Solid state thermodynamic cycle

Abstract

A method for implementing a thermodynamic cycle for an elastomeric thermal material is disclosed. The method includes increasing the stress exerted on the elastic thermal material until the stress reaches a desired stress value or the elastic thermal material transitions from austenite to martensite form, reducing the temperature of the elastic thermal material from a high value to a low value, and reducing the stress of the elastic thermal material to maintain a constant volume fraction of the corresponding martensite form during the temperature reduction, reducing the stress of the elastic thermal material until the stress reaches a minimum stress value or the elastic thermal material transitions from martensite to austenite form, and raising the temperature of the elastic thermal material from a low value to a high value, and increasing the stress of the elastic thermal material to maintain a constant volume fraction of the corresponding martensite form during the temperature rise.

Description

Technical Field

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

[0002] Recent research on the elastocaloric (EC) effect has shown its potential as a solid-state alternative to conventional vapor compression refrigeration and heat pump methods. The EC cycle exploits the superelastic behavior of shape memory alloys (SMAs) that facilitates the absorption of heat from a low-temperature source and the discharge of heat to a higher temperature sink through cyclic uniaxial loading and unloading. Elastic thermal material thermodynamic cycles have previously been modeled using conventional gas cycles. It has been shown in the literature that the reverse Brayton cycle and the reverse Stirling cycle have the best performance of elastocaloric thermal cycles. It is known from gas cycle theory that the coefficient of performance (COP) of the reverse Stirling cycle and the Carnot cycle (thermodynamic limit) are the same because both use isothermal heat discharge and absorption processes. Therefore, elastocaloric materials designed to maximize their COP will aim to implement the reverse Stirling cycle when possible. Figure 1 The key processes for the Stirling cycle are shown. As can be seen, the heat rejection and heat absorption are isothermal processes, and the heat recovery process of preheating and precooling the SMA is an isochoric or constant material volume process.

[0003] However, past modeling of the elasto-thermodynamic cycle has been done assuming a complete phase transition from austenite to martensite. True elasto-thermo materials may undergo only partial transitions between phases due to temperature or stress limitations.

[0004] Figure 2A-2D are graphs showing the relationship between stress and temperature, stress and strain, specific entropy and temperature, and specific entropy and martensite volume, respectively, when an elasto-thermal material undergoes a reverse Stirling cycle. Figure 2D It can be seen that during the heat recovery process from 2-3 (material cooling), the martensite volume increases, and during the process from 4-1 (material heating), the martensite volume decreases. It is found that the increase / decrease in martensite volume is greater in the case of higher temperature. This is due to the limited change in martensite volume during the heat discharge process due to the operating stress limitation. In addition, Figure 2BIn , the observable strain from 2-3 (cooling of the material) remains constant due to the decrease in thermal expansion and elastic strains and the increase in phase transformation strains as the martensite volume increases.

[0005] However, the amount of heat removed is related to the martensite volume, and therefore an increase causes further heat to be removed. A true heat recovery system requires both the addition and removal of heat, but in this case the heat removed is due to a fundamental process imbalance that cannot be controlled by the physical design. This is also true for the heat recovery process. This means that the heat recovery unit must handle a higher heat load. In addition, the martensite volume change during heat recovery increases with larger operating temperature differences. This is due to the smaller martensite volume increase during heat removal caused by operating stresses.

[0006]

[0006] Therefore, in view of the above, a need exists for a system and method that maintains a constant martensite volume during a heat recovery process and reduces losses due to increases in martensite volume during the heat recovery process. Summary of the invention

[0007] According to the present invention, as set forth in the accompanying claims, there is provided a method for implementing a thermodynamic cycle for an elastocaloric material. The method comprises increasing the stress applied to the elastocaloric material until the stress reaches a desired stress value or the elastocaloric material transforms from austenite to martensite form; reducing the temperature of the elastocaloric material from a high value to a low value and reducing the stress of the elastocaloric material to maintain a corresponding constant volume fraction of the martensite form during the temperature reduction; reducing the stress of 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 value to a high value and increasing the stress of the elastocaloric material to maintain a corresponding constant volume fraction of the martensite form during the temperature increase.

[0008] In an embodiment of the present invention, increasing the stress of the elastic thermomaterial to a desired stress value forms an isothermal heat discharge process, and reducing the stress forms an isothermal heat absorption process.

[0009] In an embodiment of the present invention, reducing stress to maintain a constant volume fraction of the martensite form during temperature reduction forms a polytropic temperature reduction process, and increasing stress of the elastocaloric material to maintain a constant volume fraction of the martensite form during temperature increase forms a polytropic temperature increase process.

[0010] In an embodiment of the present invention, the stress variation during the polytropic temperature increasing process and the polytropic temperature decreasing process is calculated using the following formula:

[0011]

[0012] where Δα is the thermal expansion difference between the phases, σ is the current material stress, ρΔso is the volume entropy difference between the phases which can be determined from the Clausius-Clapeyron relation, ΔS is the material stiffness, Λ is the material transformation strain, and Tpoint is the temperature change.

[0013] In an embodiment of the present invention, the change in stress is directly proportional to the change in temperature and entropy difference, and inversely proportional to the material stiffness and material transition strain.

[0014] In embodiments of the present invention, the maintenance of a constant martensite volume during the polytropic temperature ramp-up process and the polytropic temperature ramp-down process reduces the total work input of the thermodynamic cycle and increases the COP.

[0015] The present invention discloses a method of implementing a thermodynamic cycle in which latent heat emissions / absorption during heat recovery are eliminated by maintaining a constant martensite volume during the heat recovery process, and thus, the overall efficiency of the cycle is increased due to lower work input. The new thermodynamic cycle is specific only to solid-solid phase changes, and by varying stress with temperature during the heat recovery process, the partial load efficiency of elastic thermal materials is improved by 25% relative to reverse Stirling under the same conditions. The new thermodynamic cycle improves the efficiency of elastic thermal technology for heating applications or cooling applications, as well as the commercial attractiveness of SMAs, without increasing system cost or parasitic loads. In addition, due to the elimination of unnecessary energy emissions / absorption, material hysteresis is reduced, resulting in higher COP and reduced parasitic losses.

[0016] In another aspect of the present invention, a heat pump system is provided that uses a method of implementing a thermodynamic cycle.

[0017] In yet another aspect of the present invention, a refrigeration system is provided that uses a method of implementing a thermodynamic cycle.

[0018] In yet another aspect of the present invention, a system for implementing a thermodynamic cycle for an elasto-caloric material is provided. The system includes: an isothermal heat discharge module for increasing the stress applied to the elasto-caloric material until the stress reaches a desired stress value or the elasto-caloric material transforms from austenite to martensite; a polytropic temperature reduction module for reducing the temperature of the elasto-caloric material from a high value to a low value and reducing the stress of the elasto-caloric material to maintain a constant volume fraction of the corresponding martensite form during the temperature reduction; an isothermal heat absorption module for reducing the stress of the elasto-caloric material until the stress reaches a minimum stress value or the elasto-caloric material transforms from martensite to austenite; and a polytropic temperature increase module for increasing the temperature of the elasto-caloric material from a low value to a high value and increasing the stress of the elasto-caloric material to maintain a constant volume fraction of the corresponding martensite form during the temperature increase. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The invention will be more clearly understood from the following description of embodiments thereof, given by way of example only, with reference to the accompanying drawings, in which:-

[0020] Figure 1 The conventional reverse Stirling cycle is demonstrated;

[0021] Figure 2A-2D are graphs showing the relationship between stress and temperature, stress and strain, specific entropy and temperature, and specific entropy and martensite volume, respectively, when the elastic thermoelastic material undergoes a reverse Stirling cycle;

[0022] Figure 3 A new thermodynamic cycle and corresponding thermodynamic table for elasto-caloric materials according to an embodiment of the present invention are presented;

[0023] Figure 4A-4D It shows respectively when Figure 3 Plots of the relationships between stress and temperature, stress and strain, specific entropy and temperature, and specific entropy and martensite volume when the thermodynamic cycle is applied to elasto-thermal materials;

[0024] Figure 4E shows a comparison of the reverse Stirling cycle and Figure 3 Tables 1 and 2 of various parameters of the thermodynamic cycle;

[0025] Figure 5 It is a graph of COP versus stress for an isochoric cycle (i.e., reverse Stirling cycle);

[0026] Figure 6 is an isophase cycle (i.e. Figure 3 The COP versus stress curve of the thermodynamic cycle of the

[0027] Figure 7 Demonstrated for the reverse Stirling cycle and Figure 3 The “tail” of the stress-strain curve of the SMA material during the thermodynamic cycle;

[0028] Figure 8 (a)- Figure 8 (c) shows the physical implementation of the thermodynamic cycle in a hydraulic system via a pressure regulator according to an embodiment of the present invention;

[0029] Fig. 9 is a demonstration of the Figure 3 A flow chart of a method for a thermodynamic cycle; and

[0030] Fig.10 is a demonstration of the Figure 3 Block diagram of the thermodynamic cycle of the system. DETAILED DESCRIPTION

[0031] Figure 3 A new thermodynamic cycle 300 and corresponding thermodynamic table 302 for elasto-caloric materials are shown in accordance with an embodiment of the present invention.

[0032] Thermodynamic cycle 300 includes a series of four thermodynamic processes 4-1, 1-2, 2-3, and 3-4, corresponding to the transitions between states 1, 2, 3, and 4 of the elastocaloric material. The modeling of thermodynamic cycle 300 has been performed assuming a complete phase transition from austenite to martensite. However, due to temperature or stress limitations, a real elastocaloric material may only undergo a partial transition (approximately 90%) between phases. It will be apparent to one of ordinary skill in the art that thermodynamic cycle 300 can be applied to other caloric materials if they have hysteresis.

[0033] Thermodynamic cycle 300 uses an isothermal heat discharge process (process 1-2) and an isothermal heat absorption process (process 3-4), similar to the reverse Stirling cycle. However, instead of an isochoric heat recovery process during process 2-3, a constant martensite volume process is used. Due to the constant volume fraction of martensite during process 2-3, thermodynamic cycle 300 can also be called an isophase cycle. The constant martensite volume is achieved by controlling the stress applied to the material during the heat recovery process of the cycle, where the material is heated / cooled between temperature extremes. It should be noted that constant martensite and austenite volumes are achieved by controlling the stress of both processes 2-3 and 4-1.

[0034] The first thermodynamic process (process number 4-1) includes a polytropic temperature increase process during which the temperature of the elastic thermo material is increased from a cold temperature T cRaised to the hot temperature T H The first thermodynamic process occurs at a temperature T of the elastic thermomaterial. c When the temperature is T H During the first process, the elastic thermomaterial contains approximately 90% austenite and 10% martensite. During the first process (4-1), the stress of the elastic thermomaterial can be increased to maintain a constant martensite volume at a given temperature. The increase in stress during process (4-1) can be estimated based on equation (1), as explained later.

[0035] The second thermodynamic process (process number 1-2) includes an isothermal heat discharge process during which the stress applied to the elastic thermo material increases. The second thermodynamic process starts with a first state and ends with a second state when the applied stress reaches a desired value (i.e., a maximum stress value) or when ξ=1. In the second process, the elastic thermo material transforms from austenite to martensite form. ξ is the martensite volume fraction. When ξ=0, the material is fully austenite, and when ξ=1, the material is fully martensite.

[0036] The third thermodynamic process (process number 2-3) includes a polytropic temperature reduction process during which the temperature of the elastic thermal material is reduced from the hot temperature T H Reduce to cold temperature T c The third thermodynamic process occurs when the temperature of the elastic thermomaterial is T H The second state starts when the temperature of the elastic thermomaterial is less than or equal to T c The elastic thermomaterial is maintained in the martensite form during the third process. During the first process (4-1), the stress of the elastic thermomaterial can be reduced to maintain a constant martensite volume at a given temperature. The reduction of stress during the process (4-1) can be estimated based on equation (1), as explained later.

[0037] The fourth thermodynamic process (process number 3-4) includes an isothermal heat absorption process during which the stress applied to the elastic thermo material is reduced. The fourth thermodynamic process begins with the third state and ends with the fourth state when the applied stress is reduced to a minimum stress value, when ξ = 0. In the fourth process, the elastic thermo material transforms from martensite to austenite form.

[0038] The ideal stress change required during processes 2-3 and 4-1 can be calculated using the following formula:

[0039]

[0040] where Δα is the thermal expansion difference between the phases, σ is the current material stress, ρΔso is the volume entropy difference between the phases which can be determined from the Clausius-Clapeyron relation, ΔS is the material stiffness, Λ is the material transformation strain, and Tpoint is the temperature change.

[0041] As can be seen from equation (1), the change in stress is proportional to the temperature change during each phase 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 stress and temperature should change, because all other parameters are fixed for the material. However, thermal expansion and transformation strain affect the volume change required to change the stress by a certain amount. In general, if everything increases, then the stress change will need to be larger to keep the martensite volume constant.

[0042] Additionally, the designer may include an offset to reject a controlled amount of latent heat to the heat recovery system to maintain the heat recovery temperature.

[0043] Figure 4A-4D are graphs showing the relationship between stress versus temperature, stress versus strain, specific entropy versus temperature, and specific entropy versus martensite volume, respectively, when a thermodynamic cycle 300 is performed on a low temperature space heating application of an elastocaloric material.

[0044] Figure 4D The variable martensite volume (e.g., Figure 2D ), the constant martensite volume of the elastic thermal material during processes 2-3 and 4-1. When compared to the reverse Stirling cycle, it can be seen that the martensite volume is maintained during the heat recovery processes 2-3 and 4-1.

[0045] Figure 4B The stress-strain relationship of an elastic thermomaterial undergoing 300 thermodynamic cycles is shown. Figure 4B In the figure, for the same maximum operating stress, stress and volume decrease / increase during these processes. It is found that at the beginning of the heat discharge process (process 1-2), the material stress is 31 MPa lower than that of the reverse Stirling cycle, while at the beginning of the heat absorption process (process 3-4), it is 154 MPa higher.

[0046] The effect of maintaining a constant martensite / austenite volume can be seen on a stress-strain diagram, where changing the stress results in a change in strain and an overall reduction in enclosed area and resulting work input during the heat recovery process. The ideal work input into a typical thermodynamic cycle can be measured by determining the enclosed area of ​​a pressure-volume diagram or, in the case of the present invention, a stress-strain diagram. Figure 4B The stress-strain curve of Figure 2BWhen the stress versus strain graphs are compared, it is found that the work input decreases during the thermodynamic cycle 300. Figure 4E Tables 1 and 2 are shown for comparing various parameters of the reverse Stirling cycle and the thermodynamic cycle 300 (also known as the constant martensitic heat recovery cycle and the isophase cycle) under various temperature conditions. It can be seen that the thermodynamic cycle 300 has a higher theoretical seasonal coefficient of performance (SCOP) when compared to the reverse Stirling cycle. The SCOP limit of the thermodynamic cycle 300 is calculated to be 8.93, which is 26% higher than the SCOP limit of the reverse Stirling cycle. In addition, the total equivalent warming impact (TEWI) can be used to calculate the CO2 contribution of an installed system over its lifetime. The TEWI of an elastic thermal material can be calculated based on the following equation:

[0047] TEWI=[n×E 每年 ×β]+[GWP i ×m i ×(1-α i )]

[0048] in,

[0049] GWP i is the mass of any insulation or other GWP material (which is not necessarily the refrigerant), n is the operating life of the system in years, E 每年 is the energy consumed by the system per year, m i is the mass of insulation or other GWP material used, β is the amount of CO2 produced, and α is the recyclability at end of life.

[0050] Figure 5 shows a graph of COP versus stress for an isochoric cycle (i.e., a reverse Stirling cycle), and Figure 6 A graph of COP versus stress for an isophase cycle (i.e., thermodynamic cycle 300) is shown. It can be seen that thermodynamic cycle 300 eliminates the need for a minimum operating stress for elasto-thermal materials. However, for model stability and to prevent force direction reversal at low stresses, a minimum value of 10 MPa may be imposed.

[0051] The minimum operating stress is based solely on the activation temperature of the material and the current low side temperature. Thermodynamic Cycle 300 does not eliminate the need for minimum operating stress in all cases.

[0052] The material activation temperature can be raised by adding stress. Therefore, if the austenite finish temperature is too low, a minimum stress can be applied to raise it. Balancing the cycle is important because in the Stirling cycle, heat is rejected due to the martensitic transformation at 2-3 and then reabsorbed between 4-1. The same fluid is used for 2-3 and 4-1. Therefore, heat imbalance reduces the efficiency of heat recovery.

[0053] Figure 7 The "tails" of the stress-strain curves for the SMA material for the reverse Stirling cycle (represented by the dark solid black line representing the isobaric cycle) and the thermodynamic cycle 300 (represented by the light solid grey line representing the isophase cycle) are shown. It is clearly shown that in the last few % of the phase transformation, the stress-strain curves at Q are significantly higher than those at the operation at more modest phase transformation levels. 输入 Q 输出 This manifests itself as a reduction in COP. As can be seen, in process 2-3, as the temperature drops, the martensite volume changes from 80% to 90%. As an example, the thermodynamic cycle 300 will dynamically control the stress load to maintain a constant 90% martensite.

[0054] Figure 8 (a)- Figure 8 (c) illustrates the physical implementation of the thermodynamic cycle 300 in a hydraulic system 802 via a pressure regulator 804, according to an embodiment of the present invention.

[0055] During process (2-3), as the material cools from hot to cold, the pressure regulator 804 controls the hydraulic pressure on the core and therefore the material stress for constant martensitic or isophase operation based on the stress rate equation 1. Alternatively, the pressure supplied to the core can be controlled by varying the torque applied to the hydraulic system 802.

[0056] The pressure regulator 804 may be deactivated and the hydraulic system 802 may operate an isochoric or isobaric process with complete phase change ( Figure 8 (a) and Figure 8 (b)).

[0057] Although not shown, it will be apparent to one of ordinary skill in the art that the thermodynamic cycle 300 may be implemented in heat pump and refrigeration systems.

[0058] Fig. 9 is a flow chart 900 illustrating a method for implementing the thermodynamic cycle 300 .

[0059] At 902, the method includes increasing stress applied to the elasto-thermal material until the stress reaches a desired stress value or the elasto-thermal material transforms from an austenite form to a martensite form. Increasing the stress of the elasto-thermal material to the desired stress value forms an isothermal heat discharge process.

[0060] At step 904, the method includes reducing the temperature of the elasto-thermal material from a high value to a low value, and reducing the stress of the elasto-thermal material to maintain a constant volume fraction of the corresponding martensite form during the temperature reduction. Reducing the stress to maintain a constant volume fraction of the martensite form during the temperature reduction forms a multi-variable temperature reduction process.

[0061] At step 906, the method includes reducing the stress of the elasto-thermal material until the stress reaches a minimum stress value or the elasto-thermal material transforms from a martensite form to an austenite form. Reducing the stress forms an isothermal heat absorption process.

[0062] At step 908, the method includes increasing the temperature of the elasto-caloric material from a low value to a high value and increasing the stress of the elasto-caloric material to maintain a constant volume fraction of the corresponding martensite form during the temperature increase. Increasing the stress of the elasto-caloric material to maintain a constant volume fraction of the martensite form during the temperature increase forms a multi-variable temperature increase process.

[0063] Fig.10 is a demonstration of the Figure 3 A block diagram of a system 1000 of a thermodynamic cycle 300 is shown.

[0064] The system 1000 includes an isothermal heat discharge module 1002 for increasing the stress applied to the elasto-caloric material until the stress reaches a desired stress value or the elasto-caloric material transforms from austenite to martensite form; a polytropic temperature reduction module 1004 for reducing the temperature of the elasto-caloric material from a high value to a low value, and reducing the stress of the elasto-caloric material to maintain a corresponding constant volume fraction of the martensite form during the temperature reduction; an isothermal heat absorption module 1006 for reducing the stress of the elasto-caloric material until the stress reaches a minimum stress value or the elasto-caloric material transforms from martensite to austenite form; and a polytropic temperature increase module 1008 for increasing the temperature of the elasto-caloric material from a low value to a high value, and increasing the stress of the elasto-caloric material to maintain a corresponding constant volume fraction of the martensite form during the temperature increase.

[0065] In an embodiment of the present invention, the system 1000 may be implemented by a control unit for controlling various components of a thermodynamic system, such as a heat pump and a refrigeration system.

[0066] In the specification, the terms "comprise", "comprises", "comprised" and "comprising" or any variations thereof and the terms "include", "includes", "included" and "including" or any variations thereof are considered to be fully interchangeable and they should all be given the broadest possible interpretation and vice versa.

[0067] The invention is not limited to the embodiments described above but may be varied both in construction and in detail.

Claims

1. A method for implementing a thermodynamic cycle for an elasto-thermal material, the method comprising: increasing the stress applied to the elasto-thermal material until the stress reaches a desired stress value or the elasto-thermal material transforms from an austenite to a martensite form; reducing the temperature of the elastocaloric material from a high value to a low value and reducing the stress of the elastocaloric material to maintain a constant volume fraction of a corresponding martensitic form during the temperature reduction; reducing the stress of the elasto-thermal material until the stress reaches a minimum stress value or the elasto-thermal material transforms from a martensite to an austenite form; as well as The temperature of the elastocaloric material is increased from a low value to a high value, and the stress of the elastocaloric material is increased to maintain a constant volume fraction of a corresponding martensitic form during the temperature increase.

2. A method as claimed in any preceding claim, wherein: Increasing the stress of the elasto-thermal material to the desired stress value forms an isothermal heat discharge process, and reducing the stress forms an isothermal heat absorption process.

3. A method as claimed in any preceding claim, wherein: Reducing the stress to maintain a constant volume fraction of the martensite form during temperature reduction forms a polytropic temperature reduction process, and increasing the stress of the elastocaloric material to maintain a constant volume fraction of the martensite form during temperature increase forms a polytropic temperature increase process.

4. The method of claim 3, wherein: The stress changes during the polytropic temperature increase process and polytropic temperature decrease process are calculated using the following formula: where Δα is the thermal expansion difference between the phases, σ is the current material stress, ρΔso is the volume entropy difference between the phases which can be determined by the Clausius-Clapeyron relation, ΔS is the material stiffness, Λ is the material transformation strain, and Tpoint is the temperature change.

5. A method as claimed in any preceding claim, wherein: The change in stress is directly proportional to the change in temperature and entropy difference, and inversely proportional to the material stiffness and material transition strain.

6. A method as claimed in any preceding claim, wherein: The maintenance of a constant martensite volume during the polytropic temperature raising process and the polytropic temperature lowering process reduces the total work input of the thermodynamic cycle and increases the COP.

7. A hydraulic system for carrying out the method of any preceding claim, the hydraulic system comprising a pressure regulator for controlling stress to maintain a constant martensite volume during a polytropic temperature ramp-up process and a polytropic temperature ramp-down process.

8. A heat pump system for implementing a thermodynamic cycle using a method as claimed in any preceding claim.

9. A refrigeration system for implementing a thermodynamic cycle using the method according to any one of claims 1 to 7.

10. A system for implementing a thermodynamic cycle for an elasto-thermal material, the system comprising: an isothermal heat discharge module for increasing the stress applied to the elasto-thermal material until the stress reaches a desired stress value or the elasto-thermal material transforms from an austenite to a martensite form; a polytropic temperature reduction module for reducing the temperature of the elasto-caloric material from a high value to a low value and reducing the stress of the elasto-caloric material to maintain a constant volume fraction of a corresponding martensite form during the temperature reduction; an isothermal heat absorption module, the isothermal heat absorption module being used to reduce the stress of the elastic thermal material until the stress reaches a minimum stress value or the elastic thermal material transforms from martensite to austenite form; as well as A polytropic temperature ramping module is provided to ramp the temperature of the elastocaloric material from a low value to a high value and to increase the stress of the elastocaloric material to maintain a constant volume fraction of a corresponding martensite form during the temperature ramping.

11. The system of claim 10, wherein: The change in stress is calculated using the following formula: where Δα is the thermal expansion difference between the phases, σ is the current material stress, ρΔso is the volume entropy difference between the phases which can be determined by the Clausius-Clapeyron relation, ΔS is the material stiffness, Λ is the material transformation strain, and Tpoint is the temperature change.

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

13. The system of claim 10, wherein: The maintenance of a constant martensite volume reduces the total work input of the thermodynamic cycle and increases the COP.

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