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You are here: > News > June 29, 2012

Validated LeClair Cavitation Erosion Equation Predicts Cavitation Fusion Using Standard Physics

"The first validated and highly accurate general equation for cavitation erosion prediction. It is the E = MC2 of cavitation fusion. It predicts D-T fusion conditions are reached during cavitation reentrant jet impact into medium strength or higher materials. The LeClair cavitation erosion equation establishes the first sound theoretical basis for all types of cavitation fusion and is based only on well known and straightforward standard physics."

From NanoSpire
for Pure Energy Systems News

The ability to predict cavitation erosion based on material properties and flow conditions has long been sought. Cavitation erosion is seen in pumps, hydroelectric facilities, Navy ships, torpedoes and marine structures, diesel fuel injection nozzles, algae biodiesel production and many other devices. Cavitation erosion damage to all industries collectively is estimated to be in excess of $30 B annually worldwide. It is a problem with a pedigree, dating back to the days of famous fluid dynamicists such as Lord Rayleigh, who along with others began working on cavitation erosion in the early 1900's. Since this time, no one has been able to derive a general equation that is accurate for all materials. 

NanoSpire's research into nanofabrication with cavitation reentrant jets has led to the discovery of the root cause of cavitation erosion dynamics, based on first principals. The elusive general equation for cavitation erosion has been successfully derived by Mark LeClair and validated against ASTM-G32 cavitation erosion data for 22 different materials. The cavitation erosion equation also predicts the amount of cavitation processing per reentrant jet impact for processing nanophase materials in pharmaceutical and other applications, essential for accurate process control. NanoSpire's proprietary cavitation erosion equation will also allow the first predictive capability of time dependent cavitation erosion for complex 3D flows using CFD.

The LeClair cavitation erosion equation also serves another critical function, it is the E = MC2 of cavitation fusion. The equation predicts that the combination of temperatures of approximately one hundred thousand degrees K experienced by the reentrant jet passing through the hot collapsed cavitation bubble plasma just before impact, with pressures that reach into the hundreds of thousands of gigapascals at the impact surface of hard materials, satisfy the standard thermodynamic equation of state to ignite D-T fusion. This was achieved by coupling the effect of Van der Waals forces experienced during high speed cavitation reentrant jet impact with modified classical equations of high speed impact. This equation accurately predicts the effects of cavitation reentrant jet impact in our reactor, in P-F cells, and in other types of hydrodynamic cavitation overunity devices. It can also accurately predict pressures reached during ultrasonically driven bubble collapse fusion.

The significance of solving this equation is put into perspective when one considers quotes concerning the state of the art of cavitation erosion prediction, which is currently still a mystery to the other researchers in the field:

"The resistance of specific metals or other materials to liquid erosion, which is commonly evaluated by ASTM G32 (Standard Method for Vibratory Cavitation Erosion Test), does not depend on any one property, although many attempts have been made to correlate erosion damage with different intrinsic properties…hardness, true stress at fracture, corrosion fatigue strength, work hardening rate and ultimate resilience (one half the square of the ultimate strength, divided by the modulus of elasticity)…Even elaborate correlations often err by as much as 300%, and for untested materials may predict erosion rates that are in error by an order of magnitude or more from the actual rate determined by subsequent testing." (Liquid-Erosion Failures, F. Hammitt & F. Heymann, ASM Metals Handbook, vol. 10, pp. 160-167, 1975.) [Liquid Erosion Failures is an ASM (American Society of Materials) handbook, Liquid Failures is one of the chapter titles. It came out in 1975; it made a good reference to show the perspective on the state of the art of cavitation erosion over the years.]

"Despite the great deal of research the actual mechanism of cavitation erosion is still not fully clear". (On Cavitation In Fluid Power; Timo Koivula, Tampere University of Technology, Institute of Hydraulics and Automation, Proc. of 1st FPNI-PhD Symp. Hamburg (2000), pp. 371-382.)

"There is not a universal law for erosion rate (mass loss per unit time) evolution with period of exposure to cavitation. But in most cases, a little mass loss is observed at early stage of cavitation (incubation stage). This stage is often followed by a period of great increase of erosion rate (accumulation stage) or of a constant erosion rate (steady stage). After that, a decrease of erosion rate is often observed (attenuation stage)…But cavitation resistance is not an intrinsic property of material, but a system response. In spite of the nature of the material (composition, structure, heat treatment, geometry, surface roughness, residual stress, etc.), it depends largely on liquid property, flow speed, vibration characteristics, temperature, hydrostatic pressure, etc. For certain materials, cavitation resistance is related to hardness, but for most metallic materials it is more closely related to fatigue strength of materials. Resistance [19]. So, it is very difficult to establish a universal rule for materials choice to minimize cavitation erosion wear. In practical applications, laboratory tests are often used to evaluate cavitation resistance of a group of candidate materials. (Cavitation wear in plain bearing: Case study;Yan-Ming Chenaand Jacques Mongis; D'epartement Mat 'eriauxet Surfaces, CETIM, 52 Av. F'elix-Louat, 60300 Senlis, France, M'ecanique & Industries 6; pp. 195–201 (2005).)

The results of the LeClair cavitation erosion equation predictions are shown compared to the 22 different materials used in the ASTM G32 cavitation erosion data (acrylic plastic, number 23, is predicted for illustration but not part of the ASTM G32 data set). Plots of the thickness of the ultra high pressure Van der Waals zone that exists at the surface is shown, along with a plot of the prediction of the pressures during cavitation reentrant jet impact into the ASTM-G32 materials. The X-axis of the pressure plot is a proprietary material parameter:

Carbon Steel


Ausformed 12% Cr Tool Steel


Maraging Steel


Gray Cast Iron


Tool Steels H26,T1,T2,T3


SS 300 Series (18-8)


SS 410 Series


SS 630,631


Stellite 6


Stellite 6B


Stellite 12 Cast




Aluminum Alloys


Copper 260,268,280


Copper 614,953


Copper 628, 630, 955


Copper 862,863,865


Copper 713,719


Copper 903








(click on images for larger version)

Different scale...

Q. Why Don't you Publish the Equation?

On July 01, 2012 2:51 PM MDT, Mark wrote:

I have already disclosed so much to the world in my previous releases that the cat is out of the bag and can't be stopped, even if they manage to stop us. Even if it takes fifty years I will rest well knowing that the baby has been delivered.

The world's problems are political, not technological.

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Page composed by Sterling D. Allan
Last updated July 10, 2012 18:37:08 -0400 



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