Accoustic Cavitation As A Souce Of Ignition
And Its Possible Relevance To TWA Flight 800
by: JOHN D. UNSWORTH, MICHAEL
SHERAR, PH.D. and BRIAN LATTO, PH.D.
What follows are two passages from
Patent Application: U.S. 09/251,958 that introduce the description of
the invention:
Acoustic cavitation at or near the surface of liquid fuel that is
in contact with an air and fuel vapor mixture could cause ignition of
the air fuel vapor. This could occur in the absence of an electrical
discharge or other conventional ignition source.
Acoustic cavitation is the production of small bubbles in a liquid
exposed to a sound field. These bubbles can oscillate in size in a
stable manner (termed stable cavitation) or they can grow rapidly
followed by a violent collapse where temperatures of thousands of
degrees Kelvin can be produced (termed collapse cavitation). If such
a cavitation collapse event occurred at or near the surface of the
fuel, the energy produced could be sufficient to ignite the vapor
immediately above the surface. The production of collapse cavitation
in liquids has been well documented in the scientific literature.
It is possible, but unlikely that the heat produced by a collapsing
bubble of fuel vapor that contains no oxygen, could itself ignite the
fuel vapor and air above the liquid fuel stored in the tank. However,
although the temperature of a collapsing bubble can reach thousands of
degrees Kelvin, the heat is concentrated in a very tiny spot for only
a brief instant of time. The energy of the collapsing vapor bubble,
containing no oxygen, can be no greater than the sound energy that
created it, and this amount of energy would likely be quenched by the
relatively cool fuel that surrounds the collapsing bubble. For these
reasons cavitation has not been considered to be an ignition source.
What has been overlooked is that if the collapsing bubble itself
contains the fuel vapor and air mixture, that is it contains oxygen,
and it ignites as a result of the heat generated by the collapsing
bubble, much more energy is available to ignite the fuel vapor and air
mixture above the liquid fuel. This additional energy results from
the combustion of the mixture within the collapsing bubble.
A nucleating bubble containing both fuel vapor and air can occur in
a fuel tank in which the fuel is sloshing, mixing ambient air
(containing oxygen) with the fuel vapor. When the nucleating bubble
is subjected to sound having certain characteristics, the bubble will
first enlarge and then collapse. As the bubble collapses, the
temperature of the vapor in the bubble increases and ignition of the
fuel vapor and air mixture may occur. This process is the same as
occurs in diesel engines which burn kerosene fuels similar to those
burned in jet engines. Diesel engines do not rely on a spark igniting
the fuel, but instead rely on the air in the cylinder being heated
sufficiently, by the piston compressing the air, to in turn ignite the
diesel fuel. The pressure at which combustion typically occurs in a
diesel engine is instructive. The pressure just prior to ignition is
from 275 to 400 psi (1895 to 2755 kPa), far less that the maximum
pressures created by a cavitation event. Like a diesel ignition
event, the collapsing bubble of fuel vapor and air (containing oxygen)
produces sufficient heat to ignite the fuel vapor and air mixture
within the bubble. How this in turn causes the ignition of the main
fuel vapor and air chamber above the fuel depends on the varied
circumstances that exist within the sloshing fuel and air mixture.
Certainly a bubble of combusting fuel and air near the surface of the
fuel could have sufficient energy for ignition of the vapor chamber
above the fuel. The existence of foam on the surface of the fuel,
caused by sloshing, would also promote the spread of combustion into
the main fuel vapor chamber on top of the liquid fuel.
In order to calculate the minimum bubble size that upon cavitation
could ignite the fuel tank we assume that the energy E = 2 mJ is
required. From this assumption, the mass of fuel required
(mf) is given by: 
where HHV is higher heating value of the fuel. For hydrocarbons of
weight similar to kerosene constituents (we assume
C8H10), HHV = 44702 KJ/kg. Therefore the mass
of fuel required is 4.47 x 10-11 kg. The radius, r, of a
bubble that would contain this amount of fuel is determined by the
fuel/air mixture in the bubble and the atmospheric conditions. 
where r is the
bubble radius, r air is the
density of air, r f is the
density of the fuel and x is the fuel/air ratio. Rearranging gives:
The density of air (r
air) is determined by the pressure which was 50KPA at
14,000 feet (or approximately _ atmosphere). Assuming the air and
fuel in the tank were at 55 C, this gives the density of air = 0.531
kg/m3. Given that the density of kerosene (r f) is approximately
850kg/m3 and assuming a fuel air/fuel ratio (x) = 15 then
this gives an r = 0.67 mm.
The likelihood of collapse cavitation occurring is dependent on a
number of factors. These are the ambient pressure, the surface
tension of the liquid and the pre-existence of small bubbles in the
liquid (termed bubble nuclei) and the amplitude of the sound field in
the liquid. If small bubbles exist in the liquid, the threshold sound
field pressure amplitude, PT required to produce collapse
cavitation is given by the Blake threshold (Neppiras, E.A., Acoustic
Cavitation And Cyclic Processes, Ultrasonics 18, 201-209
(1980)). 
Where Ro is the bubble radius, s is the surface tension of the liquid, and
Po is the ambient pressure. For the case of low sound
frequencies and relatively large bubble sizes in the range calculated
above this equation reduces to:
In general, the
most favorable conditions for collapse cavitation to occur (i.e. when
the Blake threshold is low) are when the ambient pressure is low and
the surface tension is low. These conditions could occur in the fuel
tanks of aircraft.
An example of such conditions would exist in an airplane that has
fuel sloshing around in a near empty tank, creating small bubbles from
the agitation. Since, typically, the fuel tanks are not pressurized,
the pressure in the tanks would be low at elevated altitudes. For
example, at an altitude of 14,000 feet the ambient pressure is
approximately 0.5 atmospheres. In addition, the surface tension of
the fuel (kerosene) is naturally low compared to other liquids such as
water. At room temperature, the surface tension of kerosene is 25
dynes/cm or 0.025 Nm-1. Also, the surface tension would be
artificially low if the fuel temperature was warm due, for example to
its proximity to heat producing equipment such as an air conditioning
unit (as temperature increases, surface tension decreases). For this
example, if we assume an ambient pressure of 0.5 atmospheres and the
existence of bubbles with a radius of 0.67 mm, the Blake threshold
pressure is calculated to be 0.5 atmospheres. That is, the threshold
pressure amplitude is equal to atmospheric pressure and represents the
pressure required to put the fuel into tension. This is equivalent to
a sound intensity in the fuel (assuming a velocity of sound in the
fuel of 1500 ms-1) of 0.1 W cm-2. It is
possible that vibration caused by an electrical motor, transformer or
turning shaft in an engine could cause a sound field of this intensity
on the surface of the fuel that would be sufficient to cause collapse
cavitation, which in turn could ignite the fuel/air boundary.
The danger that acoustic cavitation could cause an explosion in a
fuel tank has not until now been appreciated. Measures to prevent
such an occurrence is the subject matter of this patent.
Also:
The relative speed of the engines may be important and
engine synchronizers that bring the operating RPM’s of the
engines closely together may cause greater cavitation when the
RPM’s are identical or approximately the same, but the phase of
the frequency generated is in an out of phase, causing constructive
and destructive interference. As the synchronizers attempt to bring
the engines into synchrony, the RPM’s of the engines get faster
and slower than each other as the identical RPM’s is located.
While this is occurring the phase of sound produced goes into and out
of phase, which may be the condition with the greatest risk of causing
cavitation.
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