Measurement of air‐gun bubble oscillations

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2009-2024 ◽  
Author(s):  
Anton Ziolkowski
Keyword(s):  
Acoustic Radiation ◽  
Bubble Radius ◽  
Real Data ◽  
Equation Of Motion ◽  
Smooth Transition ◽  
Bubble Wall ◽  
Wall Velocity ◽  
Pressure Transducers ◽  
Air Gun ◽  
Bubble Oscillations

In this paper, I provide a theoretical basis for a practical approach to measuring the pressure field of an air gun array and present an algorithm for computing its wavefield from pressure measurements made at known positions in the vicinity of the gun ports. The theory for the oscillations of a single bubble is essentially a straight‐forward extension of Lamb’s original paper and provides a continuous, smooth transition from the oscillating wall of the bubble to the far‐field, preserving both the fluid flow and the acoustic radiation, all to the same accuracy and valid for bubbles with initial pressures up to about 200 atm (3000 psi or 20 MPa). The simplifying assumption, based on an argument of Lamb, is that the particle velocity potential obeys the linear acoustic wave equation. This is used then in the basic dynamic and kinematic equations to lead, without further approximations, to the nonlinear equation of motion of the bubble wall and the wavefield in the water. Given the initial bubble radius, the initial bubble wall velocity, and the pressure variation at any point inside or outside the bubble, the algorithm can be used to calculate the bubble motion and the acoustic wavefield. The interaction among air‐gun bubbles and the resultant total wavefield is formulated using the notional source concept, in which each bubble is replaced by an equivalent notional bubble obeying the same equation of motion but oscillating in water of hydrostatic pressure, thus allowing the wavefields of the notional bubbles to be superposed. A separate calibration experiment using the same pressure transducers and firing the guns individually allows the initial values of the bubble radius and bubble wall velocity to be determined for each gun. An appendix to the paper provides a test of the algorithm on real data from a single gun.

The Behavior of Bubbles in Non-Newtonian Lubricants

1977 ◽  
Vol 99 (4) ◽  
pp. 455-461 ◽  
Author(s):  
A. Shima ◽  
T. Tsujino
Keyword(s):  
Rheological Properties ◽  
Bubble Radius ◽  
Equation Of Motion ◽  
Crude Oils ◽  
Bubble Wall ◽  
Pressure Equation ◽  
Cavitation Damage ◽  
Lubricating Oils ◽  
Cavitation Bubbles ◽  
Impulse Pressure

The behavior of cavitation bubbles and the impulse pressure occurring from the bubble in non-Newtonian lubricants are analyzed as one of the studies on cavitation which is caused on the bearing metals and oil pressure valves. That is, the equation of motion for a bubble and the pressure equation can be derived by using the Sisko model which well represents the rheological properties of lubricants (lubricating greases, and crude oils in place of lubricating oils), and the variation with time of the bubble radius and the pressure and velocity at the bubble wall in greases and crude oils are numerically obtained. In consequence, it was found that the impulse pressure occurring from the collapse of comparatively large bubbles can be a cause for the cavitation damage.

scholarly journals The Rate of Growth of Vapor Bubbles in Superheated Water

1953 ◽  
Vol 20 (4) ◽  
pp. 537-545
Author(s):  
Paul Dergarabedian
Keyword(s):  
Bubble Radius ◽  
Equation Of Motion ◽  
Heat Diffusion ◽  
Air Bubbles ◽  
Finite Range ◽  
Superheated Water ◽  
Vapor Bubbles ◽  
Bubble Wall ◽  
Air Content ◽  
Rate Of Growth

Abstract Calculations are presented for the dynamic stability of vapor and air bubbles in superheated water. These calculations indicate that the values of the bubble radii for which the equilibrium is unstable are restricted to a finite range of radii whose values are governed by the temperature of the water and the initial air content in the bubble. Two theoretical solutions for the rate of growth of these unstable bubbles are considered: (a) Solution of the equation of motion of the bubble radius with the assumption that there is no heat diffusion across the bubble wall; (b) solution which includes the effect of heat diffusion. The two solutions differ appreciably. These two solutions are then compared with the experimental data on the growth of the vapor bubbles in superheated water. This comparison shows agreement with the solution with the effect of heat diffusion included.

Resonance in nonlinear bubble oscillations

1991 ◽  
Vol 224 ◽  
pp. 531-549 ◽  
Author(s):  
Michael S. Longuet-Higgins
Keyword(s):  
Acoustic Radiation ◽  
Second Harmonic ◽  
Initial Energy ◽  
Distortion Parameter ◽  
Near Resonance ◽  
Shape Oscillation ◽  
Order Of Magnitude ◽  
Shape Oscillations ◽  
Undamped Oscillations ◽  
Bubble Oscillations

In two recent papers (Longuet-Higgins 1989a,b) the author showed that the shape oscillations of bubbles can emit sound like a monopole source, at second order in the distortion parameter ε. In the second paper (LH2) it was predicted that the emission would be amplified when the second harmonic frequency 2σn of the shape oscillation approaches the frequency ω of the breathing mode. This ‘resonance’ would however be drastically limited by damping due to acoustic radiation and thermal diffusion. The predictions were confirmed by further numerical calculations in Longuet-Higgins (1990a).Ffowcs Williams & Guo (1991) have questioned the conclusions of LH2 on the grounds that near resonance there is a slow (secular) transfer of energy between the shape oscillation and the volumetric mode which tends to diminish the amplitude of the shape oscillation and hence falsify the perturbation analysis. They have also argued that the volumetric mode never grows sufficiently to produce sound of the stated order of magnitude. In the present paper we show that these assertions are unfounded. Ffowcs Williams & Guo considered only undamped oscillations. Here we show that when the appropriate damping is included in their analysis the secular transfer of energy becomes completely insignificant. The resulting pressure pulse (figure 5 below) is found to be essentially identical to that calculated in LH2, figure 3. Moreover, in the initial-value problem considered in LH2, the excitation of the volumetric mode takes place not by a secular energy transfer but by a resonance during the first few cycles of the shape oscillation. This accounts for the amplification near resonance found in Longuet-Higgins (1990a). Finally, it is pointed out that the initial energy of the shape oscillations is far greater than is required to produce the O(ε2) volume pulsations that were studied in LH2, and which were used for a comparison with field data. This acoustic radiation was not calculated by Ffowcs Williams & Guo.

On the theory of air‐gun bubble interactions

Geophysics ◽  
1988 ◽  
Vol 53 (2) ◽  
pp. 192-200 ◽  
Author(s):  
R. C. Bailey ◽  
P. B. Garces
Keyword(s):  
Ambient Pressure ◽  
Bubble Radius ◽  
Dynamical Equations ◽  
Local Pressure ◽  
Know How ◽  
R And D ◽  
Bubble Interactions ◽  
Interaction Terms ◽  
Air Gun ◽  
Marine Air

Calculation of the seismic signatures of marine air‐gun arrays often requires that the interactions among the bubbles from air guns be taken into account. The standard method of doing this is to use the Giles‐Johnston approximation in which a time‐dependent effective ambient pressure is calculated for each bubble as the sum of the true ambient pressure and the local pressure signals of all the other bubbles in the array. These effects of interaction have a relative importance in the dynamics proportional to (R/D), where R and D are the typical bubble radius and interbubble separation, respectively. To ensure that current methods of calculating signatures are accurate, it is necessary to know how good this approximation is. This paper shows that there are no interaction terms in the full dynamical equations proportional to [Formula: see text] or [Formula: see text], and that the errors of the Giles‐Johnston approximation are only of order [Formula: see text]. The Giles‐Johnston approximation is therefore justified even for fairly accurate signature calculations for noncoalescing bubbles. The analysis here also shows how to incorporate bubble motions and deformations into the dynamical equations, so that the errors can be reduced to order [Formula: see text] if desired.

scholarly journals Bubble wall velocity from holography

2021 ◽  
Vol 104 (12) ◽  
Author(s):  
Yago Bea ◽  
Jorge Casalderrey-Solana ◽  
Thanasis Giannakopoulos ◽  
David Mateos ◽  
Mikel Sanchez-Garitaonandia ◽  
...  
Keyword(s):  
Bubble Wall ◽  
Wall Velocity

On: “The signature of an air gun array: Computation from near‐field measurements including interactions”, by A. Ziolkowski, G. Parkes, L. Hatton, and T. Haugland (GEOPHYSICS, 47, p. 1413–1421.)

Geophysics ◽  
1983 ◽  
Vol 48 (9) ◽  
pp. 1293-1293
Author(s):  
Erhard Wielandt
Keyword(s):  
Near Field ◽  
Field Measurements ◽  
Air Gun ◽  
Pressure Term ◽  
Flow Pressure ◽  
Bubble Oscillations

I wish to put forward a few arguments in favor of the after‐flow pressure term which Keller and Kolodner (1956) retain in their calculation of bubble oscillations and which Ziolkowski et al consider as “absolutely negligible.”

Simple Model for Bubble-Wall Interaction

2014 ◽  
Author(s):  
Etienne Pelletier ◽  
C. Beguin ◽  
S. Etienne
Keyword(s):  
Bubble Radius ◽  
Viscous Drag ◽  
Air Bubbles ◽  
Bubble Wall ◽  
Proposed Model ◽  
Horizontal Wall ◽  
Wall Interaction ◽  
Definition Of ◽  
Potential Pressure ◽  
Good Agreement

We have developed a model for an ellipsoidal bubble colliding with a rigid horizontal wall based on potential flow theory. The model is then compared with experiments of air bubbles surrounded by water impacting a wall. 70 impacts were observed with bubble radius between 0.3 and 2 mm and different trajectory types (helicoidal, zig-zag). Deformation and height of the first impact are the main comparison points. The proposed model is in good agreement with the height of the rebound but tends to overestimate the maximal compression for both types of trajectories. We also propose a new relation for the viscous drag coefficient correction induced by the wall confinement as well as the definition of potential pressure forces acting on bubbles close to a wall.

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