HIGH FREQUENCY THERMOACOUSTIC ENERGY CONVERTER
BACKGROUND
The present application has been at least partially funded by the Office of Naval Research contract number N00014-99-1-0705-00001.
The Field of the Invention: The present invention relates generally to thermoacoustic devices. More specifically, the invention relates to a high frequency thermoacoustic energy converter that performs a two-step energy conversion process, wherein heat is converted to sound, and then sound is converted to electricity, wherein heat is converted to sound in a high frequency range, and then the sound energy is converted to electricity by an electro- mechanical transducer.
Background of the Invention: The concept of converting heat to sound has been known for over two hundred years. Consider the "singing pipe" 10 shown in figure 1 where heat is applied to a closed end of a resonant tube 12. A metal mesh 14 within the tube 12 has a "hot" end 16 near the heated end of the resonant tube 12, and a "cold" end 18 further from the heat source 20. The terms "hot" and "cold" refer to their relative temperatures with respect to each other. The "hot" end could be at room temperature. The important parameter άs thus not the actual temperature, but the temperature gradient.
An acoustical standing wave set up in the resonator 12 forces a working fluid (a gas) within the resonator to undergo a cycle of compression, heating, expansion, and cooling. In this case, the thermal
energy is converted into acoustical energy and it maintains the standing waves .
The work of converting heat to sound has been moved forward through the development of thermoacoustical refrigerators, as disclosed in a patent application titled HIGH FREQUENCY THERMOACOUSTIC REFRIGERATOR, having serial number 09/898,539, and filed 07/02/01, which is incorporated herein by reference. Essentially, the conversion of heat to electricity by the present invention can be thought of as the opposite process performed by the thermoacoustic refrigerator. Thus, instead of applying energy to a piezoelectric element to thereby cool a device, energy is being taken and converted from a heat source itself.
Previous early attempts to create a thermoacoustic energy converter have failed for various reasons. For example, the process was performed in prior art devices operating at around 100 Hz which would convert the low frequency sound to electricity. However, the process was abandoned by those skilled in the art because of the very low efficiency of the energy conversion process at low frequencies . A prior art process for direct conversion of heat to electricity utilizes a permanent magnet and a moving coil. This process is costly because of the magnet, it is bulky and heavy, and efficiency decreases as frequency of the device increases, making high frequency operation impractical. The device itself can also cause magnetic interference with nearby magnetically sensitive devices, precluding use in certain environments.
Accordingly, it would be an advantage over the prior art to provide an efficient energy conversion
process. It would also be an advantage to operate with high output power densities.
In order to make the thermoacoustic energy conversion process practical, it is desirable to operate the device at high frequencies. High frequencies result in more efficient operation of an electro-mechanical transducer, such as a piezoelectric element that is to be used in the present invention for the conversion of sound energy to electricity. Another advantage of operation at high frequencies comes from a comparison with all of the prior art thermoacoustic devices that are relatively large compared to semiconductor devices and biological samples. Thus, it would be another advantage to make the thermoacoustic energy converter small enough to be operable with such devices and samples. It will be shown that as the operating frequency of the invention increases, there is a corresponding decrease in the size of the resonator, and hence the device. A substantial portion of the discussion of the present invention is directed towards the prime mover, so it is important to understand its operation. Figure 2 is a cross-sectional view of a prime mover 22 as taught in the prior art. The prime mover 22 is the simplest thermoacoustic engine that requires no moving parts. Steady heat producing a temperature difference across a stack 24 excites a resonator 26, thereby generating intense sound. The temperature gradient across the stack 24 forces the Brownian motion of gas molecules within the resonator 26 to diffuse down the gradient, thereby causing these to emit sharp pressure pulses at the end of the stack which then excite a sound wave in the resonator. In other words, random thermal motion of gas molecules is converted by the temperature gradient across stack 24 to coherent sound
waves. The pressure vibrations or oscillations are sustained by means of positive feedback. At the opposite ends of the stack 24 are heat exchangers 28, 29. It is noted that there is an onset temperature difference (i.e. a gradient) which initiates the oscillation, while below the onset temperature level, the oscillations do not all become coherent.
An important element of the prime mover 22 in figure 2 is the stack 24. The stack 24 is the portion of the prime mover 22 where there is a thermal interaction of the sound field with a plate or a series of plates that make up the stack 24. It is a weak thermal interaction characterized by a thermal time constant given by ωτ~l where ω is the audio pump frequency and τ is the thermal relaxation time for a thin layer of gas to interact thermally with a plate or stack 22. The amount of gas interacting with the stack 22 is determined approximately by the surface area of the stack and by a thermal penetration depth δk given by: δk = (2κ/ω)% Here K represents the thermal diffusivity of the working fluid. By increasing ω, the weak coupling condition is met by a reduction of δk and hence of τ . The amount of this gas has an important dependence on the frequency of the audio drive . In a high frequency prime mover, smaller distances and masses are utilized thus making the heat conduction process relatively quick. What is needed is a thermoacoustic energy converter that utilizes heat to generate electricity that can be used as desired, including the cooling of a device that is generating the heat driving the thermoacoustic energy converter.
Summary of Invention: It is an object of the present invention to provide a thermoacoustic energy converter that utilizes high acoustic frequencies and into the ultrasonic range to generate electricity. it is another object to provide a thermoacoustic energy converter which uses relatively small temperature differences across a stack confined within a resonator to attain the high acoustic and ultrasonic frequencies. t is another object to provide a thermoacoustic energy converter that is relatively uncomplicated, inexpensive to manufacture, and relatively compact.
Ifc. is another object to provide a thermoacoustic "energy converter that efficiently converts heat to sound which is then converted to electricity.
It is another object to provide a thermoacoustic energy converter that can be easily adapted for further miniaturization.
It is another object to provide a thermoacoustic energy converter that has a quick response and fast equilibration time for small devices.
It is another object to provide a thermoacoustic energy converter that utilizes an efficient frequency range for a piezoelectric element to produce electricity because such elements are relatively light, small, efficient, and inexpensive.
It is another object to provide a thermoacoustic energy converter in which some components, such as heat exchangers, can be fabricated using photolithography and other film technologies.
It is another object to provide a thermoacoustic energy converter in which the power density of the device is relatively high.
It is another object to provide a thermoacoustic energy converter that is suitable for operation within small electronic components or biological systems.
In a preferred embodiment, the present invention is a thermoacoustic energy converter comprised of a resonator that also functions as a housing for an electro-mechanical transducer, a stack and a pair of heat exchangers positioned on opposite sides of the stack, wherein the electro-mechanical transducer is a piezoelectric device that can operate at high frequencies that extend into ultrasonic frequencies, wherein the stack is formed from random fibers that are comprised of a material having poor thermal conductivity, wherein the heat exchangers are preferably comprised of a material having good thermal conductivity, wherein the resonator contains a working fluid, such as air or other gases, and wherein heat energy is converted to sound energy, and sound energy is converted to electricity to thereby drive electrical devices, such as a refrigeration unit for more efficient cooling.
In a first aspect of the invention, the thermoacoustic energy converter operates at a frequency of at least 2,000 Hz. In a second aspect of the invention, operating at a high frequency enables the thermoacoustic energy converter to be made relatively small in size because the wavelength at such frequencies enables use of a short resonator. In a third aspect of the invention, the size of the thermoacoustic energy converter is a function of the wavelength of the sound wave with which it operates .
In a fourth aspect of the invention, the thermoacoustic energy converter includes an elongate
resonator defining a generally cylindrical chamber whose length is a function of the wavelength of sound produced by the temperature difference across a stack.
In a fifth aspect of the invention, the thermoacoustic energy converter includes an acoustic cavity disposed at an end of the resonator opposite the electro-mechanical transducer.
In a sixth aspect of the invention, an onset temperature difference for oscillations of the thermoacoustic energy converter is lowered by utilizing the acoustic cavity.
In a seventh aspect of the invention, an array of prime movers can be utilized in order to operate in parallel, generate more power in a smaller space, and reinforce each other.
In an eight aspect of the invention, a non-random stack is provided between heat exchangers in order to provide a thermoacoustic energy converter.
In a ninth aspect of the invention, a gap is disposed between heat exchangers, the gap being filled by the working fluid, to thereby provide a thermoacoustic energy converter.
These and other objects, features, advantages and alternative aspects of the present invention will become apparent to those skilled in the art from a consideration of the following detailed description taken in combination with the accompanying drawings.
Description of the Drawings : Figure 1 is a cross-sectional side view of a singing pipe as known to those skilled in the prior art.
Figure 2 is a cross-sectional side view of a prime mover as known to those skilled in the prior art .
Figure 3 is a cross-sectional side view of a thermoacoustic energy converter that is made in accordance with the principles of the present invention. Figure 4 is a cross-sectional side view of a stack formed from random fibers .
Figure 5 is a schematic top view of a first embodiment of a heat exchanger.
Figure 6 is a schematic top view of a second embodiment of a heat exchanger.
Figure 7 is a cross-sectional side view of a thermoacoustic energy converter that is operating with an open resonator.
Figure 8 is a cross-sectional side view of a thermoacoustic energy converter that is operating with a closed resonator.
Figure 9 is a cross-sectional side view of a thermoacoustic energy converter that is operating with an acoustic cavity coupled to the resonator. Figure 10A is a cross-sectional side view of another embodiment of a thermoacoustic energy converter that utilizes a non-random stack.
Figure 10B is an end view of stack X along the lines A-A, as shown in figure 10A. Figure 11 is a cross-sectional side view of another embodiment of a thermoacoustic energy converter that utilizes a gap between heat exchangers.
Figure 12 is a perspective view of another embodiment of a thermoacoustic energy converter that is comprised of an array of prime movers in parallel.
Figure 13 is a cross-sectional side view of the embodiment of the array of prime movers shown in figure 12.
Detailed Description; Reference will now be made to the drawings in which the various elements of the present invention will be given numerical designations and in which the invention will be discussed so as to enable one skilled in the art to make and use the invention. It is to be understood that the following description is only exemplary of the principles of the present invention, and should not be viewed as narrowing the claims which follow. The presently preferred embodiment is described operating at a frequency of at least 2,000 Hz, and preferably above 5,000 Hz. It should be remembered that this is only an example, and should not be considered limiting. After gaining an understanding of the present invention, those skilled in the art will appreciate that the frequency of operation and the size of components used in the thermoacoustic energy converter can be modified in accordance with the teachings provided in order to obtain a device that will perform in an optimum manner for the given operating frequencies.
Referring now to Figure 3, a thermoacoustic energy converter is shown in a cross-sectional view, and generally indicated at 40. The thermoacoustic energy converter 40 is comprised of a resonator 42 forming an enclosure for housing the components of the thermoacoustic energy converter 40. The resonator 42 has a first closed end 44 and a second end 46, and is preferably of a generally cylindrical configuration for simplicity. However, other geometries such as rectangular, square, hexagonal, octagonal or other symmetric shapes, are also contemplated. The second end 46 can be closed, open, or be comprised of an acoustic load as will be described in other embodiments. Assume that the second end 46 is open in
figure 3 , thereby providing a quarter wavelength resonator.
Housed within the resonator 42 proximate the first closed end 44 is an electro-mechanical transducer 48. The electro-mechanical transducer 48 in the presently preferred embodiment is a piezoelectric element. The piezoelectric element 48 is capable of efficiently converting high frequency sounds that impinge upon it into electricity. The position of the piezoelectric element 48 is a function of the wavelength of the device. The piezoelectric element 48, such as a monomorph, should be placed at a pressure antinode, such that the piezoelectric element forms the closed end of a quarter wave resonator. Positioned between the piezoelectric element 48 and the second end 46 is the stack 50. The stack 50, as will be described in more detail, has a density that is inversely proportionate to the thermal penetration depth of a working fluid 52 contained within the resonator 42. The stack 50 is essentially "sandwiched" between a pair of heat exchangers 54 and 56. That is, the exchangers 54 and 56 are adjacent to and abut the ends 58 and 60, respectively, of the stack 50. Typical heat exchangers of the present invention are separated by 0.1 mm to 1 mm, depending upon the operating frequency.
In the present invention, one of the heat exchangers 54, 56 will be the "hot" exchanger. The hot exchanger will be nearest to the object from which heat is being drawn to generate electricity.
Conversely, the other heat exchanger must therefore be the "cold" exchanger. Heat is delivered to the hot exchanger via some type of thermal coupling mechanism as is known to those skilled in the art, and will be shown in figures 7, 8 and 9. However, placement of
the thermal coupling mechanism will generally depend on a factor such as the temperature of the room in which the thermoacoustic energy converter is operating. In order to produce a thermoacoustic energy converter that is relatively simple and inexpensive to manufacture, the working fluid 52 within the resonator 42 is preferably air at 1 atmosphere. This requires no special construction to provide. It is contemplated, however, that other gases and combinations of gases at higher pressures may be utilized to increase the efficiency of heat removal. Generally, the gases used as the working fluid are inert . The higher the temperature gradient across the stack 50, the greater the efficiency and the greater the electrical output of the thermoacoustic energy converter. In order to obtain a high temperature gradient, the nature of the stack 50 is critical to the invention. The stack 50 of the presently preferred embodiment is comprised of random fibers preferably in the form of cotton, glass wool, or a perforated aerogel (e.g., a silicon dioxide glass structure having a density of approximately 0.1 grams/cc) or some other similar material known in the art which will provide high surface area for interaction with sound but low acoustic attenuation. However, another material that can be used for the stack is not an open-celled material, but is instead threads of metal, such as stainless steel wool, and iron wool, as will be shown in figure 10. Finally, experimental results demonstrated a third design for the stack as will be shown in figure 11.
The first type of stack of the present invention that is shown in figure 3 is essentially a randomly
configured, open-celled material having a relatively high surface area. Such an open celled stack material allows sound to propagate and will have good thermal contact with the working gas. High frequency operation of the thermoacoustic energy converter allows the use of a relatively short stack, which for a moderate temperature difference across the stack, it can sustain a very large temperature gradient. It is noted that the heat exchangers 54, 56 are preferably comprised of a material having a high thermal conductivity such as copper and may be identical in configuration. Other materials that can be used in the heat exchangers are brass, bronze, and stainless steel. In contrast, the material of the stack is preferably a material that is not highly thermally conductive.
The components utilized in accordance with the present invention have been chosen for simplicity realizing that they are far from ideal. Those skilled in the art, however, will appreciate that various modifications to and equivalent components to those disclosed herein may increase the efficiency of the thermoacoustic energy converter without departing from the spirit and scope of the present invention. Operation of the thermoacoustic energy converter of the presently preferred embodiment is as follows. Utilizing the device shown in figure 3, heat is introduced to one of the heat exchangers 54 or 56. The side to which heat is introduced becomes the hot exchanger. A temperature gradient will form across the stack 50. A standing wave or waves are generated within the resonator 42 as explained previously. The standing waves or waves will strike the piezoelectric element 48, which in turn generates electricity. This description is the most simplistic example, where the
resonator 42 is open ended, and there is only a single stack 50 disposed therein. The basic principles described above apply for more complicated thermoacoustic energy converters, even though the specific operation is affected by several factors as will be explained.
It is noted that the specific piezoelectric element 48 utilized in the invention can be optimized for operation within specific frequency ranges and temperature ranges, and is therefore selected accordingly. However, piezoelectric devices generally experience dissipation power losses that are very small since a piezoelectric device is essentially a lossy capacitor. Another factor to consider when selecting a piezoelectric element is that when it is heated too much, it stops working. Thus, it becomes important to keep the high temperature of the thermoacoustic energy converter as low as possible because the piezoelectric element 48 is disposed at the hot end thereof.
Observations of the invention in operation demonstrate that the heat to acoustic power efficiency is 10% to 18% of a Carnot engine. A heat engine, 3 cm diameter and 3 cm long produces 60 W of acoustic power, which converts to 15 mW of electrical power. In practice, the thermoacoustic energy converter has had a length ranging from 4 cm down to 2.1 mm, the latter generating ultrasonic oscillations. It is believed that further reduction in length is possible. However, at very small lengths, all of the components of the thermoacoustic energy converter become small.
Referring now to figure 4, a cross-sectional view of the stack 50 is illustrated. Because of the relatively small size of the stack 50 of the present invention (having a thickness Δx of 1 mm or less) a
conventional stack consisting of narrow strips of Mylar to which nylon fishing line spacers are glued and then rolled into a cylindrical shape is not easy to assemble, especially when it is very short as it is difficult to maintain uniform spacing and difficult to make good thermal contact with the heat exchangers 54, 56 at each end of the stack 50. As such, the preferred embodiment of the present invention utilizes a random fiber material, such as cotton wool or a fine stainless steel mesh 70, to form the stack 50. When cotton wool 70 is used, it is pressed to the desired thickness, e.g., 0.5 mm. Cotton wool 70 has a density of approximately 0.08 g/cm3, a thermal conductivity of 0.04 W/m °C, and an average fiber diameter of 14 μm. As such, cotton wool provides a large surface area to better accommodate the transfer of heat from the working fluid 52 to the fibers and is thus quite efficient.
Figures 5 and 6 illustrate heat exchangers 54, 56, respectively, in accordance with the present invention. Figure 5 shows a heat exchanger fabricated using photolithography to form the heat exchanger 54 from a copper sheet. The heat exchanger 54 has square holes, such as holes 72, 73, and 74, having a dimension of 0.5 mm x 0.5 mm for the size of the piezoelectric element 48 previously mentioned with solid spacers, such as spacers 75 and 76 having dimensions of 0.8 mm x 0.8 mm. Such an exchanger 54 provides a sound transparency of about 50%. The heat exchanger 54 has an outer ring 78 for contacting the resonator 42 and transferring heat thereto.
The mesh shown in figures 5 and 6 can also be formed from 10 to 100 count threads of copper, stainless steel, bronze, or brass material.
Figure 6 shows another preferred embodiment of a heat exchanger 56 in accordance with the present invention. The heat exchanger 56 may be formed from a metallic screen, flattened by a press, with square holes, such as holes 81, 82 and 83 having dimensions of, for example, 0.8 mm x 0.8 mm and a wire to wire distance of 1.2 mm for adjacent wires. For such a heat exchanger, the sound transparency is approximately 44%. When such a heat exchanger 56 is utilized as the hot heat exchanger, to improve heat transfer at the hot heat exchanger (since it handles more heat than the cold one) , the heat exchanger 56 may be thermally anchored to a large (e.g., 0.5 cm thick) copper heat exchanger or heat sink (not shown) . The working fluid 52 may simply be comprised of air at one atmosphere in accordance with the present invention. The use of air provides a simple means of manufacture in that more complex pressurization and assembly techniques are not required. It is contemplated in accordance with the principles of the present invention that other gases will increase the performance of the thermoacoustic energy converter. Certain gas mixtures will result in less viscous losses. Figure 7 is a cross-sectional side view of an embodiment of the present invention. Specifically, the thermoacoustic energy converter 100 is comprised of the resonator 42, the heat exchanger 56, the stack 50, the heat exchanger 54, and the piezoelectric element 48. New to this figure that was not in figure 3 is a thermal coupling mechanism 102. The thermal coupling mechanism 102 is simply a thermally conductive material that is in contact with a device that serves as the heat source for the thermoacoustic energy converter, and the hot exchanger. In this
embodiment, the hot exchanger is the heat exchanger 54.
This embodiment describes the placement of the thermal coupling mechanism 102 between the piezoelectric element 48 and the heat exchanger 54. The resonator 42 is a quarter wavelength resonator because the second end 46 is open.
Figure 7 indicates that the thermal coupling mechanism 102 is at room temperature. For the thermoacoustic energy converter 100 to operate, it is therefore necessary that the open end 46 be cooler than room temperature. But this illustrates the fact that the present invention can operate in room temperature environments. It is noted that for operation above 1 atmosphere of pressure, the open end can be coupled to a larger cavity, thus sealing the device.
Figure 8 is a cross-sectional side view of the resonator 42 that is essentially identical to that of figure 7 with one important difference. In this embodiment of the thermoacoustic energy converter 104, the second end 46 is closed, thus reflecting the standing wave. The result is that the resonator 42 is now a half wavelength resonator. Again, this figure shows that the thermal coupling mechanism 102 is at room temperature, and the closed end 46 is being kept colder.
Note that the half wavelength resonator 42 could also be made as an integer multiple of the wavelength of the resonator.
Figure 9 is a cross-sectional side view of another thermoacoustic energy converter 110. This figure introduces an important element of an alternative embodiment of the invention. The resonator 42 now has coupled to an end opposite that
of the piezoelectric element 48 an acoustic cavity 116. It is first noted that the acoustic cavity 116 changes the resonance and thus the ideal positioning of the stack 50 when a maximum temperature gradient across the stack 50 is desired.
More importantly, it has been determined that the acoustic cavity 116 reduces the onset temperature difference. This reduction occurs because the acoustic cavity 116 reflects back sound waves (traveling waves) that leave the resonator 42.
Furthermore, it appears that the reflected sound waves are amplified by the acoustic cavity 115 as they are sent back into the resonator 42.
The onset temperature difference can be hundreds of degrees Celsius. The acoustic cavity 116 has reduced the onset temperature difference to approximately 37 to 40 degrees Celsius, and it is believed that it can be further reduced. This is important for several reasons. First, the thermoacoustic energy converter becomes a practical device for use in electronic circuitry because the present invention can operate relatively near room temperatures. Second, piezoelectric elements do not operate at relatively high temperatures . A lower ' onset temperature difference enables optimization of the piezoelectric element 48 for temperatures that are more practical.
On an experimental level it is possible to make the following observations. First, a small ultrasonic prime mover has been created at just 2.1 mm in length, having a 1 mm diameter, operating at a frequency of 20.7 kHz, and a sound level of 85 dB.
Another important factor to consider is the onset temperature difference when the prime mover begins to generate a sound wave. There is a minimum onset
temperature difference that must be reached. This difference depends upon the geometry of the device. However, it is not enough just to reach the onset temperature difference. The other factor that must be met to achieve a sound wave is an adequate temperature gradient across a stack that drives the device. The temperature gradient can be made to be very large over a short length stack using the high frequencies of the present invention. The present invention has been observed to operate with an onset temperature difference as low as 15 degrees Celsius, as long as the temperature gradient is also being met. The onset temperature difference is at a minimum when the prime mover is coupled to an acoustic cavity, as shown in figure 9.
Figure 10A is provided to illustrate another type of stack that can be used effectively. Previously, figure 4 describes a random stack. However, the present invention also operates at high and ultrasonic frequencies utilizing a non-random stack. What is meant by "non-random" is illustrated in figure 10A. Instead of random fibers or other open-celled material, a mesh can be used. This figure shows the resonator 42, the piezoelectric element 48, a first heat exchanger 54, and a second heat exchanger 56. Note that the relative dimensions of the elements shown are not to scale, and are for illustration purposes only. In place of a random stack between the heat exchangers is what appears to essentially be a third heat exchanger 90. In effect, that is an accurate description. In this figure, a stainless steel mesh is utilized as the stack 90. The stainless steel mesh can have the same dimensions , as the heat exchangers, or vary as necessary in order to obtain a desirable conformation that will have the necessary
onset temperature difference and temperature gradient across the stack 90.
Figure 10B provides an end-on view of stack 90 along lines A-A. The view is for illustration purposes only, and not intended to reflect actual thread count or spacing. As stated above, the stack 90 appears to be configured much like a heat exchanger. Thus, the arrangement of heat exchangers and stacks is essentially three heat exchangers disposed adjacent to each other. Experimentally, a stack 90 of 400 X 400 threads of stainless steel was used, with the stainless steel threads having a thickness of 1 or 2 thousands of an inch. Thus, a non-random heat exchanger can be utilized as the stack 90.
Figure 11 is provided to illustrate further embodiments of the high frequency thermoacoustic energy converter. In this figure, there are two heat exchangers 54 and 56, and a gap 92 therebetween. The gap 92 is filled with whatever gas or mixture of gases is serving as a working fluid. It has been found that the thermoacoustic energy converter 94 shown here will function even without a stack. The function of the stack is apparently being provided by a wall of the resonator 42 itself, between the last exchanger The gap 92 can be approximately 0.1 mm to 0.5 mm mm wide.
Up to this point, the specification has been explaining the elements and operation of a single prime mover used in a thermoacoustic energy converter. Figure 12 is a perspective view of another embodiment of a thermoacoustic energy converter that is comprised of an array 98 of prime movers. The prime movers 100, 102, 104, 106, and 108 are operating in parallel. Each of the prime movers is essentially identical to the others. It is preferable that the prime movers
all share the same piezoelectric element at the closed ends (away from the disk 110) . The disk 110 is a heat sink or part of a heat source such as a circuit board. Thus, the piezoelectric element (not shown) would be disposed across the ends of the prime movers that are now exposed toward the viewer.
Operation of the array 98 of prime movers 100, 102, 104, 106, and 108 results in an unusual feature. When the array 98 is heating up, each prime mover will most likely begin generating a standing wave that is out of sync with the others. However, evidence indicates that phase-locking occurs of the prime movers 100, 102, 104, 106, and 108. Phase locking most likely occurs because of the close proximity of the prime movers 100, 102, 104, 106, and 108 with each other. In other words, the prime movers 100, 102, 104, 106, and 108 start out of phase, but quickly synchronize. The effect is that the prime movers 100, 102, 104, 106, and 108 reinforce each other. The advantages of this action include more power, a more compact design, and hence a higher efficiency.
It will be appreciated that the apparatus and methods of the present invention are capable of being incorporated in the form of a variety of embodiments, only a few of which have been illustrated and described above. The invention may be embodied in other forms without departing from its spirit or essential characteristics . The described embodiments are to be considered in all respects only as illustrative and not restrictive, and the scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.