C. Martínez-Bazán

A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow

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.

Axisymmetric Bubble Pinch-Off at High Reynolds Numbers

Analytical considerations and potential-flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, rn, decreases as tau proportional to r2n sqrt[1lnr2n], where tau is the time to break up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a rn proportional to tau1/3 power law. These findings are verified experimentally.

Vortex shedding in high Reynolds number axisymmetric bluff-body wakes: Local linear instability and global bleed control

In the present work we study the large-scale helical vortex shedding regime in the wake of an axisymmetric body with a blunt trailing edge at high Reynolds numbers, both experimentally and by means of local, linear, and spatiotemporal stability analysis. In the instability analysis we take into account the detailed downstream evolution of the basic flow behind the body base. The study confirms the existence of a finite region of absolute instability for the first azimuthal number in the near field of the wake. Such instability is believed to trigger the large-scale helical vortex shedding downstream of the recirculating zone. Inhibition of vortex shedding is examined by blowing a given flow rate of fluid through the base of the slender body. The extent of the locally absolute region of the flow is calculated as a function of the bleed coefficient, Cb=qb/(πR2u∞), where qb is the bleed flow rate, R is the radius of the base, and u∞ is the incident free-stream velocity. It is shown that the basic flow become...

Transition from bubbling to jetting in a coaxial air–water jet

In this Brief Communication we study experimentally the flow regimes that appear in coaxial air–water jets discharging into a stagnant air atmosphere and we propose a simple explanation for their occurrence based on linear, local, spatiotemporal stability theory. In addition to the existence of a periodic bubbling regime for low enough values of the water-to-air velocity ratio, u=uw∕ua, our experiments revealed the presence of a jetting regime for velocity ratios higher than a critical one, uc. In the bubbling regime, bubbles form periodically from the tip of an air ligament whose length increases with u. However, when u>uc a long, slender gas jet is observed inside the core of the liquid coflow. Since in the jetting regime the downstream variation of the flow field is slow, we performed a local, linear spatiotemporal stability analysis with uniform velocity profiles to model the flow field of the air–water jet. Similar to the transition from dripping to jetting in capillary liquid jets, the analysis show...

Bubble formation in a coflowing air–water stream

Summary The present work investigates the generation of bubbles in a co-flowing air-water stream from the analytical as well as th e experimental point of view. We first study the effect of the ou ter shear layer on the stability properties of two co-flowing streams of different density moving with different velocities. On the second part of the work we concentrate on the non-linear mechanisms leading to the formation of bubbles. The analytical results given by a model proposed here are compared with experiments. Laminar co-flowing streams are present in many natural proce sses as well as engineering applications such those taking place in chemical reactors and modern material manufacturing among others. In particular, the present study focuses on some new aspects related to the formation and stability of laminar, coaxial gas-liquid jets of great relevance in bubble generation processes. Several mechanisms, previously unexplored in the literature, are expected to influence the formati on of bubbles in a submerged coaxial air-water jet configuratio n. More precisely, we study the influence of the outer shear layer generated by the difference of velocity between the external co-flowing liquid stream and the quiescent surroundi ng liquid from the analytical as well as the experimental point of view. The variety of mechanisms appearing in the bubble generation problem suggests the idea of isolating and exploring them separately. Thus the different aspects analyzed in this work are summarized as follows. We first studied the stability of two coflowing streams with fin ite crosstream extent in a cylindrical geometry. Transitio n curves from convective to absolute instability were obtained in terms of the control parameters, namely, inner to outer fluid density ratio, S, outer fluid to inner fluid velocity ratio, �, and, more importantly, external to internal nozzle diameter ratio, a. A new mode of instability caused by the external shear layer included in the velocity profile was identified. It was also found that this mode was responsible for triggering the absolute instability of configurations considered convect ively unstable in the limit a ! 1 . Moreover, it was shown that, when � = 1, the critical density ratio necessary to sustain absolute instability in axisymmetric jets decreases with t he diameter ratio as Sc / a 4 . In more general situations, where � 6 1, two modes of instability associated respectively with the inner and the outer shear layers coexist. The analysis revealed that the outer shear layer has a significant effect o n the stability of the internal interface, especially for li ght jets, corresponding to S < 1, when a is sufficiently close to unity. Furthermore, a new region of a bsolute instability was described in the a‐�‐S parameter space.

Bubbling in a co-flow at high Reynolds numbers

The physical mechanisms underlying bubble formation from a needle in a co-flowing liquid environment at high Reynolds numbers are studied in detail with the aid of experiments and boundary-integral numerical simulations. To determine the effect of gas inertia the experiments were carried out with air and helium. The influence of the injection system is elucidated by performing experiments using two different facilities, one where the constancy of the gas flow-rate entering the bubble is ensured, and another one where the gas is injected through a needle directly connected to a pressurized chamber. In the case of constant flow-rate injection conditions, the bubbling frequency has been shown to hardly depend on the gas density, with a bubble size given by db∕ro≃[6U(k*U+k2)∕(U−1)]1∕3 for U≳2, where U is the gas-to-liquid ratio of the mean velocities, ro is the radius of the gas injection needle, and k*=5.84 and k2=4.29, with db∕ro∼3.3U1∕3 for U⪢1. Nevertheless, in this case the effect of gas density is relev...

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, D 0 , breaks into exactly two fragments of sizes D and D 2 = ( D 3 0 − D 3 ) 1/3 respectively, the resulting p.d.f., f ( D ; D 0 ), must satisfy a symmetry relation given by D 2 2 f ( D ; D 0 ) = D 2 f ( D 2 ; D 0 ), which does not depend on the nature of the underlying fragmentation process. In general, for an arbitrary number of resulting particles, m ( D 0 ), we determine that the daughter p.d.f. should satisfy the conservation of volume condition given by m ( D 0 ) ∫ 0 D 0 ( D / D 0 ) 3 f ( D ; D 0 ) d D = 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, D 0 ). Although, most of the models are formulated in terms of the particle size D 0 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, D 0 ) D 2/3 0 ϵ −1/3 , with We t ~ ρ ϵ 2/3 D 0 5/3 /σ, where ρ is the density of the continuous phase and σ the surface tension.

A novel particle tracking and break-up detection algorithm: application to the turbulent break-up of bubbles

A new method has been developed to measure experimentally the break-up properties of bubbles. The technique is based on the application of a particle tracking velocimetry algorithm to high-speed video images not only to measure the velocity of the bubbles, but also to detect the break-up events. Thus the algorithm is able to associate every broken bubble with the daughter bubbles formed upon their corresponding break-up. Moreover, the lifetime, as well as the number and size of fragments resulting from the break-up process, can be measured for a large number of bubbles. Statistical processing of the information collected allows us to compute the break-up frequency and daughter size distribution of the bubbles as a function of the bubble size and the mean properties of the base flow. The method has been employed to study the break-up of a cloud of bubbles injected at the central axis of a turbulent water jet. Experimental results for the break-up frequency and daughter bubble size distribution are also presented to illustrate the performance of the technique.

THE EFFECT OF THE DIAMETER RATIO ON THE ABSOLUTE AND CONVECTIVE INSTABILITY OF FREE, COFLOWING JETS

The stability of two coflowing streams with finite cross stream extent has been studied in both axisymmetric as well as plane geometries. Transition curves from convective to absolute instability have been obtained in terms of the control parameters, namely, the density ratio, S, the velocity ratio, Λ, and, more importantly, the diameter ratio, a. A new mode of instability caused by the external shear layer included in the velocity profile has been identified. It has also been found that this mode is responsible for triggering the absolute instability of configurations considered convectively unstable in the limit a→∞. Moreover, in the present study it has been shown that, when Λ=1, the critical density ratio necessary to sustain absolute instability in axisymmetric jets decreases with the diameter ratio as Sc∝a−4, while it decreases as Sc∝a−6/5 in plane jets. In more general situations, where Λ≠1, two modes of instability associated, respectively, with the inner and the outer shear layers coexist. The an...

Global mode analysis of axisymmetric bluff-body wakes: Stabilization by base bleed

The flow around a slender body with a blunt trailing edge is unstable in most situations of interest. Usually the flow instabilities are generated within the wake behind the bluff body, inducing fluctuating forces and introducing the possibility of resonance mechanisms with modes of the structure. Base bleed is a simple and well-known means of stabilizing the wake. In the present research, we investigate the global instability properties of the laminar-incompressible flow that develops behind a cylinder with sharp edges and axis aligned with the free stream using a spectral domain decomposition method. In particular, we describe the flow instability characteristics as a function of the Reynolds number, Re=ρW∞D/μ, and the bleed coefficient, defined as the bleed-to-free-stream velocity ratio, Cb=Wb/W∞, where D is the diameter of the body and ρ and μ the density and viscosity of the free stream, respectively. For a truncated cylinder of aspect ratio L/D=5, where L is the length of the body, our calculations ...