Patent Application
20120159943
1. Field of Invention
This invention relates generally to transducers and more particularly to a Stirling cycle transducer for converting thermal energy into mechanical energy or for converting mechanical energy into thermal energy.
2. Description of Related Art
Stirling cycle heat engines and heat pumps date back to 1816 and have been produced in many different configurations. Potential advantages of such Stirling cycle devices include high efficiency and high reliability. The adoption of Stirling engines has been hampered in part by the cost of high temperature materials, and the difficulty of making high pressure and high temperature reciprocating or rotating gas seals. Furthermore the need for relatively large heat exchangers and low specific power in comparison to internal combustion engines has also hampered widespread adoption of Stirling engines. Specific power refers to output power per unit of mass, volume or area and low specific power results in higher material costs for the engine for a given output power.
Thermoacoustic heat engines are a more recent development, where the inertia of the working gas cannot be ignored as is often done in Stirling engine analysis. In a thermoacoustic engine designs, the inertia of the gas should be accounted for and may dictate the use of a tuned resonator tube in the engine. Unfortunately at reasonable operating frequencies the wavelength of sound waves is however too long to allow for compact engines and consequently results in relatively low specific power. Thermoacoustic engines are however mechanically simpler than conventional Stirling engines and do not require sliding or rotating high-pressure seals.
One promising variant of the Stirling engine is a diaphragm engine in which flexure of a diaphragm replaces the sliding pistons in conventional Stirling engines thus reducing friction and wear. Several diaphragm engines have been proposed and built, but generally have low specific power (i.e. the power produced per unit volume is low). There remains a general need for improved heat engines and heat pumps, and more specifically for improved diaphragm heat engines and heat pumps.
In accordance with one aspect of the invention there is provided a Stirling cycle transducer apparatus for converting between thermal energy and mechanical energy. The apparatus includes a housing, a compression chamber disposed in the housing and having at least a first interface operable to vary a volume of the compression chamber, an expansion chamber disposed in the housing and having a second interface operable to vary a volume of at least the expansion chamber, and a thermal regenerator in fluid communication with each of the compression chamber and the expansion chamber. The thermal regenerator is operable to alternatively receive thermal energy from gas flowing in a first direction through the regenerator and to deliver the thermal energy to gas flowing in a direction opposite to the first direction through the regenerator. The compression chamber, the expansion chamber, and the regenerator together define a working volume for containing a pressurized working gas. Each of the first and second interfaces are configured for reciprocating motion in a direction aligned with a transducer axis, the reciprocating motion being operable to cause a periodic exchange of working gas between the expansion and the compression chambers. At least one of the first and second interfaces includes a resilient diaphragm, and a cylindrical tube spring coupled between the diaphragm and the housing, the tube spring being configured to elastically deform in a direction generally aligned with the transducer axis in response to forces imparted on the tube spring by the diaphragm to cause the at least one of the first and second interfaces to have a desired natural frequency.
Each of the first and second interfaces may include a resilient diaphragm.
Each of the first and second interfaces may be configured for reciprocating motion at a natural frequency of at least about 250 Hz.
The pressurized working gas may have a static pressure of at least about 3 MPa.
The first interface may include a resilient diaphragm and the second interface may include a displacer disposed between the expansion chamber and the compression chamber and the reciprocating motion of the second interface may be operable to vary the volume of both the expansion chamber and the compression chamber.
The apparatus may include a mount for mounting the transducer apparatus, the mount being operably configured to permit reciprocating complementary vibration of the apparatus in the direction of the transducer axis to impart a reciprocating motion to the displacer at the desired phase angle.
The expansion chamber may be defined between a first surface of the displacer and a wall of the housing and the first surface of the displacer may include a flexure configured to permit reciprocating motion of the displacer, and a central portion of the wall may be offset along the transducer axis from the displacer with respect to a peripheral portion of the wall for accommodating the reciprocating motion of the displacer.
The compression chamber may be defined between a second surface of the displacer and the diaphragm and the second surface of the displacer may include a flexure configured to permit reciprocating motion of the displacer, and the central portion of the diaphragm may be offset along the transducer axis with respect to a peripheral portion of the diaphragm for accommodating reciprocating motion of the displacer.
The displacer may include a flexure, the flexure including a peripheral portion, a central portion, and an intermediate flexing portion extending between the peripheral portion and the central portion, the flexing portion configured such that during reciprocating motion of the displacer, flexing occurs substantially in the intermediate flexing portion.
The intermediate flexing portion of the flexure may have an increased thickness proximate the central portion and tapers to a reduced thickness distal to the central portion.
The peripheral portion, the intermediate flexing portion, and the central portion may together define a thickness profile for the flexure, and the thickness profile may be selected to cause the flexure to have an effective area to cause reciprocating motion of the displacer to be out of phase with the reciprocating motion of the first interface by a desired phase angle, the effective area being less than a physical area of the flexure due to deformation of the flexure during reciprocating motion.
The thickness profile of the flexure may be selected to cause the flexure to have an effective area to impart reciprocating motion to the displacer at the desired phase angle in absence of reciprocating complementary vibration of the apparatus.
The flexure may include a first flexure operable to vary a volume of the expansion chamber and the displacer may further include a second flexure operable to vary a volume of the compression chamber, the first and second flexures being spaced apart and configured for corresponding reciprocating motion and the second flexure may include a peripheral portion, a central portion, and an intermediate flexing portion extending between the peripheral portion and the central portion, the intermediate flexing portion being configured such that during reciprocating motion, flexing occurs substantially in the intermediate flexing portion.
The intermediate flexing portion of at least one of the first and second flexures may have an increased thickness proximate the central portion and tapers to a reduced thickness distal to the central portion.
The apparatus may include an insulating material disposed between the first and second flexures, the insulating material being operable to provide thermal insulation between the expansion chamber and the compression chamber.
The first and second flexures define an insulating volume therebetween, the insulating volume being operable to receive an insulating gas having a lower thermal conductivity than the working gas.
The insulating gas may include a gas selected from the group consisting of argon, krypton, and xenon.
The peripheral portion, the intermediate flexing portion, and the central portion may together define a thickness profile for the second flexure, and the thickness profile of at least one of the first and second flexures may be selected to cause the flexure to have an effective area to cause reciprocating motion of the displacer to be out of phase with the reciprocating motion of the first interface by a desired phase angle, the effective area being less than a physical area of the first and second flexures due to deformation of the flexures during reciprocating motion.
At least one of the first flexure and the second flexure may further include an additional flexure extending at least between the peripheral portion and the central portion, the additional flexure disposed between the first and second flexures and being operable to increase a stiffness associated with the at least one of the first and second flexures.
The apparatus may include a support extending between the first flexure and the second flexure, the support being operable to couple the first and second flexures.
The support may include a plurality of supports.
The support may include an annular rib.
The support may be disposed in at least one of the central portion of the respective first and second flexures and the intermediate flexing portion of the respective first and second flexures.
The first and second flexures each may include a material capable in operation of infinite fatigue life.
The apparatus may include an electro-mechanical transducer coupled to the displacer, the electro-mechanical transducer being configured for one of coupling mechanical energy to the displacer to cause the periodic exchange of the working gas between the expansion and the compression chambers, and coupling mechanical energy from the displacer to dampen reciprocating motion of the displacer.
The tube spring may include at least a portion disposed to contain the pressurized working gas.
The tube spring may be configured to provide sufficient stiffness in a direction aligned with the transducer axis to cause the at least one of the first and second interfaces to have a natural frequency of at least about 250 Hz.
The tube spring may include an outer cylindrical wall having first and second ends, the first end being coupled to the housing, and an inner cylindrical wall coaxially disposed within the outer cylindrical wall and coupled between the second end of the outer cylindrical wall and the diaphragm.
The working gas may bear on a first surface of the diaphragm and the tube spring may be coupled between a second surface of the diaphragm and the housing to define a bounce chamber between the second surface of the diaphragm, the housing, and the tube spring, the bounce chamber being operable to contain a gas volume bearing on the second surface of the diaphragm.
The tube spring may include a bore and may further include a rod mechanically coupled to the diaphragm and extending outwardly within the bore of the tube spring, the rod being operable to facilitate coupling of the transducer to an electro-mechanical transducer.
The apparatus may include a strain gauge disposed on a wall of the tube spring, the strain gauge being operably configured to produce a time varying strain signal representing an instantaneous strain in the wall of the tube spring during reciprocating motion, the time-varying strain being proportional to an amplitude of the reciprocating motion of the diaphragm and an average value of the time varying strain signal being further proportional to an average static working gas pressure.
The diaphragm may include a material capable in operation of infinite fatigue life and the diaphragm may have a thickness profile across the diaphragm that may be selected to cause stress concentrations across the diaphragm to be reduced below a fatigue threshold limit for the material.
The diaphragm may include a peripheral portion, a central portion having a thickness that may be greater than a thickness of the peripheral portion, and a transition portion extending between the peripheral portion and the central portion, the transition portion having a generally increasing thickness between the peripheral portion and the central portion.
The working gas may bear on a first surface of the diaphragm and the apparatus may further include a bounce chamber for containing a pressurized gas volume bearing on a second surface of the diaphragm.
A volume of the bounce chamber may be selected to be sufficiently larger than a swept volume swept by the diaphragm during the reciprocating motion such that pressure oscillations in the bounce chamber are reduced thereby reducing hysteresis losses associated with the gas volume in the bounce chamber.
The apparatus may include an equalization conduit for facilitating gaseous communication between the working gas in the expansion and compression chambers and the gas volume in the bounce chamber, the equalization conduit being sized to permit static pressure equalization between the working gas and the gas volume within the bounce chamber while being sufficiently narrow to prevent significant gaseous communication during time periods corresponding to an operating frequency of the transducer apparatus.
The expansion chamber may be configured to receive thermal energy from an external source for increasing a temperature of the working gas within the expansion chamber and the reciprocating motion of at least one of the first and second interfaces may alternately cause the increased temperature working gas in the expansion chamber to pass through the regenerator, thereby reducing a temperature of the working gas flowing into the compression chamber, and cause the reduced temperature working gas in the compression chamber to pass through the regenerator, thereby increasing a temperature of the working gas flowing into the expansion chamber. The reciprocating motion of at least one of the first and second interfaces facilitates expansion of the working gas when an average temperature of the working gas is increased and compression of the working gas when the average temperature of the working gas is reduced.
At least one of the first and second interfaces may include an electro-mechanical transducer coupled to the interface, the electro-mechanical transducer being operably configured to receive mechanical energy from the interface and to convert the mechanical energy into electrical energy.
At least one of the first and second interfaces may include an electro-mechanical transducer coupled to the interface for imparting the reciprocating motion to the interface and the reciprocating motion of at least one of the first and second interfaces may alternately causes the working gas in the compression chamber to pass through the regenerator, thereby reducing a temperature of the working gas flowing into the expansion chamber, and cause the working gas in the expansion chamber to pass through the regenerator, thereby increasing a temperature of the working gas flowing into the compression chamber. The reciprocating motion of at least one of the first and second interfaces facilitates compression of the working gas when an average temperature of the working gas is increased and expansion of the working gas when the average temperature of the working gas is reduced thereby causing the expansion chamber to be cooled relative to the compression chamber.
In accordance with another aspect of the invention there is provided a Stirling cycle transducer apparatus for converting between thermal energy and mechanical energy. The apparatus includes a housing, a compression chamber disposed in the housing and having at least a first interface operable to vary a volume of the compression chamber, and an expansion chamber disposed in the housing and having a second interface operable to vary a volume of at least the expansion chamber. The apparatus also includes a first heat exchanger in communication with the expansion chamber, a second heat exchanger in communication with the compression chamber, and a thermal regenerator disposed between the first and second heat exchangers and being operable to alternatively receive thermal energy from gas flowing in a first direction through the regenerator and to deliver the thermal energy to gas flowing in a direction opposite to the first direction through the regenerator. The expansion chamber, the first heat exchanger, the regenerator, the second heat exchanger, and the compression chamber together define a working volume for containing the working gas. Each of the first and second interfaces are configured for reciprocating motion in a direction aligned with a transducer axis, the reciprocating motion being operable to cause a periodic exchange of working gas between the expansion and the compression chambers. Each of the first and second heat exchangers are peripherally disposed within the housing with respect to the transducer axis and configured to receive working gas flowing to or from the respective chambers and to redirect the working gas flow through the regenerator.
Each of the first and second heat exchangers may have a greater transverse extent than height and may be configured to cause gaseous flow in a generally transverse direction through the heat exchangers.
Each of the first and second heat exchangers may include a substantially transversely extending interface in communication with the regenerator and redirection of the working gas flow occurs proximate the interface.
Each of the expansion and compression chambers may have a transverse extent significantly greater than a height of the respective chambers such that a portion of the volume that may be swept during reciprocating motion is increased as a proportion of the volume containing the working gas.
The apparatus may include a heat transport conduit disposed in thermal communication with at least one of the first and second heat exchangers, the heat transport conduit being configured to carry a heat exchange fluid for transporting heat between an external environment and the at least one of the first and second heat exchangers.
The expansion chamber may be separated from the compression chamber by an insulating wall dimensioned to provide sufficient thermal insulation to reduce heat conduction between the expansion chamber and the compression chamber, and may further include at least one access conduit for directing working gas between at least one of the expansion chamber and the first heat exchanger, and the compression chamber and the second heat exchanger.
In accordance with another aspect of the invention there is provided a hot wall apparatus for use in a Stirling cycle transducer for converting between thermal energy and mechanical energy, the transducer including a housing including an expansion chamber, a compression chamber, and a thermal regenerator together defining a volume for containing a pressurized working gas. The hot wall apparatus includes a high thermal conductivity wall, and a low thermal conductivity insulating spacer extending between the wall and the housing.
The high thermal conductivity wall may include at least one of a ceramic material including silicon carbide, a ceramic material including aluminum nitride, a ceramic material including silicon nitride (Si3N4), a material including sapphire, a refractory metal, a refractory metal including tungsten, and a carbon-carbon composite material.
The high thermal conductivity wall may include a first silicon carbide material composition having a high thermal conductivity and the low thermal conductivity insulating spacer may include a second silicon carbide material composition having a low thermal conductivity.
The high thermal conductivity wall may include a material having a first thermal expansion rate and the insulating spacer may include a material having a second thermal expansion rate, and the materials may be selected to provide a sufficiently close match between thermal expansion rates to reduce mechanical stresses at an interface between the wall and the spacer when operating at high temperature.
The high thermal conductivity wall may include a material that may have greater strength in compression than in tension and the wall may be fabricated in a dome-shape such that in operation the wall is primarily subjected to compressive stresses.
The low thermal conductivity insulating spacer may include at least one of a material including fused silica, a ceramic material including zirconia, a ceramic material including mullite, a ceramic material including alumina, and a ceramic material including sialon.
The low thermal conductivity insulating spacer may include at least one of a silicon carbide ceramic having low thermal conductivity, a silicon nitride (Si3N4) ceramic having low thermal conductivity, and an aluminum nitride ceramic having low thermal conductivity.
The high conductivity wall and the low thermal conductivity insulating spacer each may include a carbon-carbon composite having high conductivity carbon fibers oriented in a radial direction to simultaneously provide high radial conductivity and low transverse conductivity.
Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures.
In drawings which illustrate embodiments of the invention,
The output power of a Stirling engine Wout empirically follows the formula:
In a diaphragm engine, the diaphragm is usually fabricated from a metal such as steel, which restricts a maximum operating deflection of the diaphragm thus placing a constraint on the swept volume VS in Eqn 1. The swept volume constraint may be compensated for by operating at increased frequency, increased temperature differential, and/or increased pressure in order to provide a greater power output for a particular engine. The West number NW accounts for losses and an engine design that minimizes losses will have a greater West number. The West number for a range of prior art engines was found to average about NW=0.25.
The temperature differential term in Eqn 1 may be increased by increasing the hot side temperature Th. The maximum theoretical efficiency of any heat engine operating between a heat reservoir at a hot temperature Th and a colder heat reservoir at temperature Tc is the Carnot efficiency:
Heat engines will generally operate at only a fraction of this maximum theoretical efficiency. Raising the hot side temperature is a conceptually simple method of improving engine specific power and efficiency without any other detrimental side effects on the gas cycle. However limitations of conventionally used materials in Stirling engines constrain the maximum practical hot side temperature. Increased pressure further complicates material selection since the materials will then have to handle both increased temperature and pressure. Conventional engine design has generally employed stainless steel or nickel alloys resulting in maximum hot side temperatures of approximately 800° C.
Operating at higher frequencies and/or working gas pressure would appear to increase Wout in accordance with Eqn 1, but increased losses under these operating conditions may reduce the West number NW, thereby offsetting gains. For example, flow friction power dissipation increases with working gas velocity and thus increases with increasing frequency. At higher frequencies and pressures traditional Stirling engine analysis does not adequately represent engine operation as the working gas inertia becomes increasingly important and thus it is necessary to apply thermoacoustic analysis to accurately model operation of an engine.
Referring to
The apparatus 100 further includes a thermal regenerator 114 in fluid communication with each of the compression chamber 112 and the expansion chamber 114.
The compression chamber 112, the expansion chamber 110, and the regenerator 114 together define a working volume for containing a pressurized working gas. Each of the first and second interfaces 120 and 122 are configured for reciprocating motion in a direction aligned with a transducer axis 123, the reciprocating motion being operable to cause a periodic exchange of working gas between the expansion and the compression chambers. The thermal regenerator 114 is operable to alternatively receive thermal energy from gas flowing in a first direction through the regenerator and to deliver the thermal energy to gas flowing in a direction opposite to the first direction through the regenerator.
At least one of the first and second interfaces 120 and 122 includes a resilient diaphragm. In the embodiment shown in
In general, the Stirling transducer apparatus 100 will operate in any orientation. Any references to “top” or “bottom” herein is only a reference to the specific orientation depicted in the drawings and does not have any operational significance.
The Stirling cycle transducer apparatus 100 shown in
In the embodiment shown in
The apparatus 100 is shown schematically in
Referring to
In one embodiment (not shown), the flexing portion 135 may have increased thickness in a region proximate the central portion 134 and a thickness profile of the flexure 132 may taper to a reduced thickness away from the central portion, such that flexing predominantly occurs distally with respect to the central portion. The central portion 134 may be generally thicker that the flexing portion 135 to reduce flexing of the central portion during reciprocating motion.
The second interface 122 also includes supports 189 connecting the central portion 134 of the first flexure 132 and the central portion 174 of the second flexure 136 for movement together. In this embodiment the second interface 122 further includes supports 182 connecting between the flexing portions 135 and 172 of the first and second flexures 132 and 136. The supports 182 and 189 may be implemented as an annular cylindrical support or may be implemented as a plurality of posts. The second interface 122 further includes an insulating material 180, such as a porous ceramic or fibrous material. The insulating material 180 takes up space between the first and second flexures 132 and 136 that is not occupied by the supports 182, 189, and other elements such as the regenerator 114.
The apparatus 100 is shown in top cross-sectional view in
Referring back to
Referring to
In operation, the apparatus 100 is charged to a pressure Pm with a working gas such as helium or hydrogen, which occupies the expansion chamber 110, the compression chamber 112, and the passage 146. The static charge pressure of the working gas may be about 3 MPa or greater. The working gas pressure bears on a first surface 150 of the diaphragm 128, which due to the compliance of the diaphragm would cause an outwardly directed deformation of the diaphragm. However, in the embodiment shown the apparatus 100 further includes a bounce chamber 152 for containing a pressurized gas volume bearing on a second surface 154 of the diaphragm. The gas in the bounce chamber is charged to a pressure PB≈Pm to at least partially equalize forces on the first and second respective surfaces 150 and 154 of the diaphragm. The bounce chamber 152 has walls defined by the housing 102 and the diaphragm 128, and is sealed by a tube spring 156 extending between the second surface 154 of the diaphragm and the housing 102.
In one embodiment a deliberate leak may be introduced between the bounce chamber 152 and the compression chamber 112 in the form of a narrow equalization conduit 155 such as a ruby pinhole. The equalization conduit 155 facilitates gaseous communication between the working gas in the expansion chamber 110 and compression chambers 112 and the gas volume in the bounce chamber 152. The equalization conduit 155 is sized to permit static pressure equalization between the working gas and the gas volume while being sufficiently narrow to prevent significant gaseous communication at time periods corresponding to an operating frequency of the transducer apparatus.
The tube spring 156 further provides a restorative force to the diaphragm 128 during reciprocating motion. The tube spring 156, the diaphragm 128, and the rod 104 together form the first interface 120, which in
Referring back to
The conceptual operation of the apparatus 100 as a Stirling engine is described with reference to
In general, a Stirling engine receives thermal energy from an external source 200, which heats the working gas in the expansion chamber causing an average gas temperature to increase. The engine works by compressing the working gas while the average working gas temperature is generally lower and expanding the working gas while the working gas temperature is generally higher. Compressing a colder working gas requires less work than the energy provided through expansion of the hotter working gas and the difference between these energies provides a net mechanical energy output.
Referring to
Referring to
Referring to
Referring now to
Referring to
Referring to
The cycle then repeats through
Energy may be extracted from the engine in the form of mechanical work at the rod 104 and through heating of the heat exchange fluid within the heat transport conduit 142. The heat exchange fluid in the heat transport conduit 142 is heated during operation of the engine and this heat may be extracted for secondary heating purposes, for example. The temperature increase of the heat exchange fluid depends on a heat capacity and a flow rate of the heat exchange fluid. For example, a temperature rise of about 10° C. is likely for a high heat capacity heat exchange fluid such as water. A temperature of the second heat exchanger 140 would generally be at about the same temperature as the heat exchange fluid. The second heat exchanger 140 should be kept as cold as possible for best engine efficiency, and thus maintaining a low temperature of the heat exchange fluid is beneficial to engine operating efficiency. However, in some embodiments where it is desired to utilize the heat from the heat exchange fluid for a specific purpose, the engine may be operated or configured to produce a desired temperature rise for the specific use in the heat exchange fluid.
The thermal energy 200 is continuously provided to the working gas predominantly in the first heat exchanger 138 and rejected predominantly in the second heat exchanger 140 in order to maintain a temperature difference between the working gas in the expansion chamber 110 and the compression chamber 112. As long as the thermal energy 200 is provided and rejected, reciprocating motion of the first interface 120 and displacer 122 is self sustaining. Advantageously, the heat exchangers 138 and 140 have a large surface area in thermal communication with the working gas in order to limit a required temperature difference between the heat exchanger surfaces and the working gas for transfer of heat. However the surface area of the heat exchangers 138 and 140 should not be so large as to substantially impede flow of gas through the respective heat exchangers.
Referring back to
In one operational embodiment the displacer 122 provides a self initiated and self sustaining reciprocating motion by selectively balancing forces that act on the displacer surfaces 188 and 190, as described later herein. Even if first and second effective areas of the respective first and second surfaces 188 and 190 are equal, there is still a net force on the displacer 122 due to pressure swings in the expansion and compression chambers 110 and 112 not being exactly in phase due to gas viscosity and inertial effects.
The various components of the Stirling cycle transducer apparatus 100 when configured as a beta type Stirling engine as shown in
The diaphragm 128 may be fabricated from a metal such as steel, that when operated below a fatigue stress threshold exhibits infinite fatigue life. A maximum deflection of the diaphragm 128 is thus limited by the maximum infinite life fatigue stress or endurance limit of the material. The diaphragm 128, if made from the common low cost steel alloy such as 1040, will have an endurance limit stress of about 200 MPa. Endurance limit stress is about one-half of the tensile strength for steel alloys up to a maximum of about 700 MPa. Higher maximum stress is thus available using more expensive alloys. For example, using 17-4PH stainless steel should result in maximum allowable diaphragm stresses of about 500 MPa. Endurance limit stress declines with increasing temperature but Nickel super-alloys are available with maximum stress >300 MPa at 750 C. The diaphragm 128 is not operated at elevated temperature in the beta engine configuration of the embodiment shown in
In
The offset and shape of the diaphragm 128 facilitates nesting of the motion of the diaphragm and displacer. In contrast, if the first surface 150 of the diaphragm 128 were to be flat when in the equilibrium position, a larger compression chamber volume would be required to facilitate the respective reciprocating motions of the diaphragm and displacer 122. Advantageously, the diaphragm 128 allows a chamber height proximate the housing 102 to be smaller than would otherwise be the case thereby reducing a volume of the chamber 112.
The diaphragm 128 has increased thickness in a centrally disposed portion of the diaphragm generally in the region of the central portion 130. The thicker central portion 130 reduces stresses that occur in the centrally disposed portion of the diaphragm during reciprocating motion. These stresses include gas pressure stresses causes by changing pressure conditions in the working volume. The gas pressure stresses add to bending stress in a central portion 130 of the diaphragm 128 and reduces stress in peripheral regions 158 of the diaphragm. In the embodiment shown, a thickness profile of the diaphragm 128 is adjusted to equalize the stresses in the central portion 130 and the peripheral regions 158. Since gas pressure stresses are dependent on an amplitude of the periodic pressure swing in the working volume during operation, the thickness profile of the diaphragm 128 would only equalize stresses when operating at or near a design pressure amplitude. In the embodiment shown in
The central portion 130 of the diaphragm 128 has a greater thickness than the peripheral portion 158 and also includes a transition portion 160 extending between the peripheral portion 158 and the central portion 130. The transition portion 160 has a generally increasing thickness between the peripheral portion 158 and the central portion 130. The thicker central portion 130 results in a relatively rigid center portion that couples diaphragm force to the driving rod 104. The thickness profile of the transition portion 160 is selected such that stresses in this portion are below the fatigue threshold limit. The selected profile of the diaphragm 128 takes into account, not only displacement stresses but also gas pressure stresses induced by deflections of the diaphragm during reciprocating motion changing the working gas volume. The variation in thickness across the diaphragm 128 thus reduces a peak stress in the diaphragm for a given displacement to below the fatigue threshold limit for the material. In one embodiment, the thickness profile of the diaphragm 128 may be selected to even out the stress concentrations such that at maximum displacement the stresses at any point on the diaphragm are generally uniform. The thickness profile of the diaphragm 128 as shown advantageously results in a high diaphragm displacement consistently within the fatigue stress threshold for the diaphragm material.
The tube spring 156 is shown in greater detail in
Advantageously the folded back tube spring 156 as shown in
In operation, the tube spring 156 undergoes compressive and extensive strain in the direction of the reciprocating motion 128. The inner wall 164 and outer wall 162 have strains of opposite sign (i.e. if the inner wall 164 is in compression, the outer wall 162 will be in tension). The length of a tube spring 156 determines stress in the walls 162 and 164 of the tube spring for a given deflection and a minimum combined length of the inner and outer walls may be calculated to reduce stress in the tubes below the fatigue threshold limit. A wall thickness and tube length determines the spring stiffness or spring constant k. The gas pressure PB in the bounce chamber 152, which bears on the tube spring 156, may also set a minimum wall thickness of the inner and outer walls 162 and 164.
Referring back to
Since pressurized gas bears on both the first and second surfaces 150 and 154 of the diaphragm 128, the diaphragm need not be designed to withstand the full working gas pressure. Rather the diaphragm 128 is only required to withstand a differential pressure between the working gas volume and the volume of gas in the bounce chamber 152. However, due to the tube spring 156 and rod 104 coupled to the second surface 154, an area of the second surface that is exposed to the pressure PB is smaller than an area of the first surface 150 exposed to the working gas pressure Pm. Consequently, in this embodiment where the equalization conduit 155 equalizes the static pressures PB and Pm, there is a net downward force due to the imbalance. This net downward force causes a static downward deflection of the diaphragm 128 and produces a static longitudinal strain in the tube spring 156. This longitudinal strain is partially offset by a hoop stress induced longitudinal strain in an opposite direction. In general, a hoop stress is a circumferential stress in a cylindrically shaped structure as a result of internal or external pressure. In this case the tube spring 156 is subjected to the working gas pressure, which causes hoop stress in the tube spring walls 162 and 164. The hoop stress causes a corresponding hoop strain as well as a longitudinal strain, where a ratio of longitudinal strain to hoop strain may be calculated using Poisson's ratio, which is a material dependent property. For steel the Poisson's ratio is about −0.3.
The remaining deflection may be compensated by pre-loading the tube-spring to counteract this force such that in the un-deflected or equilibrium position, the tube spring urges the diaphragm upwardly to counteract the imbalance. A foil strain gauge (not shown) may be mounted on a wall of the tube-spring to provide a strain signal for adjusting this pre-load. Advantageously, during reciprocating motion the strain gauge produces a time varying strain signal representing an instantaneous strain in the tube spring during reciprocating motion of the diaphragm, which is proportional to an amplitude of the reciprocating motion of the diaphragm. Furthermore, an average or DC value of the time varying strain signal is proportional to an average static working gas pressure.
In alternative embodiments that do not include the equalization conduit 155, the imbalance may be compensated by charging the bounce chamber 152 to a greater pressure than the working gas pressure.
Advantageously, the folded back embodiment of the tube spring 156 having inner and outer walls 162 and 164 shown in
Referring to
Referring to
Referring back to
The insulating material 180 thermally separates the expansion chamber 110 and the compression chamber 112. In one embodiment the insulating material 180 comprises a porous insulating material having a distributed interior volume. The interior volume of the insulating material 180 may be charged with pressurized gas so that the gas impermeable surfaces 188 and 190 do not need to withstand the working gas pressure. The internal volumes of the insulating material 180 and of the displacer 122 may be in communication with the working gas in the expansion and/or compression chambers 110 and 112 through a narrow conduit or pinhole 184 so that when charging the apparatus 100 with the working gas, the insulating material 180 is also pressurized to the same static pressure. The narrow conduit 184 facilitates static pressure equalization while flow through the narrow conduit at on the time scale of the operating frequency is insignificant. The interior volumes of the insulating material 180 are therefore at most weakly connected to the working gas volume so the working gas pressure swings during operation are not transmitted to the insulating material 180. The flexures 132 and 136 must thus withstand only an oscillating differential pressure between the working gas and the gas pressure in the insulating material 180. As stated earlier herein, flexing of the flexures 132 and 136 occurs predominantly in the intermediate flexing portions 135 and 172 of the flexures, which are relatively thin. Under working gas pressure swings, the surfaces 188 and 190 in of the intermediate flexing portions 135 and 172 may nevertheless deform, and the supports 182 preventing such deformations occurring during operation. Advantageously the use of two flexures 132 and 136 permits the flexing surfaces 188 and 190 to provide support to each other since the pressure swings in the chambers are substantially in phase.
In an alternative embodiment, the insulating material 180 may be isolated from the working gas volume and charged with an insulating gas having a lower thermal conductivity than the working gas. In an embodiment where the working gas is a low atomic weight such as hydrogen or helium, the insulating material 180 may be isolated from the working gas volume to prevent mixing of the working gas and the insulating gas and the insulating material 180 may be charged with a heavier atomic weight gas such as argon. Argon has a lower thermal conductivity than hydrogen or helium, and would result in lower parasitic conduction loss through the insulating material 180 and thus higher engine efficiency. Advantageously, argon is in-expensive and does not add significantly toward the operating cost of the engine. Other gasses such as krypton and xenon may also be used as an insulating gas providing even lower thermal conductivity but at increased cost.
The displacement of the displacer 122 is exaggerated for sake of illustration in
The first flexure 132 of the displacer 122 is required to withstand the high working temperature within the expansion chamber 110 when configured as an engine. The top wall 126 of the housing 102 also has a shape and vertical offset configured to accommodate reciprocating motion of the displacer 122 in the expansion chamber 110. The shape and offset reduces an overall volume of the expansion chamber 110 while still permitting displacer motion without overly restricting a minimum chamber height over a central region of the displacer 122. A reduced chamber height may result in increased viscous losses, as described later herein. Advantageously, a shape and offset of the top wall 126 facilitates a smaller chamber height proximate the housing 102 than would otherwise be the case. In
Generally, it is convenient if a natural frequency of the displacer 122 is close to or coincident with the natural frequency of the first interface 120. Since the first interface 120 has greater mass (i.e. the combined mass of the diaphragm 128, rod 104, and a mass of a load driven by the rod), the displacer 122 will generally require that a stiffness of the intermediate flexing portions 135 and 172 be less than a combined stiffness of the tube spring 156 and the diaphragm 128.
In general, it is desirable to avoid the need to provide for an external drive for the displacer 122. A zero required external displacer force may be achieved by selecting an effective mass of the displacer 122, the spring constant of the intermediate flexing portions 135 and 172, the effective areas of the first and second surfaces 188 and 190, and mass of the housing 102 using the method disclosed later herein. The effective mass of the displacer 122 is defined in terms of a physical mass of an analogous rigid piston displacer, and takes into account the effect of flexures 132 and 136 and gas dynamic contributions to the mass. If additional spring force is required, it may be provided by an additional flexure 183 between either or both of the first and second flexures 132 and 136. Advantageously, adding the additional interior flexure 183 facilitates tuning of the spring constant of the displacer 122 without changing the effective areas of the surfaces 188 and 190 or the peak stresses in these surfaces. Further details are described later herein under the heading of “Thermoacoustic operational considerations”. When the forces acting on the displacer 122 are appropriately balanced, no external displacer driving force is required for the displacer motion.
Correctly predicting and then achieving by design such a balance in actual hardware requires construction of an accurate mathematical model of the specific apparatus. In one embodiment, an external drive for the displacer 122 may be provided to facilitate determination of any small residual out of balance forces, which can then be characterized and compensated for to achieve the zero drive force condition. Subsequent implementations of the compensated design may then omit the external drive. Referring back to
As stated earlier herein, flow friction power dissipation increases with working gas velocity and thus increases with increasing frequency. However, provided that increasing frequency is accompanied by a commensurate reduction in stroke, the velocity may be kept constant. However, even if the velocity of an oscillating flow is kept constant, the flow friction will still increase with frequency if the hydraulic radius of the flow passages is larger than the viscous characteristic length. The hydraulic radius or characteristic dimension rh of a flow passage is:
r
h
=V
i
/A
w Eqn 3
where Vi is the gas permeable volume inside of the gas passage; and
The viscous characteristic length is:
δv=√{square root over (2μ/ωρ)} Eqn 4
In the case of flow in a structure having a hydraulic radius substantially smaller than the viscous characteristic length, the hydraulic resistance for an oscillating flow is essentially the same as for steady, non-oscillatory flow. In this case, there is sufficient time for the flow to fully develop to a steady flow profile before flow reversal. If however the hydraulic radius is substantially larger than the viscous characteristic length, the hydraulic resistance is larger than for steady flow. The sheared fluid layer is then only approximately as thick as the characteristic length and outside of this boundary layer the flow will be an oscillating plug flow.
An analogous thermal characteristic length gives the scale of the dimensions required for oscillating heat exchange. Only the volume of a substance that is within the characteristic length of the interface separating two substances can participate in mutual heat exchange in the time available as determined by the operating frequency. The characteristic thermal length is:
δK=√{square root over (2k/ωρCp)} Eqn 5
For gases, the thermal and viscous characteristic lengths are almost the same (The Prandtl number for gasses is close to unity, the Prandtl number being a ratio between viscous diffusion rate and thermal diffusion rate). On the gas side of the heat exchanger the density depends on the pressure and thus the thermal characteristic length decreases as the pressure increases. This is because the thermal conductivity of a gas is largely independent of pressure whereas the volumetric heat capacity ρCp is proportional to the number of gas molecules and hence increases with pressure. It is thus more difficult to fully heat or cool a high-pressure gas and this is one of the limits on the operating pressure of the working gas. As the gas pressure or operating frequency is increased, the characteristic dimension of the gas flow passages in heat exchangers should shrink commensurate with the reduction in characteristic length in order to maintain similar thermal contact. Reducing the dimensions of the gas flow passages will however result in increased flow friction losses. The inventors have found that changing the aspect ratio of the regenerator in the passage 146 to have a larger frontal area and shorter flow length mitigates these increased losses.
One embodiment of the passage 146 is shown in enlarged detail in
When operating the apparatus 100 as an engine, the second heat exchanger 140 acts as a cold heat exchanger for cooling the gas. A height h2 of the second heat exchanger 140 causes a gas flow 304 to undergo a change in mean flow direction from generally vertical flow in the access conduit portion 148 to generally transverse flow through the second heat exchanger. Advantageously, this change in gas flow direction facilitates heat extraction while the gas is flowing transversely. The second heat exchanger 140 includes a plurality of vertically extending thermally conductive pins or fins 302 in the path of the gas flow 304.
The second heat exchanger 140 also includes a substantially transversely extending interface 300 in communication with the regenerator 114. In the embodiment shown, a lateral dimension of the second heat exchanger 140 is much larger than the height h2 and thus a much larger conduction area is available for heat flow through the conductive pins 302 in the vertical direction than would be available if the pins were oriented horizontally. In addition, the distance heat needs to be conducted along the pins is much shorter than if the pins were oriented horizontally. Furthermore, the second heat exchanger 140 may be wider than the regenerator 114 such that the gas flow 304 at an entrance 306 of the second heat exchanger has a minimum interaction length 308 with the conductive pins 302 before entering the regenerator 114. The gas flow 304 through the second heat exchanger 140 undergoes a further flow redirection from generally transverse flow to generally vertical flow proximate the interface 300.
When operating the apparatus 100 as an engine, the heat transport conduit 142 carries a cooling heat exchange fluid such as water. Heat extracted in the second heat exchanger from the working gas by the thermally conductive pins 302 is conducted to the heat exchange fluid. Advantageously, by redirecting gas flow as described, heat conduction occurs in the same nominal direction as the gas flow in the regenerator 114, and thus a more substantial cross-sectional area is available for heat conduction between conductive pins 302 and the heat transport conduit 142, thereby minimizing a temperature difference between the working gas and the heat transport fluid. In contrast, prior art engines have attempted to remove heat perpendicular to the regenerator gas flow direction, resulting in a much smaller cross-sectional area for heat transfer.
In this embodiment, the regenerator 114 is constructed from a matrix 310 of porous material such as a micro capillary array, porous ceramic or packed spheres. Alternatively, a stacked wire screen or wound wire regenerator, may also be used. The pore hydraulic radius of the matrix 310 calculated in accordance with Eqn 3 should be less than the thermal characteristic length calculated in accordance with Eqn 4, such that a local gas temperature in the regenerator 114 will be substantially the same as a temperature of the local matrix 310. The local temperature varies from one end of the regenerator to the other. If this condition is met, thermal relaxation losses in the gas flowing through the regenerator will be negligible. However, small pore dimensions of the matrix 310 will result in relatively large flow friction losses. Advantageously, the regenerator 114 has a large cross sectional area perpendicular to the gas flow 320, and a relatively short vertical extent h3 resulting in a short gas flow length through the matrix 310. Furthermore, the number of pores in the matrix 310 is selected such that the velocity of gas flow 320 and hence the flow friction losses are optimally balanced against regenerator heat exchange effectiveness.
In the embodiment shown, the full hot to cold temperature gradient experienced by the apparatus 100 appears across the regenerator 114 and thus the matrix 310 should be a good thermal insulator in order to reduce unproductive thermal conduction across the regenerator, which results in losses. The matrix 310 will absorb heat from the working gas during a hot to cold blow and the matrix walls will increase in temperature. This means that gas exiting the regenerator 114 toward the end of the blow will be hotter than at the beginning of the blow since the gas temperature in the regenerator is isothermal with the walls of the matrix 310. This constitutes unwanted extra heat transferred to the second heat exchanger 140, which must be removed by the second heat exchanger. Similarly, on a cold to hot blow the walls of the matrix 310 will be reduced in temperature towards the end of the blow due to the matrix transferring heat to the gas. The temperature of gas exiting the regenerator 114 will thus be colder at the end of the blow than at the beginning. This constitutes a temperature deficit that needs to be made up by the first heat exchanger 138. The matrix 310 should thus have sufficient thermal capacity to store the heat associated with a hot to cold or cold to hot blow without appreciably changing in temperature. Suitable regenerator matrices are described in U.S. Pat. No. 4,416,114 to Martini, which is incorporated herein by reference in its entirety.
When operating the apparatus 100 as an engine, the first heat exchanger 138 acts as a hot heat exchanger for heating the gas. The first heat exchanger 138 is in thermal communication with an external heat source and conducts heat to gas flowing into and out of the expansion chamber 110. A height h1 of the first heat exchanger 138 causes the gas flow 304 to undergo a further change in mean flow direction from generally vertical flow in the regenerator 114 to generally transverse flow through the first heat exchanger. As in the case of the second heat exchanger, this change in gas flow direction facilitates transfer of heat to the gas while flowing transversely. The first heat exchanger 138 includes a plurality of vertically extending thermally conductive pins or fins 312 in the path of the gas flow 304.
As the gas flow 304 leaves the regenerator 114 and through the hot exchanger, it undergoes a substantial change in mean flow direction at an interface 314 between the regenerator and the first heat exchanger 138. This change in gas flow direction makes available a larger cross-sectional area for conduction of heat into the engine. The first heat exchanger 138 may also be wider than the regenerator 114, which then provides a minimum interaction length for the gas flow 304 with the pins or fins 312. In addition, the extra width compensating for the extra width at the second heat exchanger 140 causes the flow resistance for flow path portions 316, 318, and 320 of the gas flow 304 through the regenerator 114 and first heat exchanger 138 to be very similar, even if the regenerator matrix 310 is not configured for sideways flow redistribution. Consequently, the gas flow 304 through the regenerator will be evenly distributed as shown generally at 316-320.
Referring back to
Alternatively, in other embodiments a heat transfer conduit similar to the heat transfer conduit 142 may be provided to conduct thermal energy between a hot heat transfer fluid and the first heat exchanger 138. In the engine embodiment shown in
As stated above, at high frequencies and/or pressures, neglecting to take account of the inertia of the working gas leads to inaccuracies in mathematical modeling of the operational behavior of the apparatus 100.
Referring to
The regenerator 114 keeps the working gas at substantially the same temperature as the temperature of the regenerator matrix 310, since the hydraulic radius corresponding to pores in the matrix is smaller than the thermal characteristic length (Eqns 3 and 4). The temperature gradient across the apparatus 100 appears across the regenerator 114, with the temperature increasing from the compression chamber 112 to the expansion chamber 110. Accordingly, as the working gas flows from the compression chamber 112 to the expansion chamber 110, a volume flow rate increases since the temperature is increasing, the pressure is approximately equal throughout the regenerator 114, and a mass of the working gas is conserved. This may be qualitatively understood as following from the ideal gas law PV=nRT.
Increasing volume flow amplitude corresponds to increasing acoustic power and thus the acoustic power flowing out of the regenerator 114 is larger than the acoustic power flowing into the regenerator. The regenerator 114 thus acts as an acoustic power amplifier with energy being provided by the temperature difference across the regenerator. The heat exchangers 140 and 138 function to maintain this temperature difference by transferring heat in and out of the engine. An increasing width of the dashed outline symbolizing acoustic power flow through the regenerator 114 is used to indicate this power increase, resulting in an amplified acoustic power 354.
The displacer 372 absorbs the amplified acoustic power 354 in a volume associated with the expansion chamber 110 (hereinafter the expansion space) and transfers the power back to a volume associated with the compression chamber 112 (hereinafter the compression space) as illustrated by the dotted outline 356. As depicted in
The operation, as described in connection with
In any non-idealized engine there are losses associated with the above described process. In the compression chamber 112, there are viscosity and thermal relaxation losses 360 that reduce the acoustic power. Similarly, there are losses 366 and 362 in the respective heat exchangers 138 and 140, losses 364 in the regenerator 114, and losses 368 in the expansion chamber 110. These losses all act to reduce the acoustic power by converting acoustic power to heat, and may be minimized by optimizing dimensions and design of the engine as described herein. In addition to direct acoustic power losses, there are also non-productive heat transfer losses to consider. For instance, conduction of heat through the regenerator matrix 310 does not contribute to useful engine output power. Residual ineffectiveness of the regenerator 114 also contributes additional non-productive heat transfer. Thermoacoustic theory provides suitable methods for taking these losses into account and for optimizing dimensions to achieve optimal performance of the apparatus 100.
Referring to
Referring to
The acoustic power is given by:
P
ac=½·Re[U1·P1*] Eqn 6
where U1 is the complex variable representation of the volumetric gas flow; and
From the above equation, the acoustic power removed by the diaphragm is proportional to a projection of P1 (i.e. the phasor 418) on diaphragm induced U1 (i.e. the phasor 412).
The pressure phasors in the expansion and compression spaces are however not exactly equal due to flow friction and gas inertia. Referring to
The result shown in the phasor diagram of
The displacer may be thought of as a rigid center (portions 134 and 174) with an effective mass sprung to the housing 102 and an effective spring constant due to the intermediate flexing portions 135 and 172. In such a dynamic model of the system, an effective mass of the displacer due to the peripheral portions 133 and 170 is assigned to the housing 102, since this portion of the displacer 122 is assumed to move rigidly with the housing. The rigid center of the displacer 122 moves separately from the housing and is assigned an effective moving mass. The intermediate flexing portions 135 and 172 are modeled as mass-less springs characterized by a spring constant. The vibrating motion of the housing 102 imparts a driving force on the rigid center section of the displacer 122 whenever there is a displacement of the housing relative to the center section due to flexure in the portions 135 and 172. A magnitude of this driving force may be controlled by adjusting the mass of the housing 102 and a mass of a mounting structure to which the housing is mounted. Increasing the mass of the mounting structure reduces the magnitude of the vibration of the housing 102 and thus reduces the driving force on the rigid center section of the displacer 122.
Alternatively or additionally dynamic balancing of the apparatus 100 may be employed such as adding a second cylinder to the apparatus 100, which operates 180° out of phase with the reciprocating components shown in
The magnitude and sign of the gas pressure force on the first and second surfaces 188 and 190 may be adjusted by adjusting the ratio of the first surface 188 and second surface 190 effective areas. In
The gas pressure forces acting on the displacer 122 may be computed by constructing a mathematical model of the apparatus 100 taking account of thermoacoustic effects (as described in detail later herein). In the mathematical model, the desired reciprocating motion amplitudes for the first interface 120 and the displacer 122 are specified along with a desired relative phase angle between these motions (e.g. 45°). The desired reciprocating motion forms an input for the mathematical model, which is used to calculate pressure, amplitude, and pressure phase angle, at all points throughout the working volume of the apparatus 100. Integrating pressure over both the first and second surfaces 188 and 190 of the displacer 122 results in a net computed gas pressure force acting on the displacer since the surfaces are connected together by substantially rigid supports 189. At a location proximate the peripheral supports 133 and 170, the resulting force on the surface acts primarily on the housing 102, while over the central portions 134 and 174 the same pressure force acts primarily on the effective moving mass of the rigid center of the displacer 122. A fraction of the force contributing to driving the effective mass of the center of displacer 122 at a specified radius is determined by scaling the calculated force at that radius by a ratio between the reciprocating motion amplitude at that radius and a maximum amplitude (for example, an amplitude at the center of the displacer 122). The result of the pressure integration over either the first surface 188 or the second surface 190 is a force phasor acting on the moving effective mass of the displacer as well as a force phasor acting on the housing 102.
Alternatively, the calculation may be interpreted as producing an average pressure phasor acting on an effective area of a surface of the displacer 122 that is a fraction of a true surface area of that surface. A remaining surface area multiplied by the average pressure phasor produces a force on the housing 102.
Using the above methods, force phasors representing a net force acting on the rigid center section of the displacer 122 and representing a net force acting on the housing 102 may be calculated from the gas pressure acting on the surface 188. Similarly, force phasors acting on the rigid center section 132 and housing 102 may be calculated from gas pressure acting on the second surface 190. Even if the effective areas of surfaces 188 and 190 were equal the respective forces acting on the first and second surfaces 188 and 190 are close in magnitude, but not exactly equal, and are approximately opposite in phase. The respective forces acting on the first and second surfaces 188 and 190 are not equal since the gas pressure amplitude and phase are not exactly equal in the expansion chamber 110 and compression chambers 112 due to gas viscosity and inertia. The net force acting on the moving center of the displacer 122 and the net force acting on the housing 102 is the vector sum of the respective components calculated over the first and second surfaces 188 and 190 of the displacer 122
In the same manner, the mathematical model may be applied to yield a net force on the diaphragm 128, where a separate thermoacoustic calculation is used to account for the effects of the bounce chamber 152 (if the gas volume in the bounce chamber constitutes a significant gas spring).
For the dynamic model of the system there are three significant motions. These are the motions of the first interface 120, the displacer 122 and the motion of the housing 102. The magnitude and phase of each of these three motions are conveniently mathematically represented by phasors in the complex plane. The velocity phasors thus lead their corresponding displacement phasors by 90°.
Three force phasors may thus be calculated for the displacer 122, the diaphragm, and the housing 102. These force phasors may be resolved into a components aligned with the corresponding reciprocating motion phasors, which depending on the sign of the projection behaves, as either an extra spring force or extra effective mass. Additionally, the force phasors may be resolved into components aligned with the velocity phasors, which depending on the sign of the projection is interpreted as either a damping or a drive coefficient. The resulting spring like and damping like components (calculated from the thermoacoustic model) for the displacer 122, the diaphragm, and the housing 102 are then added to the purely mechanical contributions in an otherwise standard three mass coupled oscillator calculation and the required additional external displacer and diaphragm forces calculated for the desired steady state operation. Three mass coupled oscillator calculations are described in Marion, “Classical Dynamics of Particles and Systems” 2nd edition, J. B. Marion, Academic Press (1970), which is incorporated herein in its entirety. By external displacer and diaphragm forces is meant any force that is not due to gas pressures acting on, or mechanical spring constants of the elements shown in
The calculated external force phasor on the diaphragm required for steady state operation may be resolved into a component aligned with the displacement phasor of the diaphragm and a component aligned with the corresponding velocity phasor. A non-zero component aligned with the displacement phasor corresponds to a spring like force and this external component may be eliminated by making a corresponding adjustment to the mechanical spring constant of the diaphragm 128 or tube spring 156 or to the mass of the first interface. A non-zero component aligned with the velocity phasor corresponds to an external drive or damping requirement.
If apparatus 100 is configured as an engine, it will produce power and thus at a minimum the load (not shown) attached to rod 104 should provide a damping force acting between the rod (which is part of interface 120) and the housing 102. Without such a damping force (which corresponds to making use of the power generated by the engine), an amplitude of reciprocating motion of the first interface 120 would grow, which by definition does not constitute steady state operation. A magnitude of the generator-induced damping may be adjusted by changing an apparent load resistance seen by the generator, which may be done by the power conversion electronics attached to the generator.
If the external displacer drive or damping needed for steady state operation is not zero then a displacer drive connected between the rigid center of the displacer 122 and the housing 102 must supply or remove power from the system. Given the relatively large spacing between the surfaces 188 and 190 it is possible to put a small actuator (such as the voice coil actuator shown in
Phasor representations of displacer drive taking housing vibrations and gas dynamics into account are shown in
A non-zero vector sum of the housing vibration drive contribution and the gas dynamic force contribution implies that the displacer must either be driven or power must be extracted from the displacer, depending on the sign of the sum. In either case, this may be accomplished by providing an actuator as described above, and which may be configured to provide power or to extract power from the displacer 122. It is however, advantageous in a low cost Stirling engine design to avoid the need to add a displacer drive, and thus desirable to achieve a balance resulting in zero drive requirement. A zero drive requirements may be achieved by precise selection of the effective areas of the displacer first and second surfaces 188 and 190. The expansion side force phasor 450 (Fe) shown in
In the phasor diagram example shown in
A change in effective area of one of the first and second surfaces 188 and 190 may be accomplished by changing the actual area of the surface.
Alternatively, the change in effective area may be accomplished without changing the actual area of the surface. Referring back to
where
Each differential area annulus thus contributes to the effective area in proportion to the size of its motion. Thus, the edges of the flexure that are attached to the wall 192 contribute nothing, while the moving center of the displacer contributes its full area to the calculated effective area. Similarly, the force due to pressure swings acting on a flexure surface is given by:
where
F1 is the resulting force phasor acting on the dynamic system constituted by the moving center portion of the flexure and any attached masses and springs.
The sign of the force is either positive or negative depending on the sign convention and the surface of interest. In the cases under consideration the phase of the pressure varies only slightly over the surface in which case we can often use the approximation:
F
1
≈±A
eff
·P
1(0), Eqn 9
The remaining force of the working pressure acting on the entire actual area of the surface acts on the wall 192 of the housing 102 rather than on the center dynamic system, and is given by:
F
h1≈±(A−Aeff)·P(0). Eqn 10
From Eqn 7 above, it may be appreciated that the effective area may be changed by controlling the shape of the function z(r) as was done with the diaphragm 128. The change in thickness profile z(r) may be gradual (shown in
In the case of the diaphragm where the profile is varied gradually as a function of radius there is a resultant change in shape of the deflected diaphragm. A thicker center results in more of the bending at larger radius, with the result that the effective area is larger than with a uniform thickness diaphragm.
From Eqn 1, it should be evident that increased output power for an engine may be provided by operating with a greater differential between the hot and cold side temperatures Th and Tc. It is therefore desirable to operate an engine at elevated Th, although this temperature may not be increased without limit due to material constraints. In the apparatus 100 shown in
Referring to
The engine 580 further includes a displacer 582. The displacer 582 includes first and second gas impermeable flexures 630 and 632, having a peripheral portion 606, a central portion 608, and an intermediate flexing portion 607. The peripheral portion 606 is attached to the housing 600. In this embodiment, the displacer 582 also includes supports 609, which may be annular ribs or posts for example. The displacer 582 is generally similar to the displacer 122 shown in
The displacer 582 further includes a moving insulator 610, which is fabricated from a material capable of withstanding the maximum engine temperature Th, at least at an upper surface 615. The moving insulator 610 is attached to the central portion 608 of the flexure 630 and is subjected to the same reciprocating motion as the displacer 582. The engine 580 further includes an annular insulator 611 connected to the peripheral portion 606. The annular insulator 611 may be fabricated from the same or similar material as the moving insulator 610. The moving insulator 610 moves relative to the annular insulator 611. The annular insulator 611 and moving insulator 610 together define a narrow annular gap 612, which will be hereinafter referred to as the “appendix gap”. The appendix gap 612 is in communication with a volume 613 that facilitates motion of the displacer 582 without interfering with the motion of the flexures 630 and 632. The moving insulator 610 and the annular insulator 611 provide primary insulation between the hot expansion chamber 614 and the cold compression chamber 601. The walls of the insulators 610 and 611 should be gas impermeable, while an interior of the insulators may be a porous ceramic operable to provide low thermal conductivity.
The engine 580 further includes a hot wall 616 (described in greater detail below) and the top surface 615 of the moving insulator 610 has a corresponding shape that matches a shape of the hot wall. The top surface 615 of the moving insulator 610 acts as a hot side surface of the displacer 582. An area of the top surface 615 should be similar to an effective area of the cold side of the displacer 582, but may be of slightly different area to balance forces on the displacer during operation, as described earlier herein. Since the top surface 615 is a rigid surface, its effective area is the same as its physical area. For the cold side, the effective area is less than the physical area, to take into account variations in stroke of the bottom flexure with radius, as disclosed earlier herein in connection with
The hot wall 616 has a dome shape to facilitate used of high conductivity ceramic materials such as Silicon Carbide (SiC) or Aluminum nitride (AlN), for example). Ceramic materials are known to be strong in compression but weak in tension. The domed shape of the hot wall 616, oriented as shown in
In one embodiment, the external heat source for the engine 580 may be concentrated sunlight, in which case the hot wall 616 may be fabricated as a transparent fused silica or sapphire dome. Instead of conducting heat into the engine, the transparent dome would allow sunlight radiation to enter the engine and be absorbed and converted to heat inside the engine 580.
The engine 580 further includes an insulating spacer 617, extending downwardly from the housing 600. The insulating spacer 617 provides a mounting for the hot wall 616 such that compressive stresses in the hot wall are transferred to an insulating spacer. The insulating spacer 617 may be fabricated from a low thermal conductivity refractory material such as fused silica, fully stabilized zirconia ceramic or mullite ceramic. Alternatively, the insulating spacer 617 may be fabricated from Alumina ceramic, which has high temperature capability and high strength. While a room temperature thermal conductivity of Alumina ceramic is an order of magnitude larger than that of zirconia, at elevated temperature the conductivity of Alumina ceramic drops rapidly to a value similar to that of zirconia.
It is also possible to use higher conductivity materials with the thermal conduction loss kept low enough with a longer path, thinner wall or both. Alternatively, the insulating spacer 617 may be fabricated from a more advanced material having deliberately tailored properties, such as low thermally conductive versions of SiC, AlN, Silicon Nitride (Si3N4) or Sialon ceramics. In these materials, by adjusting sintering additives and a sintering profile, the thermal conductivity may be varied by an order of magnitude without significant changes to the mechanical characteristics of the material such as coefficient of thermal expansion and mechanical strength.
The insulating ring 617 transfers the load due to the working gas pressure from the hot wall 616 to the housing 600. Thus, as is the case for the dome shaped hot wall 616, the insulating spacer 617 will also be under compressive forces, which is a preferred state of loading for a ceramic material. A remaining volume 618 between the insulating spacer 617 and the housing 600 may be filled with non-load bearing porous refractory material insulation and pressurized to the working gas pressure.
The engine 580 also includes a sealing element 620 between the dome shaped hot wall 616 and the insulating spacer 617. The sealing element 620 may be a slightly compliant ring that provides a gas tight seal such that the housing 600, spacer 617, and hot wall 6161 together provide the required pressure containment. The sealing element 620 may be a high vacuum type seal, provided by indenting a softer compliant material between the harder ceramic materials of the spacer 617 and the hot wall 616. The sealing element 620 may be fabricated from a material such as a nickel-cobalt super-alloy metal.
In one embodiment, a material having high thermal conductivity is selected for the hot wall 616, while a good thermal insulator material is selected for the insulating spacer 617. The joining between two dissimilar materials may be complicated unless the materials have similar rates of thermal expansion, since dissimilar thermal expansion rates will produce large stresses at an interface between the materials as the temperature is increased to Th. The ceramic materials Aluminum Nitride (for the hot wall 616) and Mullite (for the insulating spacer 617) provide a good thermal expansion match.
Alternatively, a carbon-carbon fiber hot wall 616 having fibers oriented radially, may be paired with a Zirconia insulating spacer 617. The radially oriented fibers of the hot wall 616 provide excellent radial heat conduction, while along a cross fiber axis the thermal expansion coefficient may be configured to be close to that of Zirconia. The carbon-carbon hot wall 616 having fibers oriented in the radial direction would not provide good strength in tension, and thus should have a dome shape oriented as shown in
Alternatively, as mentioned above the thermal conductivity of ceramics may be deliberately varied without significantly affecting the thermal expansion rate. Accordingly, the hot wall 616 and the insulating spacer 617 may be advantageously manufactured from the same material. For example, the dome could be high conductivity SiC and the ring low conductivity SiC. Both dome and insulating ring then have the same coefficient of thermal expansion, which facilitates joining. A bonding layer having a composition similar to the sintering agent for the ceramic may be used to bond the high and low conductivity versions of the ceramic material.
In another alternative embodiment, the thermally conducting hot wall 616 and the insulating spacer may be fabricated from a single composite material having anisotropic thermal conduction properties, thereby avoiding the need for a high temperature seal and/or sealing element 620. For example, the domed hot wall 616 insulating spacer 617 may be manufactured as a single piece carbon-carbon composite having all the carbon fibers oriented radially. The fibers would then be oriented perpendicular to the heat flow in the spacer portion, thus providing good insulation since thermal conductivity of a carbon composite is much lower in a cross-fiber direction than in a fiber direction. The spacer 617 would thus effectively insulate the domed hot wall portion from the housing 600. In the hot wall portion the same composite material would efficiently conduct heat into the engine 580 due to the radial fiber orientation in the dome.
The engine 580 includes a hot heat exchanger 619, regenerator 621, and cold heat exchanger 623, which are generally similar to the corresponding elements shown in
Alternatively, for a direct heated solar powered engine 580, the hot wall 616 and insulating spacer 617 may be fabricated from a single piece of fused silica, with no high temperature joint being required. Fused silica has very low thermal conductivity and would thus provide a good insulating spacer, and in such an embodiment would not be required to conduct heat into the engine and thus a dome portion (corresponding to the domed hot wall 616) would not have to have high thermal conductivity as in other embodiments.
In the process of the displacer 582 forcing the working gas back and forth from the compression chamber 601 to the expansion chamber 622, the working gas flows through the hot heat exchanger 619, the regenerator 621, the cold heat exchanger 623, and an access tube 624. The function of these components is the same as described for the lower temperature embodiment of
The engine 580 also includes a heat transport conduit 625 in thermal communication with the cold heat exchanger 623 for extracting heat from the cold side of the engine. The full temperature gradient Th-Tc thus appears across the regenerator 621, and the regenerator material should thus be a good thermal insulator in the gas flow direction. The regenerator 621 may provide a significant parasitic heat flow path given the relatively short flow length when compared to a thermal path length through the moving insulator 610. However this short thermal path length is only over the annular area of the regenerator 621, which is only a small fraction of the total cross-sectional area separating the hot and cold sides of the engine. The thermal conductivity of a matrix of the regenerator 621 is one item to be taken into account in optimizing a frontal area of the regenerator and a flow length through the regenerator for achieving optimal performance of the engine 580.
Optimizing the component dimensions for high temperature operation will generally lead to different dimensions than at lower operating temperature. All losses and effects should be considered simultaneously to produce an overall optimum design and this may be done by building a complete thermoacoustic model of the engine. A further difference between the low temperature engine of
For the design of the appendix gap 612 there are at least three choices. In a first embodiment, the gap 612 may be sufficiently narrow at some point along its length such that a flow resistance is sufficiently large that the pressure in the volume 613 at the cold end of the appendix gap 612 does not follow pressure swings in the engine 580. In this case, thermal relaxation losses are avoided in volume 613. The flexures 630 and 632 are required to withstand a differential pressure between the compression chamber 601 and the volume 613, since the pressure in the volume 613 is substantially constant, while the pressure in the chamber 601 oscillates. Fabrication of the annular insulator 611 and moving insulator 610 to provide a sufficiently narrow appendix gap 612 requires that tight manufacturing tolerances of the elements be maintained.
In an alternative embodiment, the appendix gap 612 may be sufficiently wide that volume 613 would follow the pressure swings of the engine 580. The volume 613 would then be part of the engine working volume and thus reduce the compression for a given swept volume produced by the displacer and diaphragm. Additionally, there are thermal relaxation losses due to the pressure swing in the volume 613. There are also flow losses, since the pressure changes are a result of gas flow through the appendix gap 612. There are also heat transfer losses due to hot gas flowing towards the cold side and cold gas flowing back out to the hot side. The appendix gap 612 should be narrower than the thermal characteristic length (Eqn 3) so that the gap functions as a regenerator for the gas flow that produces the pressure swing in the volume 613. All these losses are reduced if the volume 613 has a reduced volume. Reducing a radial width of the intermediate flexing portions 607 of the flexures 630 and 632 would facilitate reduction of the volume 613, which in this case is possible since if the pressure in space 613 is substantially the same as in the compression chamber 601 the flexure need not withstand any substantial differential pressure. The dual flexures 630 and 632 may then be replaced with a single thinner and narrower flexure.
A third embodiment is generally similar to the second embodiment above, except that the remaining flexure has gas passages cut into it so that volume 613 effectively becomes part of the compression chamber 601. In this case, the pressure swings in volume 613 may be supplied predominantly by flow from the compression chamber thereby reducing the flow in the appendix gap 612. In this third case, the appendix gap 612 is a parallel regenerative gas passage for a small fraction of the working gas. Appendix gap losses depend strongly on these design choices and must be included in the thermoacoustic model of the engine in order to achieve an optimal design.
While specific embodiments of the invention have been described and illustrated, such embodiments should be considered illustrative of the invention only and not as limiting the invention as construed in accordance with the accompanying claims.
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/CA10/01092 | 7/12/2010 | WO | 00 | 3/9/2012 |
| Number | Date | Country | |
|---|---|---|---|
| 61213760 | Jul 2009 | US |
