identified from the intertwined membrane responses in the parameter space of $m^{*}$-$Re$ and $m^{*}$-$Ae$. Compared to the deformed steady membrane, the flow-excited vibration produces relatively longer attached leading-edge vortices which improve the aerodynamic performance when the coupled system is near the flow-excited instability boundary. The optimal aerodynamic performance is achieved for lighter membranes with higher $Re$ and larger flexibility. Based on the global aeroelastic mode analysis, we observe a frequency lock-in phenomenon between the vortex-shedding frequency and the membrane vibration frequency causing self-sustained vibrations in the dynamic balance state. To characterize the origin of the frequency lock-in, we propose an approximate analytical formula for the nonlinear natural frequency by considering the added mass effect and employing a large deflection theory for a simply supported rectangular membrane. Through our systematic high-fidelity numerical investigation, we find that the onset of the membrane vibration and the mode transition has a direct dependence on the frequency lock-in between the natural frequency of the tensioned membrane and the vortex-shedding frequency or its harmonics. These findings on the fluid-elastic instability of membranes have implications for the design and development of control strategies for membrane wing-based unmanned systems and drones.

This paper presents an experimental study on the mechanism of interaction between a cavitation bubble and an air bubble. The cavitation bubble was generated by means of the low-voltage discharge method, and the combination of high-speed photography and a pressure measurement system allowed for simultaneous observation and measurement of the evolution of the shock wave and the change in shock wave strength with the presence of the air bubble in the vicinity. The high-speed imaging revealed the predominant roles of the relative distance φ and relative size ε between the cavitation and air bubbles in the determination of the stratification effect that the air bubble exerted on the shock wave produced from the first collapse of the cavitation bubble. The pressure measurement indicated that, when the air bubble did not merge with the cavitation bubble, the aforementioned factors, together with the angle $\alpha $ formed by the air bubble, cavitation bubble and the measuring point, would jointly affect the attenuation of the pressure peak and energy of the shock wave. Quantitatively, the attenuation magnitude was proportional to $a{(\alpha \varphi /\varepsilon )^b}$, where the values of the coefficients a and b depended on whether the shock wave was stratified or not. When the cavitation bubble and the air bubble merged, the energy and the pressure peak of the shock wave decreased to less than 40 % of the values in the absence of the air bubble. With the new insight into bubble–bubble interaction mechanisms, the findings will facilitate a better understanding and development of cavitation utilization and prevention technology in water--air two phase systems.

This work focuses on using the power of a collapsing bubble in ice breaking. We experimentally validated the possibility and investigated the mechanism of ice breaking with a single collapsing bubble, where the bubble was generated by underwater electric discharge and collapsed at various distances under ice plates with different thicknesses. Characteristics of the ice fracturing, bubble jets and shock waves emitted during the collapse of the bubble were captured. The pattern of the ice fracturing is related to the ice thickness and the bubble–ice distance. Fractures develop from the top of the ice plate, i.e. the ice–air interface, and this is attributed to the tension caused by the reflection of the shock waves at the interface. Such fracturing is lessened when the thickness of the ice plate or the bubble–ice distance increases. Fractures may also form from the bottom of the ice plate upon the shock wave incidence when the bubble–ice distance is sufficiently small. The ice plate motion and its effect on the bubble behaviour were analysed. The ice plate motion results in higher jet speed and greater elongation of the bubble shape along the vertical direction. It also causes the bubble initiated close to the ice plate to split and emit multiple shock waves at the end of the collapse. The findings suggest that collapsing bubbles can be used as a brand new way of ice breaking.

In this work, a robust, consistent, and coherent approach, termed as Modified Ghost Method (MGM), is developed to deal with the multi-medium interaction with elastic-plastic solid. This approach is simple to implement and keeps the solvers intact, and can handle multi-medium problems which involve various media including gas, liquid and solid. The MGM is first validated by two-dimensional (2D) cases and then is applied to study the interaction between elastic-plastic solid structure and the underwater explosion. The development of the wave system is described and analyzed. Furthermore, two kinds of complex solid structure subjected to underwater explosion are simulated. Finally, a complex solid structure immersed in water subjected to underwater explosion is simulated and analyzed. The numerical experiments show the viability, effectiveness and versatility of the proposed method which is able to accurately predict the wave pattern at various interfaces.

We present a moving-least-square immersed boundary method for solving viscous incompressible flow involving deformable and rigid boundaries on a uniform Cartesian grid. For rigid boundaries, noslip conditions at the rigid interfaces are enforced using the immersed-boundary direct-forcing method. We propose a reconstruction approach that utilizes moving least squares (MLS) method to reconstruct the velocity at the forcing points in the vicinity of the rigid boundaries. For deformable boundaries, MLS method is employed to construct the interpolation and distribution operators for the immersed boundary points in the vicinity of the rigid boundaries instead of using discrete delta functions. The MLS approach allows us to avoid distributing the Lagrangian forces into the solid domains as well as to avoid using the velocity of points inside the solid domains to compute the velocity of the deformable boundaries. The present numerical technique has been validated by several examples including a Poiseuille flow in a tube, deformations of elastic capsules in shear flow and dynamics of red-blood cell in microfluidic devices.

In the present article, the cell model (or self-consistent scheme) is used to derive constitutive equations for rod suspensions in non-Newtonian viscous matrices such as power-law, Ellis and Carreau fluids. It is found that the shear-thinning character of the matrix influences considerably the rod contribution to the stress tensor, but has no impact on the rod orientation dynamics: the same microstructure evolution as the one encountered in Newtonian fluids is obtained. The rod suspension behaves differently than the unfilled matrix in the sense that, depending on rod orientation, the onset of shear thinning in the composite occurs at lower or higher shear rates. Our analysis also provides a semi-analytical model for rod suspensions in an Ellis fluid, which appears to be suitable for predicting a Newtonian plateau at low shear rates and a shear-thinning behaviour at high shear rates. In addition, the model predictions are in good agreement with the shear viscosity measurements of glass-fibre-filled polystyrene melts (Chan et al., J. Rheol., vol. 22 (5), 1978, pp. 507–524), demonstrating its ability to describe the rheological behaviour of such polymer composites. Finally, the proposed approach is extended to a Carreau fluid although its solution requires the numerical solution of a set of partial differential equations.

Numerical simulation based on the Euler equation and one-step reaction model is carried out to investigate the process of deflagration to detonation transition (DDT) occurring in a straight duct. The numerical method used includes a high resolution fifth-order weighted essentially non-oscillatory (WENO) scheme for spatial discretization, coupled with a third order total variation diminishing Runge-Kutta time stepping method. In particular, effect of energy release on the DDT process is studied. The model parameters used are the heat release at q = 50,30,25,20,15,10 and 5, the specific heat ratio at 1.2, and the activation temperature at Ti = 15, respectively. For all the cases, the initial energy in the spark is about the same compared to the detonation energy at the Chapman-Jouguet (CJ) state. It is found from the simulation that the DDT occurrence strongly depends on the magnitude of the energy release. The run-up distance of DDT occurrence decreases with the increase of the energy release for q = 50 ~ 20, and increases with the increase of the energy release for q = 20 ~ 5. This phenomenon is found to be in agreement with the analysis of mathematical stability theory. It is suggested that the factors to strengthen the DDT would make the detonation more stable, and vice versa. Finally, it is concluded from the simulations that the interaction of the shock wave and the flame front is the main reason for leading to DDT.

In this work, the modified ghost fluid method is developed to deal with 2D compressible fluid interacting with elastic solid in an Euler-Lagrange coupled system. In applying the modified Ghost Fluid Method to treat the fluid-elastic solid coupling, the Navier equations for elastic solid are cast into a system similar to the Euler equations but in Lagrangian coordinates. Furthermore, to take into account the influence of material deformation and nonlinear wave interaction at the interface, an Euler-Lagrange Riemann problem is constructed and solved approximately along the normal direction of the interface to predict the interfacial status and then define the ghost fluid and ghost solid states. Numerical tests are presented to verify the resultant method.

We report on an experimental study of cavitation bubble dynamics within sub-millimetre-sized narrow gaps. The gap height is varied, while the position of the cavitation event is fixed with respect to the lower gap wall. Four different sizes of laser-induced cavitation bubbles are studied using high-speed photography of up to 430,000 frames per second. We find a strong influence of the gap height, H, on the bubble dynamics, in particular on the collapse scenario. Also, similar bubble dynamics was found for the same non-dimensional gap height η = H/Rx, where Rx is the maximum radius in the horizontal direction. Three scenarios are observed: neutral collapse at the gap centre, collapse onto the lower wall and collapse onto the upper wall. For intermediate gap height the bubble obtains a conical shape 1.4 < η < 7.0. For large distances, η > 7.0, the bubble no longer feels the presence of the upper wall and collapses hemispherically. The collapse time increases with respect to the expansion time for decreasing values of η. Due to the small scales involved, the final stage of the bubble collapse could not be resolved temporally and numerical simulations were performed to elucidate the details of the flow. The simulations demonstrate high-speed jetting towards the upper and lower walls and complex bubble splitting for neutral collapses.

The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this method, it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance, for given imposed disturbance. For a given flow geometry and fluid properties, when the maximum of the function K (a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction) in the flow field is larger than a certain critical value, it is expected that instability would occur for some initial disturbances. In this paper, using the energy gradient analysis, the equation for calculating the energy gradient function K for plane Couette flow is derived. The result indicates that K reaches the maximum at the moving walls. Thus, the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain. The critical value of K at turbulent transition, which is observed from experiments, is about 370 for plane Couette flow when two walls move in opposite directions (anti-symmetry). This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow (385-389). Therefore, it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure (symmetrical case) and shear driven flows (anti-symmetrical case).

The cavity–particle dynamics at cavitation inception on the surface of spherical particles suspended in water and exposed to a strong tensile stress wave is experimentally studied with high-speed photography. Particles, which serve as nucleation sites for cavitation bubbles, are set into a fast translatory motion during the explosive growth of the cavity. They reach velocities of ~40 ms−1 and even higher. When the volume growth of the cavity slows down, the particle detaches from the cavity through a process of neck-breaking, and the particle is shot away. The experimental observations are simulated with (i) a spherical cavity model and (ii) with an axisymmetric boundary element method (BEM). The input for both models is a pressure pulse, which is obtained from the observed radial cavity dynamics during an individual experiment. The model then allows us to calculate the resulting particle trajectory. The cavity shapes obtained from the BEM calculations compare well with the photographs until neck formation occurs. In several cases we observed inception at two or more locations on a single particle. Moreover, after collapse of the primary cavity, a second inception was often observed. Finally, an example is presented to demonstrate the potential application of the cavity–particle system as a particle cannon, e.g. in the context of drug delivery into tissue.

The dynamic interaction of a shockwave (modelled as a pressure pulse) with an initially spherically oscillating bubble is investigated. Upon the shockwave impact, the bubble deforms non-spherically and the flow field surrounding the bubble is determined with potential flow theory using the boundary-element method (BEM). The primary advantage of this method is its computational efficiency. The simulation process is repeated until the two opposite sides of the bubble surface collide with each other (i.e. the formation of a jet along the shockwave propagation direction). The collapse time of the bubble, its shape and the velocity of the jet are calculated. Moreover, the impact pressure is estimated based on water-hammer pressure theory. The Kelvin impulse, kinetic energy and bubble displacement (all at the moment of jet impact) are also determined. Overall, the simulated results compare favourably with experimental observations of lithotripter shockwave interaction with single bubbles (using laser-induced bubbles at various oscillation stages). The simulations confirm the experimental observation that the most intense collapse, with the highest jet velocity and impact pressure, occurs for bubbles with intermediate size during the contraction phase when the collapse time of the bubble is approximately equal to the compressive pulse duration of the shock wave. Under this condition, the maximum amount of energy of the incident shockwave is transferred to the collapsing bubble. Further, the effect of the bubble contents (ideal gas with different initial pressures) and the initial conditions of the bubble (initially oscillating vs. non-oscillating) on the dynamics of the shockwave-bubble interaction are discussed.