Vapour explosion under hot water depressurization

This paper continues a series of works developing a model for a high-speed boiling flow capable of describing different fluxes with no change in the model coefficients. Refining the interfacial area transport equation in partial derivatives, we test the ability of the model to describe phenomena that cannot be simulated by models that average the interfacial interaction. In the previous version, the possibility for bubble fragmentation was considered, which permitted us to reproduce an explosive boiling in rarefaction shocks moving at a speed of ${\sim}10~\text{m}~\text{s}^{-1}$ fixed in experiments on hot water decompression. The shocks were shown to be caused by a chain bubble fragmentation leading to a sharp increase in the interphase area (Ivashnyov et al., J. Fluid Mech., vol. 413, 2000, pp. 149–180). With no change in the free parameters (the initial number of boiling centres in the flow bulk and the critical Weber number) chosen for a tube decompression, the model gave close predictions for critical flows in long nozzles, $L/D\sim 100$. The formation of a boiling shock in the nozzle was shown to be the reason for the onset of autovibrated regimes (Ivashnyov & Ivashneva, J. Fluid Mech., vol. 710, 2012, pp. 72–101). However, the previous model does not simulate the phenomenon of a vapour explosion at a primary stage of a hot water decompression, when the first rarefaction wave is followed by an extended, 1 m width, several MPa amplitude compression wave in which the pressure reaches a plateau below a saturation value. The model proposed assumes initial boiling centre origination at the channel walls. Due to overflowing, the wall bubbles break up, with their fragments passing into the flow. On growing up, the flow bubbles can break up in their turn. It is shown that an extended compression wave is caused by the fragmentation of wall bubbles, which leads to the increase in the interphase area, boiling intensification and the pressure rise. The pressure reaches a plateau before a saturation state is reached due to flow momentum loss accelerating the fragments of wall bubbles. The phenomenon of pressure ‘oscillation’ fixed in some experimental oscillograms when the pressure in the compression wave increases up to a saturation pressure and then drops to the plateau value has been explained as well. The ‘illposedness’ defect of the generally accepted model for two-phase two-velocity flow with a compressible carrying phase, which lies in its complex characteristics, has been rectified. The calculations of a stationary countercurrent liquid-particle flow in a diffuser with the improved hyperbolic model predicts a critical regime with a maximal liquid mass flux, while the old non-hyperbolic model simulates the supercritical regimes with ‘numerical instabilities’. Calculations of a transient upward flow of particles have shown the formation of a superslow ‘creeping’ shock wave of particles compacting.

A Model for an Acoustically Driven Microbubble Inside a Rigid Tube

A theoretical framework to model the dynamics of acoustically driven microbubble inside a rigid tube is presented. The proposed model is not a variant of the conventional Rayleigh–Plesset category of models. It is derived from the reduced Navier–Stokes equation and is coupled with the evolving flow field solution inside the tube by a similarity transformation approach. The results are computed, and compared with experiments available in literature, for the initial bubble radius of Ro = 1.5 μm and 2 μm for the tube diameter of D = 12 μm and 200 μm with the acoustic parameters as utilized in the experiments. Results compare quite well with the existing experimental data. When compared to our earlier basic model, better agreement on a larger tube diameter is obtained with the proposed coupled model. The model also predicts, accurately, bubble fragmentation in terms of acoustic and geometric parameters.

Bubble breakup simulation in nozzle flows

Experiments on high-pressure vessel decompression have shown that vaporization occurs in ‘boiling shocks’ moving with a velocity of ${\ensuremath{\sim} }10~\mathrm{m} ~{\mathrm{s} }^{\ensuremath{-} 1} $. To explain this phenomenon, a model accounting for bubble breakup was suggested (Ivashnyov, Ivashneva & Smirnov, J. Fluid. Mech., vol. 413, 2000, pp. 149–180). It was shown that the explosive boiling was caused by chain bubble fragmentation, which led to a sharp increase in the interface area and instantaneous transformation of the mixture into an equilibrium state. In the present study, this model is used to simulate nozzle flows with no change in the free parameters chosen earlier for modelling a tube decompression. It is shown that an advanced model ensures the best correspondence to experiments for flashing flows in comparison with an equilibrium model and with a model of boiling at a constant number of centres. It is also shown that the formation of a boiling shock in a critical nozzle flow leads to autovibrations.

Considerations on bubble fragmentation models

In this paper we describe the restrictions that the probability density function (p.d.f.) of the size of particles resulting from the rupture of a drop or bubble must satisfy. Using conservation of volume, we show that when a particle of diameter, D0, breaks into exactly two fragments of sizes D and D2 = (D30−D3)1/3 respectively, the resulting p.d.f., f(D; D0), must satisfy a symmetry relation given by D22f(D; D0) = D2f(D2; D0), which does not depend on the nature of the underlying fragmentation process. In general, for an arbitrary number of resulting particles, m(D0), we determine that the daughter p.d.f. should satisfy the conservation of volume condition given by m(D0) ∫0D0 (D/D0)3f(D; D0) dD = 1. A detailed analysis of some contemporary fragmentation models shows that they may not exhibit the required conservation of volume condition if they are not adequately formulated. Furthermore, we also analyse several models proposed in the literature for the breakup frequency of drops or bubbles based on different principles, g(ϵ, D0). Although, most of the models are formulated in terms of the particle size D0 and the dissipation rate of turbulent kinetic energy, ϵ, and apparently provide different results, we show here that they are nearly identical when expressed in dimensionless form in terms of the Weber number, g*(Wet) = g(ϵ, D0) D2/30 ϵ−1/3, with Wet ~ ρ ϵ2/3D05/3/σ, where ρ is the density of the continuous phase and σ the surface tension.

Increasing the nonlinear character of microbubble oscillations at low acoustic pressures

The nonlinear response of gas bubbles to acoustic excitation is an important phenomenon in both the biomedical and engineering sciences. In medical ultrasound imaging, for example, microbubbles are used as contrast agents on account of their ability to scatter ultrasound nonlinearly. Increasing the degree of nonlinearity, however, normally requires an increase in the amplitude of excitation, which may also result in violent behaviour such as inertial cavitation and bubble fragmentation. These effects may be highly undesirable, particularly in biomedical applications, and the aim of this work was to investigate alternative means of enhancing nonlinear behaviour. In this preliminary report, it is shown through theoretical simulation and experimental verification that depositing nanoparticles on the surface of a bubble increases the nonlinear character of its response significantly at low excitation amplitudes. This is due to the fact that close packing of the nanoparticles restricts bubble compression.