EXPANSION SYSTEM

Cross-Reference to Related Applications

[0001] This application claims priority to U.S. Provisional Patent Application No. 61/590,383, filed January 25, 2012, entitled "Variable Separation Heat Transfer Device for Optimizing Heat Transfer Within a Compression and/or Expansion Device," and U.S. Provisional Patent Application No. 61/590,402, filed January 25, 2012, entitled "Wire Mesh Fin Design for Improved Heat Transfer Within a Compression and/or Expansion Device," the entireties of which are hereby incorporated by reference.

Background

[0002] The invention relates generally to systems, devices and methods for the compression and/or expansion of a gas, such as air, and particularly to a system, device and method for optimizing heat transfer during the compression and/or expansion of a gas. [0003] Some known devices, methods and systems used to compress and/or expand a gas, such as air, and/or to pressurize and/or pump a liquid, such as water, can be used, for example, within a compressed air energy storage system. In some compressed air devices and systems, a hydraulic actuator can be used to move or compress air within a pressure vessel. For example, an actuator can move a liquid within a pressure vessel such that the liquid compresses air in the pressure vessel.

[0004] Such known devices and systems used to compress and/or expand a gas and/or to pressurize and/or pump a liquid can change the temperature of the gas during, for example, a compression or expansion process. For example, compressing a gas can convert heat energy from its latent form into its sensible form, thereby increasing the temperature of the gas. Various heat transfer mechanisms can be used to remove heat energy during the compression process from the gas being compressed. In some known devices and systems, heat energy in the gas being compressed within a pressure vessel can also be transferred to the liquid used to compress the gas.

[0005] Numerous technical and commercial challenges exist with known heat transfer devices, and varying the material and structure of a heat transfer device generally results in tradeoffs in thermal efficiency, pressure drop losses, manufacturing cost and difficulty, part count, structural integrity, required size of the compression/expansion cylinder, and energy storage density (i.e., compression exhaust temperate). For example, metal extrusion-based thermal capacitors may consist of hundreds of parts individually fit together and machined to accommodate support structures. Such capacitors may have high capacitor volume fractions (i.e., the percent of cylinder volume occupied by capacitor material), but the extrusion manufacturing process limits the size and thinness of the thermal capacitor elements. Flat-plate polymer thermal capacitors suffer similar disadvantages.

[0006] Accordingly, there is a need to improve and/or optimize the heat transfer elements and methods used to transfer heat during a compression and/or expansion process between the gas and the liquid within such devices and systems used to compress and/or expand a gas.

Summary

[0007] The configuration of compressor/expander device(s) in a compressed air energy storage (CAES) system is critical to the lifetime technical and economic performance of the system. Such devices and systems used to compress and/or expand a gas, such as air, release and/or absorb heat during the thermodynamic processes. Compressor/expanders may include one or more pneumatic cylinders having heat capacitors for transferring heat to and/or from gas as it is being compressed/expanded. Since the thermodynamic cycle of the system impacts the roundtrip AC-AC efficiency, electrical power, and storage energy density of a CAES system, improvement and optimization of a thermal capacitor subsystem is desired. As such, the invention focuses on the design and configuration of heat transfer devices for the improvement of the overall performance and cost of a compression/expansion system.

[0008] Accordingly, systems, methods and devices for optimizing heat transfer within a device or system used to compress and/or expand a gas, such as air, are described herein. In some embodiments, a compressed air device and/or system can include an actuator such as a hydraulic actuator that can be used to compress a gas within a pressure vessel. An actuator can be actuated to move a liquid into a pressure vessel such that the liquid compresses a gas within the cylinder or pressure vessel. In such a compressor/expander device or system, during the compression and/or expansion process, heat can be transferred to the liquid used to compress the air. The compressor and/or expander process can include a heat transfer element that can be used to transfer heat energy between the gas and the liquid during a compression and/or expansion process. The heat transfer element may be positioned within the interior of a pneumatic cylinder of a compressor/expander device to increase the amount of surface area within the pneumatic cylinder that is in direct or indirect contact with gas, thereby improving heat transfer.

[0009] In one aspect, a compression and expansion system includes a pressure vessel having a variable volume working chamber therein. The pressure vessel has a conduit through which at least one fluid can be introduced into and discharged from the working chamber. The system further includes a heat transfer element disposed within the working chamber and including a layer and at least one of a fin and a spacing element. The pressure vessel is operable to compress fluid introduced into the working chamber such that heat energy is transferred from the compressed fluid to the heat transfer element, and is further operable to expand fluid introduced into the working chamber such that heat energy is transferred from the heat transfer element to the expanded fluid. [0010] In one embodiment, the fluid is selected from the group consisting of liquid, gas, vapor, suspension, aerosol, and combinations thereof.

[0011] In another embodiment, the heat transfer element is substantially cylindrical.

[0012] In further embodiments, an outer diameter of the heat transfer element is substantially similar to a diameter of the working chamber. [0013] In one implementation, a vertical axis of the heat transfer element is parallel to a vertical axis of the working chamber.

[0014] In yet another embodiment, the heat transfer element includes a plurality of layers. At least one of the layers may include a wire mesh. [0015] In one embodiment, the heat transfer element includes spacing elements disposed to maintain a spacing between adjacent layers of the heat transfer element.

[0016] In another implementation, the spacing elements are configured to absorb heat energy from at least one of the fluid and the layers of the heat transfer element. [0017] In another embodiment, the layers comprise a spiral from an inner diameter to an outer diameter. A fin defining a path between the inner diameter and the outer diameter may be included. The fin may define a serpentine path, and may include sheet metal. The spiral may also include sheet metal.

[0018] In a further embodiment, the heat transfer element includes at least one of an inner ring and an outer ring.

[0019] In some implementations, a density of the heat transfer element varies spatially therein. The density may vary along a vertical axis of the heat transfer element.

[0020] In yet another embodiment, the heat transfer element is operable to transfer heat energy received from the compressed fluid to an exterior of the working chamber. [0021] In a further embodiment, the pressure vessel is operable to cause heat energy transferred from the compressed fluid to the heat transfer element to be transferred from the heat transfer element to a second fluid in the working chamber.

[0022] In one embodiment, the pressure vessel is further operable to cause heat energy transferred from the second fluid in the working chamber to the heat transfer element to be transferred from the heat transfer element to the expanded fluid.

[0023] In another embodiment, the pressure vessel is further operable to cause at least a portion of a second fluid in the working chamber to be discharged to remove at least a portion of the heat energy transferred from the heat transfer element to the second fluid.

[0024] In another aspect, a method of optimizing heat transfer in a compression and expansion system includes introducing a first quantity of fluid into a variable volume working chamber of a pressure vessel of the system. The pressure vessel includes a conduit through which at least one fluid can be introduced into and discharged from the working chamber. The pressure vessel further includes a heat transfer element disposed within the working chamber and having a layer and at least one of a fin and a spacing element. The method further includes compressing the first quantity of fluid and transferring heat energy from the compressed fluid to the layer and fin or spacing element of the heat transfer element. A second quantity of fluid is introduced into the working chamber, and the second quantity of fluid is expanded. Heat energy is transferred from the layer and the fin or spacing element of the heat transfer element to the expanded fluid.

[0025] In one embodiment, the fluid is selected from the group consisting of liquid, gas, vapor, suspension, aerosol, and combinations thereof. [0026] In another embodiment, the heat transfer element is substantially cylindrical.

[0027] In a further embodiment, an outer diameter of the heat transfer element is sized to be substantially similar to a diameter of the working chamber.

[0028] In one implementation, a vertical axis of the heat transfer element is oriented substantially parallel to a vertical axis of the working chamber. [0029] In yet another embodiment, the heat transfer element includes a plurality of layers. At least one of the layers may include a wire mesh.

[0030] In further embodiments, a spacing is maintained between adjacent layers of the heat transfer element by disposing a plurality of spacing elements therebetween.

[0031] In one implementation, heat energy is absorbed with the spacing elements from at least one of the first quantity of fluid and the layers of the heat transfer element.

[0032] In another embodiment, the layers comprise a spiral from an inner diameter to an outer diameter. A fin defining a path between the inner diameter and the outer diameter may be included. The fin may define a serpentine path, and may include sheet metal. The spiral may also include sheet metal. [0033] In a further embodiment, the heat transfer element includes at least one of an inner ring and an outer ring. [0034] In some implementations, a density of the heat transfer element varies spatially therein. The density may vary along a vertical axis of the heat transfer element.

[0035] In one embodiment, heat energy received from the compressed fluid is transferred to an exterior of the working chamber. [0036] In another implementation, heat energy from the heat transfer element is transferred to a third quantity of fluid in the working chamber.

[0037] In yet another embodiment, heat energy from a third quantity of fluid in the working chamber is transferred to the heat transfer element.

[0038] In another implementation, at least a portion of a third quantity of fluid in the working chamber is discharged to remove at least a portion of the heat energy from the working chamber.

Brief Description of the Drawings

[0039] FIG. 1 is a schematic illustration of a compression and/or expansion system, according to an embodiment.

[0040] FIG. 2 is a schematic illustration of a compression and/or expansion system, according to an embodiment.

[0041] FIG. 3A is a schematic illustration of a sheet of wire mesh, according to an embodiment.

[0042] FIG. 3B is a top view of a heat transfer element incorporating a sheet of the wire mesh of FIG. 3 A. [0043] FIG. 4A is a schematic illustration of a sheet of wire mesh, according to an embodiment.

[0044] FIG. 4B is a top view of a heat transfer element incorporating a sheet of the wire mesh of FIG. 4A. [0045] FIG. 5A is a schematic illustration of a sheet of wire mesh, according to an embodiment.

[0046] FIG. 5B is a side view of the wire mesh of FIG. 5 A.

[0047] FIG. 6 is a schematic illustration of a sheet of wire mesh, according to an embodiment.

[0048] FIG. 7 is a schematic illustration of a sheet of wire mesh, according to an embodiment.

[0049] FIG. 8A is a top view of a portion of a heat transfer element manufacturing process, according to an embodiment.

[0050] FIG. 8B is a side view of the portion of the heat transfer element manufacturing process of FIG. 8A.

[0051] FIG. 9A is a top view of a portion of a heat transfer element manufacturing process, according to an embodiment.

[0052] FIG. 9B is a side view of the portion of the heat transfer element manufacturing process of FIG. 9A.

[0053] FIG. 9C is a top view of a portion of a heat transfer element manufacturing process, according to an embodiment.

[0054] FIG. 10 is a top view of a heat transfer element, according to an embodiment.

[0055] FIG. 11 is a top view of a heat transfer element, according to an embodiment.

[0056] FIG. 12 is a top view of a heat transfer element, according to an embodiment.

[0057] FIG. 13 is a top view of a heat transfer element, according to an embodiment.

[0058] FIGS. 14A-14C are schematic illustrations of a compression and/or expansion system shown in a first, second and third configuration, respectively, according to an embodiment. [0059] FIGS. 15A-15C are schematic illustrations of a compression and/or expansion system shown in a first, second and third configuration, respectively, according to an embodiment.

[0060] FIGS. 16A and 16B are schematic illustrations of a variable separation heat transfer element in a first and second configuration, respectively, according to an embodiment.

[0061] FIG. 16C is a top view of a plate included in the variable separation heat transfer element of FIG. 16A.

[0062] FIG. 17A and 17B are schematic illustrations of a compression and/or expansion system in a first and second configuration, respectively, according to an embodiment. [0063] FIG. 18A is a top view of a plate included in a variable separation heat transfer element of FIG. 17 A.

[0064] FIG. 18B is a front view of the plate of FIG. 18A.

[0065] FIG. 19A is a top view of a plate included in the variable separation heat transfer element of FIG. 17A. [0066] FIG. 19B is a front view of the plate of FIG. 19A.

[0067] FIG. 20 is a graph illustrating change in bulk temperature versus stroke time, according to an embodiment.

[0068] FIGS. 21A and 21B are graphs illustrating a comparison of pressure profiles in a simulated and actual test environment. [0069] FIGS. 22A and 22B are graphs illustrating a comparison of predicted work and ending temperature in a simulated and actual test environment.

[0070] FIGS. 23A and 23B are graphs illustrating work difference and ending temperature difference for a range of stroke speeds. Detailed Description

[0071] Systems, methods and devices used to compress and/or expand a gas, such as air, and/or to pressurize and/or pump a liquid, such as water, are described herein. Such devices and systems can be used, for example, within a CAES system. In some compression and/or expansion devices and systems, a hydraulic actuator can be used to move or compress a gas within a pressure vessel. For example, an actuator can move a liquid within a pressure vessel such that the liquid compresses the gas in the pressure vessel. Such compression devices and systems are described in U.S. Patent App. No. 12/785,086; U.S. Patent App. No. 12/785,093; and U.S. Patent App. No. 12/785,100, each titled "Compressor and/or Expander Device" (collectively referred to as "the Compressor and/or Expander Device applications"), incorporated herein by reference in their entirety. The Compressor and/or Expander Device applications describe a CAES system that can include multiple stages of compression and/or expansion. Other examples of devices and systems for expanding and/or compressing as gas are described in U.S. Patent App. No. 12/977,724 to Ingersoll, et al., filed December 23, 2010, entitled "Systems and Methods for Optimizing Efficiency of a Hydraulically Actuated System," ("the '724 application") the disclosure of which is incorporated herein by reference in its entirety.

[0072] In some compression and/or expansion devices and systems, a piston can be movably disposed within a cylinder or pressure vessel and actuated to compress air within the cylinder or pressure vessel. Such a device can include a single-acting piston configured to compress gas when moved in a single direction, or a double-acting piston configured to compress gas when moved in either direction. Examples of such compressed air devices and systems are described in U.S. Patent App. No. 61/420,505, to Ingersoll et al. ("the '505 application"), entitled "Compressor and/or Expander Device with Rolling Piston Seal," the disclosure of which is incorporated herein by reference in its entirety. [0073] In some embodiments, the devices and systems described herein can be configured for use only as a compressor. For example, in some embodiments, a compressor device described herein can be used as a compressor in a natural gas pipeline, a natural gas storage compressor, or any other industrial application that requires compression of a gas. In another example, a compressor device described herein can be used for compressing carbon dioxide. For example, carbon dioxide can be compressed in a process for use in enhanced oil recovery or for use in carbon sequestration.

[0074] In some embodiments, the devices and systems described herein can be configured for use only as an expansion device. For example, an expansion device as described herein can be used to generate electricity. In some embodiments, an expansion device as described herein can be used in a natural gas transmission and distribution system. For example, at the intersection of a high-pressure (e.g., 500 psi) transmission system and a low-pressure (e.g., 50 psi) distribution system, energy can be released where the pressure is stepped down from the high pressure to a low pressure. An expansion device as described herein can use the pressure drop to generate electricity. In other embodiments, an expansion device as described herein can be used in other gas systems to harness the energy from high to low pressure regulation.

[0075] In some embodiments, a compression and/or expansion device as described herein can be used in an air separation unit. In one example application of an air separator, a compression and/or expansion device can be used in a process to liquefy a gas. For example, air can be compressed until it liquefies and the various constituents of the air can be separated based on their differing boiling points. In another example application, a compression and/or expansion device can be used in an air separator co-located within a steel mill where oxygen separated from the other components of air is added to a blast furnace to increase the burn temperature. [0076] A compression and/or expansion system can have a variety of different configurations and can include one or more actuators that are used to compress/expand a gas (e.g. air) within a compressor/expander device. In some embodiments, an actuator can include one or more pump systems, such as for example, one or more hydraulic pumps and/or one or more pneumatic pumps that can be used to move one or more fluids within the system between various water pumps and pressure vessels. As used herein, "fluid" can mean a liquid, gas, vapor, suspension, aerosol, or any combination thereof. The Compressor and/or Expander Device applications incorporated by reference above describe various energy compression and expansion systems in which the systems and methods described herein can be employed.

[0077] As described herein, devices and systems used to compress and/or expand a gas, such as air, and/or to pressurize and/or pump a liquid, such as water, can release and/or absorb heat during, for example, a compression process. The devices and systems described herein can include one or more heat transfer mechanisms to remove heat during the compression process. In some embodiments, a heat transfer element can be used as described, for example, in U.S. Patent App. No. 12/997,679, to Ingersoll et al. ("the '679 application"), entitled "Methods and Devices for Optimizing Heat Transfer within a Compression and/or Expansion Device," the disclosure of which is incorporated herein by reference in its entirety. During an expansion process in a CAES system, when compressed air is released from a storage structure and expanded through the compressor/expander system, heat from a source can be added to the air to increase the power generated during the expansion process. In some embodiments, the source of heat can be at a relatively low temperature (e.g., between for example, about 10° C and about 50° C).

[0078] In some embodiments, a heat transfer element can be positioned within the interior of a pressure vessel of a compressor/expander device to increase the amount of surface area within the pressure vessel that is in direct or indirect contact with gas, which can improve heat transfer. The heat transfer element may be configured to minimize the distance that heat must travel through the air in order to reach the heat transfer element, such as a maximum distance of 1/8 of an inch, and other distances. The heat transfer element can provide for an increased heat transfer area both with gas that is being compressed and with gas that is being expanded (through a gas/liquid interface area and/or gas/heat transfer element interface), while allowing the exterior structure and overall shape and size of a pressure vessel to be optimized for other considerations, such as pressure limits and/or shipping size limitations. In some embodiments, the heat transfer element can be a thermal capacitor that absorbs and holds heat released from a gas that is being compressed, and then releases the heat to a gas or a liquid at a later time. In some embodiments, the heat transfer element can be a heat-transferring device that absorbs heat from a gas that is being compressed, and then facilitates the transfer of the heat outside of the pressure vessel.

[0079] In some embodiments, heat energy can be removed from a gas during compression via a liquid that is present in one or more pressure vessels of a compressor/expander device to maintain the gas that is being compressed at a relatively constant temperature. The heat energy can be transferred from the gas to the liquid and/or the compressor/expander device to a heat transfer element disposed within the pressure vessel. After gas is provided to the compressor/expander device, heat energy is removed from the gas, i.e. the gas is kept cooler as it is compressed than would be the case without the heat transfer element, and may be done to an extent that the temperature of the gas remains relatively constant. The temperature of the gas can be maintained, for example, at about 5° C, 10° C, 20° C, 30° C or other temperatures that may be desirable, until discharged to, for example, a compressed gas storage structure or a subsequent compression stage. The gas stored in the storage structure may be heated (or cooled) naturally through conductive and/or convective heat transfer if the storage structure is naturally at a higher (or lower) temperature. For example, in some cases, the storage structure may be an underground structure, such as a salt cavern constructed in a salt dome that is used for storing the compressed gas. In some embodiments, the heat transfer element can be designed such that the temperature of the gas does not remain relatively constant, but instead increases a relatively small amount, for example, 5° C, 10° C, 20° C, 30° C.

[0080] As discussed above, heat may be added to the gas during an expansion process. For example, heat can be added to the gas at some or all of the stages of a multi-stage compressor/expander system to hold gas temperatures at a substantially constant temperature, such as at about 35° C, or other temperatures, during the entire expansion process. The overall temperature change of gas during expansion may be limited by contact with substantial heat transfer surfaces, e.g. a heat transfer element. Heat may also added to the gas at some or all stages of an expansion process by introducing gas a higher temperature from another source of compressed gas.

[0081] As discussed above, heat can be transferred from and/or to gas that is compressed and/or expanded by liquid (e.g., water) within a pressure vessel. A gas/liquid or gas/heat element interface may move and/or change shape during a compression and/or expansion process in a pressure vessel. This movement and/or shape change may provide a compressor/expander device with a heat transfer surface that can accommodate the changing shape of the internal areas of a pressure vessel in which compression and/or expansion occurs. In some embodiments, the liquid may allow the volume of gas remaining in a pressure vessel after compression to be nearly eliminated or completely eliminated (i.e., zero clearance volume). [0082] A liquid (such as water) can have a relatively high thermal capacity as compared to a gas (such as air) such that a transfer of an amount of heat energy from the gas to the liquid avoids a significant increase in the temperature of the gas, while only producing a modest increase in the temperature of the liquid. This allows buffering of the system from substantial temperature changes. Said another way, this relationship creates a system that is resistant to substantial temperature changes. Heat that is transferred between the gas and liquid, or components of the vessel itself, may be moved from or to the pressure vessel through one or more processes. In some embodiments, heat can be moved in or out of the pressure vessel using mass transfer of the liquid itself. The heated liquid can be stored and later reintroduced into the pressure vessel during an expansion process. In other embodiments, heat can be moved in or out of the pressure vessel using heat exchange methods that transfer heat in or out of the liquid without removing the liquid from the pressure vessel. Such heat exchangers can be in thermal contact with the liquid, components of the pressure vessel, a heat transfer element, or any combination thereof. Furthermore, heat exchangers may also use mass transfer to move heat in or out of the pressure vessel. One type of heat exchanger that can be used to accomplish this heat transfer is a heat pipe as described in the Compressor and/or Expander Device applications and the '724 application incorporated by reference above. Thus, the liquid within a pressure vessel can be used to transfer heat from gas that is compressed (or to gas that is expanded) and can also act in combination with a heat exchanger to transfer heat to an external environment (or from an external environment).

[0083] In some embodiments, heat can be transferred from a gas (such as air) that is compressed in a pressure vessel to increase the efficiency of the compression process. Heat can be transferred from the gas to a liquid, and/or from the gas to a heat transfer element within the compression vessel, and/or from the liquid while it is inside or outside of the pressure vessel. The amount of heat transferred from an amount of gas being compressed depends on the rate of heat transfer from the gas and on the time over which the heat transfer takes place, i.e., over the cycle time during which the gas compression takes place. Thus, for a given rate of heat transfer that can be achieved by a system, the more slowly the system is operated (i.e., the longer the compression cycle times), the more closely the compression cycle can approach the theoretical ideal of isothermal compression. However, slower compression cycle times also correlate to lower gas volumetric and/or mass flow rates. In the context of a CAES system, this equates to lower energy storage rates, equivalently known as lower power. Conversely, in a gas expansion process, the more slowly the system is operated, the more heat energy can be transferred to the expanding gas (for a given heat transfer rate) and the more closely the expansion cycle can approach isothermal expansion, which may correspond to more efficient consumption of air mass relative to energy extracted/converted. However, in the context of a CAES system, the resulting lower expanding gas flow rate may equate to lower power production. In some embodiments, the CAES system can be operated at lower power rates to achieve higher efficiency or due to other system parameters (e.g., cavern storage levels, thermal storage levels, or power supply/demand).

[0084] The use of a liquid (e.g., water) as a medium through which heat passes (directly through contact between the gas and liquid, or indirectly through an intermediary material) during compression and/or expansion may allow for continuous cooling or heating at enhanced heat transfer rates and may provide a mechanism by which heat may be moved in and/or out of the pressure vessel. That is, during compression the liquid may receive heat from gas that is being compressed, and transfer this heat from the pressure vessel to the external environment continuously, both while gas is being compressed and while gas is being received by the pressure vessel for later compression. Similarly, heat addition may occur when a compressor/expander device is operating in an expansion mode both during expansion and as expanded gas is passed from the pressure vessel.

[0085] In some embodiments, a heat transfer element can be provided within a pressure vessel that can provide sufficient gas/liquid interface and sufficient thermal capacity to efficiently intermediate in the transfer of heat from the compressed gas into the liquid. A heat transfer element can be a variety of different configurations, shapes, sizes, structures, etc. to provide a relatively high surface area per unit volume or mass with the air as it is being compressed and/or at an end of the stroke of a compression cycle. The heat transfer element can be formed from one or more of a variety of different materials that provide a relatively high volumetric specific heat capacity as compared to air. The combined effects of density, volume and specific heat, and how these parameters behave per unit volume, can contribute to the absorption performance of a particular heat transfer element. For example, both water and various metals provide a relatively high volumetric specific heat as compared to air, particularly at atmospheric air density. Thus, when the metal or water absorbs the heat from the air as it is being compressed, the air and/or water temperature increases only moderately. [0086] For example, the mass specific heat values for air, water and stainless steel (one example metal that can be used) can be as follows:

air: 1,005 J/kg-K;

water: 4,183 J/kg-K; and

stainless steel: 502 J/kg-K.

[0087] The above values are only one example of the mass specific heat values for air, water and stainless steel, as specific heat of a particular material can depend on other factors such, as, for example, the temperature of the material. The heat absorbing capability per unit volume of the material is a factor of both a material's density and the mass specific heat of the material. The density of material can also depend on the temperature of the material. An example of possible material densities for air, water and stainless steel are as follows:

air: 1.2 kg/m ³ (at sea level pressure and 20 °C);

water: 998 kg/m ³ ; and

stainless steel: 8,027 kg/m ³ .

[0088] By combining the mass specific heat and density, the heat absorbing performance per unit volume (which may also be referred to as heat capacity) for air, water and stainless steel can be determined as follows:

air: 1,005 J/kg-K x 1.2 kg/m ³ = 1,206 J/m ³ -K (at sea level pressure and 20 °C); water: 4,183 x 998 kg/m ³ = 4, 174,634 J/m ³ -K; and

stainless steel: 502 J/kg-K x 8,027 kg/m ³ = 4,029,554 J/m ³ -K.

[0089] In the above example, the air has a relatively small volumetric specific heat relative to both water and stainless steel. The high heat absorbing performance of an air-to-metal interface can provide a compressor/expander device that uses metal as an intermediate absorption mechanism (between the air and the water) heat transfer to a greater extent than the direct air-to-water absorption mechanism. It should be understood that the calculation of heat absorbing performance (e.g., heat capacity) discussed above is merely one example, as the density and specific heat values of air, water and stainless steel, can vary depending on other factors, such as, for example, temperature, pressure and grade of material. For example, the density of air, and thus its heat capacity, scales approximately linearly with pressure (at a given temperature), so that the values above are higher by a factor of 10 at a pressure of 10 bar, and a factor of 100 at a pressure of 100 bar. Similarly, the density and heat capacity of air scale approximately linearly, but inversely, with temperature (at a given pressure). Thus, the values of density and heat capacity of air at 586K (313 °C) are approximately half of the values at 293K (20 °C). However, even at the higher end of the range of air pressures that can be produced by a compressor/expander device as described herein, the heat capacity of air is one or two orders of magnitude lower than water or stainless steel. In addition, other materials can be used for the heat transfer element, such as, for example, tungsten and titanium. Tungsten can have, for example, a density of 19,300 kg/m ³ and a specific heat of 132 J/kg-K to provide a heat absorbing performance per unit volume of 2,548,000 J/m ³ -K. Titanium can have for example, a density of 4,510 kg/m ³ and a specific heat of 520 J/kg-K to provide a heat absorbing performance per unit volume (or heat capacity) of 2,345,200 J/m ³ -K. As with stainless steel, the density and mass specific heat can vary depending on, for example, the temperature, pressure and particular grade of the material.

[0090] In an embodiment that uses a metal heat transfer element, the heat absorbed by the metal can be transferred to the liquid (e.g., water) in the system, which as described previously can be transferred out of the pressure vessel by other methods such as a heat exchanger (e.g., heat pipes or other mechanisms).

[0091] FIG. 1 schematically illustrates a portion of a compression and/or expansion device (also referred to herein as "compressor/expander device") according to an embodiment. A compressor/expander device 100 can include one or more pressure vessels 120 (also referred to herein as "cylinder") having a working chamber 140, an actuator 121 by which the volume of working chamber 140, and/or the portion of the volume of the working chamber 140 that can be occupied by gas, can be changed (decreased to compress the gas, increased to expand the gas), and one or more heat transfer elements 122 disposed within the working chamber 140. The compressor/expander device 100 can be used, for example, to compress or expand a gas, such as air, within the working chamber 140. The compressor/expander device 100 can be used, for example, in a CAES system. The pressure vessel 120 can include one or more gas inlet/outlet conduits 130 in fluid communication with the working chamber 140. Optionally, the pressure vessel 120 can include one or more liquid inlet/outlet conduits 128 in fluid communication with the working chamber 140. The working chamber 140 can contain, at various time periods during a compression and/or expansion cycle, a quantity of gas (e.g., air) that can be communicated to and from the working chamber 140 via the inlet/outlet conduits 130, and optionally can also contain a quantity of liquid (e.g., water) that can be communicated to and from the working chamber 140 via the inlet/outlet conduits 128. The compressor/expander device 100 can also include multiple valves (not shown in FIG. 1) coupled to the inlet/outlet conduits 128 and 130, and/or to the pressure vessel 120. The valves can be configured to operatively open and close the fluid communication to and from the working chamber 140. Examples of use of such valves are described in more detail in the Compressor and/or Expander Device applications incorporated by reference above.

[0092] The actuator 121 can be any suitable mechanism for selectively changing the volume of the working chamber 140 and/or the portion of the volume of the working chamber 140 that can be occupied by gas. For example, the working chamber 140 can be defined by a cylinder and a face of a piston (not shown in FIG. 1) disposed for reciprocal movement within the cylinder. Movement of the piston in one direction would reduce the volume of the working chamber 140, thus compressing gas contained in the working chamber 140, while movement of the piston in the other direction would increase the volume of the working chamber 140, thus expanding gas contained in the working chamber 140. The actuator 121 can thus be the piston and any suitable device for moving the piston within the cylinder, such as a pneumatic or hydraulic actuator, for example, the hydraulic actuators described in the '724 application incorporated by reference above. [0093] In some embodiments, the working chamber 140 can have a fixed volume, i.e. a volume defined by a chamber with fixed boundaries, and the portion of the volume of the working chamber 140 that can be occupied by gas can be changed by introducing a liquid into, or removing a liquid from, the working chamber 140. Thus, the working chamber 140 has a volume with a first portion containing a volume of liquid, and a second portion that can contain gas, having a volume that is the total volume of the working chamber 140 less the volume of the first portion (the volume of the liquid). In such embodiments, the actuator 121 can be any suitable device for introducing liquid into, or removing liquid from, the working chamber 140, such as a hydraulic actuator that can move a liquid in and out of the working chamber 140 via liquid inlet/outlet conduit 128. In such an embodiment, the actuator 121 can include a water pump (not shown) that drives a hydraulically driven piston (not shown) disposed within a housing (not shown) and can be driven with one or more hydraulic pumps (not shown) to move a volume of liquid in and out of the working chamber 140. An example of such a hydraulic actuator is described in the Compressor and/or Expander Device applications incorporated by reference above.

[0094] In some embodiments, the working chamber 140 can be configured to combine the techniques described above, i.e. the working chamber 140 can have a variable volume, e.g. using a cylinder and a piston as described above, and the portion of the variable volume that can be occupied by gas can be changed by introducing liquid into, or removing liquid from, the working chamber 140. In another embodiment, a constant volume of liquid can be maintained in the variable-volume working chamber 140 throughout all, or a portion, of the compression cycle.

[0095] The heat transfer element 122 can be a variety of different configurations, shapes, sizes, structures, etc. to provide a relatively high surface area per unit volume or mass that can be in contact with the gas (e.g., air) as it is being compressed or expanded within the working chamber 140. In some embodiments, it may be desirable to include a heat transfer element 122 that can be formed with a material that can provide high thermal conductivity in a transverse and a longitudinal direction within the working chamber 140. The various components of the heat transfer element 122 can be formed from one or more of a variety of different materials. For example, the heat transfer element 122 can be formed with metals (e.g. stainless steel) in various forms, such as sheet or wires, carbon fiber, nano-materials, and hybrid or composite materials (e.g. carbon polymer compounds) which have anti-corrosion properties, are lighter weight, and are less expensive than some metallic materials.

[0096] The heat transfer element 122 can be disposed at various locations within the working chamber 140 to optimize the heat transfer within the pressure vessel 120. For example, in some embodiments, the heat transfer element 122 can be disposed within the working chamber 140 near an end portion of the working chamber 140 in a portion occupied by the gas (e.g., air) near the end of a compression cycle. As the gas is compressed during the compression cycle, the work done on the gas adds heat energy to the gas. The heat energy is continuously transferred (primarily by conductive and/or convective, rather than radiant, heat transfer) to the heat transfer element 122. This heat transfer maintains the gas temperature at a lower value than would be the case without the heat transfer element 122, and moderately increases the temperature of the heat transfer element 122.

[0097] As described above, in some embodiments, the working chamber 140 can contain a liquid, and/or the actuator 121 can be used to change the portion of the working chamber 140 that is available to contain the gas, by moving a liquid (e.g., water) into and out of the working chamber 140, such that the gas (e.g., air) within the working chamber 140 is compressed by the liquid. In such embodiments, depending on the rate at which the working chamber 140 is filled with liquid and the heat transfer properties of the heat transfer element 122, the gas and the heat transfer element 122 will be relatively closer or farther from thermal equilibrium, and thus, during some or all of the compression cycle, the liquid in the working chamber 140 can be caused to contact the heat transfer element 122 and to receive from the heat transfer element 122 heat energy it received from the compressed gas. Optionally, at the end of the compression cycle, any pressurized gas remaining in the working chamber 140 can be released from the working chamber 140, and transferred to the next step or stage in the compression process or to a storage facility. Liquid can then be moved into the working chamber 140, to substantially fill the volume occupied by the gas that was released from the working chamber 140 after compression (which volume is now filled with gas at a lower pressure) by introducing more liquid and/or by reducing the volume of the working chamber 140 (e.g. by moving a piston). The heat energy stored in the heat transfer element 122 can then be transferred (again, by conductive and/or convective transfer) to the water in the working chamber 140.

[0098] In some embodiments, the heat transfer element 122 can be disposed within a substantial portion of the working chamber 140 such that air and water can flow through, along, and/or across the heat transfer element 122 as the liquid fills an increasingly larger portion of the volume of the working chamber 140 and compresses the air within the working chamber 140. In such an embodiment, the heat transfer element 122 can be in contact with both air and water from the beginning of the compression cycle, with progressively less being exposed to air, and more being exposed to water, as the cycle progresses.

[0099] In some embodiments, the heat transfer element 122 can have a density that varies spatially within the heat transfer element 122, so that the heat transfer can be tailored. For example, in some embodiments, the heat transfer element 122 can be disposed within a substantial portion of the pressure vessel 120 as described above, and have a density that varies from the bottom to the top of the heat transfer element 122. For example, the density of the heat transfer element 122 can increase as the air moves from the beginning of the compression cycle to the end of the compression cycle. In other words, the heat transfer element 122 is denser where the air is disposed near the end of the compression cycle than where the air is disposed at the beginning of the compression cycle. The density can be varied by varying the composition of the heat transfer element 122, i.e. using materials of different density. The density can also, or instead, be varied by varying the amount of heat transfer material per unit volume, e.g. by more closely packing discrete components of the heat transfer element 122, such as rods, tubes, filaments, fins, etc., such that a relatively larger portion of a given available volume is filled with heat transfer materials (and a correspondingly smaller portion of the volume can be filled with gas). Alternatively or additionally, the density can be varied circumferentially and/or radially (e.g., more or less dense toward the outer diameter relative to the inner diameter of the heat transfer element 122). [00100] In some embodiments, the heat transfer element 122 can be designed to maximize the amount of gas in the working chamber 140 to be compressed. Thus, increasing the mass of gas that can be compressed for any given size of pressure vessel 120 increases the power density of that device. As the density or volume fraction (e.g., the amount of heat transfer material per unit volume) of the heat transfer element 122 increases, the remaining volume in the working chamber 140 available for a mass of gas to be compressed decreases. Although the increased density of heat transfer element 122 improves the transfer of heat energy from the gas being compressed to the heat transfer element 122, the volume of gas being compressed with each compression cycle is reduced. Said another way, the volume of the working chamber 140 occupied by the heat transfer element 122 directly reduces the mass of gas that can be compressed within any given pressure vessel 120. Furthermore, reducing the size of the heat transfer element 122 can reduce the capital equipment costs (e.g. by savings on materials) and operating costs (e.g. decreasing the overall weight of the equipment being moved by the actuator. Thus, in some embodiments, the heat transfer element 122 can be designed such that the heat transfer element 122 has sufficient surface area to remove the heat energy generated by the compression of the gas, while minimizing the portion of the volume of the working chamber 140 occupied by the heat transfer element 122 to maximize the portion of the volume in the working chamber 140 for gas to be compressed. In some embodiments, multiple transfer elements 122 can be movable with respect to each other such that the density of the heat transfer element 122 in a given portion of the working chamber 140 can be varied throughout a compressor/expander cycle to maximize heat transfer surface area and minimize heat transfer element volume 122. [00101] In some embodiments, the working chamber 140 can be partially filled with a liquid (e.g. water) that can be communicated to and from the working chamber 140 via the inlet conduit 128 and the outlet conduit 130, respectively, or via other conduits (not shown). During the compression cycle, heat energy generated during the compression process can be transferred from the gas, to the heat transfer element 122, and then to the liquid. A volume of the heated liquid can then be discharged from the pressure vessel 120 via the outlet conduit 130 or via a separate liquid discharge conduit (not shown). As described above with respect to the heat transfer element 122, the volume of liquid that occupies a portion of working chamber 140 reduces the remaining volume of the working chamber 140 available for a mass of gas to be compressed. In other words, although the liquid in the working chamber 140 provides a mechanism by which the heat energy generated by the compression of the gas can be removed from the pressure vessel 120 (i.e. by first quenching the heat transfer element 122 to transfer the heat energy to the liquid, and then discharging the heated liquid out of the pressure vessel 120), both the liquid and the heat transfer element 122 occupy a portion of the working chamber 140, thereby reducing the mass of gas that can be compressed. In some embodiments, the heat transfer element 122 and the volume of liquid in the working chamber 140 can be designed to remove a sufficient amount of heat energy generated during the compression process, while maximizing the amount of gas in the working chamber 140 to be compressed. For example, having multiple heat transfer elements 122 that are movable with respect to each other such that the density of the heat transfer element 122 disposed in the portion of the working chamber 140 containing the gas can be varied throughout a compression cycle can reduce the volume of liquid required for quenching the heat transfer element 122.

[00102] In some embodiments, more than one heat transfer element 122 can be used. For example, in such an embodiment, more than one of the same type of heat transfer element 122 can be used, or a combination of different types or configurations of heat transfer elements 122 can be used. In addition, within a given compressor/expander device 100, one or more of the same or different combinations of heat transfer elements 122 can be used in one or more of the working chambers 140 of that system. In some embodiments, one or more heat transfer elements 122 can be positioned within the working chamber 140 such that the density of the heat transfer elements 122 is varied within the pressure vessel 120.

[00103] In some embodiments, the heat transfer element 122 can include tessellating metal plates or a stack of metal plates. The plates can be, for example, planar or curved, porous plates, or mesh screens. In some embodiments, the plates can slide with respect to each other, thereby modifying the heat transfer surface area per unit volume of air as the stroke progresses. Such an embodiment of a heat transfer element 122 based on tessellating plates may be valuable for implementing a smaller or more compact pressure vessel 120. For example, during a compression stroke that reduces the gas volume in which the heat transfer element 122 is disposed, the heat transfer element 122 may be a tessellation pack into a volumetrically compact form. This packing may be designed to occur in concert with the compression stroke. During an expansion stroke, the heat transfer element 122 may unpack and thereby volumetrically expand in concert with the expansion stroke. The plates may be moved or displaced by the engagement with a moving boundary of the working chamber 140, e.g. a piston face, and/or by liquid contained within the working chamber 140 (e.g. if the plates are buoyant), and/or by an actuator.

[00104] In some embodiments, the heat transfer element 122 can be movable or dynamic in that it can move within the working chamber 140 during a compression and/or expansion cycle. In some embodiments, the heat transfer element 122 can collapse and expand within the working chamber 140. For example, a stack of metal coils or stack of tessellating plates described above can be configured to collapse and expand within the working chamber 140. In some embodiments that include a compression and expansion device using a piston to change the volume of the working chamber 140, a heat transfer element 122 can move with the stroke of the piston, e.g. by engagement with the face of the piston. In some embodiments, the heat transfer element 122 can move (e.g., collapse and expand) in a longitudinal direction and/or vertical direction. In some embodiments, the heat transfer element 122 can move (e.g., collapse and expand) in a radial direction. In still other embodiments, the heat transfer element 122 can coil (i.e., collapse) and uncoil (i.e., expand). [00105] Heat energy transferred from the gas to the heat transfer element 122 can in turn be transferred out of the pressure vessel 120 by any suitable means, including a heat pipe, circulating fluid, etc., to a location where it can be dissipated, used in other processes, and/or stored for future use in the compressor/expander device (e.g. in an expansion cycle). In addition, or alternatively, heat energy transferred from the gas to the heat transfer element 122 can be transferred from the heat transfer element 122 to fluid contained in the working chamber 140. The heat energy can then be transferred from the fluid out of the pressure vessel 120. Similar techniques can be used to transfer heat energy from outside the pressure vessel 120 to the heat transfer element 122 and thence to the gas in the working chamber 140, e.g. during an expansion cycle.

[00106] FIG. 2 schematically illustrates a portion of a compressor/expander device according to an embodiment. A compressor/expander device 200 can include one or more pressure vessels (cylinders) 220 having a first working chamber 240 and a second working chamber 241, an actuator 221 connected to a piston 226 via a piston rod 227, and one or more heat transfer elements 222 disposed within the pressure vessel 220. More specifically, the heat transfer elements 222 can include a first heat transfer element 223 disposed within the first working chamber 240 and a second heat transfer element 224 disposed within the second working chamber 241. The compressor/expander device 200 can be used, for example, to compress or expand a gas, such as air, within the first working chamber 240 or the second working chamber 241. The compressor/expander device 200 can be used, for example, in a CAES system. The pressure vessel 220 can include an inlet conduit 228 and an outlet conduit 229 in fluid communication with the first working chamber 240 and an inlet conduit 230 and an outlet conduit 231 in fluid communication with the second working chamber 241. The first working chamber 240 and the second working chamber 241 can contain, at various time periods during a compression and/or expansion cycle, a quantity of the gas (e.g., air) and a quantity of the liquid (e.g., water) that can be communicated to and from the working chambers via the inlet/outlet conduits. Optionally, the pressure vessel 220 can include one or more additional conduits in fluid communication with the first working chamber 240 or the second working chamber 241 specifically dedicated to communicating gas or liquid to or from the first and second working chambers. The compressor/expander device 200 can also include multiple valves (not shown in FIG. 2) coupled to the inlet/outlet conduits 228, 229, 230, and 231 and/or to the pressure vessel 220. The valves can be configured to operatively open and close the fluid communication to and from the working chamber 240. Examples of use of such valves are described in more detail in the Compressor and/or Expander Device applications incorporated by reference above.

[00107] The actuator 221 can be any suitable mechanism for selectively changing the volume of the first working chamber 240 and the second working chamber 241 and/or the portion of the volume of the first working chamber 240 and the second working chamber 241 that can be occupied by gas. The actuator 221 can be for example, an electric motor or a hydraulically driven actuator such as, for example, the hydraulic actuators described in the '724 application, the disclosure of which is incorporated herein by reference in its entirety. The actuator 221 can be coupled to the piston 226 via the piston rod 227 and used to move the piston 226 back and forth within the interior region of the pressure vessel 220. For example, the working chamber 240 can be defined by the cylinder 220 and the bottom face of piston 226 disposed for reciprocal movement within the cylinder 220. Similarly, the working chamber 241 can be defined by the cylinder 220 and the top face of the piston 226. In this manner, the piston 226 is movably disposed within the interior region of the cylinder 220 and can divide the interior region between a first interior region (working chamber 240) and a second interior region (working chamber 241).

[00108] As the piston 226 moves back and forth within the interior region of the cylinder 220, a volume of the first working chamber 240 and a volume of the second working chamber 241 will each change. For example, the piston 226 can be moved between a first position (e.g., top dead center) in which the first working chamber 240 includes a volume of fluid greater than a volume of fluid in the second working chamber 241, and a second position (e.g., bottom dead center) in which the second working chamber 241 includes a volume of fluid greater than a volume of fluid in the first working chamber 240. As used herein, "fluid" means a liquid, gas, vapor, suspension, aerosol, or any combination of thereof. At least one rolling seal member (not shown) can be disposed within the first working chamber 240 and the second working chamber 241 of the cylinder 220 and can be attached to the piston 226. The arrangement of the rolling seal member(s) can fluidically seal the first working chamber 240 and the second working chamber 241 as the piston 226 moves between the first position (i.e., top dead center) and the second position (i.e., bottom dead center). Examples and use of the rolling seal member are described in more detail in the '505 application incorporated by reference above. [00109] In some embodiments, the piston 226 is moved within the pressure vessel 220 to compress a gas, such as air, within the pressure vessel 220. In some embodiments, the compressor/expander device 200 can be configured to be double acting in that the piston 226 can be actuated in two directions. In other words, the piston 226 can be actuated to compress and/or expand gas (e.g., air) in two directions. For example, in some embodiments, as the piston 226 is moved in a first direction, a first volume of a fluid (e.g., water, air, and/or any combination thereof) having a first pressure can enter the first working chamber 240 of the cylinder 220 on the bottom side of the piston 226. In addition, a second volume of the fluid having a second pressure can be compressed by the top side of the piston 226 in the second working chamber 241. The gas portion of the second volume of fluid can then exit the second working chamber 241. When the piston 226 is moved in a second direction opposite the first direction, the gas portion of the first volume of fluid within the first working chamber 240 can be compressed by the piston 226. The gas portion of the first volume of fluid can then exit the first working chamber 240 having a third pressure greater than the first pressure, and simultaneously a third volume of fluid can enter the second working chamber 241.

[00110] The heat transfer element 223 disposed within the first working chamber 240 and the heat transfer element 224 disposed within the second working chamber 241 can be a variety of different configurations, shapes, sizes, structures, etc. to provide a relatively high surface area per unit volume or mass that can be in contact with the gas (e.g., air) as it is being compressed or expanded. In some embodiments, the heat transfer element 223 disposed within the first working chamber 240 can be attached to the bottom face of the piston 226. Similarly, in such embodiments, the heat transfer element 224 disposed within the second working chamber 241 can be attached to the top face of the piston 226. In some embodiments, the heat transfer element 223 and the heat transfer element 224 are disposed within the first working chamber 240 and the second working chamber 241, respectively, such that an air gap exists between the heat transfer element 223 and the heat transfer element 224 and the piston 226. For example, in some embodiments, a 1" air gap can exist between the bottom surface of the piston 226 and the heat transfer element 223 and between the top surface of the piston 226 and the heat transfer element 224. In other embodiments, the heat transfer element 223 can be configured within the working chamber 240 such that a heat transfer volume ratio of 2: 1 can exist at the beginning of the compression stroke. For example, at the beginning of the compression stroke, the volume of air within the working chamber 240 not exposed to the heat transfer element 223 is twice as large as the volume of air that is exposed to the heat transfer element 223.

[00111] In some embodiments, it may be desirable to form the heat transfer elements 222 with a material that can provide high thermal conductivity. For example, the heat transfer elements 222 (i.e., the heat transfer element 223 and the heat transfer element 224) can be formed with metals (e.g. stainless steel) in the form of, for example, sheet or wire, carbon fiber, nano-materials, and hybrid or composite materials (e.g. carbon polymer compounds) which have anti-corrosion properties, are lighter weight, and are less expensive than some metallic materials. The heat transfer elements 222 can be, for example, substantially similar to the heat transfer element 122 described with respect to FIG. 1. Thus, the configuration, material properties, position, function, and/or the like can be similar to any of those described with respect to the heat transfer element 122. Therefore, details of the heat transfer element 223 disposed within the first working chamber 240 and the heat transfer element 224 disposed within the second working chamber 241 are not described with respect to FIG. 2 and should be considered to be any suitable configuration described herein.

[00112] FIGS. 3A and 3B schematically illustrate a heat transfer element according to an embodiment. A heat transfer element 322 can be included in, for example, a compressor/expander device (not shown in FIGS. 3A and 3B). In some embodiments, the compressor/expander device can include a pressure vessel and an actuator connected to a piston via a piston rod. The pressure vessel can define at least one working chamber in which the heat transfer element can be disposed. The compressor/expander device can be substantially similar to any compressor/expander device 100, 200 described or referenced herein.

[00113] The heat transfer element 322 can include at least one wire mesh element or fin 360. The wire mesh fin 360 can be formed from a wire mesh sheet 364. The wire mesh sheet can be a woven wire mesh sheet or a welded wire mesh, as shown in FIG. 3 A. The sheet of wire mesh 364 (also referred to herein as "mesh 364") can include any number of wires 361 that can be woven or welded together in various configurations. For example, in some embodiments, the mesh 364 can be purchased from a supplier such as, for example, Gerard Daniel Worldwide located in Hanover, PA or W.S. Tyler Screening Group located in St. Catharines, ON. The woven mesh 364 can be any suitable size range, such as 10 to 200 Mesh on the Tyler Mesh Size Scale. As used herein, the Tyler Mesh Size Scale defines the number of openings in a linear inch, measured from the center of one wire to a point one inch away. In such embodiments, the wires 361 can range in gauge from about 0.01mm to about 2mm and define an opening 362 between adjacent wires 361. The size of the openings 362 can include a range from about 1 micron to about 1 inch. In some embodiments, the openings 362 defined by the mesh 364 can be a substantially square or rectangular shape. In other embodiments, the openings 362 defined be the mesh 364 can be any suitable shape, such as, for example, hexagonal, pentagonal, and/or any other polygonal shape. In some embodiments, a woven mesh 364 can include a selvage 366 configured to prevent fraying. Similarly stated, the woven mesh 364 can include an outer edge (i.e., selvage 366) configured to prevent the mesh weave from loosening, fraying, separating, and/or otherwise failing at the edges.

[00114] The mesh 364 can be formed into any shape, configuration, and/or structure and, as such, used as a fin 360 and/or heat transfer element 322 in the compressor/expander devices described or referenced herein. For example, as shown in FIG. 3B, the heat transfer element 322 can include the mesh 364 configured to spiral outwardly from a relatively small inner diameter to a larger outer diameter. The heat transfer element 322 can include an outer ring 367 that can define a boundary of the heat transfer element 322. The heat transfer element 322 can be disposed vertically within the working chamber of the pressure vessel. Similarly stated, the heat transfer element 322 can be disposed within the working chamber of the pressure vessel such that the vertical axis defined by the spiraling mesh fins 360 is parallel to the vertical axis defined by the cylinder. Although the embodiments described herein primarily refer to the heat transfer element as including a wire mesh fin or other component, the various other structures and materials as described herein may substitute for the wire mesh. For example, the fins and other components described herein may be constructed of sheet metal. [00115] The heat transfer element 322 can be configured to extend downward from a top surface of the working chamber. More specifically, the heat transfer element 322 can be coupled (e.g., welded, bolted, clamped, fastened, and/or otherwise attached) to the top surface of the working chamber included in the compressor/expander device. In this manner, the heat transfer element 322 can be rigidly disposed within the working chamber. In such embodiments, the diameter of the outer ring 367 of the heat transfer element 322 can be substantially similar to the diameter of the pressure vessel of the compressor/expander device. Optionally, the outer ring 367 of the heat transfer element 322 can be coupled to the sidewalls of the pressure vessel. In some embodiments, the heat transfer element 322 can be coupled (e.g., welded, bolted, clamped, fastened, and/or otherwise attached) to a surface (e.g., a top and/or bottom surface) of the piston. In this manner, the heat transfer element 322 can be moved by the piston in the direction of compression and/or expansion. Therefore, in such embodiments, the outer ring 367 of the heat transfer element 322 is smaller than the diameter of the working chamber to allow free movement of the piston.

[00116] In use, a gas (e.g., air) can enter the working chamber at a first pressure and a first temperature. During a compression cycle, heat energy generated during the process can be transferred from the gas to the mesh fins 360 via convection and/or conductive heat transfer as the air flows over, through, and/or around the fins 360. At the end of the compression cycle, the gas, being compressed to a second pressure greater than the first pressure, can exit the working chamber at a second temperature that differs from (i.e. is higher than) the first temperature by an amount that is desirable or acceptable for the operation of the expansion / compression system. Similarly stated, the use and configuration of the heat transfer element 322 can cause the mesh fin 360 to absorb the heat produced by the compression of the gas, thereby allowing for a compression of the gas that is desirably or acceptably close to the theoretical ideal of isothermal. During and/or after the compression stroke, the liquid present in the working chamber can quench the mesh fins 360 and remove the heat transferred to the fins 360 during the gas compression. In this manner, the relatively warm liquid can exit the working chamber and the process can repeat. Similarly, during an expansion cycle, heat energy can be transferred to an expanding compressed gas to allow for an expansion that is desirably or acceptably close to isothermal. In some embodiments, the heat transfer between the gas and the heat transfer element 322 can be controlled to allow for a controlled, predetermined temperature change of the gas. For example, the size, shape and configuration of the heat transfer element 322 and/or the volume of liquid present in the working chamber can be configured to allow for a 5°, 10°, 15°, 20° or 25° temperature change of the gas during a compression and/or expansion cycle at a selected rate of expansion or compression.

[00117] The mesh size, wire diameter, and opening size of the mesh fin 360 can be configured to produce optimal thermal performance. For example, reducing the diameter of the wires 361 can reduce the thickness of the mesh fin 360 and allow the spiral windings (i.e., layers) of the fin to be spaced closer together, thereby increasing thermal performance of the heat transfer element 322. The layers of the mesh fin 360 may be circumferential, annular, circular, and/or cylindrical. In some embodiments, the openings 362 defined by the mesh 364 are configured to produce a turbulent flow of the gas within the working chamber as the air flows over, across, and/or through the openings 362. The turbulent flow of the gas increases the heat transfer rate from the gas to the heat transfer element 322 in comparison to laminar flow. Additionally, it may be desirable to form the mesh 364 from a material that can provide high thermal conductivity., For example, the mesh 364 can be formed with metal wires 361 (e.g., stainless steel, aluminum, copper, alloys, etc.). In some embodiments, the mesh 364 can be formed from any suitable material such as, for example, hybrid wires, carbon fiber, nano- materials, and/or composite materials (e.g. carbon polymer compounds) which have anti- corrosion properties, are lighter weight, and are less expensive than some metallic materials.

[00118] In some embodiments, the metal wires 361 can include specific coatings. The coatings can be configured to reduce corrosion, and/or trap (i.e., hydrophilic coatings) or repel (i.e., hydrophobic coatings) a liquid. For example, in some embodiments, the metal wires 361 included in the mesh 364 can be coated with a hydrophobic coating such that the mesh 364 repels a liquid (e.g., water). Thus, at the end of a compression stroke when the liquid quenches the fin 360, the coating can cause the liquid to be repelled from the surface of the fin 360. In this manner, the openings 362 of the mesh 364 can remain substantially free of water (i.e., the contact angle of the water is sufficiently large such as to not allow the water to wet the wire 361 surface). With the openings 362 substantially free from water, the hydrophobic coating can increase the heat transfer between the gas and the mesh fins 360 by ensuring a turbulent flow of the gas as it passes over the openings 362.

[00119] In some embodiments, water droplets dripping from the surface of the woven mesh fins 360 can act as a second heat transfer element. For example, after the heat transfer element 322 has been quenched by the liquid (e.g., at the end of a compression stroke) water can drip from the surface of the fins 360. As the piston begins to compress a second mass of gas, the work done on the gas adds heat energy to the gas. At least a portion of the gas can be in fluidic contact with the water dripping from the surface of the mesh fins 360. In this manner, the water can interact with the gas (e.g., air) and absorb at least a portion of the heat energy from the gas added by the compression process. Thus, as the water droplets drip from the surface of the fins 360, the water droplets act as a second heat transfer element. The working chamber can be configured so that as the water droplets drip from the surface of the fin 360, the water droplets drip into the volume of liquid included in the working chamber (e.g., the volume of liquid that is used to quench the heat transfer element 322). [00120] FIGS. 4A and 4B schematically illustrate a heat transfer element according to an embodiment. A heat transfer element 422 can be included in, for example, a compressor/expander device (not shown in FIGS. 4A and 4B). In some embodiments, the compressor/expander device can include a pressure vessel and an actuator connected to a piston via a piston rod. The pressure vessel can define at least one working chamber in which the heat transfer element can be disposed. The compressor/expander device can be substantially similar to any compressor/expander device 100, 200 described or referenced herein. The heat transfer element 422 can include at least one wire mesh (or other structure) fin 460. The wire mesh fin 460 can be formed from a wire mesh sheet 464, as shown in FIG. 4A. The sheet of wire mesh 464 (also referred to herein as "woven mesh") can include any number of wires 461 that can be woven together in various configurations and can define any number of openings 462. Additionally, the mesh 464 can include a selvage 466 configured to prevent the mesh 464 from fraying at the edges. The mesh 464 can be substantially similar to the mesh 364 described with respect to FIGS. 3 A and 3B. Therefore, details of the mesh 464 are not described in detail with respect to FIGS. 4A and 4B.

[00121] The mesh fin 460 can include a set of spacing elements 463. More specifically, the heat transfer element 422 (FIG. 4B) can include at least one mesh fin 460 configured to spiral outwardly from a relatively small inner diameter to a larger outer diameter. The spacing elements 463 can be disposed within the heat transfer element 422 to maintain a desired spacing between each adjacent layer. The spacing elements 463 can be any suitable shape, size, material, and/or configuration, including annular, circular, cylindrical, spherical, cubic, conical, and/or other structures. For example, in some embodiments, the spacing elements 463 can be metal (e.g., stainless steel) rods configured to be of similar length as the height of the mesh fin 460. While shown in FIG. 4B as having a circular cross-section, the spacing elements 463 can have any suitable cross-section such as, for example, square, rectangular, oblong, and/or the like. The spacing elements 463 may be disposed longitudinally, radially, and/or circumferentially with respect to the mesh fin 460. [00122] The spacing elements 463 can be disposed within the heat transfer element 422 in any suitable number, spacing, and/or configuration such that the desired spacing between adjacent spiral layers is maintained. For example, the diameter of the spacing elements 463 included in the heat transfer element 422 can be configured to maintain an optimal spacing between the adjacent spirals of the mesh fins 460. Convective heat transfer is inversely proportional to the distance between the adjacent windings or layers of mesh fin 460, thus, a minimal distance between adjacent windings of the fin 460 is desirable. The spacing elements 463 can be used to maintain the desired spacing between the adjacent windings of the mesh fin 460 and support the fin 460 such that movement of the fin 460 is minimized (e.g., the spacing is not increased, thus reducing the heat transfer potential).

[00123] In some embodiments, the spacing elements 463 can be heat pipes. The heat pipes can be configured to remove heat energy from the mesh fin 460 and the gas being compressed within the working chamber of the compressor/expander device. For example, the heat energy added to a gas during a compression stroke can be transferred to the heat transfer element 422. The mesh fin 460 of the heat transfer element 422 can absorb a portion of the heat energy and the spacing elements 463 (i.e., heat pipes) can also absorb a portion of the heat energy. In this manner, the spacing elements 463 (i.e., heat pipes) can be configured to absorb heat energy from the gas and/or mesh fin 460 and maintain the adjacent windings of the mesh fin 460 at a desired distance. [00124] Referring now to FIGS. 5A and 5B, a wire mesh (or other structure) fin 560 can be formed from a sheet of wire mesh 564. The mesh 564 can include any number of wires 561 that can be woven together in various configurations and can define any number of openings 562. The mesh 564 can be substantially similar to the mesh 364 described with respect to FIGS. 3A and 3B and can be included in any suitable heat transfer element described or referenced herein. Therefore, details of the mesh 564 are not described in detail with respect to FIGS. 5A and 5B.

[00125] The mesh fin 560 can also include a set of spacing elements 563. As shown in FIG. 5A, the mesh fin 560 can include spacing elements 563 configured to run the length and height of the mesh sheet 564. The spacing elements 563 can be disposed such that the horizontal spacing elements 563 (i.e., the spacing elements running the length of the mesh sheet 564) rest on top of the set of vertical spacing elements 563 (i.e., the spacing elements running the height of the mesh sheet 564), as shown in FIG. 5B. In some embodiments, the vertical spacing elements 563 can rest on top of the horizontal spacing elements 563, i.e. a welded mesh product. In some embodiments, the spacing elements 563 can be woven together, such as to increase strength, reduce welding and/or fastening, and/or allow for a modular implementation (e.g., the woven spacing elements 563 can be purchased from the suppliers named herein). In other embodiments, the spacing elements 563 can be welded together and/or to the mesh 564. The spacing elements 563 are configured to function similarly to the spacing elements 463 described with respect to FIGS. 4A and 4B. Therefore, further details are not described herein with respect to FIGS. 5 A and 5B.

[00126] Referring to FIG. 6, a wire mesh (or other structure) fin 660 can be formed from a sheet of wire mesh 664 or alternative material. The mesh 664 can include any number of wires 661 that can be woven together in various configurations and can define any number of openings 662. The mesh 664 can be substantially similar to the mesh 364 described with respect to FIGS. 3A and 3B and can be included in any suitable heat transfer element described or referenced herein. Therefore, details of the mesh 664 are not described in detail with respect to FIG. 6.

[00127] The mesh fin 660 can include a set of spacing elements 663 configured to maintain a desired spacing between adjacent fins within a heat transfer element (not shown). The spacing elements 663 can be configured to run diagonally along the surface of the mesh 664. The diagonal spacing elements 663 can be configured to impart a spiral/cyclonic flow of gas during compression and/or expansion to improve heat transfer. In some embodiments, the spacing elements 663 can be configured as a cross-woven wire included in the mesh 664. The spacing elements 664 function similarly to the spacing elements 463 described with respect to FIGS. 4A and 4B. Therefore, further details are not described herein with respect to FIG. 6.

[00128] In some embodiments, a wire mesh fin 760 can be formed from a sheet of wire mesh 764 having any number of wires 761 that can be woven together in various configurations and defining any number of openings 762 therebetween, as shown in FIG. 7. The mesh 764 can be substantially similar to the mesh 364 described with respect to FIGS. 3A and 3B and can be included in any suitable heat transfer element described or referenced herein. Therefore, details of the mesh 764 are not described in detail with respect to FIG. 7.

[00129] The mesh fin 760 can include a set of spacing elements 763 configured to maintain a desired spacing between adjacent windings or layers within a heat transfer element (not shown). The spacing elements 763 can be short rods, solid or flexible washers, or protrusions extending from a surface of the mesh 764. In some embodiments, the spacing elements 763 can be press fit into the openings 762 defined by the mesh 764. Expanding further, the spacing elements 763 can include a given shape at both ends of the spacing elements 763 (not shown in FIG. 7). For example, in some embodiments, the ends of the spacing elements 763 can include a flange, a prong, a bulb, and/or any other suitable shape. In this manner, the spacing elements 763 can be inserted into the openings 762 defined by the mesh 764 and the given shape at the ends of the spacing elements 763 can secure the spacing elements 763 within the openings 762 and maintain a given spacing between mesh fins 760. In some embodiments, a flanged end of the spacing elements 763 define a surface that can be glued to the mesh 764 using any suitable adhesive. In some embodiments, a flanged end of the spacing elements 763 define a surface that can be welded to the mesh 764. For example, the spacing elements 763 can be stud welded to the mesh 764 at one end and can include a flange at a second end. The flanged end can be inserted into an opening 762 in the mesh 764 and the flange can maintain the spacing between the mesh fins 760.

[00130] Referring now to FIGS. 8A and 8B, a manufacturing method can include a mesh 864 and a press 880. In some embodiments, the mesh 864 can be stored in a roll 865. The mesh 864 can be unrolled from the roll 865 in a manual or automated process. For example, a mechanical clamp (not shown) can clamp an end of the wire mesh 864 included in the roll 865 and pull the wire mesh 864 in a direction such that the roll 865 unrolls. In some embodiments, the wire mesh 864 can travel on a conveyer system. The press 880 can include a press plate 881 having a multitude of spikes 884 and a ram 882. The ram 882 can be a hydraulic ram, a pneumatic ram, and/or can be included in a kinematic linkage (e.g., connected to a motor via gears and chains and/or pulleys and belts). The ram 882 can move the press plate 881 in a first direction, indicated by the arrow A in FIG. 8B. In this manner, the ram 882 produces a downward force and inserts the spikes 884 included in the press plate 881 into the mesh 864. Once the spikes 884 have been inserted into the mesh 864, the ram can move the press plate 881 in a second direction, opposite the first direction, and disengage the spikes 884 from the mesh 864. The spikes 884 can create any suitable size hole or indentation in the mesh 864 and as such, a spacer (not shown in FIGS. 8A and 8B) can be inserted. The spacing elements can be substantially similar in form and function to the spacing elements 763 described with respect to FIG. 7. For example, the spikes 884 included in the press 880 can create a set of openings in the wire mesh 864 that receive a set of spacing elements (not shown in FIGS. 8A and 8B) having a flanged end configured to be welded to the wire mesh 864.

[00131] In some embodiments, a manufacturing method can include a mesh 964 and a press 980 having a roller 983 and a set of spikes 984, as shown in FIGS. 9A and 9B. In such embodiments, the mesh 964 can be stored in a roll 965. The mesh 964 can be unrolled from the roll 965 in a manual or automated process. For example, a mechanical clamp (not shown) can clamp an end of the wire mesh 964 included in the roll 965 and pull the wire mesh 964 in a direction such that the roll 965 unrolls. In some embodiments, the wire mesh 964 can travel on a conveyer system. In such embodiments, the press 980 can be configured to selectively engage the mesh 964. For example, as the wire mesh 964 travels on the conveyor system (not shown in FIGS. 9A and 9B), the spikes 984 can be inserted into the mesh 964 or can created indentations in the mesh 964. As the mesh 964 passes the press 980, the mesh 964 can spin the roller 983, such that the spikes 984 engage the mesh 964 as it passes the press 980. In some embodiments, the roller 983 can be rotated by a motor and provide a force that unrolls the roll 965 of mesh 964. Similarly stated, the roller 983 can be rotated by a motor and as the spikes 984 engage the mesh 964 during rotation of the roller 983, the roll 965 of mesh 964 is unrolled.

[00132] The spikes 984 can create any suitable size hole in the mesh 964 and as such, a spacing element (not shown in FIGS. 9 A and 9B) can be inserted. The spacing elements can be substantially similar in form and function to the spacing elements 763 described with respect to FIG. 7. For example, the spikes 984 included in the press 980 can create a set of openings in the wire mesh 964 that receive a set of spacing elements (not shown in FIGS. 9A and 9B) having a flanged end configured to be welded to the wire mesh 964. In some embodiments, the manufacturing method can include a mechanism and/or process step that inserts and fastens the spacing elements to the mesh 964 after the spikes 984 are disengaged from the mesh 964. In some embodiments, the manufacturing method can also include a mechanism and/or process step that rolls the mesh 964, including the spacing elements (not shown), into a desired shape, such as to create a heat transfer element. In this manner, the spacing elements can maintain the spacing between the adjacent rolls.

[00133] In one embodiment, a manufacturing method for a two-piece thermal capacitor design (such as that described below with respect to FIG. 12) includes a sheet metal 990a (such as aluminum) unwound from a vertical pay-out reel 992a and fed into a geared or stamping corrugation machine 994. At the exiting side of the corrugation machine 994, the sheet metal 990a is attached to the central hub up a vertical take-up reel 996. A second sheet metal 990b is unwound from a second vertical payout reel 992b and is attached to the central hub of the same take-up reel 996. As the powered take-up reel 996 turns, it pulls material from both pay-out reels 992a and 992b forming a large capacitor cylinder comprising many channels which are defined by thicknesses of the sheet metal 992a and 992b and the geometry of the gears or stamping elements of the corrugation machine 994. Wire mesh or other suitable material may be substituted for sheet metal 992a and/or sheet metal 992b.

[00134] FIG. 10 schematically illustrates a heat transfer element according to an embodiment. A heat transfer element 1022 can be included in, for example, in a compressor/expander device (not shown in FIG. 10). In some embodiments, the compressor/expander device can include a pressure vessel and an actuator connected to a piston via a piston rod. The pressure vessel can define at least one working chamber in which the heat transfer element can be disposed. The compressor/expander device can be substantially similar to any compressor/expander device described or referenced herein. The heat transfer element 1022 can include at least one folded fin 1060, which may be constructed of, for example, solid metal plate or wire mesh. The fin 1060 can include features (e.g., wires, openings, stiffening elements, and/or a selvage) that can be substantially similar to the mesh 364 described with respect to FIGS. 3A and 3B. Therefore, details of the fin 1060 are not described in detail with respect to FIG. 10.

[00135] As shown in FIG. 10, the fin 1060 can be disposed within an outer ring 1067, included in the heat transfer element 1022. The outer ring 1067 can be any suitable shape, size, or configuration, and can be formed from any suitable material. In some embodiments, the outer ring 1069 can be formed of a metal, such as, for example, aluminum, stainless steel, titanium, and/or any suitable alloy. The fin 1060 can define a path within the outer ring 1067 such that portions of the fin 1060 can bend, fold, or otherwise conform to a given geometry. For example, the heat transfer element can include an inner ring 1069, disposed in the center of the heat transfer element 1022. The inner ring 1069 can be any suitable shape, size, or configuration, and can be formed from any suitable material. In some embodiments, the inner ring 1069 can define a shaft and be formed of a metal, such as, for example, aluminum, stainless steel, titanium, and/or any suitable alloy. In other embodiments, the inner ring 1069 can be formed from a composite, a ceramic, and/or the like.

[00136] The fin 1060 can be configured to be coupled to the inner ring 1069 using any suitable coupling. For example, in some embodiments, such as those where the inner ring 1069 is a metal, the fin 1060 can be welded. In other embodiments, the fin 1060 can be mechanically fastened (e.g., using screws, pins, rivets, and/or the like) to the inner ring 1069. The fin 1060 can extend from the inner ring 1069 toward the outer ring 1067 in a radial direction. The fin 1060 can bend and/or fold to define a surface 1070 configured to couple to the outer ring 1067. Similar to the coupling of the fin 1060 to the inner ring 1069, the surface 1070 of the fin 1060 can couple to the outer ring 1067 using any suitable method. In this manner, the fin 1060 can define a serpentine path such that the fin 1060 extends from the inner ring 1069 towards the outer ring 1067 and returns to the inner ring 1069. More specifically, the fin 1060 can bend and/or fold at the outer ring 1067 and the serpentine path can return to the inner ring 1069, where the fin 1060 again bends and/or folds and the serpentine path can return to the outer ring 1067.

[00137] FIG. 1 1 schematically illustrates a heat transfer element according to an embodiment. A heat transfer element 1122 can include an outer ring 1167 and inner ring 1069, with any number of concentric rings (layers) 1 168 disposed therebetween. In some embodiments, the heat transfer element 1 122 can include a set of fins 1160, which can be substantially similar to the fin 1060 described with respect to FIG. 10. The set of fins 1160 can be coupled to adjacent rings in a back-and-forth folding, corrugated, and/or serpentine motion. For example, the fin 1 160 can be coupled to the inner ring 1069, using any suitable coupling described herein, and extend in a radial direction to couple to an adjacent concentric ring 1 168. The fin 1160 can be configured to fold, such that the fin 1160 can extend back toward the inner ring 1169. In this manner, the fins 1 160 can be configured to substantially fill the area defined by two adjacent rings, as shown in FIG. 11. [00138] In some embodiments, the heat transfer element 1122 can include a support tray (not shown in FIG. 11). The support tray can be formed from any suitable material described herein including, for example, woven mesh. In this manner, the support tray can support the heat transfer element 1122 as well as provide a mounting surface to mount the heat transfer element 1122 to a piston and/or pressure vessel. In such embodiments, conduits or other support members can be incorporated into the spirals and/or concentric rings 1 168 to allow access to mounting hardware, such as bolts.

[00139] As shown in FIG. 12, in some embodiments, the rings (layers) 1268 of the heat transfer element 1222 can be configured to form a continuous spiral such as, for example, discussed with respect to FIGS. 3B and 4B. The spiral may be constructed of one or more sheets of solid metal plate or wire mesh. In such embodiments, the set of fins 1260 can follow a similar corrugated path as described above and having, for example, a sinusoidal or triangle pattern. Furthermore, in some embodiments, the fins 1260 can be formed from a single sheet of solid metal plate or wire mesh as the spiral configuration defines a continuous path to be occupied by the fins 1260. The layers 1268 of the spiral and fin 1260 may interleave as they spiral outward from the inner ring 1269. The inner ring 1269 may be configured as a separate core structure to which one end of the spiral configuration and/or fin 1260 are affixed. In another embodiment, the above-described configuration does not include the inner ring 1269.

[00140] In some embodiments, a heat transfer element 1322 can include an outer ring 1367 and a mesh (or other structure) fin 1360, as shown in FIG. 13. In such embodiments, the mesh fin 1360 can be coupled to a first portion of the outer ring 1367 and extend toward a second portion of the outer ring 1367 opposite the first portion. The mesh fin 1360 can be configured to bend to define a surface 1370 that can be coupled to the outer ring 1367. The mesh fin 1360 can form substantially parallel fins and extend to fill the area defined by the outer ring 1367. [00141] FIGS. 14A-14C schematically illustrate a compressor/expander device according to another embodiment. A compressor/expander device 1400 can include one or more pressure vessels (cylinders) 1420 having a first working chamber 1440 and a second working chamber 1441, an actuator 1421 connected to a piston 1426 via a piston rod 1427, and one or more heat transfer elements 1422 disposed within the pressure vessel 1420. More specifically, the heat transfer elements 1422 can include a heat transfer element 1423 disposed within the first working chamber 1440 and a heat transfer element 1424 disposed within the second working chamber 1441. The compressor/expander device 1400 can be used, for example, in a CAES system. The pressure vessel 1420 can include an inlet conduit 1428 and an outlet conduit 1429 in fluid communication with the first working chamber 1440 and an inlet conduit 1430 and a conduit 1431 in fluid communication with the second working chamber 1441. The first working chamber 1440 and the second working chamber 1441 can contain, at various time periods during a compression and/or expansion cycle, a quantity of the gas (e.g., air) and a quantity of the liquid (e.g., water) that can be communicated to and from the working chambers via the inlet/outlet conduits. Optionally, the pressure vessel 1420 can include one or more additional conduits in fluid communication with the first working chamber 1440 or the second working chamber 1441 specifically dedicated to communicating gas or liquid to or from the first and second working chambers.

[00142] The actuator 1421, the piston 1426, and the piston rod 1427 can be structurally and functionally similar to the actuator 221, the piston 226, and the piston rod 227 in FIG. 2 and can be actuated to compress and/or expand, for example, a gas. Thus, further details are not described with respect to FIG. 14A-14C and should be considered to be any suitable configuration described herein. The heat transfer element 1423 and 1424 can be used to facilitate the removal heat energy from the air within the first working chamber 1440 and the second working chamber 1441, respectively, by providing an increased amount of surface area that is in direct contact with the air being compressed.

[00143] The heat transfer elements 1422, shown with respect to FIGS. 14A-14C, include multiple plates 1432 that are coupled together in a stack. The plates 1432 can be metal, carbon fiber, nano-materials, and hybrid or composite materials (e.g. carbon polymer compounds). In some embodiments, the plates 1432 can be coupled to the piston 1426 such that the piston 1426 collapses the plates 1432 as the stroke progresses. For example, the plates 1432 can be coupled together with one or more linkages (not shown in FIGS. 14A-14C). The linkages can also be used to couple the plates 1432 to an interior wall of the pressure vessel 1420, and/or the piston 1426. The heat transfer element 1423 and the heat transfer element 1424 within the first working chamber 1440 and the second working chamber 1441, respectively, can be any length within the pressure vessel 1420. In some embodiments, for example, the heat transfer element 1422 can have a length or height that extends substantially along the length or height of the respective working chamber of the pressure vessel 1420. In other embodiments, for example, the heat transfer element 1422 can have a length or height that extends along only a portion of the length or height of the respective working chamber of the pressure vessel 1420.

[00144] In use, the compressor/expander device 1400 can be used to compress a gas, such as air. As shown in FIG. 14A, a first mass of gas at a first pressure can be introduced through the inlet conduit 1430 into the second working chamber 1441 of the pressure vessel 1420. Optionally, a volume of a relatively cool liquid (e.g., water) can be introduced through the inlet conduit 1430 or through a separate liquid inlet conduit (not shown). The actuator 1421 can be actuated to move the piston 1426 in the direction of the arrow A to compress the first mass of gas within the second working chamber 1441. In some embodiments, a combination of the piston moving in the direction of the arrow A and the liquid entering the second working chamber 1441 can compress the first mass of gas. As the piston 1426 moves from its position at bottom dead center (FIG. 14A) in the direction of the arrow A, the plates 1432 of the heat transfer element 1424 disposed within the second working chamber 1441 begin to collapse upon each other and the plates 1432 of the heat transfer element 1423 disposed within the first working chamber 1440 begin to separate, as shown in FIG. 14B. As the actuator 1421 continues to move the piston 1426 in the direction of arrow A to the top dead center position (i.e., the end of the stroke), the plates 1432 further collapse and form a relatively dense stack at the end of the compression cycle as shown in FIG. 14C.

[00145] During the compression cycle, heat energy generated during the process can be transferred from the gas to the heat transfer element 1424 as described above for previous embodiments. As the heat transfer element 1424 collapses upon itself during the compression cycle, the heat transfer element 1424 becomes denser and the distance between any given gas molecule and the heat transfer element 1424 becomes smaller, thus, facilitating heat transfer between the gas being compressed and the heat transfer element 1424. The first mass of gas at a second pressure, greater than the first pressure, can exit the second working chamber 1441 via the outlet conduit 1431. During and/or after the compression stroke, the liquid present in the second working chamber 1441 can quench the plates 1432 and remove the heat transferred to the plates 1432 during the gas compression. In this manner, the warmed liquid can exit the second working chamber 1441 via the outlet conduit 1431. In some embodiments, only a portion of the warmed liquid is discharged through the outlet conduit 1431. Optionally, the liquid can be discharged through a separate liquid outlet conduit (not shown). The compressor/expander device 1400 can be configured to perform a substantially similar process in the opposite direction to compress a volume of gas within the first working chamber 1440.

[00146] The linkage (not shown in FIGS. 14A-14C), can be any suitable linkage system, examples of which are described herein. The linkage can be moveably coupled to the plates 1432 and the piston 1426 and maintain each of the plates 1432 at a substantially equal distance from the adjacent plates throughout the stroke. Similarly stated, the linkage can be coupled to the stack of plates 1432 such that a uniform spacing exists between the plates 1432 throughout the stroke. For example, the spacing between the plates 1432 of the heat transfer element 1424 is substantially equal and the spacing between the plates 1432 of the heat transfer element 1423 is substantially equal as shown in FIG. 14A. As the actuator 1421 moves the piston 1426 in the direction of the arrow A, the plates 1432 of the heat transfer elements 1424 begin to collapse such that the spacing between the plates 1432 decreases equally and the plates 1432 of the heat transfer element 1423 begin to separate such that the spacing between the plates 1432 increases equally as shown in FIGS. 14B and 14C. In some embodiments, the linkage can be coupled to the stack of plates 1432 such that non-uniform spacing exists between the plates 1432 throughout the stroke. Moreover, the plates 1432 can be configured to collapse such that liquid quenches all or substantially all of the plates 1432 at the end of a compression stroke.

[00147] FIGS. 15A-15C schematically illustrate a compressor/expander device according to another embodiment. A compressor/expander device 1500 can include one or more pressure vessels (cylinders) 1520 having a first working chamber 1540 and a second working chamber 1541, an actuator 1521 connected to a piston 1526 via a piston rod 1527, and one or more heat transfer elements 1522 disposed within the pressure vessel 1520. More specifically, the heat transfer elements 1522 can include a heat transfer element 1523 disposed within the first working chamber 1540 and a heat transfer element 1524 disposed within the second working chamber 1541. The compressor/expander device 1500 can be used, for example, in a CAES system. The pressure vessel 1520 can include an inlet conduit 1528 and an outlet conduit 1529 in fluid communication with the first working chamber 1540 and an inlet conduit 1530 and an outlet conduit 1531 in fluid communication with the second working chamber 1541. The first working chamber 1540 and the second working chamber 1541 can contain, at various time periods during a compression and/or expansion cycle, a quantity of the gas (e.g., air) and a quantity of the liquid (e.g., water) that can be communicated to and from the working chambers via the inlet/outlet conduits. Optionally, the pressure vessel 1520 can include one or more additional conduits in fluid communication with the first working chamber 1540 or the second working chamber 1541 specifically dedicated to communicating gas or liquid to or from the first and second working chambers.

[00148] The actuator 1521, the piston 1526, and the piston rod 1527 can be structurally and functionally similar to the actuator 221, the piston 226, and the piston rod 227 in FIG. 2 and can be actuated to compress and/or expand, for example, a gas. Thus, further details are not described with respect to FIG. 15A-15C and should be considered to be any suitable configuration described herein. The heat transfer elements 1523 and 1524 can be used to remove heat energy from the gas within the first working chamber 1540 and the second working chamber 1541, respectively, by providing an increased amount of surface area that is in direct contact with the gas being compressed.

[00149] The heat transfer elements 1522, shown with respect to FIGS. 15A-15C, include multiple metal plates 1532 coupled together in a stack by a linkage system (not shown in FIGS. 15A-15C). The heat transfer elements 1522 can be of similar form and function as the heat transfer elements 1422 described with respect to FIGS. 14A-14C. Although the plates 1432 of the expansion/compression device 1400 extended the approximate length of the working chamber 1440 and 1441, respectively, the plates 1532 of the compressor/expander device 1500 extend for a portion of the working chamber 1540 and 1541, respectively. Similarly stated, the plates 1532 initially occupy less height within the respective working chamber than the plates 1432 of FIGS. 14A-14C. The linkage system can be configured to provide a distance and/or air gap between a surface of the piston 1526 and the closest plate 1532, as shown in FIGS. 15A-15C. The air gap between the piston 1526 and the closest plate 1532 can be configured to provide optimal conditions within the pressure vessel 1520, such as, for example, an optimal ratio of heat transfer potential to weight or an optimal ratio of heat transfer potential to flow loss potential. In this manner, the compression expansion device 1500 can perform a similar process of compression as the compressor/expander device 1400, going between the bottom dead center position (FIG. 15A), through an intermediate position (FIG. 15B), to the top dead center position (FIG. 15C). [00150] FIGS. 16A and 16B schematically illustrate a heat transfer element according to an embodiment. A heat transfer element 1622 can be included in, for example, a compressor/expander device (not shown in FIGS. 16A and 16B). In some embodiments, the compressor/expander device can include a pressure vessel and an actuator connected to a piston via a piston rod. The pressure vessel can define at least one working chamber in which the heat transfer element 1622 can be disposed. The compressor/expander device can be substantially similar to any compressor/expander device 100, 200, 300, 1400 described or referenced herein.

[00151] The heat transfer element 1622 can include multiple plates 1632 coupled together in a stack by multiple linkages 1650. As described above with respect to FIGS. 14A-14C and FIGS. 15A-15C, the plates 1632 can be coupled to a piston such that the piston collapses the plates 1632 as the stroke progresses (i.e., causing the spacing between plates 1632 to decrease). More specifically, at least a portion of the linkage 1650 can be used to couple the plates 1632 to the piston. The heat transfer element 1622 can be any length within the pressure vessel (not shown). In some embodiments, the heat transfer element 1622 can have a length or height that extends substantially along the length or height of the respective working chamber of the pressure vessel. In other embodiments, an air gap can exist between the piston and the bottom plate 1632 of the heat transfer element 1622. The air gap can be of any suitable size such as, for example, a size that can provide an optimal heat transfer potential to weight ratio.

[00152] In use, the compressor/expander device can be used to compress and/or expand a gas, such as air. A mass of gas having a first pressure and a first temperature can be introduced into a working chamber of a pressure vessel using any suitable method described herein. Optionally, a volume of a relatively cool liquid (e.g., water) can also be introduced into the pressure vessel. A piston can be moved within the pressure vessel in a direction for compression. As the piston moves the liquid and the gas in the direction of compression, it also drives the linkage 1650. The plates 1632 of the heat transfer element 1622 disposed within the working chamber begin to collapse upon each other as the piston is moved in the direction of compression. Similarly, an expanding compressed gas can be communicated to a working chamber of a pressure vessel. The expanding compressed gas can move the piston in a direction for expansion causing the plates 1632 of the heat transfer element 1622 to separate in a uniform fashion as controlled by the linkage 1650. [00153] The linkage 1650 is configured to compress the plates 1632 in a helical motion, as shown by the arrows B in FIG. 16B. Similarly stated, the linkage 1650 is configured to create a rotational motion of each plate 1632 as the heat transfer element 1622 is collapsed. In some embodiments, the linkage 1650 can be a rigid member with a given shape configured to slide against the walls of the working chamber. As the piston moves the linkage 1650 in the direction of compression, the linkage 1650 can pivot at a top and bottom pivot point. The pivoting motion of the linkage 1650 can cause the plates 1632 to compress in the helical motion. In other embodiments, the linkage 1650 can be coupled to the piston and the piston can rotate within the pressure vessel, thereby rotating the plates 1632 as they are collapsed. The linkage 1650 can be configured to maintain each of the plates 1632 at a substantially equal distance from the adjacent plates throughout the stroke. Similarly stated, the linkage 1650 can be coupled to the stack of plates 1632 such that a uniform spacing exists between the plates 1632 throughout a compression and/or expansion stroke. For example, as the piston moves the linkage 1650, the plates 1632 begin to collapse in a uniform process and equally spaced throughout the compression and/or expansion cycle.

[00154] During the compression cycle, heat energy generated during the process can be transferred from the gas (e.g., air) to the plates 1632 of the heat transfer element 1622 via convection and/or conductive heat transfer as the air flows over, through, and/or around the plates 1632. As the piston causes the plates 1632 to collapse upon each other during the compression cycle, the heat transfer element 1622 becomes denser and the distance between any given gas molecule and the heat transfer element 1622 becomes smaller, thus, facilitating heat transfer between the gas being compressed and the heat transfer element 1622. At the end of the compression cycle, the gas, being compressed to a second pressure, can exit the working chamber at a second temperature substantially similar to the first temperature. Similarly stated, the use and configuration of the heat transfer element 1622 can cause the plates 1632 to absorb the heat produced by the compression of the gas, thereby allowing for a substantially isothermal compression of the gas. During and/or after the compression stroke, the liquid present in the working chamber can quench the plates 1632 and remove the heat transferred to the plates 1632 during the gas compression. In this manner, the relatively warm liquid can exit the working chamber and the process can repeat. Similarly, during an expansion cycle, heat energy can be transferred to an expanding compressed gas to allow for substantially isothermal expansion. In some embodiments, the heat transfer between the gas and the heat transfer element 1622 can be controlled to allow for a controlled, predetermined temperature change of the gas. For example, the size, shape and configuration of the heat transfer element 1622 and/or the volume of liquid present in the working chamber can be configured to allow for a 5°, 10°, 15°, 20° or 25° temperature change of the gas during a compression and/or expansion cycle.

[00155] Referring now to FIG. 16C, the plates 1632 included in the heat transfer element 1622 can include, for example, a wire mesh. The wire mesh can be any suitable configuration such as to provide optimal heat transfer. For example, in some embodiments, the wire mesh can be a woven wire mesh material. In some embodiments, the woven wire mesh material can be [80 Square Mesh Market Grade (Stainless steel), 24x1 10 single plain weave (Stainless steel), or 10 Square Mesh (0.047" wire diameter, Stainless Steel)] available from Gerard Daniel Worldwide located in Hanover, PA or from W.S. Tyler Screening Group located in St. Catharines, ON. In such embodiments, the size of the openings defined by the woven wires included in the wire mesh can be any size or shape. For example, the size of the openings can be large enough that the air can flow through the openings, increasing the surface area of the wire mesh plate 1632 that contacts the gas, thus, increasing the heat transfer efficiency. Additionally, the diameter of the wire used in the wire mesh can any suitable diameter. In some embodiments, the diameter of the wires used in the mesh can vary, thereby producing a specific heat transfer through the wire mesh plate 1632. The wire mesh plate 1632 can include an outer ring over which the wire mesh can wrap. The wire mesh plate 1632 can therefore be drawn tight around outer ring and reduce potential deflection of the plate 1632 during compression. The wire mesh can be made from any suitable material such as, for example, copper, aluminum, stainless steel, other pure metals or metal alloys, carbon fiber, nano- materials, or hybrid or composite materials (e.g. carbon polymer compounds). In some embodiments, the wire mesh material can be a welded wire mesh such as, for example, 2" x 2" stainless steel mesh having 0.047" wire diameter available from Gerard Daniel Worldwide.

[00156] FIGS. 17A and 17B schematically illustrate a compressor/expander device according to another embodiment. The compressor/expander device 1700 can include a pressure vessel 1720 and an actuator 1721 connected to a piston 1726 via a piston rod 1727. The pressure vessel can define at least one working chamber 1740 in which at least one heat transfer element 1722 can be disposed. The compressor/expander device 1700 can be substantially similar to any of the compressor/expander devices described or referenced herein.

[00157] The heat transfer element 1722 can include multiple plates 1732 coupled together in a stack by multiple linkages 1750. As described above with respect to FIGS. 14A-14C, the plates 1732 can be coupled to the piston 1726 such that the piston 1726 collapses the plates 1732 as the stroke progresses (i.e., causing the spacing between the plates 1732 to decrease). More specifically, at least a portion of the linkage 1750 can be used to couple the plates 1732 to the piston 1726. The heat transfer element 1722 can be any length or height within the working chamber 1740. In some embodiments, for example, the heat transfer element 1722 can have a length or height that extends substantially along the length or height of the respective working chamber 1740, as shown in FIGS. 17A and 17B. In other embodiments, an air gap can defined between the piston 1726 and the bottom plate 1732 of the heat transfer element 1722. The air gap can be of any suitable size such as, for example, a size that can provide an optimal heat transfer potential to weight ratio. [00158] In use, the compressor/expander device 1700 can be used to compress a gas, such as air. A first mass of gas having a first pressure and a first temperature can be introduced into a working chamber 1740 of the pressure vessel 1720 via an inlet conduit 1728. Optionally, a volume of a relatively cool liquid (e.g., water) can also be introduced into the pressure vessel 1720 via the inlet conduit 1728 or via a separate conduit specifically dedicated to liquids. The piston 1726 can be moved by the actuator 1721 within the pressure vessel 1720 in a direction of the arrow C to compress the first mass of gas within the working chamber 1740. As the piston 1726 moves from its first position (FIG. 17A) in the direction of the arrow C to compress the first mass of gas, it also moves the linkage 1750 such that the plates 1732 of the heat transfer element 1722 begin to collapse upon each other, as shown in FIG. 17B. [00159] The linkage 1750 can be configured to collapse and expand utilizing a scissor-style mechanism. More specifically, the linkage 1750 can include a plurality of linkage arms 1751 and linkage nodes 1752. The linkage arms 1751 can be rigid members coupled to the linkage nodes 1752 for pivoting motion. The linkage nodes 1752 can be any suitable node configured to allow pivoting motion. For example, a pair of linkage arms 1751 can be adjacently coupled to the linkage node 1752 via a pivot pin that can be inserted into a receiving opening defined by the linkage arms 17651. As the piston 1726 moves the linkage 1750 in the direction of arrow C, the linkage arms 1751 begin to pivot at the linkage nodes 1752 causing the linkage 1750 to collapse. As the linkage 1750 collapses, the plates 1732 also begin to collapse and the space between adjacent plates 1732 is reduced. Similar to the heat transfer element 1622 described with respect to FIGS. 16A and 16B, the plates 1732 are coupled to the linkage 1750 such that as the linkage 1750 collapses, the space between adjacent plates 1732 is uniformly reduced (i.e., there is consistent spacing between the plates 1732 at any time of the compression cycle).

[00160] During the compression cycle, heat energy generated during the process can be transferred from the gas to the plates 1732 of the heat transfer element 1722 via convection and/or conduction heat transfer as the gas flows over, through, and/or around the plates 1732. As the plates 1732 collapse upon each other during the compression cycle, the heat transfer element 1722 becomes denser and the distance between any given gas molecule and the heat transfer element 1722 becomes smaller, thus, facilitating heat transfer between the gas being compressed and the heat transfer element 1722. At the end of the compression cycle, the first mass of gas is compressed to a second pressure, greater than the first pressure, and can exit the working chamber 1740 via the outlet conduit 1730 at a second temperature substantially similar to the first temperature. Similarly stated, the use and configuration of the heat transfer element 1722 can cause the plates 1732 to absorb the heat energy produced by the compression of the gas, thereby allowing for a substantially isothermal compression of the gas. During and/or after the compression stroke, the liquid present in the working chamber can quench the plates 1732 and absorb the heat energy transferred to the plates 1732 during the gas compression. In this manner, the warmed liquid can exit the working chamber and the process can repeat.

[00161] Referring now to FIGS. 18A-19B, the plates 1732 of the heat transfer element 1722 can include a plurality of first plates 1733 (FIG. 18A) having a first diameter Di (FIG. 18B) that is substantially similar to the diameter of the cylinder 1720 and a plurality of second plates 1736 (FIG. l 9A) having a second diameter D ₂ (FIG. 19B), smaller than the first diameter Di. The first plate 1733 can define an aperture 1734 in the center of the plate 1733 and a set of slits 1735. Similarly, the second plate 1736 can define a set of slits 1737. The set of slits 1735 in the first plate 1733 and the set of slits 1737 in the second plate 1736 provide an opening through which the linkage 1750 is disposed. [00162] Referring back to FIGS. 17A and 17B, the plurality of first plates 1733 and the plurality of second plates 1736 can be arranged in an alternating pattern (i.e., every first plate 1733 is adjacent to the second plate 1733. The slits 1735 and 1737, respectively, can be any suitable size, shape, or configuration as to provide the necessary clearance for the linkage 1750 to operate. In use, for example, in the compression cycle described with respect to FIGS. 17A and 17B, the gas can flow across the surface of the first plate 1733 and through the aperture 1735. Similarly, the gas can flow across the surface of the second plate 1736. As described above, the first diameter Di of the first plate 1733 is substantially similar to the diameter of the cylinder. Therefore, as the gas contacts the surface of the first plate 1733, the gas is forced to flow through the aperture 1734. The second plate 1736, having the second diameter D2 smaller than the first diameter Di, creates an annulus between the edge of the second plate 1736 and the walls of the cylinder 1720. Therefore, as the gas passes through the aperture 1734 defined by the first plate 1733, the gas can contact the surface of the second plate 1736 and flow along the surface and through the annulus defined by the second plate 1736 and the cylinder 1720. The arrangement of the first plate 1733, the second plate 1736, and the cylinder 1720 creates a gas flow path with a "figure 8" pattern. In this manner, contact between the gas and the surface areas of the first plate 1733 and the second plate 1736 is maximized, thus providing enhanced heat transfer.

[00163] While the aperture 1734 is described as being at the center of the first plate 1733, the aperture 1734 can be disposed at any location on the first plate 1733. Additionally, in some embodiments, the second plate 1736 can include an aperture. The first plate 1733 and/or second plate 1736 can define any number of apertures, openings, and/or extrusions configured to manipulate the flow of gas within the working chamber 1740. The first plate 1733 and the second plate 1736 can also include any suitable coating, texture, and/or fin arrangement configured to manipulate the flow and or heat transfer characteristics. For example, in some embodiments, the first plate 1733 and the second plate 1736 can include dimples similar to the surface of a golf ball. The dimples can be configured to create a turbulent flow of the gas being compressed and increase the surface area of the plates, thus increasing the heat transfer potential. [00164] FIG. 20 is a graph illustrating the change in bulk air temperature versus stroke time at different simulated ("Model") and example experimental conditions during a 2.5x volume reduction (e.g., pressure ratio). In the illustrated examples, the high-pressure water pump ("HPWP") fin test included a laboratory-scale device that included a 21" inner diameter pressure vessel with a 16" stroke. The "air gap" distance denotes the starting level of a volume of water beneath a set of fins included in a heat transfer element at the beginning of the stroke. The "WW" is a spiral woven wire architecture similar those described herein, with respect to FIGS. 3B and 4B, while the "Al Ex" is an aluminum extrusion fin architecture provided for benchmarking and comparison purposes. The "WW" fins are spaced with diagonal spacing wires (approx. 15 degrees), similar to the woven wire mesh fin 660, described with respect to FIG. 6. The "WW" fins define approximately a 13% volume fraction (0.67mm thick, 2mm spacing, 50% porosity), while the Al Ex fins define approximately a 20% volume fraction (lmm thick, 3mm gap, clearance spacing due to geometric constraints). The "Model" lines represent predictions for the same geometries described above using a proprietary computer modeling system.

[00165] As shown in FIG. 20, the experimental data confirms the computer simulations for the given parameters described above. Furthermore, the experimental data and computer simulations indicate the pressure vessel configuration including the woven wire fin design with the 5" air gap (represented in FIG. 20 as the diamond shape points and the dashed and dotted line, respectively) result in the lowest change in bulk temperature (i.e., air temperature). In this manner, the experimental data confirms that a heat transfer element including a woven wire mesh fin transfers heat at a faster rate than extruded aluminum fins.

[00166] As described above, the extrusion manufacturing process limits the minimum thickness of fin elements in a thermal capacitor. For example, extrusion fin element thickness is generally limited to approximately 0.5mm; however, smaller thicknesses such as approximately 0.05mm are more desirable given the fundamental principles of heat transfer. As further described below, it can be shown that a corrugated capacitor configuration such as that depicted in FIG. 12 offers a significant improvement in heat transfer capability, enabling substantial improvements in the performance of a CAES system incorporating the heat transfer device, including improvements in roundtrip AC-AC efficiency, electrical power, and storage energy density. [00167] The heat transfer to a fluid from a capacitor subsystem is defined by Equation (1) below, where Q is the heat flow rate, h is the heat transfer coefficient, A is the heat transfer surface area, T _c is the capacitor temperature and Tf is the fluid temperature.

Equation (1) : Q = hA T _c — T )

[00168] The heat transfer surface area density, the amount of heat transfer area in a given chamber volume, can be readily computed using Equation (2), where t is the thickness of the capacitor material, V is the chamber volume, and CVF is the "capacitor volume fraction," defined as the ratio of capacitor volume to chamber volume.

A 2 (CVF)

Equation (2) : — =

[00169] As such, for the same capacitor volume fraction, a heat wheel-like capacitor ("hw") could have approximately 10 times the heat transfer surface area density as an extrusion-based capacitor ("ex") given the aforementioned material thickness limitations for each construction method.

Equation (3) : « 10

r/v) _ex ^thw

[00170] Moreover, the heat transfer coefficient for a heat wheel-based capacitor will be larger than for an extrusion-based system. The heat transfer coefficient is defined in terms of the non-dimension Nusselt number, Nu, the thermal conductivity of the fluid, k, and the hydraulic diameter of the capacitor, Z¾. See Equation (4). In the case of fully developed laminar fluid flow, and uniform capacitor temperature, the Nusselt numbers for each type of capacitor can be assumed to be constant and defined by the cross sectional profiles of their channels. The extrusion-based channels are approximated as infinite parallel plates with Nusselt equal to 7.54, and the sinusoidal channels of the heat wheel capacitors are considered to be equilateral triangles with a Nusselt number of 2.49.

Nu k

Equation (4) : h = —— [00171] The hydraulic diameter for each channel type are given by Equations (5) and (6), where g is the spacing between the infinite plates and the interior height of the equilateral triangles. The calculation of the channel spacing in each case can be determined by Equations (7) and (8), below, assuming a certain capacitor volume fraction and material thickness.

2t(l - CVF)

Equation (5): Dj{ = 2g = ο~γρ

2 2 (3t - 2tCVF\

Equation (6): 9 CVF

Equation (7): CVF _ex =

t + g

3t

Equation (8): CVF _hw =

2t + g

[00172] Using 0.5mm and 0.05mm for the extrusion and heat wheel-based thicknesses, respectively, and a 0.2 CVF, the hydraulic diameters in each case are calculated to be 4mm and 0.43mm. As such, it can be shown with these assumptions and Equation (9) that the heat transfer coefficient for the heat wheel-type capacitor is approximately three times larger than that of the extrusion-comprised system. h _hw 4.98t _ex (l— CVF)

Equation (9) :

h _ex 5.03(3t _ftw - 2tCVF)

[00173] Finally, combining the results from Equation (3) and Equation (9), it is shown that for a given temperature differential, the heat transfer rate for the heat wheel capacitors can in this example is nearly thirty times larger than the extrusion-based capacitors.

Equation (10) : —— = « 30

[00174] However, the pressure drops across the capacitors in this example are also substantively different. For channel flow, the pressure loss is given by Equation (1 1), where / is the non-dimensional Darcy friction factor, L is the channel length, p is the fluid density, and v is the fluid velocity.

Equation (11) : ΔΡ = f

[00175] As shown in Equations (12) and (13), for fully developed laminar channel flow, the Darcy friction factor in each case depends on the non-dimensional Reynolds number, given by Re = ^ΣΕ ^ where μ is the dynamic viscosity of the fluid.

Equation (12) : f _ex = —

Re

53.2

Equation (13) : f _hw

~Re

[00176] In this example, the pressure drop for the heat wheel-based capacitor is substantially larger than that of the extrusion-comprised capacitor, as given below in Equation (15). Nonetheless, an assessment of the magnitude the pressure drop is required, as it may be inconsequential in comparison to the average pressure of the CAES system. Equation « 47

[00177] The figures described below illustrate test results obtained using a model that predicts the thermodynamic performance of CAES systems having thermal capacitors within their compression/expansion cylinders. A dedicated test setup was also used to investigate the performance of thermal capacitors and to validate the accuracy of the aforementioned model. The model and test rig are capable of examining capacitor performance over a range of conditions including stroke time, and pressure ratio. The model and test rig exhibit good correlation, providing confidence in the absolute and relative performance of different capacitor designs. [00178] FIGS. 21A and 21 depict the pressure profiles from example compression and expansion strokes, respectively. In these examples, compared to the measurements from the test setup, the model over-predicts the compression work and ending temperature and under- predicts the expansion work and ending temperature. [00179] The performance of the an optimized corrugated capacitor design, defined by element thickness of 0.30mm, pleat height of 2.9mm, and pleat width of 7.6mm, has been verified. A subset of analysis is presented below in which simulation results are compared to test rig measurements for a given pressure ratio and a range of stroke speeds. FIG. 22A presents the percent difference in predicted work between the model and the test setup, as well as the difference in predicted ending temperature, for compression cycles that range in stroke time by a factor of 10. FIG. 22B gives the same comparison for a set of expansion cycles. As shown, the model demonstrates solid correlation with the test rig for these series of comparisons.

[00180] For commercial scale CAES systems, the performance benefits of using a corrugated-type capacitor over an extrusion-based design can be substantial. Using the model, the optimized corrugated capacitor, specified above, is compared to an extrusion-type capacitor each residing in the same size compression/expansion chamber. Each capacitor is assumed to be constructed of the same material (aluminum), have the same capacitor volume fraction (20%) and height, and have similar channel spacing (approximately 4mm). FIGS. 23A and 23B show the work difference (percentage between pleated and extrusion geometries) and ending temperature difference (pleated minus extrusion) for a range of compression and expansion stroke speeds, respectively. For the shortest stroke times, the corrugated design outperforms the extrusion capacitor substantially, demonstrating over 6% less compression work and over 5% more expansion work. Moreover, at the fastest stroke speed, the air leaving the compression cylinder at storage pressure is an estimated 50° C cooler for the pleated design, offering a substantial advantage for the energy storage density of the CAES system.

[00181] While various embodiments have been described above, it should be understood that they have been presented by way of example only, and not limitation. Where methods and steps described above indicate certain events occurring in certain order, those of ordinary skill in the art having the benefit of this disclosure would recognize that the ordering of certain steps may be modified and that such modifications are in accordance with the given variations. Additionally, certain of the steps may be performed concurrently in a parallel process when possible, as well as performed sequentially as described above. The embodiments have been particularly shown and described, but it will be understood that various changes in form and details may be made.

[00182] For example, although various embodiments have been described as having particular features and/or combinations of components, other embodiments are possible having any combination or sub-combination of any features and/or components from any of the embodiments described herein. Although certain embodiments of a heat transfer element are described with respect to a particular embodiment of a compressor/expander device, it should be understood that the various embodiments of a heat transfer element can be used in any of the various embodiments of a compression and/or expansion device described herein and in other embodiments of a compression and/or expansion device not described herein.

[00183] Additionally, although some embodiments of a compression and/or expansion device include a heat transfer element disposed at a particular location within the pressure vessel, it should be understood that a heat transfer element could be disposed at different locations than those illustrated and described. The specific configurations of the various components of a compression and/or expansion device can also be varied. For example, the size and specific shape of the various components can be different from the embodiments shown, while still providing the functions as described herein.

[00184] What is claimed is: