Cavitation Bubble Trackers. By Y. LECOFFRE. Balkema, pp. ISBN 90 9. 75 Hfl. – Volume – J. R. Blake. Cavitation and bubble cloud dynamics are of importance in various fields front tracking[14] and Mixed-Eulerian-Lagrangian/boundary integral. : Cavitation Bubble Trackers () by Yves Lecoffre and a great selection of similar New, Used and Collectible Books available now.

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Cavitation is the transition from a liquid to a vapour phase, due to a drop in pressure to the level of the vapour tension of the fluid.

Two kinds of cavitation have been reviewed here: As acoustic cavitation in engineering systems is related to the propagation of waves through a region subjected to liquid vaporization, the available expressions of the sound speed are discussed. One of the main effects of hydrodynamic cavitation in the nozzles and orifices of hydraulic power systems is a reduction in flow permeability.

Different discharge coefficient formulae are analysed in this paper: The latest advances in the characterization of different cavitation regimes in a nozzle, as the cavitation number reduces, are presented.

The physical cause of choked flows is explained, and an analogy between cavitation and supersonic aerodynamic flows is proposed.

Cavitation: bubble trackers

The main approaches to cavitation modelling in hydraulic power systems are also reviewed: The homogeneous-mixture models are further subdivided into barotropic and baroclinic models. The advantages and disadvantages of an implementation of the complete Rayleigh—Plesset equation are examined. Cavitation is responsible for issues such as erosion [ 12 ], noise and vibration [ 34 ], which can lead to the malfunctioning of various turbo-machines [ 5 ] and positive displacement machines.

In general, the occurrence of cavitation has a negative effect on the proper functioning of a hydraulic system. However, in some particular cases, it can also have a positive effect, as it can lead to a drag reduction, as in the case of submarine vehicles [ 6 ], or to a better liquid atomization, as in tracksrs case of fuel injector holes [ 7 ]. It is important to be able to understand the physics behind the two-phase flow phenomenon buubble order to reduce the negative effect, or to increase its positive influence.

In this sense, obtaining detailed knowledge on the basic theoretical aspects cavitatino cavitation, and studying bubnle dynamics in simple geometries, such as pipes and nozzles, is one way of achieving this goal [ 8 ].

After this limit has been exceeded, a general explosive growth of the gaseous nuclei can be observed. The value of the tensile strength of a liquid depends on the presence of weak spots in the bubbld, which provide the nuclei for the development of cavitationn phase transition process. Because the mass of the vaporized phase is usually much smaller than the mass of the liquid phase, the amount of heat consumed locally to vaporize trackeers amounts of liquid can be neglected in a macroscopic analysis.

Hence, the global evolution of the cavitating flow can be regarded as an isothermal process, although the heat of vaporization of the liquid is not negligible.

The macroscopic traciers of thermodynamic evolution on cavitation have been analysed in [ 10 ]: Cavitation desinence tracker to the process by which the vapour phase vanishes from the liquid, as a result of a pressure increase in the liquid flow that surrounds the bubbles.

During the final collapse stage of the bubbles, the temperature and pressure can become extremely high inside the bubbles, due to the inertia and compressibility of the gas-vapour bubble content. These high temperatures, and the presence of intense and high-frequency pressure waves, which are triggered by the peak pressure values that are reached after the bubble has collapsed, lead to the possible production of light emission sonoluminiscence and to erosive wear of the surfaces of the hydraulic systems.

Erosion occurs because the pressure waves remove the layer of oxides that had previously formed on the hydraulic system walls, and the air content in the liquid can therefore oxidize a new layer on these walls, which progressively become thinner.

A possible classification of vaporous cavitation can be made on the basis of the reasons for the pressure reduction. Acoustic cavitation is induced by the presence of pressure waves that propagate through the liquid region [ 1112 ]. This often takes place in hydraulic power systems, such as high-pressure diesel injection apparatus, continuously variable transmission systems, anti-lock braking systems and traction control systems. In such cases, acoustic cavitation can be accurately studied by means of refined, unsteady, one-dimensional models [ 13 — 16 ].

Hydrodynamic cavitation occurs when the reduction in pressure to the vapour tension level is caused by the hydrodynamic motion of the fluid, the features of which in turn depend on the geometrical layout of the flow passages [ 1718 ]. The liquid pressure can decrease locally, below the vapour tension level, according to Bernoulli’s equation, as a result of augmenting the gravitational energy, or the kinetic energy, of a fluid. An increase in gravitational energy can occur in a piping system, when the pipe elevation increases locally; an increase in kinetic energy can result from an abrupt reduction in the cross-section of the flow passages, such as in diesel injector holes [ 171920 ], but also because of a particular design of the walls that delimitate the flow, for example, around the rotor blades of dynamic pumps or in marine propellers [ 21 ].


Decreases in the local pressure caused by concentrated losses at the inlet of positive displacement and vane pumps, particularly when special valves are installed at the pump inlet to control the flow rate, can also result in cavitation. It is necessary to use two-dimensional or three-dimensional models to conduct an accurate simulation of hydrodynamic cavitation, because of its local nature.

Unlike acoustic cavitation, which is initiated by unsteady pressure waves that travel throughout the liquid, hydrodynamic cavitation can also take place in steady-state flows. Some typical hydrodynamic cavitation problems of engineering relevance in hydraulic power applications are those related to straight or conical nozzles and to orifices: Experimental methods generally provide a reliable basis to analyse hydrodynamic cavitation flows, but studies on cavitation in engineering components of reduced size, such as injector holes, orifices and miniaturized hydraulic valves, are difficult, because of the special equipment and techniques necessary to measure and visualize the flow.

In these cases, hydrodynamic cavitation can be studied using the hydrodynamic similarity theory [ 2223 ]. Different nozzle prototypes have been realized with optical materials, such as quartz and methacrylate, which allow the velocity components inside the nozzles to be visualized [ 24 ]: Observations in the laboratory can be extrapolated to natural-scale flows [ 33 — 36 ], through the use of a scale model and different fuels, and the obtained results can then be integrated with data from a few experimental studies on cavitation in real-size orifices [ 353738 ].

An alternative methodology to the experimental investigation of hydrodynamic cavitation is represented by its numerical computation. Models based on Navier—Stokes equations and standard turbulence models have become very attractive for the prediction of cavitating flow fields of arbitrary scales, because they are able to cope with the evaluation of secondary scale effects.

Furthermore, the governing partial differential equations of the model can be arranged in dimensionless form, in order to exploit the advantages of hydrodynamic similarity.

: Cavitation: Bubble Trackers () : : Books

However, two-dimensional and three-dimensional computation approaches to cavitation are not yet at a fully mature stage, as the single-phase calculations of acoustic cavitation instead are, and they still need improvements and practice in order to increase confidence in the results [ 39 ]. The conditions necessary to allow the experimental observations of a cavihation flow in one bibble to be transferred to another scale, according to the theory of hydrodynamic similarity [ 3334cavitagion41 ], are the geometrical similarity of the flows and the identification of some dimensionless groups, which are defined with some macroscopic quantities.

Thermal aspects, any local features of the problem, including details on the nozzle geometry for example, conicity of the nozzle and roundness at its entrycavitattion the fluid dynamic characterization of two-phase structures can initially be disregarded in an bubboe that is focused on the macroscopic effects of cavitation.

The nozzle discharge buble, C dcan be expressed as a function of the following dimensionless numbers in a turbulent field [ 4243 ]:. The functional dependencies stated in equation 2. On the other hand, experiments have also shown that real flows do not always obey the classical scaling theory, and discrepancies can occur between cavitation flows under natural and large-scale conditions [ 46 ].

The reasons for these discrepancies are: In other words, the scale effects associated with the micro-geometry of the system, the local flow phenomena cavvitation the liquid quality should have a negligible effect on the considered tests in tackers to make equation 2. As long as this condition is verified, only those discrepancies concerning the details of the cavitation description will occur if real- and large-scale nozzles are compared; otherwise micro-geometrical, local-flow and liquid-quality-scale effects should be characterized and modelled in an appropriate manner.

As can be inferred from figure 1cavitation takes place in the low-pressure region that forms at the nozzle entry [ 57 ], and in the zone around the section at which the jet flow area is at the minimum this section of area A c is referred to as the vena contracta.

The figure shows that the separation zone with length L sep and the cavitation zone with cavitatiln L cav do not generally coincide: After the main stream has reattached to the wall, the pressure reduction in the subsequent piece of the straight nozzle is due to wall friction, and a boundary layer starts growing from the reattachment point up to the nozzle exit [ 43 ]. The value of the cavitation number, i. Figure 2 schematically illustrates the influence of p 2 on the length of the cavitation region for a one-dimensional de Laval nozzle x is the axial coordinate along the nozzle.

If p 2 is diminished even further, the cavitation region, in which the pressure is equal to p vprogressively extends towards the nozzle exit. The pressure recovery from p v up to p 2 occurs in the divergent part of the de Laval nozzle, downstream of the cavitation region.

A classification of the cavitation regimes has been made in figure 3where L cav is the length of the cavitation region cf. Observations on small-scale nozzles have revealed the presence of bubbly flow and bubble foam patterns in the incipient, sub-cavitation and early transitional cavitation stages, while sheet-type cavitation, with the presence of long strips and vapour films, has been observed well into the transitional cavitation sub-regime, and in the supercavitation regime [ 51 ].

In other words, the features of the vapour structures at cavitation inception are almost the same regardless of the nozzle geometry, and the development and early evolution of these structures is not affected by this geometry. However, the shape of the cavitation structures, during the deep transitional regime and the supercavitation regime, depends on the nozzle geometry to a significant extent.


The high-speed photography of supercavitation flows [ 58 ] has revealed their unsteady and unstable nature. As soon as the flow starts to enter the supercavitation regime, a rapid collapse of the cavitation pockets can occur between the liquid core and the walls, according to a re-entrant jet mechanism [ 59 ].

It is believed that the re-entrant jet is created by the expansion of the flow in the closure region behind the cavity; this flow impinges on the wall and establishes a local stagnation point. On the upstream side of this stagnation point, conservation of the momentum forces the liquid to flow beneath the fixed cavity. The jet progresses towards the nozzle inlet and, even though no liquid layer can completely separate the vapour phase from the walls [ 54 ], it pinches off the fixed cavity and a vapour cloud is formed [ 54 ].

As the cloud is shed, the remaining cavity at the nozzle inlet again begins to grow. The separated cloud that is convected downstream eventually collapses in the relatively high-pressure region behind the flow-reattachment point. The motion of the re-entrant liquid jet is central to the periodic shedding of the cavitation cloud, but the mechanism that drives the phenomenon is still not fully known [ 54 ].

It has been observed [ 60 ] that the re-entrant jet is dominant during the earlier stages of the instability, whereas a propagating shock wave appears during the later stages for the intensive cloud-shedding phase [ 61 ].

This is illustrated in figure 3where the L cav versus CN curve exhibits a vertical inflection point between transitional cavitation and supercavitation. On the other hand, when the outflow is into a gas, experiments [ 2363 ] have shown that the liquid flow is unable to reattach to the nozzle walls at the lowest CN values. Cavitation disappears, and a jet that consists entirely cavktation liquid a glass-like flow [ 63 ] becomes completely detached from ttrackers nozzle cavitatioh The latter circumstance causes minimum values of the discharge coefficient [ 63 ], and thus reduces the liquid flow penetration in the downstream environment, which in turn results in altered spray characteristics.

Nevertheless, hydraulic flip also determines a sudden reduction in friction losses, because there is no contact between the liquid flow and the nozzle walls. Rounded inlet corners of straight nozzles also affect the recirculation flow that forms at the nozzle throat: L sep reduces and transition to hydraulic flip is more unlikely [ 67 ]. The nozzle discharge coefficient represents the hydraulic resistance of a nozzle to the flow passage.

It can cxvitation defined as. Different expressions of C d are available in the literature: Term C c is the contraction coefficient, which is defined as. As already mentioned, CN represents the main parameter necessary for the characterization of C d during cavitation [ 23 ].

CN is sometimes replaced by the following dimensionless number, which is a special form of the Euler number [ 5369 ]:. Figure 4 emphasizes the relationship between C d and CN: The data plotted in figure 4 a,bwhich refer to inside the cavitation region, that is, where C d depends significantly on CN, have been interpolated using equation 4.

Dependence of C d on CN. The dependence of C d on CN is not significant in the liquid flow regime, where the mass flow rate depends almost linearly on the square root of the pressure drop across the nozzle, i. A slight increase in C d can be observed in the initial cavitation stage in figure 4 cin line with the results of other visualization experiments [ 65 ].

This particular phenomenon may be explained by considering that the very small amount of bubbles, located at the inlet corner of the nozzle, smooth the internal flow, and thus improve the discharge coefficient [ 65 ].

A criterion that has been proposed to detect cavitation inception, which is related to the appearance of the first bubbles [ 24 ], pertains to the identification of CN start this is the CN value that corresponds to cavitation inception through the use of the value of CN that corresponds to the maximum of C d [ 62 ]. Mass flow rate, cavitation and choking conditions for diesel oil p 1 is constant and p 2 changes [ 24 ].

Online cavitatikn in colour.

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The greyscale images that are included in figure 5 refer to internal flow visualizations of the nozzle cavitarion by tracker of an optical system [ 24 ]. The cavitation zones are dark, and the darkness intensity bubbke as the cavitation intensity increases.

It can be observed that bubbles are already present in the spray within the nozzle before choking takes place. An empirical correlation that is often used to describe both the effects of Re and the aspect ratio on the discharge coefficient of the cylindrical nozzle is [ 70 ]. Figure 6 refers to water and a cylindrical nozzle with fixed L and d values.

The tests have been conducted by varying the upstream pressure p 1 for different levels of p 2and the solid line interpolates the experimental data in the liquid field, according to the formula that is reported in the graph.