METHOD OF OPERATING A HEAT CYCLE SYSTEM, HEAT CYCLE SYSTEM AND METHOD OF MODIFYING A HEAT CYCLE SYSTEM
20250382901 · 2025-12-18
Assignee
Inventors
Cpc classification
F01K11/00
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F25B11/02
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F01K21/005
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F01K13/006
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
International classification
F01K13/00
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F01K11/00
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F01K21/00
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F25B11/02
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
Abstract
A method of operating a heat cycle system, wherein the heat cycle system comprises a working fluid, which is cycled through a circuit comprising a compressor, a condenser, an expander unit, and an evaporator and wherein the expander unit is configured to generate a rotating mechanical motion, comprises operating the evaporator at an evaporator working fluid evaporation capacity that is at least about 110% of the nominal evaporator working fluid evaporation capacity. There is also disclosed a heat cycle system as well as a method of modifying a heat cycle system.
Claims
1. A method of operating a heat cycle system, wherein the heat cycle system comprises a working fluid, which is cycled through a circuit comprising a compressor (10), a condenser (11), an expander unit (130), and an evaporator (140), wherein the expander unit (130) is configured to generate a rotating mechanical motion, wherein the method comprises: operating the compressor (10) to receive the working fluid in a first state, with a first pressure (P1), a first temperature (T1) and a first enthalpy (H1), and to compress the working fluid to a second state with a second pressure (P2), a second temperature (T2) and a second enthalpy (H2), operating the condenser (11) to receive the working fluid in the second state, and to condense the working fluid to a third state with a third pressure (P3), a third temperature (T3) and a third enthalpy (H3), operating the expander unit (130) to receive the working fluid in the third state, and to expand the working fluid to a modified fourth state with a modified fourth pressure (P40), a modified fourth temperature (T40) and a modified fourth enthalpy (H40), operating the evaporator (140) to receive the working fluid in the modified fourth state, and to evaporate the working fluid to the first state, wherein a nominal evaporator working fluid evaporation capacity is defined as an amount of an enthalpy reduction (H2H3) provided by the condenser less an amount of an enthalpy increase (H2H1) provided by the compressor, characterized by operating the evaporator at an evaporator working fluid evaporation capacity that is at least about 110% of the nominal evaporator working fluid evaporation capacity, and a working fluid pressure drop over the evaporator is less than about 5 bar.
2. The method as claimed in claim 1, wherein power (mf(H1H40)) provided to the working fluid by the evaporator is greater than a power required to essentially isobarically raise an entropy of the working fluid from an entropy level (H3) at a condenser outlet to an entropy level (H1) corresponding to saturation (H1).
3. The method as claimed in claim 1, wherein an evaporator power transferred to the working fluid corresponds to a sum of a heat power (mf(H2H3)) removed from the working fluid by the condenser and a power (mf(H3H40)) generated by the working fluid at the rotatable expander less a power (mf(H2H1)) provided to the working fluid by the compressor.
4. The method as claimed in claim 1, wherein a working fluid pressure drop over the evaporator is about 0.50-0.75 bar; about 0.75-1.00 bar; about 1.00-1.25 bar; about 1.25-1.50 bar; about 1.50-1.75 bar; about 1.75-2.00 bar; about 2.00-2.25 bar; about 2.25-2.50 bar; about 2.50-2.75 bar; about 2.75-3.00 bar; about 3.00-3.25 bar; about 3.25-3.50 bar; about 3.50-3.75 bar; about 3.75-4.00 bar; about 4.00-4.25 bar; about 4.25-4.50 bar; about 4.50-4.75 bar; or about 4.75-5.00 bar.
5. The heat cycle system as claimed in claim 1, wherein the expander unit (130) is selected from a group consisting of a rotation type expander, a swing type expander, a scroll type expander, a GE rotor type expander, a reciprocating type expander, a screw type expander and a radial turbo type expander.
6. The method as claimed in claim 1, wherein a generator (131) is mechanically connected to the expander unit (130) for generating electricity, and wherein the generator (131) is operated to generate electric power as the rotatable expander (130) is caused to rotate during the expansion of the working fluid.
7. The method as claimed in claim 1, further comprising subcooling the working fluid downstream of the condenser (11) and upstream of the expander unit (130).
8. The method as claimed in claim 7, wherein the working fluid downstream of the condenser (11) and upstream of the expander unit (130) is caused to exchange heat with the working fluid upstream of the compressor (10) and downstream of the evaporator (140).
9. The method as claimed in claim 1, further comprising causing at least some of the working fluid downstream of the expander unit (130) and upstream of the evaporator (140) to undergo further expansion in an expansion valve (162).
10. The method as claimed in claim 9, wherein the working fluid exiting from the expander unit (130) is selectively distributed between the expansion valve (162) and a bypass connection (161), which bypasses the expansion valve (162).
11. The method as claimed in claim 9, wherein the expansion valve (162) is operable based on a condition downstream of the evaporator (140), preferably immediately downstream of the evaporator (140).
12. The method as claimed in claim 1, wherein the condenser (11) is caused to exchange heat with a first external working fluid in the form of a gas.
13. The method as claimed in claim 1, wherein the evaporator (140) is caused to exchange heat with a second external working fluid in the form of a gas.
14. A heat cycle system, comprising: a working fluid, which is cycled through a circuit comprising a compressor (10), a condenser (11), an expander unit, and an evaporator (140), wherein the expander unit is configured to generate a rotating mechanical motion, wherein a nominal evaporator working fluid evaporation capacity is defined as an amount of an enthalpy reduction (H2H3) provided by the condenser less an amount of an enthalpy increase (H2H1) provided by the compressor, characterized by the evaporator is sized and adapted to provide an evaporator working fluid evaporation capacity that is at least 110% of the nominal evaporator working fluid evaporation capacity, and a working fluid pressure drop over the evaporator is less than about 5 bar.
15.-29. (canceled)
30. A method of modifying a heat cycle system, wherein the heat cycle system comprises: a working fluid, which is cycled through a circuit comprising a compressor (10), a condenser (11), an expansion valve (13), and a first evaporator (14), wherein the method comprises: replacing the expansion valve (13) with an expander unit that is configured to generate a rotating mechanical motion, and replacing the first evaporator (14) with a second evaporator (140) having greater working fluid evaporation capacity than the first evaporator (14).
Description
DRAWINGS
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[0102]
[0103]
[0104]
[0105]
[0106]
DETAILED DESCRIPTION
[0107] The inventive concept will be disclosed with reference to
[0108] The system shown in
[0109] Hence, in
[0110] In some embodiments, the heat cycle system may be formed as a refrigeration circuit for use in an air conditioning system in a fixed construction, in a vessel or in a vehicle.
[0111] In other embodiments, the heat cycle system may be formed as a heat pump system for use in a fixed construction, such as a building, in a vessel or in a vehicle.
[0112] The system comprises a compressor 10 having a compressor input where the working fluid is in a first state with a first pressure P1, a first temperature T1 and a first enthalpy H1, and a compressor output where the working fluid is in a second state with a second pressure P2, a second temperature T2 and a second enthalpy H2.
[0113] The compressor 10 is configured to increase the pressure of the working fluid, such that P2>P1.
[0114] The compressor may be electrically powered.
[0115] The system further comprises a condenser 11 having a condenser input which is connected to the compressor output to receive the working fluid in the second state, and a condenser output, where the working fluid is in a third state P3, T3, H3.
[0116] The condenser 11 may be configured to exchange heat with a heat delivery circuit 12, wherein heat is delivered from the condenser 11, whereby the enthalpy of the working fluid may be reduced, such that H3<H2.
[0117] Alternatively, the condenser 11 may be configured to deliver heat to an airflow, or to merely dissipate heat to the surrounding environment, as could be the case in a refrigeration system.
[0118] The system further comprises a rotatable expander 130, which replaces the expansion valve 13 (
[0119] An expander input is connected to receive the working fluid in the third P3, T3, H3 state from the condenser 11.
[0120] The rotatable expander 130 is configured to allow the working fluid to expand to a modified fourth state P40, T40, such that the working fluid, at an expander output has a lower pressure and enthalpy than the third state, such that P40<P3 and H40<H3.
[0121] The rotatable expander 130 may be characterized as operating close to isentropic, which causes not only a pressure loss but also a loss in enthalpy, such that in the fifth state modified fourth state P40, T40, the enthalpy H40 is less than that (H3) of the third state.
[0122] The system further comprises an evaporator 140, which may be configured to exchange heat with a heat supplying circuit 15, wherein heat is received by the evaporator 140, whereby the enthalpy of the working fluid is increased and the working fluid is vaporized, such that H40<H1.
[0123] The heat supplying circuit 15 may be a cooling circuit in a cooling device or an air conditioning device. Alternatively, the heat supplying circuit 15 may be configured to pick up heat from e.g. air, ground, bedrock or water in a heat pump system.
[0124] An evaporator input is connected to receive the working fluid in the modified fourth state from the rotatable expander 130. An evaporator output is connected to the input of the compressor 10.
[0125]
[0126] In
[0127] In
[0128] In the system of
[0129] However, in the system of
[0130] The rotatable expander 130 may operate entirely below a saturation curve of the working fluid, such that the working fluid is in a two-phase state throughout the expansion. Alternatively, the rotatable expander may operate on the saturation curve or outside of the saturation curve.
[0131] In the evaporator 14, used in the system shown in
[0132] The evaporator 140 will need to add more enthalpy to the working fluid in the system of
[0133] Hence, the evaporator 140 will have to evaporate the working fluid by adding enthalpy corresponding to the difference between the enthalpy in the first state and the modified fourth state, i.e. the enthalpy H1H40 is added in the evaporator 140.
[0134] Therefore, the capacity of the evaporator 140 in
[0135] Additionally, it may be advantageous to minimize pressure drop in the evaporator 140. Ideally, the heating of the working fluid in the evaporator 140 would take place under constant pressure, but in reality there will be some pressure losses, depending on the design of the evaporator, so that P4>P1. In particular the pressure drop in the evaporator 140 may be less than about 3 bar, preferably less than about 2 bar or less than about 1.5 bar.
[0136] The pressure drop reduction can be achieved by increasing the number of flow paths through the evaporator 140 and/or by increasing a flow area of the evaporator 140.
[0137] It may also be advantageous to shorten the connection between the rotatable expander 130 and the evaporator 140.
[0138] As illustrated in
[0139] Referring to
[0140] However, other types of rotatable expanders may also be used.
[0141] The rotatable expander 130 is mechanically connected to a generator 131 for generating electric power.
[0142] The rotatable expander 130 receives a flow mf of the working fluid in the third state P3, T3 with an enthalpy H3 from the output of the condenser 12.
[0143] In the rotatable expander 130, the working fluid is isentropically expanded, with the working fluid being below the saturated liquid line, such that the working fluid is in two phase form.
[0144] The rotatable expander 130 outputs the working fluid at a lower pressure P40 and temperature T40, referred to as the modified fourth state, with also a lower enthalpy H40.
[0145] The rotation of the rotatable expander 130 drives the generator 131, which outputs electric power corresponding to P (exp), except for losses.
[0146] Referring to
[0147] The evaporator 140 is connected to the output of the rotatable expander 130, such that it receives the flow mf of the working fluid in the modified fourth state P40, T40, H40.
[0148] A connection 141 between the output of the rotatable expander 130 and the evaporator 140 may be made as short and straight as possible.
[0149] The connection 141 connects to a distributor 142, which divides the flow of working fluid into a plurality of evaporator channels 143a, 143b, 143c, each of which providing an evaporator subflow.
[0150] The subflows are merged by a collector 144 into an evaporator output 145, which connects to the compressor 10.
[0151] Each of the evaporator channels 143a, 143b, 143c may be formed as a respective flow path, such as a pipe, a tube or a hose, which may be connected to cooling flanges (not shown) for increasing heat exchange efficiency with a gaseous fluid.
[0152] Alternatively, the evaporator channels 143a, 143b, 143c may be formed by channels in a heat exchanger for heat exchange with a liquid.
[0153] The number of flow paths, and optionally the surface area of each flow path, can be selected to provide a desired pressure drop of less than 3 bar over the heat exchanger, with due consideration taken to the type of working fluid used in the relevant application.
[0154] From a power balance point of view, the system in
[0155] Consequently, the evaporator will be dimensioned such that P(evap)=P(cond)+P(exp)P(comp).
Experimental Data
[0156] In order to verify the principles of the system disclosed in
[0157] The modified system was modified as follows:
[0158] The expansion valve was replaced with a scroll type expander of the type DENSO SCSA06C 447220-6572 HFC134a. The scroll type expander was modified by removal of its non-return check valve and by increasing the flow area of the expander input to a diameter of about 14 mm.
[0159] The expander was connected to a brake, in the form of a Delta AC Servo Modell ECMA-J11330R4 KW 3,0/3000 rpm from Delta Electronics (Sweden) AB, which was used to emulate a generator connected to the outgoing axle of the rotatable expander 130.
[0160] The evaporator was replaced with an evaporator having higher capacity and lower pressure drop.
[0161] The evaporator was constructed by two open gable evaporator blocks of the type AIR0332 600600-4R, available from Aircoil AB (SE). The evaporator blocks were connected in parallel and mounted with the blocks in a V formation with a 90 degree angle.
[0162] In total, the evaporator 140 comprises 16 channels having an internal diameter of 6.4 mm and an average length of about 1400 mm.
[0163] A 500 mm long pipe was used to connect the output of the rotatable expander 130 to the distributor of the evaporator.
[0164] The systems were further fitted with pressure and temperature sensors as follows.
[0165] The modified system was fitted with pressure sensors GP01, GP02 immediately upstream and downstream of the compressor 10; temperature sensors GT03 and GT01 immediately upstream and downstream of the compressor 10; pressure sensors GP03 and GP04 immediately upstream and downstream of the rotatable expander 130; temperature sensors GT02, GT504 immediately upstream and downstream of the rotatable expander 130, and a temperature sensor GT503 at the inlet of the rotatable expander, downstream of the temperature sensor GT02.
[0166] The modified system was also fitted with temperature sensors GT501 and GT502 in the air stream immediately upstream and downstream of the evaporator 140.
[0167] All pressure sensors were Carel 0-10 bar/0-10V/SPKT0011CO 45/20, available from Carel Industries S.p.A (IT).
[0168] All temperature sensors were of the type PT1000, which are available from Regin Controls Sverige AB (SE).
[0169] Pressure and temperature data was logged using EXOcompact Ardo, which is available from Regin Controls Sverige AB (SE).
[0170] The systems were installed in a climate chamber, at an ambient temperature of 33-34 degC and a relative humidity of 25-30%.
[0171] The systems were installed in parallel and in the same environment, such that their operating conditions would be identical.
[0172] The resulting data for the original system and for the modified system are disclosed in the table below.
[0173] The condenser was caused to exchange heat with ambient air in the climate chamber.
[0174] The evaporator of the modified system was caused to exchange heat with an air stream moving at 9550 m3/h in another climate chamber having a temperature of 25-35 degC and a relative humidity of 35-46%, driven by the fan provided in the original system.
[0175] The values of GP01-GP04 and GT01-GT03 for the original system are residual values from an installation run of the system. These values were not used for calculating the COPc for the original system.
[0176] During an operating cycle of 15 minutes for the original system, the following data was collected by the temperature sensors GT501, GT502, GT503 and GT504 (
TABLE-US-00001 No GP01 GP02 GP03 GP04 GT01 GT02 GT03 GT501 GT502 GT503 GT504 1 14.31 14.33 10.11 10.10 22.31 22.38 22.27 23.56 9.33 23.48 23.27 2 14.32 14.34 10.11 10.10 22.33 22.41 22.36 23.65 9.26 23.48 23.29 3 14.33 14.35 10.12 10.11 22.37 22.48 22.33 23.54 9.26 23.48 23.38 4 14.34 14.36 10.11 10.10 22.35 22.49 22.32 23.73 9.26 23.48 23.39 5 14.35 14.37 10.11 10.10 22.40 22.51 22.42 23.78 9.22 23.51 23.44 6 14.36 14.38 10.12 10.11 22.43 22.55 22.42 23.64 9.30 23.55 23.48 7 14.37 14.39 10.12 10.11 22.46 22.54 22.46 23.89 9.24 23.59 23.60 8 14.37 14.39 10.12 10.10 22.45 22.61 22.50 24.04 9.27 23.59 23.68 9 14.38 14.39 10.12 10.11 22.50 22.68 22.53 24.24 9.34 23.66 23.70 10 14.39 14.40 10.12 10.12 22.55 22.67 22.54 24.54 9.27 23.70 23.80 11 14.39 14.41 10.12 10.12 22.54 22.68 22.59 24.38 9.35 23.71 23.87 12 14.40 14.42 10.13 10.12 22.59 22.71 22.58 24.01 9.34 23.81 23.92 13 14.41 14.42 10.13 10.12 22.60 22.75 22.61 23.75 9.26 23.81 23.94 14 14.42 14.43 10.13 10.13 22.66 22.76 22.66 24.12 9.59 23.86 24.00
[0177] Except for Pc, the following values were calculated for the original system:
TABLE-US-00002 No dPex dP23 dP41 Qev[kW] Pc COP* 1 0.02 4.22 4.22 24.39 9.21 2.65 2 0.01 4.23 4.22 24.65 9.21 2.68 3 0.01 4.23 4.23 24.46 9.21 2.66 4 0.01 4.24 4.24 24.79 9.21 2.69 5 0.01 4.26 4.25 24.94 9.21 2.71 6 0.01 4.26 4.25 24.57 9.21 2.67 7 0.01 4.27 4.26 25.11 9.21 2.73 8 0.01 4.27 4.26 25.29 9.21 2.75 9 0.01 4.27 4.27 25.53 9.21 2.77 10 0.01 4.28 4.27 26.16 9.21 2.84 11 0.01 4.29 4.28 25.76 9.21 2.80 12 0.00 4.29 4.27 25.15 9.21 2.73 13 0.01 4.28 4.29 24.83 9.21 2.70 14 0.00 4.29 4.29 24.91 9.21 2.70
[0178] The pressure differentials were calculated as follows: dPex=GP04GP03; dP23=GP02GP03; dP41=GP04GP01.
[0179] Qev was calculated as 5040*0.34*(GT501GT502), where the value 5040 from equipment supplier is the amount of air in m3/h per fan for the original system and the value 0.34 is a well known conversion factor from m3/h to kg/s for air at 285 K and 1 bar.
[0180] Pc is the standard power input value for the original system. COP was calculated as Qev/Pc.
[0181] The average COP for the original system was thus 2.72.
[0182] During an operating cycle of 45 minutes for the modified system, the following data was collected by the pressure sensors GP01, GP02, GP03, GP04, and the temperature sensors GT01, GT02, GT03, GT04, GT501, GT502, GT503 and GT504:
TABLE-US-00003 No GP01 GP02 GP03 GP04 GT01 GT02 GT03 GT501 GT502 GT503 GT504 1 9.1 18.9 18.7 10.3 75.3 33.0 11.6 22.9 12.9 28.2 15.1 2 9.3 19.1 18.6 10.4 76.3 33.7 11.8 22.9 13.2 28.6 16.1 3 9.4 19.7 19.2 10.6 77.8 34.8 12.0 23.7 13.7 29.9 16.7 4 9.4 19.6 19.4 10.8 78.0 34.8 12.2 23.8 13.9 30.0 16.8 5 9.4 21.1 21.0 10.6 81.2 36.6 12.9 24.1 14.0 32.2 16.6 6 9.3 21.7 21.5 10.7 84.1 37.5 13.8 23.9 14.0 33.0 16.6 7 9.5 21.4 21.1 10.8 83.8 37.4 13.6 25.2 14.6 32.9 17.2
[0183] In the same manner as for the original system, values for pressure differences, Qev, Pc and COP were calculated based on the measured values for the modified system as follows:
TABLE-US-00004 No dPex dP23 dP41 Bf rpm Pex[W] Qev[kW] Pc COP* 1 8.60 0.27 1.3 40 520 206.9 33.5 7.46 4.63 2 8.65 0.52 1.2 40 640 254.7 32.5 7.68 4.38 3 9.08 0.48 1.2 45 590 264.1 33.4 7.90 4.38 4 8.78 0.21 1.4 45 600 268.6 33.1 7.94 4.32 5 10.55 0.14 1.2 58 435 251.0 33.8 7.94 4.40 6 11.01 0.15 1.3 58 395 227.9 33.1 7.95 4.29 7 10.60 0.35 1.3 52 425 219.9 35.5 8.04 4.53
[0184] Measurement data of the torque ratio Bf and rpm were provided by the brake. Bf was measured as a percent of the brake's maximum torque.
[0185] Pex was calculated as (2n)/60MnBf, where n is the rpm, Mn is the maximum torque and Bf is the torque ratio.
[0186] With an average value of Qev of 33.6 and an average value of Pc of 7.84, it is concluded that the average value of COP was 4.42.
[0187] As can be concluded from the table above, the COP of the modified heat pump system is improved as compared with the original system in terms, and the modified system is also able to generate an additional 0.2 KW of electric power, which corresponds to about 1700 kWh for 365 days of continuous operation. By comparison, an average electric power consumption of a normal single-family house in Sweden will be in the interval 5000-20000 kWh per year, depending on which heating method is used (the lower part of the interval would be for houses with district heating).
[0188] The results achieved with the modified system are deemed to be conservative, in that measured values of electric power have been as high as 0.3-0.35 KW, in a system where e.g. connecting pipes are longer than they would have been in a properly packaged and optimized system. It is estimated that at least 0.4-0.5 KW should be achievable.
[0189]
[0190] In the following, only differences relative to the heat cycle in
[0191] The heat cycle system illustrated in
[0192] The provision of a subcooler 110 may increase the amount of liquid working fluid available at the inlet of the expander unit 130, which may in turn reduce leakage in the expander and thus increase expander efficiency.
[0193] The subcooler 110 may be caused to exchange heat with the working medium at a point upstream of the compressor 10, such as immediately upstream of the compressor, such that heat is effectively transferred from the working medium downstream of the condenser 11 to the working medium upstream of the compressor 10.
[0194] Tests were made with a modified version of the system described above. In particular, a heat exchanger in the form of an Aircoil 600200 3R Air 0331 was connected downstream of the condenser by means of a in connector.
[0195] A second modification can be made in the portion between the expander unit 130 and the evaporator 140, in that an expansion valve 162 may be connected in series with the expander unit 130 upstream of the evaporator 140. The expansion valve 162 may be operable in response to a condition downstream of the evaporator 140, in particular immediately downstream of the evaporator 140.
[0196] The expansion valve 162 may form part of an expansion arrangement 160, which may comprise a bypass connection 161 that makes the outlet of the expander unit 130 directly connectable to the evaporator 140, thus bypassing the expansion valve 162. One or more control valves 163, 164, 165 may be provided for shifting and/or adjusting the flow between the expansion valve 162 and the bypass channel 161. For example, the expansion arrangement 160 may be controlled based on measurements of pressure and/or temperature downstream of the evaporator 140. The control valves 163, 164, 165 may be adjustable between certain distributions, such as 50-50, 70-30, or the like. The provision of the expansion arrangement 160 allows for fine tuning the amount of liquid working medium that is input to the evaporator 140, which, in turn, enhances the efficiency of the evaporator 140.
[0197] The system may further comprise one or more service valves 151, 152, which may be binary valves or valves that can be adjustable continuously or stepwise.
[0198] The arrangement of a subcooler and the expansion arrangement 160 has proven effective in increasing the COP of the system from about 2.8 to about 3.8, which is significant.
[0199] In order to verify the function of the modifications described with reference to
TABLE-US-00005 System Qev(kW) Pc (kW) COP* Original 22.5 8.00 2.81 Original 21.3 8.02 2.66 Original 22.9 8.30 2.76 First modified 22.7 8.43 2.84 First modified 22.0 7.79 2.98 First modified 18.1 7.66 2.47 Second modified 27.9 7.65 3.86 Second modified 24.7 7.65 3.43 Second modified 28.0 7.76 3.82 Second modified 28.8 7.88 3.83 Second modified 29.5 7.70 3.98
[0200] From the tests, it was noted that for the original system, the average COP* was 2.74 and for the first modified system, the average COP* was 2.77. However, for the second modified system, the average COP* was 3.78. It is concluded that the second modified system provides for a substantial improvement in efficiency.
[0201] 10