Forced oscillations of spherical bubbles in a compressible viscous liquid (water) are calculated numerically. The response of bubbles to sound fields for a special parameter set is given along with examples of the pressure distribution around a single bubble during oscillation.To understand the emission of noise in liquids irradiated by sound with an intensity beyond the cavitation threshold knowledge is required of the response of bubbles to sound fields of different frequencies and different pressure amplitudes. Response curves have previously been given for bubbles oscillating in an incompressible liquid [1]. In this paper numerical calculations are given for bubbles in a compressible liquid. The compressibility becomes important as soon as bubble wall velocities become comparable with the speed of sound in the liquid.
The Bubble ModelThe GILMORE model [2] is based on the KIRKWOOO-BETHE hypothesis [3] which consists in specifying an invariant of the motion. For a compressible liquid two families of characteristic curves, xa(t) and xS(t), may be defined covering the r-t plane. The motion is then completely specified by two quantities, Xa and XS, which are such that Xa is an invariant of xa(t) and Xs is an invariant of xS(t). A fruitful approach to the solution of such problems has been the suggestion of KIRKWOOD and BETHE, that the function G = r (h + u2/2) is an adequate approximation to the invariant X a , when the other invariant Xs is everywhere constant. Here h is the specific enthalpy of the liquid, u is the particle speed and r is the distance from the middle of the bubble.A val ue of G is propagated along a curve xatt) with a speed u + c in such a manner that it remains ~nchanged. Here c is the local speed of sound. From this condition we may derive GILMORE's equation of motion of the interface:
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