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  • 1
    Electronic Resource
    Electronic Resource
    On the Sound Radiated by a Turbulent Bubbly Flow (1998)
    Springer
    Journal of engineering mathematics 34 (1998), S. 45-55 
    Details
    ISSN: 1573-2703
    Keywords: turbulence ; bubbly flow ; acoustics ; Mach number ; mixture.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract In this paper the sound emitted by a turbulent bubbly liquid is investigated, in particular for very dilute mixtures. The results are compared with those obtained by previous investigators, and with available experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004303401475
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    Paper (German National Licenses)
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  • 2
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    Gravity waves over a non-uniform flow (1969)
    Cambridge University Press
    Details
    Publication Date: 1969-12-15
    Description: This paper is concerned with the propagation of small amplitude gravity waves over a flow with non-uniform velocity distribution. For such a flow Burns derived a relation for the velocity of propagation in terms of the velocity distribution of the mean flow. This result is derived here in another way and some of its implications are discussed. It is shown that one of these is hardly acceptable physically. Burns's result holds only when a real value of the propagation velocity is assumed; the mentioned difficulties vanish if complex values are allowed for, implying damping or growth of the waves. Viscous effects which are the cause of damping or growth are important in the wall layer near the bottom and also at the critical depth, which is present when the wave speed is between zero and the fluid velocity at the free surface.In § 2 the basic equations for the present problem are given. In § 3 exchange of momentum and energy between wave and primary flow is discussed. This is analogous to what happens at the critical height in a wind flow over wind-driven gravity waves. In § 4 the viscous effects at the bottom are included in the analysis and the complex equation for the propagation velocity is derived. Finally in § 5 illustrations of the theory are given for long waves over running flow and for the flow along a ship advancing in a wavy sea. In these examples a negative curvature of the mean velocity profile is shown to have a stabilizing effect.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 3
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    Flow in the exit of open pipes during acoustic resonance (1980)
    Cambridge University Press
    Details
    Publication Date: 1980-07-25
    Description: The flow near the mouth of an open tube is examined, experimentally and theoretically, under conditions in which resonant acoustic waves are excited in the tube at the other end. If the edge of the tube is round, separation does not occur at high Strouhal numbers, which enables us to verify theoretical predictions for dissipation in the boundary layer and for acoustic radiation. Observation with the aid of schlieren pictures shows that in the case of a sharp edge vortices are formed during inflow. The vortices are shed from the pipe during outflow. Based on these observations a mathematical model is developed for the generation and shedding of vorticity. The main result of the analysis is a boundary condition for the pressure in the wave, to be applied near the mouth. The pressure amplitudes in the acoustic wave measured under resonance are compared with theoretical predictions made with the aid of the boundary condition obtained in the paper. © 1980, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    Wave Propagation in Gas–Liquid Media. By V. E. Nakoryakov, B. G. Pokusaev and I. R. Shreiber. CRC Press, 1993. 222 pp. ISBN 0-8493-9906-8. (1994)
    Cambridge University Press
    Details
    Publication Date: 1994-08-10
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    The mean rise velocity of pairwise-interacting bubbles in liquid (1993)
    Cambridge University Press
    Details
    Publication Date: 1993-06-01
    Description: This paper is concerned with calculations regarding a collection of small gas bubbles rising under buoyancy in a clear liquid. For dilute mixtures interactions can be restricted to those between two bubbles. In the analysis of binary interactions it is assumed that the Reynolds number for relative motion between bubbles and liquid is large, that surfactants, if present, do not modify the condition of zero tangential stress at the bubble-liquid interface, and that bubbles bounce at an encounter. A two-bubble probability density is derived from the analysis, valid on a short timescale associated with the interaction. It is shown that on a long timescale, based on viscous dissipation, clustering together of pairs takes place, most likely even when triple encounters are allowed for. An analysis is given of the vertical motion of pairs, followed by a calculation of the mean vertical bubble velocity with help of the (short timescale) probability density function. The result is compared with experimental data. © 1993, Cambridge University Press
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
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    On the equations of motion for mixtures of liquid and gas bubbles (1968)
    Cambridge University Press
    Details
    Publication Date: 1968-09-02
    Description: On the basis of previous work by the author, equations are derived describing one-dimensional unsteady flow in bubble-fluid mixtures. Attention is subsequently focused on pressure waves of small and moderate amplitude propagating through the mixture. Four characteristic lengths occur, namely, wavelength, amplitude, bubble diameter and inter-bubble distance. The significance of their relative magnitudes for the theory is discussed. It appears that for high gas content the dispersion is weak and then the conservation of mass and momentum lead to equations similar to the Boussinesq equations, describing long dispersive waves of finite amplitude on a fluid of finite depth. For waves propagating in one direction only, the corresponding equation is similar to the Korteweg–de Vries equation.It is shown that for mixtures of low gas content the frequency dispersion is in most cases not small. Finally, solutions of the Korteweg–de Vries equation representing cnoidal and solitary waves in a bubble–liquid mixture are given explicitly.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
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    Mechanics and physics of gas bubbles in liquids: a report on Euromech 98 (1978)
    Cambridge University Press
    Details
    Publication Date: 1978-08-01
    Description: Euromech 98 was held in Eindhoven inNovember 1977 with the authors as chairmen. The Colloquium was attended by 48 participants from a number of European countries. Bubbles play an important role in many areas of technology: Propeller-induced cavitation in ship building, cavitation in fluid machinery, nucleate boiling in reactorsand similar devices, and many processes (centrifuges, mixers) in the chemical process industry. A wide variety of research, both of fundamental and of more applied nature, is going on in universities and in industrial laboratories. Representatives from all theabove areas were included among the participants and consequently the topics raised in the presentations and discussions covered a very broad field. © 1978, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
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    Hydrodynamic interaction between gas bubbles in liquid (1976)
    Cambridge University Press
    Details
    Publication Date: 1976-09-09
    Description: A calculation is given of the velocity which a cloud of identical gas bubbles acquires when the liquid in which the cloud is immersed is impulsively accelerated. From the results an expression follows for the effective virtual mass of a bubble in a gas-bubble/liquid mixture. Further consideration is given to that part of the momentum flux in the mixture associated with relative motion between liquid and bubbles. An expression for this quantity is derived which appears to differ from the one used in practice. It is shown that qualitative support for the expression obtained here is provided by experimental observations reported in the literature. © 1976, Cambridge University Press. All rights reserved.
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    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 9
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    Two-phase flow equations for a dilute dispersion of gas bubbles in liquid (1984)
    Cambridge University Press
    Details
    Publication Date: 1984-11-01
    Description: Equations of motion correct to the first order of the gas concentration by volume are derived for a dispersion of gas bubbles in liquid through systematic averaging of the equations on the microlevel. First, by ensemble averaging, an expression for the average stress tensor is obtained, which is non-isotropic although the local stress tensors in the constituent phases are isotropic (viscosity is neglected). Next, by applying the same technique, the momentum-flux tensor of the entire mixture is obtained. An equation expressing the fact that the average force on a massless bubble is zero leads to a third relation. Complemented with mass-conservation equations for liquid and gas, these equations appear to constitute a completely hyperbolic system, unlike the systems with complex characteristics found previously. The characteristic speeds are calculated and shown to be related to the propagation speeds of acoustic waves and concentration waves. © 1984, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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