1. Cavitation and Bubble Dynamics
Ch.3 Cavitation Bubble Collapse

2. Cavitation and Bubble Dynamics
Bubble collapse
Thermally controlled collapse
Thermal effects during collapse
Nonspherical Shape
Cavitation noise
Luminescence

3. r is distance from center of bubble
Bubble Collapse
Collapse is a major concern because of damage and noise caused by high velocities, pressures and temperatures that occur
When the bubble contains some noncondensable gas or when thermal effects become significant, the solution to the Rayleigh-Plesset equation becomes more complex since pressure inside the bubble is no longer constant
Compressibility of gas in the bubble is important because of shock waves formed during the rebounding phase that follows collapse. Little effect on bubble dynamics.
Hickling and Plesset found the amplitude of the pressure pulse that radiates into the liquid has a peak amplitude
r is distance from center of bubble

4. Thermally Controlled Collapse
Introduce a new time scale for thermal effects to become significant during collapse, tc4
Recalling Thermodynamic effect from CH. 2:
If thermally controlled growth will begin early in the collapse phase
From Ch.2, the time for total collapse from R=Ro to R=0:
With positive-time pressure:

5. Thermal Effects during Collapse
Thermal effects are important in the final stages of collapse when bubble contents are highly compressed
Since collapse occurs on a small time scale, fractions of a millisecond, the noncondensable gas is treated as adiabatic
Fujikawa and Akamatsu (1980) found conditions at the center of the bubble in water at STP to be 848 bar and 6700°K
Interface temperature was 3400°K
time scale of this collapse was approximately 2μs
After this point interface was 300°K

6. Nonspherical Shape during Collapse
2 important stages in collapse
Early stage; before thermal effects dominate
Characterized by behavior
Rebound; wherein switches sign and takes on a very large positive value
Instabilities in bubble during collapse manifest several ways:
A bubble made entirely of vapor that collapses to a size orders of magnitude smaller than the maximum radius rebounds as a cloud of smaller bubbles
Bubble filled with gas are less unstable and rebound nearly spherically

7. Nonspherical Shape during Collapse
Reentrant microjet forms because of asymmetry in the acceleration of the interface, often due to a boundary
Jet is aimed at the boundary
Gravity can affect collapse enough to form a jet

8. Nonspherical Shape during Collapse
Other bubbles can also affect the acceleration of the bubble interface
Collapse will direct jet at the center of the inner bubble in a cloud or group of bubbles

9. Nonspherical Shape during Collapse
Free surface can cause faster acceleration
Jet is directed away from free surface
Microjet causes a 2-3x larger pressure pulse than a remnant cloud collapse

10. Noise is often the first indicator of cavitation
Cavitation Noise
Recalling the basic force balance with zero mass transport at the interface and substituting volume V(t) for bubble radius R(t), we can get the pressure result in the far field at distance r:
Noise is often the first indicator of cavitation
Cavitation noise has been identified to have the trend
Spectral Power (RMS of acoustic pressure) above 5kHz drastically increased when the flow reaches the incipient cavitation number

11. Cavitation Noise
Acoustic power spectra from a model spool valve operating under noncavitating (σ=0.523) and cavitating (σ= and 0.342) conditions.

12. In acoustic cavitation, this phenomenon is called Sonoluminescence
Spike in pressure and temperature causes light emission during bubble collapse due to ionization of the noncondensable gas
Spherical, inward-propagating shock waves that focus on the center of the bubble
Nonspherical collapse (ie: in a fluid flow) do not allow significant shock focusing so the effect is rare
In acoustic cavitation, this phenomenon is called Sonoluminescence
Surface tension and vapor pressure play important roles determining the sonoluminescent flux
Conduction of heat in the noncondensable gas is important, therefore the breakup of the bubble could completely eliminate it