The transient evolution of the bubble-size probability density functions resulting from the breakup of an air bubble injected into a fully developed turbulent water ow has been measured experimentally using phase Doppler particle sizing (PDPA) and image processing techniques. These measurements were used to determine the breakup frequency of the bubbles as a function of their size and of the critical diameter D_c defined as D_c = 1.26 (σ/ρ)^3/5ε^−2/5, where ε is the rate of dissipation per unit mass and per unit time of the underlying turbulence. A phenomenological model is proposed showing the existence of two distinct bubble size regimes. For bubbles of sizes comparable to D_c, the breakup frequency is shown to increase as (σ/ρ)^−2/5ε^−3/5 √D/D_c−1, while for large bubbles whose sizes are greater than 1.63D_c, it decreases with the bubble size as ε^1/3D^−2/3. The model is shown to be in good agreement with measurements performed over a wide range of bubble sizes and turbulence intensities.

Based on energy principles, we propose a statistical model to describe the bubble size probability density function of the daughter bubbles resulting from the shattering of a mother bubble of size D₀ immersed in a fully developed turbulent water flow. The model shows that the bubble size p.d.f. depends not only on D₀, but also on the value of the dissipation rate of turbulent kinetic energy of the underlying turbulence of the water, ε. The phenomenological model is simple, yet it predicts detailed experimental measurements of the transient bubble size p.d.f.s performed over a range of bubble sizes and dissipation rates ε in a very consistent manner. The agreement between the model and the experiments is particularly good for low and moderate bubble turbulent Weber numbers, We_t = ρΔ u²(D₀)D₀/σ where the assumption of the binary breakup is shown to be consistent with the experimental observations. At larger values of We_t, it was found that the most probable number of daughter bubbles increases and the assumption of tertiary breakup is shown to lead to a better fit of the experimental measurements.

We consider the statistical description of the break-up of an immiscible fluid lump immersed into a fully developed turbulent flow. We focus on systems where there is no relative velocity between the continuous and dispersed phases. In this case, particle fragmentation is caused only by turbulent velocity fluctuations. The most relevant models proposed for the particle break-up frequency and for the shape of the daughter particle size distribution are reviewed. Their predictions are compared to recent experimental data, obtained for the break-up of an air cavity immersed into a high Reynolds number, turbulent water jet. Models based on purely kinematic arguments show the best agreement with the experimental data

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) ∫₀^D₀ (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*(We_t) = g(ϵ, D₀) D^2/3₀ ϵ^−1/3, with We_t ~ ρ ϵ^2/3D₀^5/3/σ, where ρ is the density of the continuous phase and σ the surface tension.

This paper presents some results on the performance of hydrogen-based engines. In particular, the following aspects are addressed: Benefits associated with specific fuel and energy consumption, net thrust, turbine entry temperature, and hardware changes needed in the upgrading process from kerosene to hydrogen. Hydrogen is a high-energy clean-burning fuel whose main combustion product is water vapour plus traces of nitrogen oxides. This fact suggests that, provided that the technology is available, the use of hydrogen could offer some opportunities for the environmentally friendly development and sustained growth of commercial aviation. The study has been performed in the frame of the Liquid Hydrogen Fuelled Aircraft — System Analysis (CRYOPLANE) project. This is a Fifth Framework Programme, supported by the European Commission, whose objective was to assess the feasibility of using hydrogen as a clean energy source for air transportation systems.