Solid Thermodynamic Cycle

Abstract

A method for performing a thermodynamic cycle on an elastocaloric material is provided. [Solution] The method includes increasing a stress applied to the elastocaloric material until a desired stress value is reached or the elastocaloric material transitions from austenite to martensite form; decreasing a temperature of the elastocaloric material from a high temperature to a low temperature, decreasing the stress of the elastocaloric material to maintain a corresponding volume fraction of the martensite form constant during the temperature decrease; decreasing the stress of the elastocaloric material until a minimum stress value is reached or the elastocaloric material transitions from martensite to austenite form; and increasing a temperature of the elastocaloric material from a low temperature to a high temperature, increasing the stress of the elastocaloric material to maintain a corresponding volume fraction of the martensite form constant during the temperature increase.

Description

[Technical field]

[0001] The present disclosure relates to thermodynamic cycles, and more particularly to thermodynamic cycles for elastocaloric materials. [Background technology]

[0002] Recent research on the EC (elastocaloric) effect has demonstrated the potential of EC as a solid-state alternative to conventional vapor compression refrigeration and heat pumping technologies. The EC cycle utilizes the superelastic behavior of SMAs (shape memory alloys), which facilitates heat absorption from a cold source and heat dissipation to a hotter side by uniaxial loading and unloading. Thermodynamic cycles for elastocaloric materials were previously modeled using conventional gas cycles. The inverse Brayton cycle and the inverse Stirling cycle are described in the literature as the best representatives of thermodynamic cycles for elastocaloric materials. According to gas cycle theory, it is known that the COP (coefficient of performance) of the inverse Stirling cycle and the Carnot cycle (in the thermodynamic limit) are identical since both use isothermal heat dissipation and endothermic processes. Therefore, elastocaloric materials to maximize the COP are used to implement the inverse Stirling cycle whenever possible. In Figure 1, the main processes in the Stirling cycle are shown. As shown in the figure, heat dissipation and endothermic processes are isothermal processes, and the heat recovery process of preheating and precooling the SMA is an isochoric or constant volume material process.

[0003] However, elastocaloric thermodynamic cycles have been modeled assuming a complete phase change from austenite to martensite. In reality, due to temperature or stress limitations, elastocaloric materials may only partially transform.

[0004] 2A-2D show graphs of stress vs. temperature, stress vs. strain, specific entropy vs. temperature, and specific entropy vs. martensite volume, respectively, when a reverse Stirling cycle is performed on an elastocaloric material. As shown in FIG. 2D, during the heat recovery process of 2-3 (material cooling), the martensite volume increases, and during the process of 4-1 (material heating), the martensite volume decreases. Such an increase or decrease in martensite volume is greater the higher the temperature. This is because the change in martensite volume during the heat dissipation process is limited due to the working stress limit. Also, in FIG. 2B, the strains seen in 2-3 (material cooling) remain constant due to thermal expansion, as well as the decrease in elastic strain and the increase in phase change strain with the martensite volume.

[0005] However, the amount of heat release is related to the martensite volume, so its increase causes further heat release. A real heat recovery system requires heating and heat release, but in this case the heat release is due to an imbalance in the underlying process that cannot be controlled by the physical design. The same is true for the heat recovery process. This means that the heat recovery equipment has to handle high heat loads. Furthermore, the change in martensite volume during heat recovery is larger with increasing operating temperature delta. This is because the increase in martensite volume for heat release is countered by the working pressure. Summary of the Invention [Problem to be solved by the invention]

[0006] In view of the above, therefore, there is a need for a system and method for maintaining a constant martensite volume during a heat recovery process and reducing losses that occur due to an increase in martensite volume in the heat recovery process. [Means for solving the problem]

[0007] According to the present invention, there is provided a method of performing a thermodynamic cycle on an elastocaloric material as claimed in the accompanying claims, comprising increasing a stress applied to the elastocaloric material until a desired stress value is reached or the elastocaloric material transitions from austenite to martensite form, decreasing a temperature of the elastocaloric material from a high temperature to a low temperature, decreasing the stress of the elastocaloric material to maintain a corresponding volume fraction of the martensite form constant during the temperature decrease, decreasing the stress of the elastocaloric material until a minimum stress value is reached or the elastocaloric material transitions from martensite to austenite form, and increasing a temperature of the elastocaloric material from a low temperature to a high temperature, increasing the stress of the elastocaloric material to maintain a corresponding volume fraction of the martensite form constant during the temperature increase.

[0008] In one embodiment of the present invention, increasing the stress of the elastocaloric material to a desired stress value corresponds to an isothermal heat dissipation process, and decreasing the stress corresponds to an isothermal heat absorption process.

[0009] In one embodiment of the present invention, maintaining the volume fraction of martensite form constant during a temperature decrease by decreasing stress corresponds to a polytropic temperature decrease process, and maintaining the volume fraction of martensite form constant during a temperature increase by increasing stress in an elastocaloric material corresponds to a polytropic temperature increase process.

[0010] In one embodiment of the present invention, the stress change during the polytropic temperature ramp-up and ramp-down process is calculated using the following formula:

number

[0011] In one embodiment of the present invention, the stress change is directly proportional to the temperature change and entropy difference, and inversely proportional to the material stiffness and material transformation strain.

[0012] In one embodiment of the present invention, by maintaining the martensite volume constant during the polytropic temperature ramp-up and ramp-down process, the overall work input of the thermodynamic cycle is reduced and the COP is increased.

[0013] The present invention discloses a method for implementing a thermodynamic cycle in which the release / absorption of latent heat during heat recovery is eliminated by maintaining a constant martensite volume during the heat recovery process, thereby increasing the overall cycle efficiency while reducing the work input. The novel thermodynamic cycle is specific to solid-state phase change and improves the part-load efficiency of elastocaloric materials by 25% over the reverse Stirling cycle under identical conditions by varying stress with temperature during the heat recovery process. The novel thermodynamic cycle increases the efficiency of elastocaloric technologies used for heating or cooling applications without increasing system costs or parasitic loads, thereby increasing the commercial attractiveness of SMAs. Additionally, the elimination of unnecessary energy release / absorption reduces material hysteresis, resulting in increased COP and reduced parasitic losses.

[0014] In another aspect of the present invention, a heat pump system is provided that employs a method for implementing a thermodynamic cycle.

[0015] In yet another aspect of the present invention, a refrigeration system employing a method for implementing a thermodynamic cycle is provided.

[0016] In yet another aspect of the invention, a system is provided for performing a thermodynamic cycle on an elastocaloric material, the system comprising: an isothermal heat release module that increases a stress applied to the elastocaloric material until a desired stress value is reached or the elastocaloric material transitions from austenite to martensite form, a polytropic temperature reduction module that reduces the temperature of the elastocaloric material from a high temperature to a low temperature and reduces the stress of the elastocaloric material to maintain a corresponding volume fraction of the martensite form constant during the temperature reduction, an isothermal heat absorption module that reduces the stress of the elastocaloric material until a minimum stress value is reached or the elastocaloric material transitions from martensite to austenite form, and a polytropic temperature increase module that increases the temperature of the elastocaloric material from a low temperature to a high temperature and increases the stress of the elastocaloric material to maintain a corresponding volume fraction of the martensite form constant during the temperature increase.

[0017] The invention will be more clearly understood from the following description of an embodiment, given by way of example only, with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0018] [Figure 1] 1 shows a conventional reverse Stirling cycle. [Figure 2A] 1 shows a graph of stress versus temperature when a reverse Stirling cycle is performed on an elastocaloric material. [Figure 2B] 1 shows a graph of stress versus strain when a reverse Stirling cycle is performed on an elastocaloric material. [Figure 2C] 1 shows a graph of specific entropy versus temperature when a reverse Stirling cycle is performed on an elastocaloric material. [Figure 2D] 1 shows a graph of specific entropy versus martensite volume when a reverse Stirling cycle is performed on an elastocaloric material. [Diagram 3] 1 illustrates a novel thermodynamic cycle and corresponding thermodynamic table for an elastocaloric material, according to an embodiment of the present invention; [Figure 4A] 4 shows a graph of stress versus temperature when the thermodynamic cycle of FIG. 3 is applied to an elastocaloric material. [Figure 4B] 4 shows a graph of the relationship between stress and strain when the thermodynamic cycle of FIG. 3 is applied to an elastocaloric material. [Figure 4C] 4 shows a graph of specific entropy versus temperature when the thermodynamic cycle of FIG. 3 is applied to an elastocaloric material. [Figure 4D] 4 shows a graph of the relationship between specific entropy and martensite volume when the thermodynamic cycle of FIG. 3 is applied to an elastocaloric material. [Figure 4E] Tables 1 and 2 are provided to compare various parameters of the reverse Stirling cycle and the thermodynamic cycle of FIG. [Diagram 5] 1 shows a COP-stress graph for an isochoric cycle, i.e., a reverse Stirling cycle. [Figure 6] 4 shows a COP-stress graph for an isophase cycle, i.e., the thermodynamic cycle of FIG. 3. [Figure 7] 4 shows the "tail" of the stress-strain curve of the SMA material for the reverse Stirling cycle and the thermodynamic cycle of FIG. [Figure 8] 1 illustrates a physical implementation of a thermodynamic cycle in a hydraulic system via a pressure regulator, in accordance with an embodiment of the present invention; [Figure 9] 4 shows a flow chart of a method for implementing the thermodynamic cycle of FIG. 3. [Figure 10] FIG. 4 shows a block diagram of a system for implementing the thermodynamic cycle of FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0019] FIG. 3 illustrates a novel thermodynamic cycle 300 and corresponding thermodynamic table 302 for an elastocaloric material according to one embodiment of the present invention.

[0020] Thermodynamic cycle 300 includes a sequence of four thermodynamic processes 4-1, 1-2, 2-3, and 3-4, which correspond to the transitions between states 1, 2, 3, and 4 of the elastocaloric material. Thermodynamic cycle 300 was modeled assuming a complete phase change from austenite to martensite. However, in reality, due to temperature or stress limitations, elastocaloric materials may only undergo a partial phase transformation (approximately 90%). It will be apparent to one skilled in the art that thermodynamic cycle 300 can be applied to other caloric materials if they exhibit hysteresis.

[0021] Thermodynamic cycle 300 uses an isothermal heat release process (process 1-2) and an isothermal heat absorption process (process 3-4) similar to the reverse Stirling cycle. However, instead of the isochoric heat recovery process of process 2-3, a constant volume martensite process is used. Thermodynamic cycle 300 may also be referred to as an isophase cycle since the volume fraction of martensite in process 2-3 is constant. By adjusting the stress applied to the material in the heat recovery process of the cycle, the martensite volume is constant and the material is heated / cooled between maximum and minimum temperatures. Note that by adjusting the stress in both processes 2-3 and 4-1, the martensite volume and austenite volume are constant.

[0022] The first thermodynamic process (process number 4-1) is when the temperature of the elastocaloric material is reduced to a low temperature T C From high temperature T H The first thermodynamic process involves a polytropic temperature rise process in which the temperature of the elastocaloric material rises to T C The fourth state starts when the temperature is T H During the first process, the elastocaloric material contains approximately 90% austenite and 10% martensite. During the first process (4-1), the stress of the elastocaloric material is increased to maintain a constant martensite volume at a given temperature. As described below, the stress increase in process (4-1) can be estimated based on equation (1).

[0023] The second thermodynamic process (Process No. 1-2) involves an isothermal heat release process where the applied stress to the elastocaloric material is increased. The second thermodynamic process starts at a first state and ends at a second state when the applied stress reaches a desired value, i.e., the maximum stress value or when ξ=1. In the second process, the elastocaloric material transforms from austenite to martensite form, where ξ is the volume fraction of martensite. When ξ=0, the material is fully austenitic and when ξ=1, the material is fully martensite.

[0024] The third thermodynamic process (process number 2-3) is when the temperature of the elastocaloric material increases to a high temperature T H From low temperature T C The third thermodynamic process involves a polytropic temperature drop process in which the temperature of an elastocaloric material drops to T H Starting at the second state when , the temperature of the elastocaloric material rises to T C A third state is reached when: In the third process, the elastocaloric material remains in the martensite form; During the first process (4-1), the stress of the elastocaloric material is reduced and may maintain a constant martensite volume at a given temperature; As described below, the stress reduction in process (4-1) may be estimated based on equation (1).

[0025] The fourth thermodynamic process (Process No. 3-4) involves an isothermal endothermic process in which the applied stress to the elastocaloric material is reduced. The fourth thermodynamic process begins at the third state and ends at the fourth state when the applied stress is at the lowest stress value or ξ=0. In the fourth process, the elastocaloric material transforms from martensite to austenite form.

[0026] The ideal change in stress required in processes 2-3 and 4-1 can be calculated using the following formula:

[0027]

number

[0028] As shown in equation (1), the stress change is directly proportional to the temperature change between the phases and the entropy difference between the phases, and inversely proportional to the material stiffness and material transformation strain. During processes 4-1 and 2-3, only the stress and temperature are changed, while all other parameters should be fixed for the material. However, thermal expansion and transformation strain can affect the volume change required to change the stress by a certain amount. In general, if all are increased, a larger stress change is required to keep the martensite volume constant.

[0029] Additionally, a correction may be made by the designer to not include the amount of latent heat to the heat recovery system that is adjusted to maintain the heat recovery temperature.

[0030] 4A-4D show graphs of stress vs. temperature, stress vs. strain, specific entropy vs. temperature, and specific entropy vs. martensite volume, respectively, when thermodynamic cycle 300 is performed for a low temperature space heating application using an elastocaloric material.

[0031] In Figure 4D, the constant martensite volume of the elastocaloric material in processes 2-3 and 4-1 is shown compared to the variable martensite volume of the elastocaloric material in processes 2-3 and 4-1 of the reverse Stirling cycle (see Figure 2D). It can be seen that the martensite volume is maintained in the heat recovery processes 2-3 and 4-1 when compared to the reverse Stirling cycle.

[0032] In Fig. 4B, the stress-strain relationship of the elastocaloric material during the thermodynamic cycle 300 is shown. In Fig. 4B, the stress and volume increase and decrease during these processes with respect to the same maximum applied stress. It was found that the material stress at the start of the heat release process (process 1-2) is 31 MPa lower than the reverse Stirling cycle, and at the start of the heat absorption process (process 3-4) is 154 MPa higher.

[0033] The effect of keeping the martensite / austenite volume constant can be seen in the stress-strain diagram, where the change in stress in the heat recovery process results in a change in strain, reducing the overall closure range and therefore the work input. The ideal work input for a typical thermodynamic cycle can be measured by determining the closure range of the pressure-volume diagram, in this case the pressure-strain diagram. Comparing the stress-strain graph in FIG. 4B with FIG. 2B, it can be seen that the work input is reduced in the thermodynamic cycle 300. In FIG. 4E, Tables 1 and 2 are shown to compare various parameters of the reverse Stirling cycle and the thermodynamic cycle 300 (also referred to as constant volume martensite heat recovery cycle and isophase cycle) at various temperature conditions. Compared to the reverse Stirling cycle, it can be seen that the thermodynamic cycle 300 has a higher theoretical SCOP (seasonal coefficient of performance). The SCOP limit value of the thermodynamic cycle 300 is calculated to be 8.93, which is 26% higher than the reverse Stirling cycle. Also, TEWI (Total Equivalent Warming Factor) may be used to calculate the CO2 contribution of an installed system over its lifetime. The TEWI of an elastocaloric material may be calculated based on the following formula:

[0034]

number

[0035] In Figure 5, a COP-stress graph is shown for an isochoric cycle, i.e., a reversed Stirling cycle, and in Figure 6, a COP-stress graph is shown for an isophasic cycle, i.e., thermodynamic cycle 300. It can be seen that thermodynamic cycle 300 eliminates the need for a minimum applied stress for elastocaloric materials. However, a minimum of 10 MPa may be applied for model stability and to prevent reversal of force direction at low stresses.

[0036] The minimum applied stress is based purely on the material activation temperature and the current cold side temperature. Thermodynamic cycle 300 may not require a minimum applied stress in all circumstances.

[0037] The material activation temperature can be increased by increasing the stress. Thus, if the final temperature of the austenite is too low, a minimum stress may be applied to increase it. Balancing the cycle is important in the Stirling cycle, since heat is released by the transformation of martensite in 2-3 and absorbed again in 4-1. The same fluid is used in 2-3 and 4-1. Thus, a thermal imbalance reduces the heat recovery efficiency.

[0038] In FIG. 7, the “tails” of the stress-strain curves of the SMA material are shown for a reverse Stirling cycle (an example of an isobaric cycle shown in solid dark black lines) and a thermodynamic cycle 300 (an example of an isophase cycle shown in solid light grey lines). in and Q out, it can be clearly seen that the last few percent of phase transformation is more difficult than the more gradual phase change levels. This is manifested as a drop in COP. As shown, in process 2-3, as the temperature is lowered, the martensite volume can change from 80% to 90%. As an example, thermodynamic cycle 300 can adjust the dynamically applied stress to hold the martensite at a constant 90%.

[0039] 8(a)-8(c) show a physical implementation of the thermodynamic cycle 300 in a hydraulic system 802 via a pressure regulator 804, according to one embodiment of the present invention.

[0040] During process (2-3), as the material cools from hot to cold, the pressure regulator 804 adjusts the hydraulic pressure and therefore the material stress on the core to perform a constant volume martensite or isophase process based on the stress rate equation 1. Alternatively, the pressure applied to the core can be adjusted by changing the torque applied to the hydraulic pump 802.

[0041] The pressure regulator 802 may cease its operation and the hydraulic system 802 may perform an isochoric or isobaric process (FIGS. 8(a) and 8(b)) in the situation where the phase change is complete.

[0042] Although not shown, it will be apparent to one skilled in the art that thermodynamic cycle 300 can be implemented in heat pumps and refrigeration systems.

[0043] In FIG. 9, a flow chart 900 of a method for implementing the thermodynamic cycle 300 is shown.

[0044] At 902, the method includes increasing a stress applied to the elastocaloric material until the stress reaches a desired stress value or the elastocaloric material transitions from an austenitic to a martensite form, Increasing the stress of such an elastocaloric material to a desired stress value corresponds to an isothermal heat dissipation process.

[0045] In step 904, the method includes ramping down the temperature of the elastocaloric material from a high temperature to a low temperature and reducing the stress of the elastocaloric material to maintain a corresponding volume fraction of the martensite form constant during the temperature ramp down. Maintaining a constant volume fraction of the martensite form during the temperature ramp down with such stress reduction corresponds to a polytropic temperature ramp down process.

[0046] In step 906, the method includes reducing the stress in the elastocaloric material until the stress reaches a minimum stress value or until the elastocaloric material transforms from martensite to austenite form, such a stress reduction corresponding to an isothermal endothermic process.

[0047] In step 908, the method includes increasing the temperature of the elastocaloric material from a low temperature to a high temperature and increasing the stress of the elastocaloric material to maintain a corresponding volume fraction of the martensite form constant during the temperature increase. Such an increase in the stress of the elastocaloric material to maintain a constant volume fraction of the martensite form during the temperature increase corresponds to a polytropic temperature increase process.

[0048] FIG. 10 shows a block diagram of a system 1000 for implementing the thermodynamic cycle 300 of FIG.

[0049] The system 1000 includes an isothermal heat release module 1002 that increases the stress applied to the elastocaloric material until a desired stress value is reached or the elastocaloric material transitions from austenite to martensite form; a polytropic temperature reduction module 1004 that reduces the temperature of the elastocaloric material from a high temperature to a low temperature, decreasing the stress of the elastocaloric material to maintain a constant volume fraction of the corresponding martensite form during the temperature reduction; an isothermal heat absorption module 1006 that reduces the stress of the elastocaloric material until a minimum stress value is reached or the elastocaloric material transitions from martensite to austenite form; and a polytropic temperature increase module 1008 that increases the temperature of the elastocaloric material from a low temperature to a high temperature, increasing the stress of the elastocaloric material to maintain a constant volume fraction of the corresponding martensite form during the temperature increase.

[0050] In one embodiment of the present invention, the system 1000 may be implemented via a control unit that controls various components of a thermodynamic system, such as a heat pump and a refrigeration system.

[0051] As used herein, the terms "comprise, comprises, comprised, and comprising" or any variation thereof, and "include, includes, included, and including" or any variation thereof, are considered to be fully interchangeable and should all be given the broadest possible interpretation, and vice versa.

[0052] The invention is not limited to the embodiments described above, which may be modified both in arrangement and detail. [Explanation of symbols]

[0053] 300 Thermodynamic Cycle 302 Thermodynamics Table 802 Hydraulic System 804 Pressure Regulator 1000 Systems 1002 Isothermal heat dissipation module 1004 Polytropic Temperature Decrease Module 1006 Isothermal Endothermic Module 1008 Polytropic Temperature Rise Module

Claims

1. 1. A method of performing a thermodynamic cycle on an elastocaloric material, comprising: increasing the stress applied to the elastocaloric material until a desired stress value is reached or the elastocaloric material transitions from austenitic to martensite form; decreasing the temperature of the elastocaloric material from an elevated temperature to a lower temperature to reduce stress in the elastocaloric material to maintain a corresponding martensite volume fraction constant during the temperature decrease; reducing the stress in the elastocaloric material until the stress reaches a minimum stress value or the elastocaloric material transforms from martensite to austenite form; and increasing the temperature of the elastocaloric material from a low temperature to a high temperature, increasing the stress of the elastocaloric material to maintain a corresponding martensite volume fraction constant during the temperature increase.

2. The method of claim 1 , wherein increasing the stress of the elastocaloric material to the desired stress value corresponds to an isothermal heat dissipation process and the stress reduction corresponds to an isothermal heat absorption process.

3. 3. The method of claim 1, wherein maintaining the volume fraction of the martensite form constant during a temperature decrease by decreasing the stress corresponds to a polytropic temperature decrease process, and maintaining the volume fraction of the martensite form constant during a temperature increase by increasing the stress of the elastocaloric material corresponds to a polytropic temperature increase process.

4. The stress change during the polytropic temperature increase and decrease process is calculated using the following formula: [0010] where Δα is the difference in thermal expansion between the phases, σ is the current material stress, and ρΔs ０ 4. The method of claim 3, wherein ΔS is the difference in volume entropy between the phases, which may be determined from the Clausius-Clapeyron equation, ΔS is the material stiffness, Λ is the material transformation strain, and T is the temperature change.

5. The method of claim 1 , wherein the stress change is directly proportional to the temperature change and the entropy difference, and inversely proportional to the material stiffness and the material transformation strain.

6. 2. The method of claim 1, wherein maintaining a constant martensite volume during the polytropic temperature ramp-up and ramp-down process reduces the overall work input of the thermodynamic cycle and increases COP.

7. 13. A hydraulic system for carrying out the method of claim 1, comprising: A hydraulic system with a pressure regulator that adjusts the stress to maintain a constant martensite volume during the polytropic temperature increase and decrease process.

8. 13. A heat pump system using the method of claim 1 to implement a thermodynamic cycle.

9. 10. A refrigeration system using the method of claim 1 to implement a thermodynamic cycle.

10. 1. A system for performing a thermodynamic cycle on an elastocaloric material, comprising: an isothermal heat dissipation module that increases the stress applied to the elastocaloric material until a desired stress value is reached or the elastocaloric material transitions from austenitic to martensite form; a polytropic temperature reduction module that reduces the temperature of the elastocaloric material from a high temperature to a low temperature and reduces stress in the elastocaloric material to maintain a corresponding martensite volume fraction constant during the temperature reduction; an isothermal heat absorption module that reduces the stress in the elastocaloric material until the stress reaches a minimum stress value or the elastocaloric material transforms from martensite to austenite form; a polytropic temperature ramp module that ramps the temperature of the elastocaloric material from a low temperature to a high temperature and increases the stress of the elastocaloric material to maintain a corresponding martensite form volume fraction constant during the temperature ramp.

11. The stress change is calculated using the following formula: [0025] where Δα is the difference in thermal expansion between the phases, σ is the current material stress, and ρΔs ０ 11. The system of claim 10, wherein ΔS is the difference in volume entropy between the phases, which may be determined from the Clausius-Clapeyron equation, ΔS is the material stiffness, Λ is the material transformation strain, and T is the temperature change.

12. The system of claim 10 , wherein the stress change is directly proportional to the temperature change and the entropy difference, and inversely proportional to the material stiffness and the material transformation strain.

13. The system of claim 10 , wherein maintaining the martensite volume constant reduces the overall work input of the thermodynamic cycle and increases COP.

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