### Cavitation

October 16, 2017

We think of liquids and gases as being soft materials, far too soft to damage anything as hard as steel. I discovered that this is not always the case when I was asked to design a sensor to detect the onset of cavitation in an hydraulic pump. Mechanical action on a liquid can create bubbles through a rapid decrease in pressure. When this is followed by a a rapid change to higher pressure, these bubble will implode to generate an intense shock wave.

While the impact from a bubble might not be enough to dislodge material from a metal, all metals are subject to cyclic fatigue damage in which repeated pulling and pushing (tension and compression) weakens the material. Cavitation damage can be seen in ship propeller blades (see figure), pump impellers, and pipe bends that cause sudden change in the direction of rapidly moving liquid.

Cavitation damage on a ship propeller.

(US National Park Service photo)

Although the term, "cavitation," wasn't used, the phenomenon was first mentioned by Leonhard Euler (1707-1783) in his 1754 paper, "Théorie plus complette des machines qui sont mises en mouvement par la réaction de l'eau (A more complete theory of machines that are set in motion by reaction with water).[1] The term, "cavitation," was coined by R. E. Froude and first used by Barnaby and Thornycroft in 1893.[2] Barnaby and Parsons discovered that cavitation was responsible for the propeller failure of the British warship, HMS Daring. Parsons built a water version of a wind tunnel in 1895 to assess cavitation damage.[2]

The physics of cavitation was investigated by Rayleigh, who analyzed the collapse of a void in a large liquid mass in 1917.[3] The Rayleigh–Plesset equation, which is an ordinary differential equation describing the dynamics of cavitation, makes the simplifying assumption that the void is spherical. The voids are actually more like hemispheres, since they need to be nucleated on a surface.

Mechanical action is not the only way to create cavitation. Creating a transient local heating in the liquid, as by a focused laser pulse or an electrical discharge, will create a bubble. During bubble collapse, the temperature and pressure of the gases in the bubble soar to extremes, with temperatures often rising to thousands of kelvins, and pressure approaching hundreds of atmospheres. Cavitation can cause sonoluminescence (see figure).

A bubble acoustically created in a noble gas saturated liquid will produce light during cavitation collapse. It's believed that the high temperature of the gas inside the collapsing bubble excites the gas to cause light emission.

Wikimedia Commons image (simplified) by Aolzick.

A spectacular demonstration of cavitation is found in the many YouTube videos of the "breaking (beer) bottle trick" in which sharply striking the top of the bottle breaks its bottom. Now a team of scientists from Utah State University (Logan, Utah), the Tokyo University of Agriculture and Technology (Tokyo, Japan), the Naval Undersea Warfare Center (Newport, Rhode Island), and Brigham Young University (Provo, Utah) has done a detailed analysis of the cavitation system of the breaking bottle to develop an equation that more accurately predicts cavitation.[4-5] Their experimental results are presented in an article in the Proceedings of the National Academy of Sciences.[4]

A more forceful demonstration of the "breaking bottle trick" using a rubber mallet.

(Utah State University image.)

The conventional way to quantify cavitation is by a variant of a dimensionless parameter, called the Euler number. While this cavitation number is good at predicting the onset of cavitation for fluid flow, as around propellers and in pumps, it doesn't accurately predict cavitation in sharply accelerated liquids, as in the breaking bottle case.[4-5] says Tadd Truscott, an associate professor of mechanical engineering at Utah State University and lead author of the study,
"The traditional formula would tell us cavitation won't happen by smacking your palm against the top of a bottle... but experience tells us otherwise. The bottle will usually shatter, and now we have photographic evidence of cavitation bubbles forming in the bottle and their subsequent collapse and shockwaves. This tells us the conventional cavitation number doesn't always work correctly."[5]
The research team proposed an alternative cavitation number that's better at predicting the onset of cavitation caused by a sudden acceleration rather than a large fluid velocity.[4] This new cavitation number is based on acceleration and fluid depth, and not merely on velocity.[4] Cavitation breakage of dropped test tubes was analyzed using high-speed photography. When an empty glass test tube was dropped from a 200 millimeter height onto the floor, the impact with the floor did not break the glass when it was empty. However, when the tube was filled with silicone oil, a cavitation bubble forms at t = 0.25 ms, and it collapses at 0.35 ms. Fracture immediately develops at the location of the cavitation bubble collapse (see photos).[4]

Cavitation by dropping a sealed test tube filled with silicone oil. Note that the drop, itself, doesn't break the tube; rather, the cavitation bubble formed at the inside surface does. (Utah State University image.)[4]

To validate this new number, experiments were conducted to determine the threshold for cavitation in a variety of systems. Their new cavitation equation correctly determined the onset of cavitation.[5] This can have consequences beyond engineered fluid systems, since some brain injuries are the result of acceleration-induced cavitation.[5]

Two routes to cavitation by acceleration. Top impact (left) and bottom impact (right) give a change in the water column height. (Schematic based on fig. 2 of ref. 4.)[4]

### References:

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