Patent Publication Number: US-6711905-B2

Title: Acoustically isolated heat exchanger for thermoacoustic engine

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This Non-Provisional Utility Patent Application claims the benefit of the filing date of U.S. Provisional Application Ser. No. 60/369,760, filed Apr. 5, 2002, entitled “ACOUSTICALLY ISOLATED HEAT EXCHANGER FOR THERMOACOUSTIC ENGINE.” 
    
    
     THE FIELD OF THE INVENTION 
     The present invention relates to a thermoacoustic engine for converting acoustic energy to thermal energy or for converting thermal energy to acoustic energy. More particularly, the present invention relates to a thermoacoustic engine with an acoustically isolated heat exchanger. 
     BACKGROUND OF THE INVENTION 
     Thermoacoustic engines have developed as an attractive alternative to more traditional piston and turbine devices for heating, cooling, and electric power generation applications. Thermoacoustic engines are generally highly reliable due to the limited number of moving parts and the abrogated need for lubrication. Furthermore, thermoacoustic systems are environmentally friendly as they can utilize air or a noble gas as a heat transfer medium and working fluid rather than poisonous or ozone layer damaging substances, such as FREON, which are commonly used in conventional piston and turbine devices. In what follows the terms heat transfer medium and working fluid will be used interchangeably for brevity, unless otherwise indicated. 
     FIG. 1 illustrates a typical thermoacoustic engine  10  including an acoustic resonator  12  and a drive tube  14 . Drive tube  14  is a hollow, elongated member typically having a closed end  16  and an open end  18 . Open end  18  is connected or sealed to acoustic resonator  12 . Drive tube  14  contains a first thermal element  20 , a regenerator  24 , and a second thermal element  22 . As illustrated, first thermal element  20  is positioned further from acoustic resonator  12  than second thermal element  22 , and regenerator  24  is positioned between first thermal element  20  and second thermal element  22 . First thermal element  20  is commonly a heat source and second thermal element  22  is commonly a heat sink. Acoustic resonator  12  and drive tube  14  are generally filled with a heat transfer medium  26 , which is typically air or a noble gas. Heat transfer medium  26  flows through and between first thermal element  20 , regenerator  24 , and second thermal element  22  to facilitate thermal exchange. 
     During operation, heat is supplied to first thermal element  20  while heat is simultaneously removed from second thermal element  22  to establish a sufficient temperature gradient across regenerator  24  to activate thermoacoustic engine  10 . Upon activation, thermoacoustic engine  10  may function as a Carnot engine in which first thermal element  20  is heated to induce movement in heat transfer medium  26  to produce a high intensity sound in acoustic resonator  12 . Alternatively, acoustic energy is introduced to heat transfer medium  26  which is employed to establish thermal transition from the cold sink, i.e., second thermal element  22 , across regenerator  24 , to the heat source, i.e., first thermal element  20 , to function as a refrigerator. 
     Typical thermoacoustic engines, such as thermoacoustic engine  10 , depend on thermal conduction through the drive tube walls at first and second thermal elements  20  and  22 . In particular, heat exchangers or electric elements are commonly attached to the inside or outside of the drive tube  14 , such as at the first and/or second thermal elements  20 ,  22  located within drive tube  14 , to add or remove heat from the respective elements. 
     The typical thermoacoustic engines have low thermal efficiency, low power density, and tend to be significantly larger than their piston or turbine driven counterparts. A significant factor contributing to the aforementioned disadvantages of thermoacoustic engines is a difficulty in supplying or removing heat to or from the active areas or thermal elements of the thermoacoustic engine while maintaining acceptable acoustic losses. 
     To avoid the shortcomings of the above-discussed thermoacoustic engines and for other reasons presented in the Description of the Preferred Embodiments, a need exists for a thermoacoustic engine which supplies and removes heat from the respective portions of the drive tube in a more efficient manner so as to maintain acceptable levels of acoustic losses. 
     SUMMARY OF THE INVENTION 
     One aspect of the present invention provides a thermoacoustic engine for acoustically driving a thermal exchange. The thermoacoustic engine includes a hollow drive tube, a heat transfer medium, an acoustic resonator, and a first thermal element. The hollow drive tube partially contains the heat transfer medium and is connected to and opens into the acoustic resonator. The acoustic resonator is adapted to store acoustic energy and deliver at least one acoustic wave to the heat transfer medium. The first thermal element includes a first channel and a first working fluid. The first channel is positioned to cross and open into the hollow drive tube, at least partially contains the first working fluid, and is sized to decrease the propagation of the at least one acoustic wave within the first channel. The first thermal working fluid is adapted to interact with and undergo thermal exchange with the heat transfer medium by conduction. 
     In one embodiment, the first channel is sized to procure exponential decay of the acoustic waves within the first channel. Additionally, the first channel has a duct-cut off frequency smaller than a frequency of the hollow drive tube (i.e. a critical dimension smaller than a dimension required for propagation of the at least one acoustic wave). In one embodiment, the first thermal element further includes an external heat exchanger connected and open to a first end and a second end of the first channel. The heat exchanger is adapted to alter the thermal energy of the first working fluid. 
     In another embodiment, the thermoacoustic engine further includes a second thermal element spaced from the first thermal element. The second thermal element includes a second channel at least partially containing a second working fluid. The second channel is positioned to cross and open into the hollow drive tube and is sized to decrease propagation of the at least one acoustic wave within the second channel. The second working fluid is adapted to interact and undergo thermal exchange within the heat transfer medium. 
     Another aspect of the present invention provides a thermoacoustic engine for producing at least one acoustic wave. The thermoacoustic engine includes a drive tube, an acoustic resonator, a heat transfer medium, a first thermal element, and a second thermal element. The drive tube is connected to and opens into the acoustic resonator, and the drive tube and acoustic resonator contain the heat transfer medium. The first thermal element includes a first channel positioned to cross and opens into the drive tube. The first working fluid is at least partially contained in the first channel and is adapted to interact and undergo thermal exchange with the heat transfer medium by conduction. The second thermal element is spaced from the first thermal element and is adapted to induce thermal exchange between the second working fluid and the heat transfer medium. Thermal exchange between the first thermal element and the heat transfer medium and between the second thermal element and the heat transfer medium produces an acoustic wave in the heat transfer medium. The first channel is sized to decrease propagation of the acoustic wave within the first channel. 
     Another aspect of the present invention provides a method of acoustical thermal exchange. The acoustical method includes providing a thermoacoustic engine, inducing an acoustic wave, and exchanging thermal energy. The thermoacoustic engine provided includes a drive tube, a heat transfer medium contained in the drive tube, a first channel, and a first working fluid at least partially contained in the first channel. The first channel is positioned to cross and open into the drive tube. Introducing an acoustic wave to the drive tube induces flow within the heat transfer medium. The first channel is sized to decrease propagation of the acoustic wave within the first channel. Exchanging thermal energy occurs between the heat transfer medium and the first working fluid by conduction. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic illustration of a conventional thermoacoustic engine. 
     FIG. 2 is a schematic illustration of one embodiment of a thermoacoustic engine in accordance with the present invention. 
     FIG. 3A is a schematic illustration of one embodiment of a channel of a thermoacoustic engine in accordance with the present invention. 
     FIG. 3B is a schematic illustration of another embodiment of a channel of a thermoacoustic engine in accordance with the present invention. 
     FIG. 4 is a schematic illustration of another embodiment of a thermoacoustic engine in accordance with the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the following detailed description of the preferred embodiments, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced. It is to be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present invention. The following detailed description, therefore, is not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims. 
     FIG. 2 generally illustrates a thermoacoustic engine  30  for converting thermal energy to acoustic energy or for converting acoustic energy to thermal energy in accordance with the present invention. Generally speaking, thermoacoustic engine  30  includes a drive tube  32 , a regenerator  34 , an acoustic resonator  36 , a heat transfer medium  38 , a first thermal element  40 , and a second thermal element  42 . Regenerator  34  is contained within drive tube  32 , and drive tube  32  is connected to and opens into acoustic resonator  36 . Drive tube  32  and acoustic resonator  36  contain heat transfer medium  38 . First thermal element  40  and second thermal element  42  are each positioned to open into drive tube  32  on either side of regenerator  34 . 
     During operation, an acoustic wave is introduced to thermoacoustic engine  30 . Acoustic resonator  36  stores acoustic energy from the acoustic wave and delivers acoustic energy back to heat transfer medium  38 , thereby, imparting oscillatory motion into heat transfer medium  38 . The oscillatory flow establishes a standing wave in heat transfer medium  38  through drive tube  32 . In particular, heat transfer medium moves in a circuit through the thermal elements  40  and  42  and drive tube  32  by convection. As heat transfer medium  38  passes through first thermal element  40 , first thermal element  40  transmits heat to or removes heat from heat transfer medium  38  by conduction. Heat transfer medium  38  continues from first thermal element  40  and is entrained in the standing acoustic wave in the drive tube  32 , delivering heat to regenerator  34  and through second thermal element  42 . As heat transfer medium  38  passes regenerator  34  and into second thermal element  42 , second thermal element  42  delivers heat to or removes heat from heat transfer medium  38 , preferably performing the opposite thermal exchange as first thermal element  40 . 
     In one preferred embodiment, drive tube  32  is an elongated, hollow member as is known in the art. Drive tube  32  includes a wall  50  and defines a proximal end  52 , a distal end  54 , and a hollow cavity  56 . Wall  50  extends between proximal end  52  and distal end  54  and encompasses hollow cavity  56 . In one embodiment, wall  50  is open at proximal end  52  and closed or capped at distal end  54 . Regenerator  34  is contained within hollow cavity  56 . Preferably, regenerator  34  is positioned within hollow cavity  56  nearer distal end  54  than proximal end  52 . Preferably, regenerator  34  is a regenerative stack, as is known in the art, such as a stack of metal or other material chosen to have an appropriate thickness, thermal capacity, thermal conductivity, and separation to maximize thermal and acoustic efficiency. In one embodiment, regenerator  34  has a high lateral thermal conductivity and a low conductivity along the length of the tube. Regenerator  34  is designed to allow incoming heat transfer medium  38  to oscillate back and forth across the regenerator  34  to heat or cool internal surfaces (not shown) of regenerator  34 . The heated or cooled internal surfaces serve to further heat or cool outgoing heat transfer medium  38  as it is directed towards second thermal element  42 . 
     Proximal end  52  of drive tube  32  is connected and open to acoustic resonator  36 . Acoustic resonator  36  is a hollow, preferably metallic, container for storing acoustic energy and delivering acoustic energy to heat transfer medium  38 . Acoustic resonator  36  includes an opening  56  to receive proximal end  52  of drive tube  32 , such that heat transfer medium  38  can flow freely between acoustic resonator  36  and drive tube  32 . Preferably, drive tube  32  is sealed to acoustic resonator  36  to prevent leakage of heat transfer medium  38  from the connection between drive tube  32  and acoustic resonator  36 . Acoustic resonator  36  defines a cavity  62  and is adapted to store and deliver acoustic energy from an intense or large amplitude acoustic wave to heat transfer medium  38 . As is known in the art, the acoustic energy will induce an oscillatory flow in heat transfer medium  38  and, consequently, will drive a standing wave in heat transfer medium  38  through drive tube  32  between proximal end  52  and distal end  54 . 
     In one embodiment, acoustic resonator  36  is a Helmholtz resonator as is known in the art. The Helmholtz resonator is a rigid-walled volume that supports an acoustic wave having an acoustic wavelength larger than a wavelength typically implied by the dimensions of acoustic resonator  36 . Typically, Helmholtz resonators have a main body  64  and a neck  66  leading to drive tube  32 . Helmholtz resonators involve bulk fluid flow (as opposed to standing waves in the resonator body) and, therefore, require additional considerations in the design of first and second thermal elements as described in detail below. 
     Heat transfer medium  38  flows within and fills drive tube  32  and acoustic resonator  36 . Heat transfer medium  38  is any heat transfer medium known in the art for use with acoustic resonators. For example, heat transfer medium  38  may be a compressible thermodynamic fluid. In a preferred embodiment, heat transfer medium  38  is air or an environmentally friendly noble gas. 
     In one embodiment, in which distal end  54  of drive tube  32  is capped, the acoustic wave, and therefore heat transfer medium  38 , travels through drive tube  32  and is reflected back towards acoustic resonator  36  as a standing wave. In an alternative embodiment, a loop (not shown) is added to distal end  54  and the acoustic wave and heat transfer medium  38  travels from acoustic resonator  36  through drive tube  32  and back around to acoustic resonator  36 . The looped acoustic wave forms a traveling wave in heat transfer medium  38  and lessens reliance upon acoustic resonator  36 . The remaining description focuses on the use of standing waves, however, modifying thermal acoustic engine  30  to utilize traveling waves, as apparent to those of ordinary skill in the art, is equally acceptable. 
     In one embodiment, first thermal element  36  includes a first branch or channel  70  and a working fluid  72 . First channel  70  is an elongated hollow member that defines a first channel cavity  74  and an external surface or first channel wall  76 . Working fluid  72  is similar to heat transfer medium and at least partially contained within cavity  74 , such that working fluid  72  can flow through first channel cavity  74 . Notably, the distinction between heat transfer medium  38  and first working fluid  72  is a temporal description such that at a given instance in time, the heat transfer medium is the fluid contained in the drive tube  32  and first working fluid  72  is the fluid contained in first channel  70 . In actuality, heat transfer medium  38  and first working fluid  72  freely interact and interchange with one another. First channel  70  crosses, connects, and opens to drive tube  32 . More particularly, first channel wall  76  connects to and opens to drive tube  32  proximal to regenerator  34  and distal to acoustic resonator  36 . In one embodiment, first channel wall  76  opens to drive tube  32  nearer regenerator  34  than acoustic resonator  36 . 
     In one embodiment, first working fluid  72  is heated or cooled such that first channel  70  functions as an external heat exchanger or a portion of an external heat exchanger. In one embodiment, first channel  70  includes a first end  71  and a second end  73  opposite first end  71 . In this embodiment, first thermal element  36  further includes a heat exchanger  75 , which can be implemented with any suitable heat exchanger known in the art defining an internal cavity (not shown), an inlet  77 , and an outlet  78 . The internal cavity extends between inlet  77  and outlet  78 . Inlet  77  and outlet  78  receive first end  71  and second end  73  of first channel  70 , respectively. First working fluid  72  flows within and between first channel cavity  74  and the internal cavity of heat exchanger  75 . Heat exchanger  75  is adapted to alter the thermal energy of the first working fluid  72  by absorbing heat from or providing heat to first working fluid  72 . In one embodiment, heat exchanger  75  cools first working fluid  72  such that first thermal element  40  functions as a heat sink to thermoacoustic engine  30 . 
     In one embodiment, first thermal element  40  includes a plurality of first channels  70 . Each of the plurality of first channels  70  includes a cavity and a channel wall, wherein each of the cavities contains a working fluid in a similar manner as described above for first channel  70 . In one embodiment, each of the channel walls connects to drive tube wall  50  such that channel  70  opens to drive tube  32  such that working fluid  72  contained within each of the plurality of channels  70  can mix or flow with heat transfer medium  38 , contained within drive tube  32 . As such, working fluid  72  is heated or cooled by conduction from heat transfer medium  38 . In another embodiment, the plurality of channels  70  are bundled together. 
     In the embodiment incorporating a plurality of first channels  70 , each of the plurality of first channels  70  defines a first end  71  and a second end  73  opposite the first end  71 . Similar to first channel  70 , the plurality of first channels  70  are connected at their first end  71  to inlet  77  and at their second end  73  to outlet  78 . As such, in one embodiment, inlet  77  and outlet  78  each contain a plurality of connection points (not shown) to receive the plurality of channels or may be fitted with a separate connection piece to facilitate connection of the channels  70  to heat exchanger  75 . 
     In one embodiment, the connection between first channels  70  and inlet  77  or outlet  78  is constructed by drilling a hole corresponding to the cross-section of each first channel  70  in a thick plate to support first channels  70  and rigidly connecting the plate to heat exchanger  75 . In another embodiment, the connection between first channels  70  and inlet  77  or outlet  78  is constructed by forming a hole in a thick plate to support the entire plurality of first channels  70 . In a plate connection, the hole diameter is preferably selected to be less than half the plate thickness. Notably, each of the plurality of channels may be connected to the plate and/or cut at different angles. However, other methods of connection are known in the art and equally acceptable. 
     Second thermal element  42  includes a second branch or channel  80 , a heat exchanger  82 , and a second working fluid  84 . Second branch or channel  80  is a hollow elongated member defining and extending between a first end  86  and a second end  88 . Second channel  80  defines a second channel cavity  90  enclosed by a second channel wall  92 . Heat exchanger  82  can be implemented with any suitable heat exchanger adaptable to have an inlet  94 , an outlet  96 , and an internal cavity (not shown). The internal cavity extends between inlet  94  and outlet  96 . First end  86  of second channel  80  is connected to inlet  94  and second end  88  is connected to outlet  96 . Second working fluid  84  is similar to heat transfer medium and flows within and between second channel cavity  90  and the internal cavity of heat exchanger  82 . Heat exchanger  82  is adapted to alter the thermal energy of second working fluid  84  by absorbing heat from or providing heat to second working fluid  84 . In one embodiment, heat exchanger  82  provides heat to second working fluid  84  such that second thermal element  42  functions as a heat source to thermoacoustic device  30 . 
     Second channel wall  92  connects to drive tube wall  50  distal to regenerator  34  and proximal to distal end  54  of drive tube  32 . More particularly, second channel  80  connects and opens to drive tube  32 , thereby, allowing second working fluid  84  to physically mix with heat transfer medium  38  and to foster thermal exchange between heat transfer medium  38  and second working fluid  84  by conduction. Notably, the distinction between heat transfer medium  38  and second working fluid  84  is a temporal description such that at a given instance in time, the heat transfer medium  38  is the fluid contained in the drive tube  32  and the second working fluid  84  is the fluid contained in second channel  80 . In actuality, heat transfer medium  38  and second working fluid  84  freely interact and interchange with one another. 
     In one embodiment, second thermal element  42  includes a plurality of channels  80 . Each of the plurality of channels  80  defines first end  86 , second end  88 , cavity  90 , and channel wall  92 . Similar to second channel  80 , each channel first end  86  of the plurality of channels  80  is connected to inlet  94 , and each channel second end  88  is connected to outlet  96 . As such, inlet  94  and outlet  96  may each contain a plurality of connection points to receive the plurality of channels  80  or may be fitted with a separate connection piece to facilitate connection of the channels  80  to heat exchanger  82 . In one exemplary embodiment, the connection between each second channel  80  and heat exchange inlet  94  or heat exchange outlet  96  may be constructed by drilling a hole corresponding to the cross-section of each second channel  80  in a thick plate to support second channel  80  and rigidly connecting the plate to heat exchanger  82 . In another embodiment, the connection between second channels  80  and inlet  94  or outlet  96  is constructed by forming a hole in a thick plate to support the entire plurality of second channels  80 . In a plate connection, the hole diameter is preferably selected to be less than half the plate thickness. Notably, each of the plurality of channels may be connected to the plate and/or cut at different angles. However, other methods of connection known in the art are equally acceptable. 
     Each cavity within the plurality of channels contains and allows flow of a working fluid in a similar manner as described above for second channel  80  and second working fluid  84 . Similarly, each channel  80  connects and opens into drive tube  32  such that the working fluid contained within each of the plurality of channels can mix or flow with heat transfer medium  38 , contained within drive tube  32 . As such, the working fluid contained within each of the plurality of channels is heated or cooled upon interaction with heat transfer medium  38  by conduction. In one embodiment, the plurality of channels  80  are bundled together. In order for thermoacoustic engine  30  to function in an efficient manner, first channel  70 , second channel  80 , and/or the plurality of channels are acoustically isolated to decrease the amount of oscillatory flow within each channel  70  or  80 . Acoustically isolating first and second channels  70 ,  80 , decreases or prevents the first and second channels  70 ,  80  from intercepting or detracting from the acoustic waves traveling within drive tube  32  to decrease oscillatory flow, consequently, decreasing overall acoustic losses within thermoacoustic engine  30 . Furthermore, by acoustically isolating first and second channels  70 ,  80 , the thermal exchange design is decoupled from the acoustic design, thereby allowing each design to be independently optimized within economic constraints. 
     In order to be acoustically isolated from drive tube  32 , first channel wall  76 , second channel wall  92 , and/or the plurality of channel walls must be sufficiently rigid to satisfy the boundary conditions. In one embodiment, the boundary condition is satisfied by ensuring that the ratio of the cross-section of cavity  74  or  84  to the thickness of the corresponding channel wall  76  or  86  is sufficiently small. In an alternative embodiment, the boundary condition is satisfied by bundling the plurality of channels together to support each other, thereby allowing thinner individual channel walls to be utilized. 
     To limit oscillatory flow and acoustic losses and to effectively decouple the acoustic and thermal aspects of thermoacoustic engine  30 , first and second channels  70 ,  80  are sized to prevent propagation of the acoustic wave within the first or second channel  70 ,  80 . In general, first channel  70  and second channel  80  each have a small channel cross-section compared to the wavelength of the acoustic wave produced by acoustic resonator  36 . A relatively small channel cross-section prevents propagation of the wave and causes the wave to decay exponentially along the length of the channel. In particular, for any channel (e.g., rectangular or circular) there are wave modes that will propagate down the tube and, thereby, cause acoustic losses to the wave within drive tube  32 . However, when both side lengths of a rectangular channel or a diameter of a circular channel drops below a critical dimension relative to the wavelength of the acoustic wave within drive tube  32 , the acoustic wave will no longer propagate down the channel. Rather, if the side length or diameter is below the critical dimension, the intensity of the acoustic wave decays exponentially, dependent on the ratio of the wavelength to the diameter or length of the tube, along the length of the channel. The frequency at which an acoustic wave ceases to propagate within a channel is called the duct cutoff frequency. As such, first and second channels  70 ,  80  are sized to have duct cutoff frequencies lower than the duct cutoff frequency of the acoustic resonator  36  and/or drive tube  32 , as further described below. 
     FIG. 3A generally illustrates a portion of one embodiment of a first or second channel  70  or  80  as a rectangular channel  100 . Rectangular channel  100  is formed from rigid sides or boundaries and has a constant rectangular cross-section. The cross-sectional dimensions are L min  and L max . For purposes of duct cutoff frequency, L max  is a critical dimension L c . The lowest propagating wave mode (k lm ) for rectangular channel  100  is given by the following equation:          k   lm     =     π     L   c                       
     As such, any wave having a mode less than π/Lc is a non-propagating wave otherwise known as an evanescent wave. Further, any sound propagating into rectangular channel  100  can be reduced to any arbitrary level by designing rectangular channel  100  to have a sufficiently small ratio of critical dimension L c  to a wavelength λ and sufficiently long channel length z to allow for full decay of the wave within rectangular channel  100 , thereby, limiting oscillatory flow within rectangular channel  100 . The basis for this reasoning is the following wave equation and solution known in the art (e.g., see Lawrence E. Kinsler, et al.,  Fundamentals of Acoustics  (3d ed. John Wiley &amp; Sons 1982)): 
     
       
           P   lm   =A   lm  cos( k   lm   x )cos( k   my   y )exp( k   z   z ) e   jwl  and  
       
       
         
           
             
               k 
               z 
             
             = 
             
               ( 
               
                 - 
                 
                   
                     
                       k 
                       lm 
                       2 
                     
                     - 
                     
                       
                         ( 
                         
                           2 
                            
                           
                             π 
                             λ 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               ) 
             
           
         
         
         
             
         
       
     
     Substituting the k lm  value for rectangular channel  100  into the wave equation, the exponential in the wave equation can be written as the following:        exp        (       -       [       π   2     -       (     2          π                   L   c       λ       )     2       ]              (     z     L   c       )       )                     
     Accordingly, as the ratio of critical dimension L c  to the wavelength λ becomes small compared to k lm , the constant term of the exponent will approach π. In order for this approximation to hold true to within about one percent, the ratio of critical dimension L c  to the wavelength λ must be less than about 0.141 times the wavelength. Thus for practical situations the wave propagating into rectangular channel  100  can be reduced by a factor of twenty decibels if the length of rectangular channel  100  is at least:          z     L   c       =       2.303   3.141     =   0.829                     
     Notably, the ratio between length z of rectangular channel  100  and critical dimension L c  is preferably chosen to be as small as possible within economic restraints and in view of other considerations to limit the distance the evanescent wave penetrates into rectangular channel  100 , to reduce acoustic losses in thermoacoustic engine  30  and oscillatory flow in rectangular channel  100 . 
     FIG. 3B generally illustrates a portion of one embodiment of a first or second channel  70  or  80  as a circular channel  110 . Circular channel  110  is formed of rigid sides or boundaries. Circular channel  110  has a constant cross-section, a radius a, and a diameter D, wherein diameter D is the critical dimension L c  for duct cutoff frequency purposes. The lowest propagating wave mode (k lm ) for circular channel  110  is given by the following equation:          k   lm     =     1.841   a                     
     As such, any wave having a mode less than 1.841/a is an evanescent wave. The acoustic wave propagating into circular channel  110  can be reduced to any arbitrary level by designing circular channel  110  to have a sufficiently small ratio of critical dimension L c  to a wavelength λ and a sufficiently long length z to allow for full decay of the wave within circular channel  110 . The basis for this reasoning is the wave equation and the solution utilized above with respect to rectangular channel  100 . Substituting the values for circular channel  110  into the wave equation, the exponential in the wave equation can be written as the following:        exp        (       -       [       1.841   2     -       (       π                   L   c       λ     )     2       ]              (     z     L   c       )       )                     
     Accordingly, as the ratio of critical dimension L c  to wavelength λ becomes small compared to k lm , the constant term of the exponent will approach 1.841. In order for this approximation to hold true to within about one percent, the ratio of critical dimension L c  to the wavelength λ must be less than about 0.108 times the wavelength. Thus, for practical situations the wave propagating into circular channel  110  can be reduced by a factor of twenty decibels if the length of circular channel  110  is at least:          z     L   c       =       2.303   1.841     =   1.25                     
     Notably, as described above the lower the ratio of length z of circular channel  110  to the critical dimension the lower the acoustic losses in thermoacoustic engine  30  and the lower the oscillatory flow within circular channel  110 . Accordingly, rectangular channel  100  more efficiently reduces loss and oscillatory flow based upon the ratio of channel length to critical dimension. However, it should be noted that rectangular channel  100  is more difficult to machine, which typically leads to increased losses in rectangular channel  100 . As such, which channel type has lower amounts of oscillatory flow and leads to fewer acoustic losses within thermoacoustic engine  30  is a function of multiple machine and design variables. 
     In a preferred embodiment, critical dimension L c  is small compared to the wave length of the highest significant harmonic present in the acoustic wave. In addition, channel length z is preferably similar to a length L R  of regenerator  34 . More preferably, channel length z is less than a length L D  of drive tube  32 . Moreover, channel length z is commonly determined based upon additional factors such as required working flow rate and achievable pressure, heat, and friction losses at inlet  94 , through heat exchanger  82 , and at outlet  96 . 
     Further considerations must be taken when designing channels for use with Helmholtz resonator, described above. In particular, the cross-sectional dimensions of the channel are selected to have a significantly higher Helmholtz mode than the Helmholtz resonator. A resonant frequency ω for a Helmholtz resonator is expressed as:        ω   =       c        (     A       L   ′        V       )         1   /   2                       
     Where c is a speed of sound, A is an effective cross-sectional area of channel  100  or  110 , L′ is the effective length of neck  66 , and V is the volume of acoustic cavity  56 . Preferably, the channels are designed such that the Helmholtz resonance frequency is as small as possible. More particularly, the channels are designed so as the ratio of effective channel area A to effective length L′, i.e. A/L′, is as small as possible, consistent with other restraints, such that first and second thermal elements  40 ,  42  will have a significantly different (preferably lower) Helmholtz resonance, as is known in the art, than acoustic resonator  36 . 
     Although illustrations and calculations are provided for channels having rectangular or circular cross-sections, channels having other cross-sections remain within the scope of the present invention. Furthermore, although the design process is enumerated for first channel  70  and second channel  80  similar considerations and calculations would comprise the design of a plurality of channels  70  or  80  in either first thermal element  40  or second thermal element  42 . Notably in practice either plurality of channels  70  or  80  may contain hundreds of channels. In one embodiment, each plurality of channels  70  and  80  contains 10-30 channels. Within each of the plurality of channels  70  and  80 , the ratio of channel length z to critical length L c  may be the same or may vary for each channel within the plurality of channels. Likewise, the cross-sectional shapes of each channel may be the same or may vary within the plurality of channels. 
     Referring again to FIG. 2, during use of thermoacoustic engine  30 , acoustic resonator  36  stores and transfers an acoustic wave to heat transfer medium  38 , thereby driving heat transfer medium  38  through drive tube  32  by oscillatory flow. Heat transfer medium  38  passes through drive tube  32  past first thermal element  40 , through regenerator  34 , and past second thermal element  42 . In a preferred embodiment, first working fluid  72  is pre-cooled and functions to cool heat transfer medium  38  by conduction as heat transfer medium  38  contacts or mixes with first working fluid  72 . In one embodiment, pre-cooled first working fluid  72  is continuously or periodically injected into the first channel  70  of the first thermal element  40 . The now cooled heat transfer medium  38  passes through regenerator  34  cooling the internal surfaces of regenerator  34 . 
     Being driven through drive tube  32  by the acoustic wave, heat transfer medium  38  passes from regenerator  34  past and through second thermal element  42 , which is either pre-heated or pre-cooled by heat exchanger  82 . The interaction and thermal difference between heat transfer medium  38  and second working fluid  84  induces thermal exchange by conduction between heat transfer medium  38  and second working fluid  84 . In one embodiment, second thermal element  42  provides heat to heat transfer medium  38 . Accordingly, heat transfer medium  38  absorbs heat from second working fluid  84  to effectively heat transfer medium  38  and cool second working fluid  84 . As such, in this embodiment thermoacoustic engine  30  functions as a refrigerator. Following thermal exchange between heat transfer medium  38  and second thermal element  42  in a standing wave embodiment, the acoustic wave within the heat transfer medium  38  is reflected off distal end  54  and redirected back towards resonator  36  to repeat the cyclic process. 
     Notably, after being cooled by heat transfer medium  38 , second working fluid  84  is continually routed or circulated through and heated by heat exchanger  82 , routed back to drive tube  32  in a pre-heated state, cooled again by heat transfer medium  38 , and routed through the cyclic process again. In this manner, conduction between heat exchanger  82  and second working fluid  84  not only heats second working fluid  84  but also cools heat exchanger  82 . In an alternative embodiment, first heat exchanger  40  may provide heat to heat transfer medium  38  and second heat exchanger  42  may absorb heat from heat transfer medium  38  such that thermoacoustic engine  30  functions as a heating apparatus. 
     For other embodiments in which first thermal element  40  includes a plurality of channels  70 , each channel within the plurality of channels  70  functions in a similar manner as described above with respect to first channel  70 . Similarly, for embodiments in which second thermal element  42  includes a plurality of channels  80 , each channel within the plurality of channels  80  functions in a similar manner as described above with respect to second channel  80 . 
     FIG. 4 generally illustrates another embodiment of the first and second thermal elements generally at  40 ′ and  42 ′. First thermal element  40 ′ includes a first channel  70 ′ and a first working fluid  72 . First channel  70 ′ is sized and shaped according to similar considerations as described above with respect to first channel  70 . However, rather than being connected to heat exchanger  75  (FIG.  2 ), first channel  70 ′ forms a closed loop. The closed loop is routed through an external device or environment  98 , and first channel  70 ′ independently contains first working fluid  72 . 
     During operation, first working fluid  72  flows through first channel  70 ′ through external device  98 . External device  98  absorbs heat from or provides heat to first working fluid  72  by conduction. First working fluid  72  flows through first channel cavity  90  from external device  98  into drive tube  32  where it interacts with and undergoes thermal exchange with heat transfer medium  38 . Preferably, the thermal exchange of first working fluid  72  with external device  98  is the opposite of the thermal exchange of first working fluid  72  with heat transfer medium  38 . For example, if first working fluid  72  absorbs heat from external device  98 , first working fluid  72  preferably provides heat to heat transfer medium  38 . Alternatively, if first working fluid  72  provides heat to external device  98 , first working fluid  72  preferably absorbs heat from heat transfer medium  38 . In this manner, first channel  70 ′ and first working fluid  72  interact to function as a heat exchanger eliminating the need for an additional heat exchanger and, therefore, reducing the weight and cost of themoacoustic engine  30 . However, the increase in the channel length of first channel  80  would likely require active pumping of first working fluid  72 , and thereby, introduce moving parts and additional reliability obstacles to thermoacoustic device  30 . In one embodiment, first thermal element  40 ′ includes a plurality of first channels  70 ′. Each of the plurality of channels  70 ′ has similar properties as described with respect to first channel  70 ′. 
     Second thermal element  42 ′ is formed in a similar manner as described with respect to first thermal element  40 ′. As such, second thermal element  42 ′ includes a second channel  80 ′ and second working fluid  84 . Second channel  80 ′ forms a closed loop, which is routed through an external device  100 , and second channel  80 ′ independently contains second working fluid  84 . Accordingly, second thermal element  42 ′ functions to absorb or provide heat to heat transfer medium in a similar manner as described above with respect to first thermal element  40 ′. In one embodiment, second thermal element  42 ′ includes a plurality of second channels  80 ′. Each of the plurality of channels  80 ′ has similar properties as described with respect to second channel  80 ′. 
     Notably, in one embodiment, thermoacoustic engine  30  includes first thermal element  40  and second thermal element  42 ′ or first thermal element  40 ′ and second thermal element  42 . In another embodiment, a plurality of looped channels extend from drive tube  42 . Each of the plurality of channels functions in a similar manner as described above with respect to the second channel  80 ′ In yet another embodiment, thermoacoustic engine  30  may include one of first or second thermal element  40  or  42  in accordance with the present invention while including the remaining thermal element  40  or  42  in accordance with prior art. 
     The acoustically isolated heat element of the present invention provides an efficient system and method of thermal exchange for use with a thermoacoustic engine. The external thermal elements decrease structural interference and are designed to prevent wave propagation within the external thermal elements thereby decreasing overall acoustic losses with the thermoacoustic engine. Moreover, the acoustically isolated design of the external thermal element(s) decouples the design of acoustic chambers and corresponding heat exchangers to allow for independent optimization of both such elements of a thermoacoustic engine. 
     Although specific embodiments have been illustrated and described herein for purposes of description of the preferred embodiment, it will be appreciated by those of ordinary skill in the art that a wide variety of alternate and/or equivalent implementations calculated to achieve the same purposes may be substituted for the specific embodiments shown and described without departing from the scope of the present invention. Those with skill in the chemical, mechanical, electromechanical, electrical, and computer arts will readily appreciate that the present invention may be implemented in a very wide variety of embodiments. This application is intended to cover any adaptations or variations of the preferred embodiments discussed herein. Therefore, it is manifestly intended that this invention be limited only by the claims and the equivalents thereof.