Transient cavitation

Tullis, J.P. Hydraulics of Pipelines Pumps, Valves. Cavitation. Transients. John Wiley Sons, Inc.. New York. NY. 1990,... 

Figure 8.1.13 Regions of stable cavitation, transient cavitation and dissolving bubbles for a frequency of 20 kHz in water at ambient temperature and a static pressure of 1 bar. Bubble radius R is normalized by the resonant bubble radius R,.

The main advantages of hydrophones are (1) the relative ease of use, (2) the fact that FFT analysis can be carried out, a feature which gives information on the type of cavitation (transient vs stable, access to chaos via a cascade of period doubling in the acoustic emissions from pulsating bubbles), (3) the topology of the reactors, (4) the shape of a pulsed signal in pulsed ultrasound, etc. ... 

It was expected that the cavitational transient pressures could improve the general conditions, in analogy with the positive effect of sonication on the addition of amines to acrylic esters (Eq. The sonochemical Baylis-Hillmarm reactions are somewhat disappointing, and the effect of sonication remains weak. Attempts to use different catalysts (e.g., amines adsorbed on various solid... 

The cycloaddition step can be influenced by the cavitational transient high pressures, but mechanistic elements are missing to go further in this analysis. 

Conventionally, either the yields are low or the conversion times are rather long. Under sonication, excellent yields are obtained in much shorter times. Mechanistically, the reaction is extremely complex, and an enormous number of isomers can theoretically be formed. It is then interesting to observe that sonication accelerates the overall process without inducing the presence of some of the by-products. In this respect, the simple interpretation, the rate increase of a biphasic process, can be insufficient. Since the cage compounds are, among the products, those with a smaller molecular volume, the role of the cavitational transient high pressures can be questioned. 

This chapter deals only with established regime (steady-state) flows in a hydranhc circuit. In this framewoik, we emphasize the difference between flows in convergent and divergent pipes, discuss the effect of turbulence on pipe flows, and tackle the problem of cavitation. Transient flows in hydraulic circuits will be dealt with in Chapter 6, when discussing water hammer phenomena. 

Fig. 1. Transient acoustic cavitation the origin of sonochemistry and sonoluminescence.

Cavitation Loosely regarded as related to water hammer and hydrauhc transients because it may cause similar vibration and equipment damage, cavitation is the phenomenon of collapse of vapor bubbles in flowing liquid. These bubbles may be formed anywhere the local liquid pressure drops below the vapor pressure, or they may be injected into the hquid, as when steam is sparged into water. Local low-pressure zones may be produced by local velocity increases (in accordance with the Bernouhi equation see the preceding Conservation Equations subsection) as in eddies or vortices, or near bound-aiy contours by rapid vibration of a boundaiy by separation of liquid during water hammer or by an overaU reduction in static pressure, as due to pressure drop in the suction line of a pump. 

Atomization = Eotvos numher, Eo Two-phase flows, free surface flows Compressible flow, hydraulic transients Cavitation... 

Cavitation Formation of transient voids or vacuum bubbles in a liquid stream passing over a surface is called cavitation. This is often encountered arouna propellers, rudders, and struts and in pumps. When these bubbles collapse on a metal surface, there is a severe impact or explosive effec t that can cause considerable mechanical damage, and corrosion can be greatly accelerated because of the destruction of protective films. Redesign or a more resistant metal is generally required to avoid this problem. 

Spall is the process of internal failure or rupture of condensed media through a mechanism of cavitation due to stresses in excess of the tensile strength of the material. Usually, a dynamic failure is implied where transient states of tensile stress within the body are brought about by the interaction of stress waves. Free surfaces are assumed to be well removed from the material point of interest and play no role in the spall process. 

Cavitations generate several effects. On one hand, both stable and transient cavitations generate turbulence and liquid circulation - acoustic streaming - in the proximity of the microbubble. This phenomenon enhances mass and heat transfer and improves (micro)mixing as well. In membrane systems, increase of fiux through the membrane and reduction of fouling has been observed [56]. 

There are two types in acoustic cavitation. One is transient cavitation and the other is stable cavitation [14, 15]. There are two definitions in transient cavitation. One is that the lifetime of a bubble is relatively short such as one or a few acoustic cycles as a bubble is fragmented into daughter bubbles due to its shape instability. The other is that bubbles are active in light emission (sonoluminescence (SL)) or chemical reactions (sonochemical reactions). Accordingly, there are two definitions in stable cavitation. One is that bubbles are shape stable and have a long lifetime. The other is that bubbles are inactive in SL and chemical reactions. There exist... 

In Fig. 1.1, the parameter space for transient and stable cavitation bubbles is shown in R0 (ambient bubble radius) - pa (acoustic amplitude) plane [15]. The ambient bubble radius is defined as the bubble radius when an acoustic wave (ultrasound) is absent. The acoustic amplitude is defined as the pressure amplitude of an acoustic wave (ultrasound). Here, transient and stable cavitation bubbles are defined by their shape stability. This is the result of numerical simulations of bubble pulsations. Above the thickest line, bubbles are those of transient cavitation. Below the thickest line, bubbles are those of stable cavitation. Near the left upper side, there is a region for bubbles of high-energy stable cavitation designated by Stable (strong nf0) . In the brackets, the type of acoustic cavitation noise is indicated. The acoustic cavitation noise is defined as acoustic emissions from... 

Fig. 1.1 The regions for transient cavitation bubbles and stable cavitation bubbles when they are defined by the shape stability of bubbles in the parameter space of ambient bubble radius (R0) and the acoustic amplitude (p ). The ultrasonic frequency is 515 kHz. The thickest line is the border between the region for stable cavitation bubbles and that for transient ones. The type of bubble pulsation has been indicated by the frequency spectrum of acoustic cavitation noise such as nf0 (periodic pulsation with the acoustic period), nfo/2 (doubled acoustic period), nf0/4 (quadrupled acoustic period), and chaotic (non-periodic pulsation). Any transient cavitation bubbles result in the broad-band noise due to the temporal fluctuation in the number of bubbles. Reprinted from Ultrasonics Sonochemistry, vol. 17, K.Yasui, T.Tuziuti, J. Lee, T.Kozuka, A.Towata, and Y. Iida, Numerical simulations of acoustic cavitation noise with the temporal fluctuation in the number of bubbles, pp. 460-472, Copyright (2010), with permission from Elsevier...

From Fig. 1.1, it is seen that stable cavitation bubbles are tiny bubbles of a few pm in ambient radius or relatively large bubbles of about 10 pm or more in radius at 515 kHz. The range of ambient radius for transient cavitation bubbles becomes... 

The temperature is higher than 5000 K for bubbles of 0.28 3.5 pm in ambient radius. For the linear resonance radius of 11 pm, it is only about 1000 K. In Fig. 1.9b, the rate of production of chemical species is shown. It is above 10s s 1 for bubbles of 0.28 8 pm in ambient radius. The minimum ambient radius coincides with the Blake threshold radius (Rgiake) f°r transient cavitation (active bubbles). It is calculated by the following formula [6]. 

Ashokkumar M, Lee J, Iida Y, Yasui K, Kozuka T, Tuziuti T, Towata A (2009) The detection and control of stable and transient acoustic cavitation bubbles. Phys Chem Chem Phys 11 10118-10121... 

Apart from the classification based on the mode of generation of cavities, cavitation can also be classified as transient cavitation and stable cavitation [3]. The classification is based on the maximum radius reached (resonant size), life time of cavity (which decides the extent of collapse) in the bulk of liquid and the pattern of cavity collapse. Generation of transient or stable cavitation usually depends on the set of operating parameters and constitution of the liquid medium. Depending on the specific application under question, it is very important to select particular set of operating conditions such that maximum effects are obtained with minimum possible energy consumption. 

Transient cavitation is generally due to gaseous or vapor filled cavities, which are believed to be produced at ultrasonic intensity greater than 10 W/cm2. Transient cavitation involves larger variation in the bubble sizes (maximum size reached by the cavity is few hundred times the initial size) over a time scale of few acoustic cycles. The life time of transient bubble is too small for any mass to flow by diffusion of the gas into or out of the bubble however evaporation and condensation of liquid within the cavity can take place freely. Hence, as there is no gas to act as cushion, the collapse is violent. Bubble dynamics analysis can be easily used to understand whether transient cavitation can occur for a particular set of operating conditions. A typical bubble dynamics profile for the case of transient cavitation has been given in Fig. 2.2. By assuming adiabatic collapse of bubble, the maximum temperature and pressure reached after the collapse can be estimated as follows [2]. 

Fig. 2.2 Radius and pressure profiles in the case of Transient Cavitation (Typical profile at frequency of irradiation = 20 kHz, Intensity of irradiation = 0.12 W/m2 and initial radius of the nuclei = 0.001 mm)...

The bubble formed in stable cavitation contains gas (and very small amount of vapor) at ultrasonic intensity in the range of 1-3 W/cm2. Stable cavitation involves formation of smaller bubbles with non linear oscillations over many acoustic cycles. The typical bubble dynamics profile for the case of stable cavitation has been shown in Fig. 2.3. The phenomenon of growth of bubbles in stable cavitation is due to rectified diffusion [4] where, influx of gas during the rarefaction is higher than the flux of gas going out during compression. The temperature and pressure generated in this type of cavitation is lower as compared to transient cavitation and can be estimated as ... 

Cavitation threshold, Intensity of cavitation, rate of chemical reaction Transient threshold Size of the nuclei (cavitation threshold)... 

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