Supercavitation

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Underwater Speed Limits
(Following is the full text submitted to Scientific American. The published version was shortened for editorial reasons.)

"There appear to be two conceptual ways of approaching supercavitation. The generally accepted one derives from propeller cavitation theory and holds that the water is essentially boiled by dropping its pressure via abrupt acceleration. This creates a source of gaseous water vapor which creates the cavitation bubble. It is generally assumed that the cavitation bubble is filled with this water vapor. Indeed, in low speed (say torpedoes) supercavitation applications the cavity size is usually enhanced with ventilation gases. This fits well with the understanding that gas creates the bubble in the first place and appears to work well within that context. It also fits comfortably in the general framework of marine engineering.

Last September, at an ONR sponsored Supercavitation Conference, Dr. Kirschner (of Anteon Corporation) and I were discussing the idea of a theoretical speed limit for supercavitating objects, assuming material strength issues could be overcome. As previously mentioned, conventional wisdom holds that the cavity is created by the water vapor and therefore, at some speed, the volumetric rate at which vapor can be generated will become insufficient to support the formation of a cavitation bubble which will clear the body. In other words, at some velocity the rate at which the water boils will become insufficient to fill the volume of the "hole" in the water created by the passage of the projectile and the cavity will collapse.

For whatever reason, I have a different mental picture of how the bubble is created, perhaps due to my background in hypersonics in graduate school. In that field discontinuities and rarified flows are encountered in the course of normal business. I do not know if anyone else shares this view but Dr. Kirschner and I have discussed it at some length. In any case, I believe the process is fundamentally one of momentum transfer. The cavitator, be it a disk or cone or whatever, imparts a significant radial velocity (relative to the axis of flight) to the water it comes in contact with. In effect the water is thrown violently to the side. It therefore has a high radial momentum that is resisted by the pressure of the water around it. This pressure serves to slow its radial velocity and will bring it to a stop over a finite time. The accepted definition of cavitation number is compatible with this idea. In the meantime, assuming a circularly symmetric cavitator, a round "hole" has been created in the water. What is in this hole, other than the projectile? I believe it is a vacuum, at least initially. Of course the water on the interior face of the bubble begins to boil, but it can only boil so fast, even in a hard vacuum. At slow velocities the rate of boiling can create a fairly decent partial pressure of water vapor in the cavity. In the limit case, as velocity increases, the pressure inside the cavity in the vicinity of the projectile will go to zero. Eventually the pressure acting on the water will reverse its radial velocity and cause the cavity to close. However, the projectile will be long gone by that point. If this approach is correct then, except for finding a material to withstand the steady state stagnation pressure, there may be no hydrodynamic upper limit to the velocity of a supercavitating body.

In any case, perhaps there is room for both viewpoints. In fact, they may very well be opposite sides of the same theoretical coin. I would certainly be interested to know what other people in the field thought of this approach. Perhaps it would provide an interesting topic of discussion within the article?"

 

I cannot discuss about supercavitation, as I have not enough knowledge about it.
But I have a question for you. I have been following the '300 knots torpedo' thread, and I wonder what happens to the tremendous amount of energy that is put into the creation of the cavitation bubble and the torpedo propulsion. When the bubble collapses all this energy is suddenly liberated and I imagine bounces back creating a huge shock wave, something like a submarine explosion all along the torpedo wake...Am I right or not? I'd greatly appreciate your comments.

 

It stands to reason that it is not only water vapor in the cavitation bubble, but also whatever dissolved gases such as oxygen are in the water. So you would expect the rate of vacuum-mediated water vaporization to be only part of the limiting factor of gases in the cavitation envelope.

Water vapor is much denser than other gases, so I would think it would tend to give a different resistance signature.

 

I don't see any conflict between the two explanations. The boiling explanation does a good job of predicting incipient cavitation and the collapse of cavitation bubbles as they pass into higher pressure regions. At higher speeds, one can do a good job of predicting the outer flowfield by just considering the potential flow, like say, a jet of water hitting a small disk, and not pay any attention to the composition of what's inside the dividing streamline. At very high speeds, you're going to get more rarefied gas in the cavity. It's just all more of the same principles.

As you know from hypersonic flow, one can add additional species equations to the usual conservation equations for mass, momentum, and energy, and these species equations can track the conversion of liquid water into vapor. Or even the dissociation of water vapor into atomic hydrogen and oxygen, and the chemical recombination to HO, H20, O2 and H2, if it comes to that.

I don't know of any physical limit to the speed at which a rod penetrates a solid, so why would there be any limit to the speed at which a projectile can penetrate water? At high enough speeds, it's all going to be fluid anyway.