Abstract:
An oscillating-wave engine or refrigerator having a regenerator or a stack in which oscillating flow of a working gas occurs in a direction defined by an axis of a trunk of the engine or refrigerator, incorporates an improved heat exchanger. First and second connections branch from the trunk at locations along the axis in selected proximity to one end of the regenerator or stack, where the trunk extends in two directions from the locations of the connections. A circulating heat exchanger loop is connected to the first and second connections. At least one fluidic diode within the circulating heat exchanger loop produces a superimposed steady flow component and oscillating flow component of the working gas within the circulating heat exchanger loop. A local process fluid is in thermal contact with an outside portion of the circulating heat exchanger loop.

Description:
STATEMENT REGARDING FEDERAL RIGHTS 
     This invention was made with government support under Contract No. W-7405-ENG-36 awarded by the U.S. Department of Energy. The government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to oscillating wave engines and refrigerators, and, more particularly, to Stirling engines, Stirling refrigerators, orifice pulse tube refrigerators, thermoacoustic engines, thermoacoustic refrigerators, and hybrids and combinations thereof. 
     BACKGROUND OF THE INVENTION 
     Historically, Stirling&#39;s hot-air engine of the early 19th century was the first heat engine to use oscillating pressure and oscillating volume flow rate in a working gas in a sealed system, although the time-averaged product thereof was not called acoustic power. Since then, a variety of related engines and refrigerators have been developed, including Stirling refrigerators, Ericsson engines, orifice pulse-tube refrigerators, standing-wave thermoacoustic engines and refrigerators, free-piston Stirling engines and refrigerators, and thermoacoustic-Stirling hybrid engines and refrigerators. Combinations thereof, such as the Vuilleumier refrigerator and the thermoacoustically driven orifice pulse tube refrigerator, have provided heat-driven refrigeration. 
     Much of the evolution of this entire family of acoustic-power thermodynamic technologies has been driven by the search for higher efficiencies, greater reliabilities, and lower fabrication costs. FIGS. 1,  2 , and  3  show some prior art engine examples in which simplicity, reliability, and low fabrication costs have been achieved by the elimination of moving parts, especially elimination of moving parts at temperatures other than ambient temperature. 
     FIG. 1 shows a free-piston Stirling engine  10  integrated with a linear alternator  12  to form a heat-driven electric generator. High-temperature heat, such as from a flame or from nuclear fuel, is added to the engine at hot heat exchanger  14 , ambient-temperature waste heat is removed from the engine at ambient heat exchanger  16 , and oscillations of working gas  18 , piston  22 , and displacer  24  are thereby encouraged. The oscillations of piston  22  cause permanent magnet  26  to oscillate through wire coil  28 , thereby generating electrical power, which is removed from the engine to be used elsewhere. 
     The conversion of heat to acoustic power occurs in regenerator  32 , which is a solid matrix smoothly spanning the temperature difference between hot heat exchanger  14  and ambient heat exchanger  16  and containing small pores through which working gas  18  oscillates. The pores must be small enough that working gas  18  in the pores is in is excellent local thermal contact with the solid matrix. Proper design of the dynamics of moving piston  22  and displacer  24 , their gas springs  34 / 36 , and working gas  18  throughout the system causes the working gas in the pores of regenerator  32  to move toward hot heat exchanger  14  while the pressure is high and toward ambient heat exchanger  16  while the pressure is low. The oscillating thermal expansion and contraction of the working gas in regenerator  32 , attending its oscillating motion along the temperature gradient in the pores, is therefore temporally phased with respect to the oscillating pressure so that the thermal expansion occurs while the pressure is high and the thermal contraction occurs while the pressure is low. 
     The absence of crankshafts and connecting rods contributes to the simplicity, reliability, and low fabrication costs of the free-piston Stirling engine. 
     FIG. 2 shows a “toroidal” regenerator-based engine: a thermoacoustic-Stirling hybrid engine delivering acoustic power to an unspecified load  42  (e.g., a linear alternator or any of the aforementioned refrigerators) to the right. See, e.g., U.S. Pat. No. 6,032,464, “Traveling Wave Device with Mass Flux Suppression, issued Mar. 7, 2000, to Swift et al. and U.S. Pat. No. 6,314,740, “Thermoacoustic System,” issued Nov. 13, 2001, to deBlok et al. High-temperature heat, such as from a flame, from nuclear fuel, or from ohmic heating, is added to the engine at hot heat exchanger  44 , most of the ambient-temperature waste heat is removed from the engine at main ambient heat exchanger  46 , and oscillations of the working gas are thereby encouraged. Mass flux suppressor  50  acts to minimize time-averaged mass flux of the working gas and attendant heat loss. The oscillations deliver acoustic power to load  42 . 
     FIG. 3 shows a “cascade” thermoacoustic-Stirling hybrid engine comprising a standing-wave thermoacoustic engine and a Stirling engine in series, without any piston therebetween, as described in U.S. patent application Ser. No. 10/125,268 “Cascaded Thermoacoustic Devices,” G. W. Swift et al., filed Apr. 18, 2002. High-temperature heat is added at the two hot heat exchangers  52 ,  54 ; ambient-temperature waste heat is removed at the three ambient heat exchangers  56 ,  58 ,  62 ; and oscillations of the working gas are thereby encouraged. The oscillations deliver acoustic power to a load  64 , such as a linear alternator or a pulse tube refrigerator, below the bottom of FIG.  3 . The conversion of heat to acoustic power occurs in regenerator  66  according to the same processes as described in the context of FIG. 1 above. Stack  68  has larger pore sizes than regenerator  66 , and conversion of heat to acoustic power in stack  68  occurs by a similar process, but with some different details regarding time phasing, as described in the &#39;268 patent application. 
     The simplicity, reliability, and low fabrication cost of the toroidal thermoacoustic-Stirling hybrid engine and of the cascade thermoacoustic-Stirling hybrid engine, compared to earlier Stirling engines, comes from the elimination of pistons previously needed. 
     FIG. 4A shows a piston-driven orifice pulse tube refrigerator, as described for example by R. Radebaugh in “A review of pulse tube refrigeration,” Adv. Cryogenic Eng., volume 35, pages 1191-1205 (1990). The motion of piston  70  causes oscillations in the working gas throughout the refrigerator. Low-temperature heat is removed from a load by the refrigerator at cold heat exchanger  72 , and ambient-temperature waste heat is rejected from the refrigerator at the two ambient-temperature heat exchangers  74 ,  76 , the larger of which is commonly called the aftercooler, i.e., heat exchanger  74 . Heat pumping up the temperature gradient occurs in regenerator  78  because the working gas in the pores of regenerator  78  is caused to move toward cold heat exchanger  72  while the pressure is high and toward aftercooler  74  while the pressure is low. This necessary time phasing between oscillating pressure and oscillating motion is created by acoustic impedance network  82  above pulse tube  84 , which sets the relative amplitudes and time phasing of the pressure and velocity at its entrance. Earlier Stirling refrigerators achieved the correct time phasing by means of a cold piston (whose motion was coordinated with that of the drive piston) instead of by means of the acoustic impedance network. However, the technical challenge of sealing around such a piston at cryogenic temperatures was severe. Hence, the simplicity, reliability, and low fabrication cost of the orifice pulse tube refrigerator compared to earlier Stirling refrigerators comes from the elimination of the cold piston. 
     Although much progress has recently been made in the elimination of moving parts from these oscillating-wave engines and refrigerators, the simplification of the heat exchangers offers a second opportunity for dramatic improvement in simplicity, reliability, and low fabrication cost, particularly in engines and refrigerators of high power. All engines and refrigerators must reject waste heat to ambient temperature, and the ambient temperature is often present as a flowing fluid stream, such as a fan-driven air stream or a flowing water stream. Engines must also accept heat from a source at a higher temperature, which may be in the form of a flowing stream of combustion products from a burner. Refrigerators must withdraw heat from a load at lower temperature, which is sometimes in the form of a flowing stream; examples include a stream of indoor air to be cooled and dehumidified, or a stream of methane to be cooled and cryogenically liquefied. Hence, the typical heat exchanger in these engines and refrigerators must transfer heat between a steadily flowing “process fluid” stream and an oscillating “working gas” stream that is the thermodynamic working substance of the oscillating-wave engine or refrigerator. The working gas is often pressurized helium gas. At small power levels, simple geometries such as stacks of copper screens suffice as heat exchangers, but at higher powers the thermal conductivity of solids is insufficient to carry the required heats, so that geometrically complicated heat exchangers must usually be used to bring the process fluid and working gas into intimate thermal contact. 
     M. Mitchell, “Pulse tube refrigerator,” U.S. Pat. No. 5,966,942, Oct. 19, 1999, teaches a design to avoid a geometrically complicated heat exchanger for the ambient heat exchanger  76  (FIG. 4A) at the ambient end of the pulse tube  84  of an orifice pulse tube refrigerator. As illustrated in FIG. 4B, which is adapted from FIGS. 1 and 11 in the &#39;942 patent, ambient heat exchanger  76  and orifice  86  can be replaced by a dissipative heat-transfer loop  88  containing one or more (two are shown in FIG. 4B) fluidic diodes  92 ,  94  that convert some of the oscillatory power in the oscillating wave into circulating flow of the working gas around loop  88 . The dissipation in fluidic diodes  92 , 94  and other oscillatory dissipation in loop  88  serve the function of orifice  86 , and the surface area along the entire path length of loop  88  serves the function of heat exchanger  76 . 
     A shell and tube heat exchanger  102 , illustrated in FIGS. 5A and 5B, is typical of the complicated, geometries that must otherwise be used at high power throughout oscillating-wave engines and refrigerators. Working gas  104  oscillates through the insides of the many tubes  106 , while process fluid  108  flows around and between the outsides of tubes  106 . 
     Particular features of oscillating-wave engines and refrigerators impose size constraints on such heat exchangers as they are scaled up to higher powers. Higher power demands more heat-transfer surface area for efficient heat transfer. However, tube diameters cannot be increased, because this would reduce the total heat-transfer coefficient on the working-gas side, thereby decreasing the efficiency. Tube lengths cannot be increased, because having such tube lengths greater than the oscillatory displacement of the working gas does not help transfer more heat. 
     The usual solution to the scaleup of heat exchangers is to increase the number of tubes in proportion to the power, keeping the length and diameter of each tube constant. Such heat exchangers can have hundreds or thousands of tubes. Building such heat exchangers is expensive (because many parts must be handled, assembled, and joined) and such heat exchangers are unreliable (because so many joints must be leak tight). Thermally induced stress imposes an additional challenge to reliability when a geometrically complex heat exchanger is at an extreme temperature, such as a red-hot temperature for an engine or a cryogenic temperature for a refrigerator. Sometimes a pool boiler or heat pipe must be used to enforce isothermality in these circumstances so that thermally induced stresses are eliminated. 
     Another shortcoming of oscillating-wave engines and refrigerators is that their heat exchangers often must be located close to one another, simply because each heat exchanger must typically be adjacent to one end or the other of the nearest stack or regenerator or pulse tube or thermal buffer tube, and these components themselves are typically short. The practical importance of this shortcoming is easily appreciated by considering the food refrigerator in the typical American kitchen. The “vapor compression” (also known as “reverse Rankine”) cooling technology employed therein allows complete flexibility in the geometrical separation of the cold heat exchanger, where heat is absorbed from the inside of the cold box, and the ambient heat exchanger, where waste heat is rejected outside, to the air in the kitchen. The cold heat exchanger is typically located inside, above, or under the freezer, and the ambient heat exchanger is typically located behind or under the refrigerator cabinet. Not only can these heat exchangers be located freely, but their shapes can be chosen as needed for their circumstances, e.g., to accommodate fan-driven or natural convection as chosen, and to fit in and around the desired shape of the cold box or cabinet. In contrast, when one tries to adapt an oscillating-wave refrigerator to this application, the cold heat exchanger and main ambient heat exchanger must be very close together, separated only by the regenerator whose length is typically only a few inches. Hence, in, order to put the cold heat exchanger and the main ambient heat exchanger into thermal contact with the inside of the cold box and with the outside air, respectively, intermediate heat transfer means, such as heat pipes or pumped fluid heat transfer loops, must typically be employed. These add complexity and cost, and reduce efficiency. 
     Accordingly, it is highly desirable to provide simplicity, reliability, and low fabrication cost of heat exchangers for oscillating-wave engines and refrigerators. More specifically, the present invention is directed to eliminating the need for massively parallel heat-exchanger structures in oscillating-wave engines and refrigerators of high power. The present invention also allows the heat exchangers of oscillating-wave engines and refrigerators to be located distant from one another and from the nearest regenerator or stack. 
     Those skilled in the art understand that “ambient” temperature, referring to the temperature at which waste heat is rejected, need not always be a temperature near ordinary room temperature. For example, a cryogenic refrigerator intended to liquefy hydrogen at 20 Kelvin might reject its waste heat to a liquid-nitrogen stream at 77 Kelvin; for the purposes of this particular cryogenic refrigerator, “ambient” would be 77 Kelvin. 
     Those skilled in the art also understand that fluidic diodes are typically much less perfect than electronic diodes. Fluidic diodes usually offer a difference between forward and backward flow resistances of less than a factor of ten, and sometimes even less than a factor of two, whereas the difference in forward and backward resistances in electronic diodes is typically orders of magnitude. Fluidic diodes include the vortex diodes described in &#39;942, the valvular conduit described by Nikola Tesla in U.S. Pat. No. 1,329,559, Feb. 3, 1920, and the conical and tapered structures called jet pumps in many recent publications such as U.S. Pat. No. 6,032,464, “Traveling Wave Device with Mass Flux Suppression,” supra; S. Backhaus, et al., “A thermoacoustic-Stirling heat engine: Detailed study,” J. Acoust. Soc. Am., volume 107, pages 3148-3166 (2000); G. W. Swift,  Thermoacoustics: A unifying perspective for some engines and refrigerators , to be published by The Acoustical Society of America, 2002. 
     Various objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to an oscillating-wave engine or refrigerator having a regenerator or a stack in which oscillating flow of a working gas occurs in a direction defined by an axis of a trunk of the engine or refrigerator, and having an improved heat exchanger. First and second connections branch from the trunk at locations along the axis in selected proximity to one end of the regenerator or stack, where the trunk extends in two directions from the locations of the connections. A circulating heat exchanger loop is connected to the first and second connections. At least one fluidic diode within the circulating heat exchanger loop produces a superimposed steady flow component and oscillating flow component of the working gas within the circulating heat exchanger. A local process fluid is in thermal contact with an outside portion of the circulating heat exchanger loop. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings, which are incorporated in and form a part of the specification, illustrate embodiments of the present invention and, together with the description, serve to explain the principles of the invention. In the drawings: 
     FIG. 1 is a cross-sectional view of a free piston Stirling engine. (Prior art) 
     FIG. 2 schematically depicts a toroidal thermoacoustic-Stirling hybrid engine. (Prior art) 
     FIG. 3 schematically depicts a cascade thermoacoustic-Stirling hybrid engine. (Prior art) 
     FIG. 4A schematically depicts an orifice pulse tube refrigerator. (Prior art) 
     FIG. 4B schematically depicts an orifice pulse tube refrigerator with heat-transfer loop at the ambient end of the pulse tube driven by a fluidic diode. (Prior art) 
     FIGS. 5A and 5B schematically depict a conventional shell-and-tube heat exchanger. (Prior art) 
     FIG. 6A schematically depicts a portion of an oscillating-wave engine or refrigerator. (Prior art) 
     FIG. 6B schematically depicts a portion-of an oscillating-wave engine or refrigerator, employing a circulating heat exchanger according to the present invention. 
     FIG. 7A schematically depicts a portion of an oscillating-wave engine. (Prior art) 
     FIG. 7B schematically depicts a portion of an oscillating-wave engine, employing a resonant circulating hot heat exchanger according to the present invention. 
     FIG. 7C graphically depicts the volume flow rate in one resonant circulating hot heat exchanger as a function of position and time. 
     FIG. 8A schematically depicts a portion of an oscillating-wave refrigerator. (Prior art) 
     FIG. 8B schematically depicts a portion of an oscillating-wave refrigerator, employing a resonant circulating cold exchanger according to the present invention. 
     FIG. 9A schematically depicts a portion of an oscillating-wave engine. (Prior art) 
     FIG. 9B schematically depicts a portion of an oscillating-wave engine, employing a non-resonant circulating hot heat exchanger according to the present invention. 
    
    
     DETAILED DESCRIPTION 
     The improved heat exchanger of the present invention is generally explained with reference to FIGS. 6A and 6B. FIG. 6A shows a portion of an oscillating-wave engine or refrigerator  112 , containing a prior art heat exchanger  114  as described above. In FIG. 6A, heat exchanger  114  is below stack or regenerator  116 , and is above pulse tube, thermal buffer tube or open duct  118 . Heat exchanger  114  is of traditional design, such as shell-and-tube or finned tube. The oscillating flow  122  of the working gas, e.g. pressurized helium, is indicated by the double-headed straight-line arrows. The steady flow  124  of the process fluid, e.g., water, is indicated by the wavy arrows. The axial direction along which these oscillations occur in regenerator/stack  116  and pulse tube/thermal buffer tube/open duct  118  is referred to herein as “the axis” and vessel  120  containing these components is referred to herein as “the trunk,” where the trunk extends in two directions from regenerator or stack  116 , and pulse tube/open duct/thermal buffer tube  118 . 
     FIG. 6B shows the same portion  112  of an oscillating-wave engine or refrigerator, but with a circulating heat exchanger  126  according to the present invention. Circulating heat exchanger  126  comprises a long, narrow pipe  128 , each end of which is attached to trunk  120  at an axial location between stack/regenerator  116  and pulse tube/thermal buffer tube/or open duct  118 . The preferred axial location is where a prior-art heat exchanger would be expected. Oscillating flow  122  of the working gas in trunk  120  is again indicated by the double-headed straight-line arrows. 
     The flow  132  of the working gas in circulating heat exchanger  126  is a superposition of oscillating flow and steady flow, indicated by adjacent double-headed straight-line arrows and single-headed straight-line arrows. The steady flow therein is caused by the interaction of the oscillating flow with fluidic diode  134  and is in the direction of least resistance through fluidic diode  134 . In turn, the oscillating flow in circulating heat exchanger  126  is caused by the pressure oscillations in trunk  120 . The steady flow of the process fluid is again indicated by the wavy arrows. Process fluid  136  flows past circulating heat exchanger  126  (either substantially perpendicular to it, as shown in FIG. 6B, or substantially parallel to it, or anything in between). 
     Thus, heat exchanger  114  of FIG. 6A, which is expensive to build because it comprises a multiplicity of parallel passages, and which must abut regenerator or stack  116 , has been replaced by circulating heat exchanger  126  shown in FIG. 6B, which is inexpensive because it is essentially just a single long pipe, and which allows the heat exchange between the working gas and process fluid  136  to take place far from regenerator or stack  116 . 
     The distinction between the invention shown in FIG.  6 B and the fluidic diode configuration shown by the &#39;942 patent (FIG. 4B) is the topology. As shown in FIG. 4B, vessel  85  terminates at tee  90 , while trunk  120  of the present invention extends in both directions from circulating heat exchanger  126 . Heat-transfer loop  88  in FIG. 4B carries all of the oscillating flow that exists in vessel  85 . In contrast, circulating heat exchanger  126  in FIG. 6B carries only a fraction of the oscillating flow in trunk  120 , that fraction designed to be as small as possible. The &#39;942 patent teaches only the context of the heat exchanger at the warm end of the pulse tube in a pulse tube refrigerator, which is a unique location in a specific type of oscillating-wave refrigerator where all of the trunk flow can indeed be carried by the two branches together, without harm to the function of the refrigerator. In contrast, the present invention is applicable to any of the heat exchangers of any oscillating-wave engine or refrigerator. 
     Referring first to a resonant embodiment of the present invention, the oscillating flow in the trunk is perturbed only a small amount, while creating a surprisingly strong steady flow in the circulating heat exchanger. Resonant embodiments are described in the context of hot heat exchangers  142  and  146  of oscillating-wave engine  140 , shown in FIGS. 7A and 7B, and in the context of cold heat exchangers  162  and  168  of oscillating-wave refrigerator  160  shown in FIGS. 8A and 8B. A non-resonant embodiment of the is present invention perturbs the oscillating flow in the trunk considerably, leading in some situations to a requirement for a larger pulse tube or thermal buffer tube. A non-resonant embodiment is described in the context of the hot heat exchanger of an oscillating-wave engine as shown in FIGS. 9A and 9B. 
     A resonant embodiment of the present invention is illustrated with reference to FIGS. 7A and 7B. FIG. 7A shows a portion of an oscillating-wave engine  140 , employing a traditional hot heat exchanger  142 , such as a shell-and-tube heat exchanger, located adjacent to regenerator/stack  144  contained within trunk  145 . FIG. 7B shows the use of a resonant circulating hot heat exchanger  146  according to the present invention, instead of traditional hot heat exchanger  142 . Resonant circulating hot heat exchanger  146  comprises pipe  148  with a length equal to one wavelength of sound in the working gas, at the frequency of the oscillation of the working gas, and has two fluidic diodes  152 ,  154  in pipe  148 , each located a quarter wavelength from an end of pipe  148 . The wavelength is that of the working gas at the temperature in pipe  148 , which, might be far from ambient temperature. 
     The oscillating and steady flows of the working gas, and the steady flow of the process fluid (here, a hot gas such as the combustion products from a burner) are similar to the flows shown in FIGS. 6A and 6B. However, the fact that the oscillating flow is wavelike in character and the fact that the length of pipe  148 .in FIG. 7B is one wavelength of sound lead to some unexpected synergistic features. Fluidic diodes  152 ,  154  are located where the oscillating volume flow rate is a maximum along pipe  148  so that fluidic diodes  152 ,  154  can create a large steady flow, as explained more fully below. Meanwhile, the ends of pipe  148  are locations of minimal oscillating volume flow rate of working gas within pipe  148 , so that connecting pipe  148  to trunk  145  only minimally perturbs the oscillations in trunk  145 . Thus, circulating heat exchanger  146  extracts from and delivers to trunk  145  a large steady flow, while only minimally perturbing oscillations in trunk  145 . 
     One specific design of this type for an engine has been further investigated, with a hot heat exchanger  142  or  146  required between regenerator  144  above hot heat exchanger  142  or  146  and a thermal buffer tube  150  below, as shown in FIGS. 7A and 7B. The engine operates at 40 Hz, with a helium working gas at an average pressure of 3.1 MPa. The design with traditional heat exchanger  142 , as shown in FIG. 7A, is compared with the design with circulating heat exchanger  146 , as shown in FIG.  7 B. 
     The geometry of the traditionally designed heat exchanger  142  is shell-and-tube. Heat exchanger  142  was designed to deliver 63 kW of heat to the engine, keeping the hot, lower face of regenerator  144  at 936 K. Heat exchanger  142  comprised 375 tubes in parallel, each having a length of 20 cm and an inside diameter of 6 mm, so that the total surface area presented to the helium was 1.5 square meters. The amplitude of the oscillating pressure in the helium in and near heat exchanger  142  was 240 kPa, and 2.7 kW of acoustic power was consumed in viscous and thermal-hysteresis loss in heat exchanger  142 , while 55 kW of acoustic power passed through it. Even with this much surface area, it was estimated that a 40 degree average difference in temperature is required to drive the heat from the metal into the helium. This would be a very complex heat exchanger to fabricate because the high temperature weakens metals and the difficulty of ensuring tube-to-tube temperature uniformity as the combustion-product process fluid flows through the shell is extreme. 
     The geometry of the circulating heat exchanger  146  for this application is illustrated in FIG.  7 B: pipe  148  one wavelength long, with two fluidic diodes  152 ,  154  at the quarter-wavelength positions. Circulating heat exchanger  146  was, as above, designed to deliver 63 kW of heat to the engine, keeping the hot, lower face of regenerator  144  at 936 K. The amplitude of the oscillating pressure in the helium working gas below regenerator  144  was 240 kPa, while 55 kW of acoustic power passed down from regenerator  144 , as above. Heat exchanger  146  comprised one pipe  148 , having a length of 43 m, and an inside diameter of 7.1 cm, so that the total surface area presented to the helium working gas was 10 square meters. 
     The dramatic increase in surface area of circulating heat exchanger  146  relative to traditional heat exchanger  142  means that temperature differences, both process fluid to metal and metal to helium, are greatly reduced, as long as the steady flow is vigorous and the heat transfer coefficient per unit area is reasonably large. The long length of pipe  148  means that some length can be devoted to tubing runs without heat exchange, in order to place the heat exchanger at a convenient location remote from the regenerator, where the heat-exchange portion of pipe  148  can be coiled for compactness. Each of the two fluidic diodes  152 ,  154  is a truncated cone, with the large end matched to pipe  148  and the small end having an area equal to 40% of the area of pipe  148 , and with a length of 43 cm. The lip at the abrupt diametral transition from the small-diameter end of the cone back to the pipe diameter is preferably generously rounded so that the minor loss coefficient for flow into the small end, K in , is approximately 0.05 or less (see, e.g.,  Introduction to Fluid Mechanics , R. W. Fox and A. T. McDonald (Wiley, 1985)). 
     The dissipation of acoustic power in circulating heat exchanger  146  was estimated to be 7.6 kW total, with 1.9 kW lost in fluidic diodes  152 ,  154  and 5.7 kW of viscous and thermal-hysteresis losses elsewhere in pipe  148 . The extra 4.9 kW of acoustic power dissipated in heat exchanger  146 , relative to the traditional heat exchanger  142 , is minor in view of the simplicity of fabrication and reliability in operation that results from the one-pipe geometry. 
     The steady volume flow rate created in circulating heat exchanger  146  was 0.06 m 3 /sec. The amplitude of the oscillating volume flow rate at the entrance and exit of circulating heat exchanger  146 , where it is attached to trunk  145 , was only 0.032 m 3 /sec, while the amplitude of the oscillating volume flow rate along trunk  145  at that location was 0.5 m 3 /sec. The amplitude of the oscillating volume flow rate in fluidic diodes  152 ,  154  was 0.33 m 3 /sec. Qualitative features of some of these flow rates are shown in FIG. 7C, which shows the instantaneous volumetric flow rate U(x,t) as a function of position x in circulating heat exchanger  146  at four equally spaced times t in one cycle of the wave. The sign and origin of position coordinate x are shown in FIG. 7B, and the position x is normalized by wavelength λ in FIG.  7 C. The four equally spaced times are labeled by ωt, where ω=2πf is the radian frequency of the oscillations and f is the frequency of the oscillations. Hence, ωt=2π represents a full temporal cycle of the oscillations. The zero of time has been chosen to be when the oscillating pressure in trunk  145  reaches a maximum. This oscillating pressure creates the entire wave U(x,t), with the amplitude of U largest at x/λ=0.25 and 0.75 where fluidic diodes  154 ,  152  induce the temporally steady and spatially uniform volume flow rate, here 0.06 m 3 /s, Thus, a substantial steady flow rate is created through a heat exchanger with a very large surface area, while consuming a relatively small amount of oscillating flow from the trunk, and this is accomplished with no moving parts. 
     It will be appreciated by those skilled in the art that acoustic power at such a high temperature is inherently less valuable than acoustic power at ambient temperature, according to the principles of exergy accounting in thermoacoustics (G. W. Swift,  Thermoacoustics: A unifying perspective for some engines and refrigerators , supra). Thus the extra 4.9 kW of acoustic power consumed by the circulating heat exchanger appears even less important in this application. 
     The calculations described above were performed using a conventional design code for oscillating-wave engines and refrigerators, such as DeltaE (available at www.lanl.gov/thermoacoustics/) or Sage (available from Gedeon Associates, Athens, Ohio, dgedeon@compuserve.com). The estimation of the acoustic power consumed by the fluidic diodes, the steady pumping effect of the fluidic diodes, and the resulting steady flow is accomplished as follows. The time-averaged pressure difference {overscore (Δp fd )} developed across each fluidic diode due to the time-dependent flow through it can be estimated using                  Δ                   p   fd       _     =       ω     2                 π                   A   2              [         ∫     t   1         π   /   ω     -     t   1                K   in          1   2            ρ        (              U   1             sin                 ω                 t     +     U   m       )       2             t         -       ∫       π   /   ω     -     t   1           2                   π   /   ω       +     t   1                K   out          1   2            ρ        (              U   1             sin                 ω                 t     +     U   m       )       2             t           ]               Eqn   .              1                                
     where K out  and K in  are the minor loss coefficients for the two directions of flow through the fluidic diode, A is the area on which the K&#39;s are based (conventionally the smallest area of the fluidic diode), ρ is the gas mass density, |U 1 | is the amplitude of the oscillating volumetric flow rate at the small diameter of the fluidic diode, |U m | is the steady volumetric flow rate, t is time, and t 1  is the time at which the volumetric flow rate crosses zero, i.e., t 1  satisfies |U 1 | sin ωt 1 +U m =0 (where the solution with −π/2&lt;ωt 1 &lt;0 is chosen). Equation 1 is a straightforward extension of Equation 7.76 in G. W. Swift,  Thermoacoustics: A unifying perspective for some engines and refrigerators , supra. 
     Assuming that ρ, K out  and K in  are independent of time, performing the integrals in Equation 1 and simplifying yields                  Δ                   p   fd       _     =         ρ               U   1          2         8        A   2              (       K   out     -     K   in       )     ×     {       (     1   +     2                   ɛ   2         )     -           K   out     +     K   in           K   out     -     K   in                2   π          [         (     1   +     2                   ɛ   2         )          sin     -   1          ɛ     +     3                 ɛ          1   -     ɛ   2             ]           }               Eqn   .              2                                
     where ε=U m /|U 1 |. This equation is used to estimate the pressure difference developed across the fluidic diode. 
     A time-averaged pressure gradient also exists throughout the rest of the circulating heat exchanger because U m  flows throughout the circulating heat exchanger. To estimate the total pressure difference Δp hx  in the rest of the circulating heat exchanger, standard results of fluid mechanics are used (e.g., Fox and McDonald, supra), so that                  Δ                   p   hx       =     k        1   2            ρ        (       U   m       A   hx       )       2          L   D         ,           Eqn   .              3                                
     where L is the total length, D is the diameter, A hx  is the cross-sectional area, and k is the conventional Moody friction factor, which depends on Reynolds number and surface roughness. 
     Using Equations 2 and 3 and setting {overscore (Δp fd )}=Δp hx  allows U m  to be found. This is done numerically because of the complicated nature of Equation 2. 
     The acoustic power consumed by each fluidic diode due to the time-dependent flow through it is estimated using                  Δ   _            E   .       2   ,   fd         =         ω     2                 π                   A   2              [         ∫     t   1         π   /   ω     -     t   1                K   in          1   2            ρ        (              U   1             sin                 ω                 t     +     U   m       )       3             t         -       ∫       π   /   ω     -     t   1           2                   π   /   ω       +     t   1                K   out          1   2            ρ        (              U   1             sin                 ω                 t     +     U   m       )       2             t           ]       .             Eqn   .              4                                
     Again assuming that ρ, K out  and K in  are independent of time, performing the integrals in Equation 4 and simplifying yields                    Δ   _            E   .       2   ,   fd         =         ρ               U   1          3         3                 π                   A   2              (       K   out     +     K   in       )     ×     {         (     1   +       11   4          ɛ   2         )            1   -     ɛ   2           +       3   4          ɛ        (     3   +     2                   ɛ   2         )            sin     -   1          ɛ     -           K   out     -     K   in           K   out     +     K   in              (         9                 π                 ɛ     8     +       3                 π                   ɛ   3       4       )         }         ,           Eqn   .              5                                
     which can be readily used. 
     The use of resonant circulating heat exchanger  168  as the cold heat exchanger in an orifice pulse tube refrigerator  160  has also been investigated for one application. FIG. 8A illustrates this case with a traditional shell-and-tube heat exchanger  162 , and FIG. 8B illustrates the application with circulating heat exchanger  168 , both having regenerator  164 , pulse tube  166 , and trunk  165 . Again, the working gas was helium gas at an average pressure of 3.1 MPa, oscillating at 40 Hz. Refrigerator  160  was designed to provide 20 kW of cooling power at 100 K. The amplitude of the oscillating pressure in the helium in and near the heat exchanger  162  or  168  was 240 kPa. 
     Traditional heat exchanger  162 , illustrated in FIG. 8A, comprised 5,500 tubes in parallel, each having a length of 1.5 inches and an inside diameter of 0.148 inch, so that the total surface area of metal in contact with the helium was 2.4 square meters. A total of 400 W of acoustic power was consumed in viscous and thermal hysteresis loss in heat exchanger  162 . 
     The corresponding circulating heat exchanger  168  for this application is shown in FIG.  8 B: pipe  172  one wavelength long, with two fluidic diodes  174 ,  176  at the quarter-wavelength positions. Pipe  172  had a length of 44 feet and a diameter of 2.4 inches, so that the total surface area presented to the helium was 2.5 square meters. The long length of circulating heat exchanger  168  means that some length can be devoted to tubing runs without heat exchange, in order to place the process fluid heat-transfer surfaces at a convenient location remote from regenerator  164 , where the heat-exchange portion of pipe  172  can be coiled for compactness. Each of fluidic diodes  174 ,  176  was a truncated cone, with its large end matched to the pipe diameter and its small end having an area equal to 40% of that of the pipe, and with a length of 37 cm. The lip at the abrupt diametral transition from the small-diameter end back to the pipe diameter was generously rounded, as described above. The dissipation of acoustic power in this circulating heat exchanger was estimated to be 760 W. Even though the energy cost of this dissipation at low temperature is relatively high, the extra 360 W, relative to the traditional design described above, is again a minor performance penalty in view of the simplicity of fabrication and reliability in operation that results from the simple, one-pipe geometry as compared to the 5,500 small tubes of the traditional design. 
     The steady volume flow rate created in circulating heat exchanger  168  was 0.023 m 3 /sec. The amplitude of the oscillating volume flow rate at the entrance and exit of circulating heat exchanger  168 , where it is attached to trunk  165 , was only 0.003 m 3 /sec. Thus, a substantial steady flow rate is created through a heat exchanger with a large surface area, while consuming a relatively small amount of oscillating flow and of acoustic power, and this is accomplished with no moving parts and with a reduction by orders of magnitude in the number of joints that must be made leak tight during fabrication. 
     FIGS. 9A and 9B illustrate a non-resonant embodiment of the present invention, discussed here in the context of the hot heat exchanger of an oscillating-wave engine  180  having regenerator or stack  184 , thermal buffer tubes  186  and  190  forming trunks  185 ,  195 . FIG. 9A shows a portion of engine  180 , employing a traditional shell-and-tube heat exchanger 182 with the helium working gas oscillating through the tubes and the steady flow of the combustion gases flowing through the shell. FIG. 9B shows the use of a non-resonant circulating hot heat exchanger  188  according to the present invention, instead of traditional hot heat exchanger  182 . Non-resonant circulating hot heat exchanger  188  is a pipe network  192  with a length less than a quarter wavelength of sound in the gas in the pipe, at the frequency of the oscillation of the working gas in engine  180 , and having one or more (two are shown in FIG. 7B) fluidic diodes  194 ,  196  in the pipe. The oscillating and, steady flows of the working gas, and the steady flow of the process fluid (here, a hot gas such as the combustion products from a burner) are similar to those shown in FIG.  6 . Fluidic diodes  194 ,  196  are located where the oscillating volume flow rate is a maximum, near the connections to trunk  195 , so that fluidic diodes  194 ,  196  can create the largest possible steady flow. Heat exchanger passages  192  can be subdivided into several passages in parallel, as shown in FIG. 9B, although the number of passages can be considerably smaller than the number of passages in heat exchanger  182  shown in FIG.  9 A. 
     Preliminary estimates were made for one specific design of this type for an engine, with hot circulating heat exchanger  188  connected between regenerator  184  above it and thermal buffer tube  190  below it, as shown schematically in FIG. 9B, but with only one fluidic diode. The engine was designed to operate at 40 Hz, with helium at an average pressure of 3.1 MPa and the amplitude of the oscillating pressure in the helium below the regenerator of 310 kPa. 
     The heat to be transferred from combustion gas to helium was 3 MW, keeping the hot, lower face of regenerator  184  at 936 K. This would be a large system. For example, the small diameter of the conical fluidic diode was chosen to be 40 cm, in order to accommodate an oscillating volume flow rate amplitude of 20 m 3 /sec and to dissipate only 85 kW of acoustic power in the diode. The estimates showed that the fluidic diode would then pump a steady volumetric flow rate of 8 m 3 /sec against a steady pressure head of 5 kPa, so the impedance of heat exchanger  188  was designed accordingly. One design of such a heat exchanger  188  then resulted in 75 kW of acoustic power dissipation in the heat exchanger, for a total acoustic power dissipation of 160 kW. 
     This acoustic power dissipation is acceptable because there is no prior-art way to build a hot heat exchanger for such a large oscillating-wave engine. A traditional heat exchanger design was not even considered since the fabrication of such a large traditional heat exchanger for this application did not appear feasible. No oscillating-wave engine has ever been built with such a large power. 
     For non-resonant circulating heat exchanger  188 , the oscillating volume flow rate at each connection between circulating heat exchanger  188  and trunk  195  is larger than the steady volume flow rate, because no acoustic wave or resonance phenomena are used to increase the oscillations at the location(s) of the fluidic diode(s) relative to their amplitudes at the connections. Hence, getting a large enough steady volume flow rate requires an oscillating volume flow rate that is not insignificant relative to the oscillating volume flow rate in trunk  195 . Therefore, to accommodate this increased oscillating volume flow rate, thermal buffer tube  190  must be enlarged, as shown in FIG.  9 B. 
     In the oscillating-wave engines and refrigerators discussed above, the oscillating flows within a given regenerator or stack are essentially parallel, such as through the short dimension of a regenerator shaped with the proportions of a hockey puck. However, the same principles apply to oscillating-wave engines and refrigerators in which a stack or regenerator is shaped like a cylindrical annulus, with the, oscillating flow in the radial direction and to other geometries as well. 
     The discussion has focused on fluidic diodes having no moving parts, but fluidic diodes with moving parts, such as check valves or any other means of partially or fully rectifying oscillating flow, can also be employed. The discussion has focused on one or two fluidic diodes used per heat exchanger, but more can be employed if a greater steady volume flow rate is desired. The fluidic diodes are best placed at locations of large oscillating volume flow rate, but the location need not be exactly at the relative maxima of the oscillating volume flow rate as described in the context of FIGS. 6B and 7B. 
     The discussion of the resonant circulating heat exchanger described a pipe length of one wavelength, but other lengths can accomplish the same resonant conditions leading to low oscillating flow rate at the connections between the pipe and the trunk, high oscillating flow rate at the location(s) of fluidic diode(s), and large surface area. Obviously two or a larger integer number of wavelengths would perform in a similar manner, albeit with increased losses. Acousticians also appreciate that variations in the cross section of the pipe along its length can be used to alter the oscillation amplitudes as functions of position in the pipe, with resulting total lengths of pipe either shorter or longer than a wavelength while still maintaining the important features. 
     The discussion has focused on only one circulating heat exchanger per engine or refrigerator, but obviously more than one can be employed. Two or more of the heat exchangers in an engine or refrigerator can be made according to the present invention. Also, two or more circulating heat exchangers, in parallel, according to the present invention can be employed as one heat exchanger if more heat transfer surface area is needed. 
     When the present invention is employed adjacent to a pulse tube or thermal buffer tube, it is preferable to employ means to ensure that the pulse tube or thermal buffer tube experiences substantially thermally stratified oscillating flow. Such means includes, e.g., flow straightener  155  spanning the cross sectional area of thermal buffer tube  150  at the end adjacent to circulating heat exchanger  146 , as illustrated in FIG.  7 B. Flow straightener  155  can have sufficient solid heat capacity to store heat during a fraction of the oscillation period, helping the heat transfer between circulating heat exchanger  146  and the nearby stack or regenerator  144 . 
     Gravity-driven convection of the working gas in the circulating heat exchanger can also create steady flow, if the connections to the trunk and the parts of the circulating heat exchanger having thermal contact to the process fluid are at different heights. This feature can be useful in starting an engine using the present invention by providing convective heat transfer between the process fluid and the regenerator or stack before the oscillations begin. 
     The embodiments discussed herein are directed to oscillating-wave engines and refrigerators with few or no moving parts, but the invention is also well suited to oscillating-wave engines and refrigerators that depend on moving pistons, such as traditional Stirling engines and refrigerators. The resonant form of the invention is particularly well suited to such applications, because it does not require increased oscillating volume flow rate in the trunk and hence does not require increased piston motion. 
     The foregoing description of the invention has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. 
     The embodiments were chosen and described in order to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.