Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-06T01:21:36.856Z Has data issue: false hasContentIssue false

6 - Homogeneous Bubbly Flows

Published online by Cambridge University Press:  05 October 2013

Christopher Earls Brennen
Christopher Earls Brennen
Affiliation:
California Institute of Technology
Get access

Summary

Introduction

When the concentration of bubbles in a flow exceeds some small value the bubbles will begin to have a substantial effect on the fluid dynamics of the suspending liquid. Analyses of the dynamics of this multiphase mixture then become significantly more complicated and important new phenomena may be manifest. In this chapter we discuss some of the analyses and phenomena that may occur in bubbly multiphase flow.

In the larger context of practical multiphase (or multicomponent) flows one finds a wide range of homogeneities, from those consisting of one phase (or component) that is very finely dispersed within the other phase (or component) to those that consist of two separate streams of the two phases (or components). In between are topologies that are less readily defined. The two asymptotic states are conveniently referred to as homogeneous and separated flow. One of the consequences of the topology is the extent to which relative motion between the phases can occur. It is clear that two different streams can readily travel at different velocities, and indeed such relative motion is an implicit part of the study of separated flows. On the other hand, it is clear from the results of Section 5.11 that any two phases could, in theory, be sufficiently well mixed and the disperse particle size sufficiently small so as to eliminate any significant relative motion.

Type
Chapter
Information
Cavitation and Bubble Dynamics , pp. 145 - 181
Publisher: Cambridge University Press
Print publication year: 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G.K. (1969). In Fluid Dynamics Transactions, 4, (eds: W., FizdonP., Kucharczyk, and W.J., Prosnak). Polish Sci. Publ., Warsaw.
Campbell, I.J. and Pitcher., A.S. (1958). Shock waves in a liquid containing gas bubbles. Proc. Roy. Soc. London, A, 243, 534–545.Google Scholar
Carstensen, E.L. and Foldy, L.L. (1947). Propagation of sound through a liquid containing bubbles. J. Acoust. Soc. Amer., 19, 481–501.Google Scholar
Chahine, G.L. (1982). Cloud cavitation: theory. Proc. 14th ONR Symp. on Naval Hydrodynamics, 165–194.
Chahine, G.L. and Duraiswami, R. (1992). Dynamical interactions in a multibubble cloud. ASME J. Fluids Eng., 114, 680–686.Google Scholar
Chapman, R.B. and Plesset, M.S. (1971). Thermal effects in the free oscillation of gas bubbles. ASME J. Basic Eng., 93, 373–376.Google Scholar
Crespo, A. (1969). Sound and shock waves in liquids containing bubbles. Phys. Fluids, 12, 2274–2282.Google Scholar
d'Agostino, L., and Brennen, C.E. (1983). On the acoustical dynamics of bubble clouds. ASME Cavitation and Multiphase Flow Forum, 72–75.Google Scholar
d'Agostino, L., and Brennen, C.E. (1988). Acoustical absorption and scattering cross-sections of spherical bubble clouds. J. Acoust. Soc. Am., 84, 2126–2134.Google Scholar
d'Agostino, L., and Brennen, C.E. (1989). Linearized dynamics of spherical bubble clouds. J. Fluid Mech., 199, 155–176.Google Scholar
d'Agostino, L., Brennen, C.E., and Acosta, A.J. (1988). Linearized dynamics of two-dimensional bubbly and cavitating flows over slender surfaces. J. Fluid Mech., 192, 485–509.Google Scholar
Foldy, L.L. (1945). The multiple scattering of waves. Phys. Rev., 67, 107–119.Google Scholar
Fox, F.E., Curley, S.R., and Larson, G.S. (1955). Phase velocity and absorption measurements in water containing air bubbles. J. Acoust. Soc. Am., 27, 534–539.Google Scholar
Gouse, S.W. and Brown, G.A. (1964). A survey of the velocity of sound in two-phase mixtures. ASME Paper 64-WA/FE-35.
Hanson, I., Kedrinskii, V.K., and Mørch, K.A. (1981). On the dynamics of cavity clusters. J. Appl. Phys., 15, 1725–1734.Google Scholar
Henry, R.E. and Fauske, H.K. (1971). The two-phase critical flow of one-component mixtures in nozzles, orifices, and short tubes. ASME J. Heat Transfer, 93, 179–187.Google Scholar
Karplus, H.B. (1958). The velocity of sound in a liquid containing gas bubbles. Illinois Inst. Tech. Rep. COO-248.
Kumar, S. and Brennen, C.E. (1991). Non-linear effects in the dynamics of clouds of bubbles. J. Acoust. Soc. Am., 89, 707–714.Google Scholar
Kumar, S. and Brennen, C.E. (1992). Harmonic cascading in bubble clouds. Proc. Int. Symp. on Propulsors and Cavitation, Hamburg, 171–179.
Kumar, S. and Brennen, C.E. (1993). Some nonlinear interactive effects in bubbly cavitation clouds. J. Fluid Mech., 253, 565–591.Google Scholar
Macpherson, J.D. (1957). The effect of gas bubbles on sound propagation in water. Proc. Phys. Soc. London, 70B, 85–92.Google Scholar
Maneely, D.J. (1962). A study of the expansion process of low quality steam through a de Laval nozzle. Univ. of Calif. Radiation Lab. Rep. UCRL-6230.
Minnaert, M. (1933). Musical air bubbles and the sound of running water. Phil. Mag., 16, 235–248.Google Scholar
Mørch, K.A. (1980). On the collapse of cavity cluster in flow cavitation. Proc. First Int. Conf. on Cavitation and Inhomogenieties in Underwater Acoustics, Springer Series in Electrophysics, 4, 95–100.Google Scholar
Mørch, K.A. (1981). Cavity cluster dynamics and cavitation erosion. Proc. ASME Cavitation and Polyphase Flow Forum, 1–10.
Muir, T.F. and Eichhorn, R. (1963). Compressible flow of an air-water mixture through a vertical two-dimensional converging-diverging nozzle. Proc. 1963 Heat Transfer and Fluid Mechanics Institute, Stanford Univ. Press, 183–204.
Neusen, K.F. (1962). Optimizing of flow parameters for the expansion of very low quality steam. Univ. of Calif. Radiation Lab. Rep. UCRL-6152.
Noordzij, L. (1973). Shock waves in mixtures of liquid and air bubbles. Ph.D. Thesis, Technische Hogeschool, Twente, Netherlands.
Noordzij, L. and van Wijngaarden, L. (1974). Relaxation effects, caused by relative motion, on short waves in gas-bubble/liquid mixtures. J. Fluid Mech., 66, 115–143.Google Scholar
Omta, R. (1987). Oscillations of a cloud of bubbles of small and not so small amplitude. J. Acoust. Soc. Am., 82, 1018–1033.Google Scholar
Petroff, C. (1993). The interaction of breaking solitary waves with an armored bed. Ph.D. Thesis, Calif. Inst. of Tech.
Silberman, E. (1957). Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am., 18, 925–933.Google Scholar
Symington, W.A. (1978). Analytical studies of steady and non-steady motion of a bubbly liquid. Ph.D. Thesis, Calif. Inst. of Tech.
Tangren, R.F., Dodge, C.H., and Seifert, H.S. (1949). Compressibility effects in two-phase flow. J. Appl. Phys., 20, No. 7, 637–645.Google Scholar
van Wijngaarden, L. (1964). On the collective collapse of a large number of gas bubbles in water. Proc. 11th Int. Cong. Appl. Mech., Springer-Verlag, Berlin, 854–861.
van Wijngaarden, L. (1972). One-dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech., 4, 369–396.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×