THERMOACOUSTIC RESONATOR

BACKGROUND OF THE INVENTION

The subject invention originates from twenty-two years research by the inventor, into engines and resonators that operate on the principles of thermoacoustic physics. For purposes of this application for patent, the term “thermoacoustic” refers to traveling energy impulses, normally detected as pressure fluctuations, propagating along velocity vectors that move thermal energy through an elastic medium that is typically a compressible working fluid. For purposes of this application for patent, thermoacoustic energy includes both shockwaves (supersonic and hypersonic pressure waves) and sound waves (pressure waves traveling at the sonic velocity of the working fluid under locally extant conditions).

The research background data in heat, acoustic wave phenomena and gas mechanics includes the shock tube research performed by government and institutional scientists during the 1950’s and 1960’s, relevant examples of which can be found in the Proceedings of the Seventh International Shock Tube Symposium, University of Toronto Press 1970, ISBN 0-8020-1729-0; as well as research into thermoacoustic waves generated by chemical explosives, The Chemistry of Powder and Explosives, Volume I, 1941, Volume II, 1943, by Tenney L. Davis, Ph.D., ISBN 0913022-00-4; published research in atmospheric physics, including Lightning, by Martin A. Uman, McGraw-Hill 1969; The Flight of Thunderbolts, 2^nd ed., B.F.J. Schonland, Clarendon Press 1964; Graphic Survey of Physics, by Alexander Taffel, Oxford Book Company 1960; Matter and Motion, by James Clerk Maxwell, 1877, Dover Publications 1991 (reprint); Laboratory Exercises in Physics, Fuller and Brownlee, Allyn and Bacon 1913; Laboratory Experiments in Elementary Physics, by Newton Henry Black, Macmillan Company, 1944; Modern Physics, by Williams, Metcalfe, Trinklein and Lefler, 1968, Holt, Rinehart and Winston Publishers; Physics of Lightning, D.J. Malan, The English Universities Press Ltd., 1963; which includes thermoacoustic phenomena generated by natural lightning and man-made electric arcs.

Other relevant published research includes work in pulse tube refrigeration, including The Influence of Heat Conduction on Acoustic Streaming, Nikolaus Rott, Journal of Applied Mathematics and Physics (ZAMP), vol. 25, pp. 417-421, 1974; A Review of Pulse Tube Refrigeration, Ray Radebaugh, Cryogenic Engineering Conference, pp. 1-14, 1989; Flow Patterns Intrinsic to the Pulse Tube Refrigerator, J. M. Lee, P. Kittel, K. D. Timmerhaus, R. Radebaugh, National Institute of Standards and Technology, pp. 125-139, 1993. The cryogenics department at NASA-Ames is a premier focus of pulse tube refrigeration research. Pulse tubes differ from thermoacoustic devices in that they are typically non-resonant devices in which a mechanical piston, driven by an external power source, generates compression waves (pulses) that move in one direction through a series of heat exchangers, and cause thermal energy to be transported between those heat exchangers. Pulse tubes are typically used in cryogenic refrigeration applications. Pulse tubes are similar to thermoacoustic devices in that traveling pressure waves in a working fluid are the mode of operation.

The research history involving prime movers with associated thermoacoustic characteristics includes Stirling Cycle Machines, by Graham Walker, PhD, 1973, Oxford University Press; various Stirling engine technical research reports, 1937 – 1978, issued by The Philips Company Laboratories, Eindhoven, Netherlands; and Stirling Cycle Engines, by Andy Ross, 1977, published by Solar Engines, Phoenix, Arizona.

The device described herein is a traveling-wave Thermoacoustic Cycle (TAC) engine-generator set, herein referred to as a Thermoacoustic Resonator (TAR), comprised of an acoustically resonant cavity containing a multiplicity of thermally resonant heat exchangers and a compressible working fluid, in which a train of acoustic traveling waves is generated, and in which said acoustic traveling waves are amplified by a thermal gradient across the device, causing an increase in pressure and temperature amplitudes, and wave propagation velocity, and said acoustic traveling waves impinge upon a moveable piston-armature assembly, causing it to reciprocate within a magnetic field and generate electrical energy.

Thermoacoustic Cycle (TAC) engines are well known to acoustic science, are in USPTO Class 310 and International Class H01L 041/08, and have been explored extensively by Peter H. Ceperley, George Mason University; Steven Garrett of Penn State University and Gregory Swift of Los Alamos National Laboratory. Thermoacoustic related patents searched include:

6,054,775 Apr., 2000 Vocaturo 290/1R

6,032,464 Mar., 2000 Swift, et al 60/517

5,953,920 Sep., 1999 Swift, et al 60/520 X

5,892,293 Apr., 1999 Lucas 290/1R

5,673,561 Oct., 1997 Moss 62/6

5,659,173 Aug., 1997 Putterman, et al 250/361

5,647,216 Jul., 1997 Garrett 62/6

5,519,999 May., 1996 Harpole, et al 60/520 X

5,515,684 May., 1996 Lucas, et al 62/6

5,456,082 Oct., 1995 Keolian, et al 62/6

5,319,938 Jun., 1994 Lucas 62/6

5,303,555 Apr., 1994 Chrysler, et al 62/6

5,295,355 Mar., 1994 Zhou, et al 62/6

5,275,002 Jan., 1994 Inoue, et al 62/6

5,269,147 Dec., 1993 Ishizaki, et al 62/467

5,263,341 Nov., 1993 Lucas 62/6

5,165,243 Nov., 1992 Bennett 62/6

4,722,201 Feb., 1988 Hoffler, et al 62/467

4,686,407 Aug., 1987 Ceperley 60/721

4,599,551 Jul., 1986 Wheatley, et al 322/2R

4,398,398 Aug., 1983 Wheatley, et al 62/467

4,355,517 Oct., 1982 Ceperley 60/721

4,114,380 Sep., 1978 Ceperley 60/721

A Thermoacoustic Cycle engine is typically comprised of a resonant cavity in the approximate shape of a cylinder, tube or torus, in which a working fluid resides, and in which an applied difference in thermal potential, across internal isothermal heat exchangers that are separated by a regenerative heat exchanger (stack) and spaced along the length of the resonant cavity by a nominal wavelength or fraction thereof, produce and amplify acoustic waves which transport thermal energy from one heat exchanger to another, and maintain a state of oscillation, or periodic thermal and acoustic flux, in the working fluid. To extract useful work from the engine, the oscillating pressure component can be applied to a mechanical member, such as a piston, in order to perform reciprocating work, and thereby used to perform tasks such as pumping fluids or generating electrical energy. The maxima, or peak pressure points in the traveling thermoacoustic wave train, also transport thermal energy in accordance with the pressure-temperature relationship in a gas, as described in Charles Law, and this property can be employed in a reverse entropy cycle to produce refrigeration.

Thermoacoustic Cycle engines have been researched for several decades, and researchers at the Los Alamos National Laboratory, the Naval Post Graduate School, The University of Texas, Penn State University and other institutions have written numerous research papers on the genre, primarily concerning standing-wave thermoacoustic physics. A standing-wave thermoacoustic refrigerator developed by Steven Lurie Garrett was flown aboard the space shuttle Discovery in 1991 as an experimental package. It is mentioned (project 511) along with this inventor’s Acoustic Cycle engine (project 503) in the 1993 Rolex Awards For Enterprise, published December, 1992. Currently, there are approximately thirty relevant patents in the field.

The most significant problem with prior art thermoacoustic engines and refrigerators is that they have a very low power density. They are typically much larger and more massive for the amount of output work they produce, than other types of engines and refrigerators. Until 1998, disregarding non-resonant pulse tubes, most researchers working in the field, including Gregory Swift’s Los Alamos group, concentrated their efforts largely on thermoacoustic engines that employed standing wave physics. The power output of standing wave systems is limited by the inherent physical characteristics, to wit; standing wave systems rely on the forward-going wave being inverted and reflected uniformly back along the resonator at nearly the same propagation velocity. If too much energy is extracted from the forward-going wave in the cold-side heat exchanger the propagation velocity of the return wave is changed, and the forward-going wave and the return wave will be out of phase, and will interfere with each other. This adds impedance to the cycle, and tends to damp the oscillation. This inherent characteristic severely limits the quantity of energy per cycle that is available to perform useful work, resulting in large engines with low power density.

Traveling-wave engines and pulse tubes, by comparison, do not rely on reflected waves to maintain system oscillation. Traveling-wave engines ideally propagate thermoacoustic energy in only one direction, eliminating the reflected wave, thus reducing the impeding effects of a change in wave propagation velocity on the system, and increasing the amount of useful energy that can be extracted from the system.

In 1998-99, Greg Swift of Los Alamos attempted to improve the art by coupling Ceperley’s torus-shaped traveling-wave engine with a cylindrical standing-wave resonator, in an effort to produce greater output power from the traveling-wave component, without damping the standing-wave oscillator. Even so, the compound engine develops low energy density because the design still relies mainly on geometry to produce an engine that is acoustically resonant.

The subject invention described herein is a traveling-wave thermoacoustic engine that conquers the problem of low power density through use of a design methodology and fabrication process conceived and developed by the inventor, in which the specific heat and thermal conductivity of the heat exchanger materials and the working fluid are tailored, in accordance with the designer’s desires, to derive a combination of properties that produce specific values of thermal energy capacitance and reactance.

Thermal capacitance is the property that determines the natural period of thermal energy oscillation in matter. The thermal capacitance of a specific artifact, such as a heat exchanger in a thermoacoustic engine, is determined by design, by manipulating elemental matter with known properties, to produce alloys and compounds with different properties, to wit; artifacts with unique properties of specific heat and thermal conductivity with relation to their temperature swing, mass and geometry. In some cases, pure elements can exhibit the required thermal capacitance for optimal operation of a thermoacoustic engine, but this will occur only in cases where the engine designer has specifically chosen to engineer the engine around the natural properties of an element, rather than for a useful purpose, and even in such rare cases, the designer must still manipulate the surface area per unit mass and the energy coupling factors between components in order to derive a working engine. In other words, when intentionally designed to do so, thermal capacitance regulates the periodic oscillation of energy within the solid-state materials and the working fluid of a thermoacoustic resonator.

The principal difference between prior Stirling Cycle and Thermoacoustic Cycle engines and the Fellows TAC engine is that these prior art machines depend upon an acoustic pressure oscillation in the working fluid that is derived from the sonic velocity of the fluid and the geometry of the resonant cavity; while the Fellows engine relies upon the thermal resonance of the materials in the heat exchangers.

The advantage of this thermal capacitance approach, and the improvement gained thereby to the prior art, is that the solid-state materials that comprise the heat exchangers exhibit thousands of times the volumetric energy density of typical working fluids, therefore, the greatest quantitative portion of the oscillating energy flux is concentrated in the solid-state materials, and when tapped by the subject design methodology, far exceeds the effect of the geometric dimensions of the resonator in determining the frequency of oscillation, the propagation velocity of the wave-train and the energy that can be extracted from the thermoacoustic engine. The effect of this design methodology and fabrication process on the energy density of the invention is so great that, in terms of power output per unit size, energy density is increased by two or three orders of magnitude, over those examples of the prior art in thermoacoustic engines that are known to the inventor.

BRIEF SUMMARY OF THE INVENTION

The principal improvement on prior art is a significant increase in power density. This is accomplished by the development of an applied engineering design and construction process, by the inventor, in which the Principle of Thermal Resonance of Materials, a property determined by the thermal energy capacitance of materials, is applied in a proprietary design methodology in order to manipulate the acoustic properties of a thermoacoustic machine by means of the periodic thermal energy properties of the heat exchanger materials and working fluids, in conjunction with the geometric design of the resonant cavity, rather than by means of the geometry of the cavity and the acoustic properties of the working fluid alone.

This Thermal Resonance of Materials Principle constitutes a new invention of process, a new art, by which periodic thermal energy flux in matter can be measured, calculated, predicted and manipulated, and these material properties used to increase the energy density of thermoacoustic engines. This principle and the affected material properties are described in US Provisional Patent application No. 60, 151,349, Oscar L. Fellows, Inventor, August 30, 1999.

In the subject invention, multiple heat exchangers reside within an acoustic cavity. A minimum of two heat exchangers is required. The hot-side heat exchanger (HX_h), which introduces thermal energy into the working fluid; the cold-side heat exchanger (HX_c), which removes thermal energy from the working fluid; and the thermal capacitor (C_t), a type of regenerative heat exchanger that acts as a thermal metronome. C_t conserves energy in the cycle, aids in amplifying the traveling wave and helps sustain the thermoacoustic flux in the working fluid of the engine. In the minimal design described herein, HX_h and C_t comprise one unit with multiple functions.

This heat exchanger arrangement is similar to prior art, but the invention is novel in the design methodology and fabrication process of the heat exchangers, in that the geometry, physical properties and operating theory of said heat exchangers are based on the inventor’s theory of thermal capacitance, and thermal resonance of materials principle.

Two of the heat exchangers, HX_h and HX_c, are considered isothermal in that the external thermal gradient across them is considered steady state. In actuality, though the external energy source is ideally injecting energy into the engine at a steady rate, and the external energy sink is removing energy from the engine at a steady rate, the internal thermal gradient across HX_h and HX_c is in harmonic flux with the resonator frequency, and the heat exchangers are so designed. HX_h introduces thermal energy into the working fluid, and HX_c removes thermal energy from the working fluid in periodic pulses. These pulses are coincidental with the traveling thermoacoustic waves.

Traveling waves transiting HX_h and HX_c inside the engine cavity, periodically present to the heat exchangers a mass of working fluid that is high in density, high in energy amplitude and high in thermal conductivity. In between these periods of high density, are intervals when the working fluid in contact with the heat exchangers is relatively low in density, low in energy content and low in thermal conductivity. When the energy gradient and the relative thermal conductivity are greatest, energy flows between the working fluid and the heat exchangers. When the energy gradient and thermal conductivity are least, the energy flow is least, and results in a dwell period. Another way of looking at it is that traveling waves remove thermal energy from HX_h and deposit it in HX_c.

These propagating energy pulses, if graphed as a waveform, will appear to be inversely proportional in amplitudes between genesis and decay, or rise and fall times, appearing as a saw tooth waveform in which the rise and fall times of the wave are inverted on opposite sides of the wave maxima, the slope of the amplitude vector. In practice, the rising and falling amplitude angles will be slightly asymmetrical. The approximate waveform is illustrated in the graph labeled “Energy Cycle in Thermal Capacitors.” These cyclical heat exchangers operate in harmony with, and amplify, an injected waveform to produce a high amplitude fluctuating thermal pressure gradient across the resonator.

As in provisional patent application No. 60, 151,349, Oscar L. Fellows, Inventor, August 30, 1999; construction of this invention applies a design process methodology developed solely by the inventor, which shall now be described in depth.

The design of the heat exchangers, C_t-HXh and HXc, involves specifically tailored and manipulated Thermal Resonance of Materials properties, and specific geometry, that make them thermally resonant at a desired frequency, and thereby establish the acoustic period of the engine and working fluid. In other words, the materials are tailored so that they exhibit a natural period of energy oscillation that establishes a synchronous thermal energy flux in the working fluid.

To further clarify, this design process methodology takes into account those material properties that combine to produce thermal capacitance, and permits accurate design of passive and active components so that they acquire and discharge thermal energy to and from a working fluid in harmonic resonance with the acoustic period of a traveling wave, when the working fluid is at the desired operating temperature and pressure. The elemental properties of the solid materials are adjusted by doping with other materials to form compounds with specific thermal properties, by surface treating components to create a desired surface effect, and by creative geometry, such as forming metal structures of reticulated foam or plates that exhibit desired surface area to mass and volume ratios. This particularly affects C_t, in which the swing in thermal energy amplitude is greatest.

The physical properties of the matter comprising the heat exchangers and working fluid, such as their specific heat, thermal conductivity, thermal hysteresis, thermal capacitance, mass, cross-section, surface area, fluid mass-flow-rate, impulse frequency, dwell angle and propagation velocity determine the amount of thermal energy that can be stored in a given mass of material at a given temperature, and the rate at which said thermal energy is conveyed through the mass and coupled to the working fluid.

As stated above, these properties are rarely exhibited, in the correct interacting values for a given resonator, by pure elements. Compound components and alloys must be created to adjust these values. In some cases, the alloys must be surface treated by plating, ion implantation, plasma deposition and other means to bring the various values into specification. These physical properties, the physical dimensions and geometry of the materials, along with the quantity of thermal throughput energy, and various thermal and frictional impedances, determine the thermodynamic operation of the invention. The heat exchanger materials must absorb and emit thermal energy in harmonic step with the cyclic rhythm, or frequency, of the traveling wave.

The flow of thermal energy in the heat exchangers exhibits many properties that are similar in effect to energy flow in an electrical capacitor. For example, thermal reactance and thermal hysteresis are caused by a combination of the change of specific heat of a given material over a temperature range, because it determines the amount of energy required to "charge" a given mass of the material up to a desired thermomotive potential (temperature); and the reciprocal change in the thermal conductivity of the material, which is the inverse of "resistance" to the flow of thermal "current". These variable properties determine the time required for a given quantity of energy to be conveyed through the materials, including the working fluid, of the resonator.

Materials store thermal energy by increasing the relative distance of their atomic orbitals, analogous to a population inversion in a laser cavity, wherein electrons are pumped to energy levels above the ground state. In the same way, specific heat is linked to atomic structure. So is thermal conductivity. Materials convey thermal energy via transfer of energy between adjacent atoms. The ionic and covalent bonds of materials vary, as do their specific heats, and the field strength of these bonds vary with distance, thereby changing the energy absorption properties of the materials with respect to the tension, or amplitude, of the charge. This phenomenon is linked to latent energy storage in matter, a phenomenon that is well documented in the scientific literature. Said phenomenon often precedes a change of state, said change of state including changes in energy fields, such as magnetism and quantum states.

In the following table, Cp = specific heat, k = thermal conductivity, and L = latent energy. Specific heat is in cal/gm/C^o, total and latent energy is in cal/gm, and thermal conductivity is in Watts/cm/C^o.

Material	Cp @100K	Cp @300K	k@100K	k@300K	Total Energy	L cal/gm
Aluminum	0.115	0.215	3.00	2.37	43	20
Beryllium	0.049	0.436	4.138	2.18	87.2	77.4
Magnesium	0.016	0.243	1.69	1.59	48.6	45.4

TABLE SHOWING LATENT ENERGY OF SOME MATERIALS

In the materials shown, thermal conductivity varies inversely with specific heat, diminishing the value of the latent energy available per cycle. The thermal impedance in aluminum increases by twenty percent (20%) over the temperature range shown. This is not the case with magnesium, which exhibits a significant latent energy swing and almost no change in thermal conductivity. Magnesium then, is a better thermal capacitor, even though its specific thermal conductivity is less than aluminum, because it exhibits less reactance and hysteresis than aluminum. Beryllium may be the best choice, for though its conductivity is cut in half over the temperature range, latent energy increases by a factor of ten.

Examples of engineered materials with low reactance include iron lattices with grown silver whiskers. Such combinations exhibit entirely different properties from the individual metals. Doped silicon, glasses, ceramics, carbon compounds, metal oxides, carbides and deposited films are all appropriate materials, depending on the operating parameters desired in a TAR.

Each material, because of its engineered thermal capacitance and reactance, is resonant at a different frequency, a frequency at which the energy oscillation within the material reaches a maximum value. Because of these design characteristics, the energy levels in such materials can be pumped at a frequency that is resonant, or “natural”, to a given artifact, causing it to exhibit a periodic swing in dynamic amplitude that is alternately significantly greater, and significantly less, than it would be in the same materials under non-resonant conditions. This increases the amplification factor. This property of thermal energy swing amplification is adjustable, by means of changing the pumping period of the energy source, and by changing the energy resonance, or more properly the internal capacitance, of the artifact, via manipulation of the physical properties and geometries of the materials.

Viewed in terms of thermal energy flow rate (power), this amplification is a manifestation of the inherent non-linear relaxation period, the dwell period, or more appropriately the energy-leveling period, of a given material that is undergoing a change in temperature in which both latent and sensible energy is being transferred. It holds true for fluids as well as solids. The inherent leveling period, which is determined by the changing values of specific heat and thermal conductivity, determines the quantitative energy flow per unit of time, the frequency at which a substance may be pumped in order to achieve the greatest energy swing amplification.

As can be seen in the table, because of its large ratio of latent capacity to total energy, and its relatively unchanging thermal conductivity, magnesium has a shorter dwell period than aluminum, and less memory, or hysteresis, at the bottom of its energy well. The change in the apparent specific heat, and the relatively fixed thermal conductivity of the material, result in a high rate of energy transfer, and a greater amplification of the pressure-temperature oscillation of the wave than can be attributed to simple conduction between the heat exchangers and the working fluid. These properties are of little benefit in conventional steady state flow thermal systems, but become extremely important in high frequency cyclical systems such as thermoacoustic and Stirling Cycle engines.

A simpler way of looking at the invention is in terms of apparent overall system impedance. In the prior art, a regenerative heat exchanger creates a small but abrupt change of temperature and pressure within the thermoacoustic wave, a transition in energy amplitude, altering its acoustic wavelength, phase angle and wave propagation velocity. The result is a small periodic pressure-temperature swing between the isothermal heat exchangers that can be output as useful work, and the wave becomes slightly asynchronous (out of phase), losing waveform symmetry. This has heretofore been viewed as a necessary, but performance-limiting, impedance, both in standing wave and traveling-wave prior art. The inventor’s design process maintains the synchronicity of the traveling wave in relation to the energy transfer capabilities of the heat exchangers, by application of this thermal resonance of materials principle, thereby reducing apparent overall system impedance and producing a greater amount of output work, in comparison to the total internal energy flux of the engine, than is possible with the prior art. This is essentially impedance matching through resonant coupling. The resulting increase in energy density over the prior art is measured in multiple orders of magnitude.

In the preferred embodiment, C_t and HX_h are physically coupled into a single component. C_t-HX_h acts as both the metronome and the heat injection point, the primary thermal oscillator. The external input energy to C_t-HX_h is preferably isothermal, but the internal extension of C_t-HX_h, that portion in contact with the internal working fluid, exhibits thermal capacitance, an engineered tendency to resonate internal energy at a particular frequency, and is induced by the signal injection means to couple with the working fluid in such a way that it takes up energy from the external source and injects it into the working fluid in a periodic oscillatory manner. This material resonance principle causes the injected signal to be reinforced and amplified more effectively than can be accomplished with the simple addition of thermal energy, as is the case with prior art. It operates in conjunction with HX_c, the working fluid and the injected acoustic wave train, to establish the resonant period of the resonator. As a separate component, C_t can also be configured as a regenerative device that reduces the amount of waste energy rejected through the cold-side heat exchanger by extracting a portion of the energy from the wave before it is rejected to HX_c, and reintroducing it to succeeding waves before they enter HX_h, as wave preheat energy. This energy conserving function can reduce the total input-to-output energy ratio of the engine, and increase overall thermal efficiency.

These components, their novel arrangement, and the proprietary design process applied in the making of them, as described below, tend to reduce the physical size and increase the power density, operating efficiency, cost effectiveness and design predictability of the invention, thereby improving the art toward widespread commercial applications. The invention, including the design process, operating theory and design characteristics described herein, is a thermoacoustic, microelectromechanical system (MEMS) that uses acoustic waves to transform thermal energy into electrical energy. In function, the device is a micro miniature traveling wave Thermoacoustic Cycle engine and generator, and is herein referred to as a Thermoacoustic Resonator (TAR).

Described simply, the TAR is an acoustic cavity containing a compressible working fluid, in which an injected train of traveling waves is amplified by manipulating the thermal flux within the device, and the resulting periodic pressure fluctuation in the working fluid performs work on a freely reciprocating piston-armature assembly. The invention physically incorporates said reciprocating piston-armature assembly, electrical conductors, a magnetic field generating means, a signal injection means and multiple heat exchangers into the acoustic cavity. The heat exchangers in the TAR are separated by a substrate that is a thermal insulator, also called a thermal break, that reduces short-circuit thermal conduction between components with differing temperature gradients, in order to limit the path of maximum throughput energy exchange, as much as possible, to the working fluid. The component parts of the TAR are disposed within an integral case, or housing. The housing is preferably comprised of metal, though ceramics and thermoplastics can also be used. The TAR can be further encapsulated within an external package, to meet varying conditions of use.

TARs can be made in single autonomous units. Multiple unitary TARs can be ganged together to form an array. Multiple TARs can also be manufactured as an integrated panel array, on a common substrate, with a common housing, a common power conditioning circuit, and connected by printed wiring. A single TAR can range in size from approximately that of a microchip, with a piston less than one-fourth centimeter in diameter, to more than ten centimeters in diameter. As shown in the table labeled TAR.WKS, power output depends on the physical dimensions of the pistons and heat exchangers in the device, the static pressure of the working fluid, the magnetic field strength, the thermal gradient across the device, the energy throughput, the frequency of the internal pressure fluctuations, the travel of the attendant piston-armature oscillating within the magnetic field, and the electrical capacity of the internal conductors.

In operation, a thermal gradient is established between the external isothermal heat exchangers by heating and cooling means, and coupled to the TAR housing. A train of acoustic impulses, also called traveling waves, is injected by the signal injection means and causes the piston-armature to begin oscillating. As the internal components of the TAR attain normal operating conditions, the energy amplitude of the traveling wave increases, converting the heat supplied by the thermal energy source into an electrical output current.

The frequency of operation is determined by the engineered properties of all the heat exchangers, and to a lesser extent, by the geometry of the acoustic cavity. The propagation velocity of the traveling waves is determined by the nature and operating conditions of the working fluid. Said traveling waves propagate through the working fluid from HX_h to HX_c, transporting thermal energy between the two. Said traveling waves take up energy from one heat exchanger, causing said traveling waves to increase in pressure and temperature amplitude in accordance with Charles Law, and reject energy via another heat exchanger. The amplified traveling waves cause a large fluctuation, or oscillation, in the pressure of the working fluid. The oscillation in pressure in the working fluid causes the piston-armature assembly to reciprocate within a magnetic field, and generates an electric current in an electrical conductor. Said electrical conductor is connected to the separate sides of the TAR casing by electrically conducting means, so as to form opposite polarity terminals, in order to convey the electrical energy from within the TAR to an external load.

The outer opposing flat surfaces of the TAR housing are designed for contact with the isothermal heat exchangers by which both thermal and electrical energy enter and exit the TAR. The TAR can be configured so that one or both electric poles are isolated from the thermal casing, if desired. This is a minor detail, and not intrinsic to the operation of the TAR.

Thermally conductive strips can also be bonded to the opposing faces of the TAR casing during manufacture, as a means to connect the TAR to heat source and heat sink. The TAR can then be potted in a non-conductive package, with the conductive strips exposed. The conductive strips can be omitted by bonding the TAR directly to conductive hot and cold plates (external heat exchangers), with the TAR sandwiched between the plates. This works well for ganged arrays designed to achieve a multiplied power output.

The preferred manufacturing methods for the micro miniature TARs include the formation of the internal heat exchangers, thermal breaks and wiring by those techniques common to the semiconductor industry, including photolithography and chemical machining, ion implantation, doping, material deposition and laser ablation, much like large scale integrated circuits are created on computer chips. Integrated TAR thermal-to-electric generator panels with specific power conditioning and load capacities can be produced by these means.

When affixed to a blackened metal absorber panel, or other radiant-energy absorbing material, and to a cooling means on its opposite face, the TAR can convert heat from radiant energy, such as sunlight, into electrical energy. In this respect, the TAR responds to a wider bandwidth of radiant energy than photovoltaic cells. It can absorb and use wavelengths that are below the photovoltaic threshold for most materials. It is possible to configure the device to absorb and convert electromagnetic energy such as radio waves and microwaves into a different wavelength, such as 60 Hertz power, by first converting the absorbed energy to heat.

The TAR can operate across a wide temperature range. The operating range with common materials is from 100 Kelvins to 1200 Kelvins. Higher temperatures, and thus a wider absolute range, are possible with development of TARs using advanced materials, such as ceramics, special composites and high-temperature metal alloys.

Energy conversion efficiencies are directly related to the temperature gradient across the TAR. A theoretical (Carnot) efficiency of 92% (1200K-100K/1200K=0.9167), and realizable efficiencies of 58% (0.92*0.63=0.58) are possible within the nominal limits of current materials and architecture.

Thermal energy is admitted to, and emitted from, the TAR via conduction and radiation, at the outer case surfaces of the device. The external case surfaces of the TAR operate as isothermal heat exchangers. The interior side of the heat exchangers is comprised of a matrix, which is of the proper mass, specific heat, thermal conductivity and surface area to alternately store and transfer the thermal energy to and from the working fluid within a period of time that “matches” the thermal resonance period of the TAR heat exchangers.

A variety of working fluids are employed in the manufacture of TARs. Each working fluid has unique physical properties. Air and helium are the working fluids preferred for the TAR. An example of the calculations involved in determining the working fluid charge is given below:

The acoustic velocity of a compression wave in air is:

V = Ö 1.4p/d

Where p is the pressure and d the density. The coefficient, 1.4, will vary with the type of working fluid employed. As shown below the velocity of propagation of the traveling high-density wave, also varies directly with temperature.

V = V_o Ö 1+t/273

V = V@STP + nt

Where velocity is meters/second, n is a coefficient of velocity change for a given working fluid per unit change in temperature, and t is temperature in C^o.

When the dimensions of the working fluid passages, which comprise the resonant cavity, are matched to the acoustic velocity of the working fluid under given dynamic temperature and pressure parameters, and with the thermal reactance of the thermal capacitors, a resonant frequency, or natural harmonic period of oscillation, is established for the device. Operation under these conditions yields maximum efficiency. In the design of the TAR, physical size limitations and the energy throughput required for a particular application are the principal determinants of the resonant frequency of the working fluid passages, and therefore, their length and diameter for a given resonant frequency.

The fundamental frequency of an air column in a closed pipe, for example, is:

n_o = V/4L

V is the wave propagation velocity and L is the length of the air column. In practice, an empirical correction proportional to the diameter of the tube is applied for greater accuracy. The approximate dimensions of the gas passages would then be calculated by the following formula:

Wavelength = (L + 0.4d)

where d is the diameter of the gas passage and L the length. These formulas can be found in the 55th edition of the CRC Handbook of Chemistry and Physics.

For maximum efficiency, the armature must reciprocate at the resonant frequency of the working fluid, and the traveling wave must arrive at the reflecting surfaces of the moving piston-armature assembly, in phase with it. The piston-armature assembly is a reciprocating mass, with an oscillation period designed to coincide with the resonant frequency of the working fluid under extant conditions. If a resonant condition between the armature and the acoustic velocity of the working fluid does not exist, a sub-optimal operating efficiency will result. This condition will cause the compression wave to be out of phase with the motion of the armature and the device will tend to damp its own oscillation and hence reduce its efficiency.

The period required for transit of thermal energy through the heat exchangers and thermal capacitors must be calculated so that these components also accrete and discharge thermal energy in phase with the acoustic wave train. Mass flow rates through the matrices of these components, specific heat of the materials and their thermal conductivity determine their porosity, web thickness and area per unit volume. In this transient-flow cycle, these factors translate into thermal capacitance (C_t), thermal reactance (X_t) and thermal impedance (Z_t).

The period required for complete energy leveling in a heat exchanger or thermal capacitor is divided into five parts, or five time constants. This is done because the rate of energy exchange between components is not linear, and work or power is measured as the rate of flow per unit of time. In any such non-linear system, peak power is usually achieved by cycling the system in a period that is less than the complete energy-leveling period. In the TAR, the rate of energy exchange between components during the first time constant is sixty-three percent (63%) of the available energy. To extend the working cycle for four additional time constants, in order to harvest the remaining thirty-seven percent (37%), would decrease the overall power of the system. The rate of energy exchange changes logarithmically, and this is why thermal reactance and hysteresis are critical. For example, if total available energy is 100 Joules, 63 Joules will flow during the first time constant, 23.3 Joules during the second time constant, 8.63 Joules during the third time constant, 3.2 Joules during the fourth time constant, and 1.87 Joules during the fifth time constant. If the thermodynamic cycle is one time constant in duration, the average rate of flow, or power, is 63 Joules per cycle. If the cycle is two time constants in duration, the average rate of flow is 63 + 23 / 2 = 43 Joules per cycle. Therefore, the system has a greater power output if the cycle is limited to one time constant in duration.

GRAPH OF QUANTITATIVE ENERGY FLOW PER TIME CONSTANT

As illustrated in the graph above, during each time-constant, 63% of the energy remaining in the energy donor is transferred to the energy recipient. The actual quantity depends upon temperature swing and duration of the swing, and the change in specific thermal conductivity and specific heat of the elements of the system over the temperature swing. This design knowledge permits specification of all heat exchangers in the machine so that they are closely matched to the energy transfer cycle desired through the machine, since it takes the acoustic velocity of the working fluid and the thermal impedances of all other interacting elements into account.

In a periodic flow system, the thermal reactance (X_t) of any component will be the average of the angle of the amplitude and period of the energy transferred during the half-cycle. This will always be 0.63 of the available energy. The available energy is a factor of the reactance and hysteresis of the material. The value of the available energy in one time-constant is used in the inventor's formula to calculate the optimum quantity of energy exchanged in a given period in a transient-flow cycle. There are five time-constants in the cyclic swing between the minimum and maximum energy storage capacity of an element, during a period of alternating amplitude energy exchange. This number is the resulting coefficient multiplied against the Carnot number that yields the nominal actual performance of the device. Other factors, such as frictional losses within the gas passages, non-ideal gas behavior of the working fluid, cross-conduction of thermal energy, tangential reflection of acoustic energy and other impedances can affect the actual final energy conversion efficiency.

The elements in the system appear to the energy flow as thermal impedances (Z_t), the Z_t of an individual element being determined by its X_t, hysteresis and the acoustic resonance of the system. Overall system impedance is determined by the system designer, the object being to design for minimal Z_t, and synchronous, or harmonic operation among all the interacting elements. The point expressed here is that the parameters of all the system elements interplay to create the machine’s performance, and that by using the inventor's proprietary design methodology, these parameters can be calculated to achieve consistent, optimum results.

The TAR is physically comprised of three principal sections; the hot-side heat exchanger; the cold-side heat exchanger; and sandwiched between them, a non-conductive thermal break. The thermal break serves as a substrate into which the component parts of the TAR are assembled. It contains passages for the working fluid, and a centrally located cavity that houses a piston-armature assembly, said piston-armature assembly comprised of a piston-armature suspension, armature electrical conductors and a field magnet structure. These three principal sections are housed, or sandwiched, between two separate layers that comprise an electrically and thermally conductive outer casing, or envelope. In the case of multiple TARs manufactured as an integrated panel array on a common substrate, the outer casing will be comprised of contiguous conductive layers laminated to both sides of the non-conductive substrate, which is a contiguous thermal break, to form a single panel, with said multiple TARs and their connecting printed wiring sandwiched between. The TAR components and the working fluid are disposed within the casing.

C_t-HX_h is a specially engineered heat exchanger, with integrated wave-guide. It couples the thermal source energy to the internal working fluid of the TAR, vectors traveling waves in the proper direction and maintains system impedance. C_t-HX_h exhibits thermal resonance properties that couple most efficiently with traveling waves of a specific frequency, and less efficiently with the stagnant medium (the working fluid) through which the traveling waves propagate.

A multiplicity of holes, or ports, extend through the thermal break in order to communicate thermoacoustic energy between the hot side heat exchanger and the cold side heat exchanger. The traveling waves exit C_t-HX_h at an amplified temperature and pressure, and continue on through the connecting ports in the thermal break, through connecting passages, toward the piston-armature assembly. Said piston-armature assembly and passages are separated from the cold-side heat exchanger (HX_c) by an inertance plate. The traveling waves are slowed and phase shifted between the piston-armature assembly and the inertance plate, where peak pressure is attained, and they perform work on the piston-armature assembly, causing the piston-armature assembly to reciprocate in step with the pressure fluctuations of the working fluid, and convert said pressure fluctuations into electrical energy.

Thermal energy remaining in the traveling waves is metered through the orifice in the inertance plate, into the internal matrix of the cold-side heat exchanger (HX_c), where the remaining energy is transmitted, via conduction, through the thermally conductive outer casing of the TAR to an external heat sink.

When the high-pressure maxima of the wave train are within the cavity between the piston-armature assembly and the inertance plate (the dwell cavity), the low-pressure node is within HX_h. The piston-armature assembly resists the pressure of the traveling wave, pushing it back toward HX_h, and also pushing it through the metering orifices of the inertance plate into HX_c. Stirling Cycle compression occurs in the dwell cavity for a period corresponding to eight to twelve degrees (8^o –12^o) of the cycle. The cooler pressure wave tends to rebound, driven both by the displacement of the rebounding armature mass and the physical oscillation caused by the changing pressure in the working fluid, back into Ct-HXh. The TAR engineer strives to extract maximum energy to the piston-armature assembly, to dump whatever remains of the energy into HXc, and to minimize the reflected wave, which represents impedance.

The energy in the return wave is counter to the velocity vector of the wave train, and if improperly controlled, will conflict with succeeding traveling waves entering Ct-HXh from the signal injecting means. The TAR engineer strives to time the arrival of the reflected wave so that it arrives at Ct-HXh during the nodal portion (minimal energy flow) of the injected signal, thereby reducing destructive impedance and reinforcing the oscillation.

The drop in system pressure, caused by the loss of energy through HX_c, now offers a large thermal gradient across HX_h, and energy flows to the working fluid, causing a rapid increase in temperature and pressure within HX_h, and generating a new, high density wavefront that moves through the device toward HX_c, thereby repeating the cycle.

The periodic oscillation and energy exchange that takes place within the internal elements is illustrated in the following graph. The time-constants inherent in the energy exchange are also depicted. The amplitude, or swing, of the temperature and pressure gradients is greatest across Ct-HXh, but the energy exchange through HXc, and the oscillation period of the piston-armature must coincide with the rising and falling pressure of the traveling wave in order to realize peak efficiency from the device. The graph shows approximately one-and-two-thirds cycles.

The function of Ct-HXh is to transfer an external energy stream to an internal working fluid in a periodic manner, in order to maximize the pressure swing in the cycle, and to establish the baseline period of the oscillating pressure-temperature gradient of the traveling wave.

In operation, the piston-armature assembly synchronously reciprocates with the oscillations in pressure. The armature is comprised of magnet-steel laminates and electrical conductors so disposed that they cut the lines of magnetic flux created by the magnetic field generating means, and produce an electric current in said electrical conductors. The armature is suspended between the poles of the magnetic-field generating means, a permanent magnet or electromagnet, by mechanical bearings and the flexible suspension of the piston. The fluctuating pressure gradient within the working fluid causes the armature to reciprocate within the magnetic field, thereby causing an electric current to be induced in the armature conductors. Said electric current is conveyed, via conducting means, from the armature to the outer casing of the TAR, and to an external load.

In the working cycle, thermal energy is transferred from the hot-side heat exchanger to the cold-side heat exchanger via traveling waves that traverse the working fluid in periods of typically less than a few milliseconds. At a frequency of ten kilohertz (10 kHz) for example, the period of sonic oscillation is one hundred microseconds (100 uSec).

Gas pressure in a confined volume increases with increases in temperature on the order of 1/273 units, or 0.0037 per K^o. For example, a static pressure of 10 kg/cm² will become 13.8 kg/cm² with a 100 C^o increase in temperature. This pressure fluctuation of 3.8 kg/cm² will result in a force that is a multiple of the area it acts upon, which in this case, is the area of the piston.

For example, assume the area of the piston is one square centimeter, and the resultant force is: (1 cm² * 3.8 kg/cm² = 3.8 kgf). Assume that the piston travel is 2.0 millimeters and the TAR is operating at a frequency of 5340 HZ. The TAR in this example will develop theoretical work of approximately 40.5 kg-m/sec, or 400 Watts. If the hot-side temperature is 500K, and the cold-side temperature is 400K, the Carnot efficiency will be:

E = T1 - T2 / T1

500K – 400K / 500 = 0.20

Our thermal capacitance theory gives a maximum of sixty-three percent (0.63) of Carnot:

0.20 * 0.63 = 0.126, = 12.6% eff.

Therefore, our 400 Watts of potential becomes (400 * 0.126 =) 50 Watts. Not bad from a disk that fits in the palm of your hand.

If the temperature delta is increased to 300C^o, for example:

700K – 400K = 300K / 700 = 0.429

0.429 * 0.63 = 0.27, or 27% eff.

400 Watts * 0.27 = 108 Watts

Some of the design parameters and dynamic resultants for an arbitrarily sized TAR are illustrated in the table (TAR.WKS) shown below:

TAR.WKS