OPTIMIZATION, CONTROL , AND IMPLEMENTATION OF CO 2 TRANSCRITICAL AIR CONDITIONING SYSTEMS By Ahmed A li Okasha A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Mechanical Engineering Doctor of Philosophy 20 20 ABSTRACT OPTIMIZATION, CONTROL , AND IMPLEMENTATION OF CO 2 TRANSCRITICAL AIR CONDITIONING SYSTEMS By Ahmed A li Okasha The US EPA listed R134a as unacceptable refrigerant for newly light - duty vehicles manufactured or sold in the United States as of model year 2021. Carbon dioxide CO 2 (R744) has been revived as a natural environmentally friendly refrigerant and is considere d a strong alternative to R134a as it has a global warming potential (GWP) of 1 compared to 1300 for R134a. In an air - conditioning system and due to the different thermodynamic properties of CO 2 , the heat rejection process at the high - pressure side will ta ke place above the critical point for high ambient/sink temperatures. Therefore, for a given ambient temperature, the GC pressure (high - side pressure) can be optimized and controlled independently. Either through simulations or experiments, researchers hav e been focusing on developing control correlations for the GC pressure to maximize the COP using offline control correlations or online methods. Maximizing COP does not mean that the system is working at its highest cooling/heating capacity that might be d esired for example in a transient start - up operation to cool down or heat up the car cabin in the shortest possible time. In addition, offline control correlations suffer deviation from the true optimum as they rely on the system model. Online methods, on the other hand, can be more accurate but often lack the fast convergence to the optimum solution. The aim of this thesis was to develop a new strategy to optimize and control the CO 2 transcritical air conditioning system for not only optimum COP, but also optimum cooling/heating capacity or a tradeoff solution based on the system state i.e. transient, steady state, or capacity demand. To find the Pareto Front or the best non - dominated solutions between the COP and the cooling capacity for any set of operati ng conditions, the existing Non - Dominated Sorting Genetic Algorithm II (NSGA - II) is used , and the results are generated based on a transcritical CO 2 thermodynamic model. The best solutions of both objectives COP and cooling capacity are presented by a Pare to Front for a given operating conditions. Each solution of the Pareto Front has a unique GC pressure and superheat. An optimization parameter that ranges from 0 to 1 is introduced to easily select maximum COP, maximum cooling capacity, or any of trade - off solutions. Based on the system operating conditions, the high - level optimizer signals the system actuators , the GC pressure , and superheat reference values. The proposed optimization and control approach can be employed as a hybrid offline and online s trategy. Based on the current operating conditions, the high - level optimizer will provide an initial estimate of the optimum solution to the online optimizer , which will start searching for the true optimum online from this close initial guess. An optional online optimizer can be integrated in the loop e.g. before the controller, resulting in conjunction with the offline optimizer in a hybrid solution. Such hybrid solution can reduce the time to approach the desired operating point compared to online only m ethods. Compared to offline only methods, this can additionally enhance COP and based on the actual system characteristics, while it is also able to adapt to changing system characteristics. While the results in this thesis are presented in terms of the cooling capacity, the same findings can be applied for the heating capacity. For further experimental investigations of the transcritical cycle, a modular transcritical CO 2 heat pump system and its coolant system have been constructed at the MSU Turbomachinery Lab that support cooling, heating, and dehumidification modes. Several parameters effects on the system performance have been analyzed and the experimental results are reported. Copyright by AHMED A LI OKASHA 20 20 v To my beloved F ather, M other, and B rother Ali, Mona, and Mohamed, Thank you for your unlimited love , patience, and support vi ACKNOWLEDGEMENT S In the name of Allah, the most Merciful and Beneficent . All praise is due to God (Allah) Almighty , the Lord of the world, the Master of day of J udgement, for the all the blessing, the strength, and the determination t o successfully complete this thesis wor k. My sincere gratitude goes to my main adviser, Prof. Norbert Müller for his constant support and motivation from the early stage of my research . I thank him a lot for all the hours of meetings ; his judgment of my work ; and his clear and persuasive , directions, comments , and feedback. A big thank s to Ford Motor Company for their generous support of this research and special thanks to Ford PI, James Gebbie, for his immense feedback and insights on my work from the early stage of the project. Likewise, I thank James Dyson Foundation for the Fellowship award while I was working on this research work. Many thanks to Prof. Kalyanmoy Deb whom I learn ed a lot from his evolutionary multi - objective class at MSU and for his time a nd fruitful discussion s on my thesis optimization portion. His innovative way of teaching made me love optimization and evolu tionary methods . In addition, I extend my sincere gratitude to Prof. Abrah a m Engeda and Prof. Neil Wright for their support and enc ouragement of this work and being in this thesis committee. Special thanks to my brother Mohamed for his help in designing the control circuits for the variable frequency driver s . I must also acknowledge Duy Nguyen , Ian Albert, Do Thong , and Basil Ahmed fo r their support in the experimentation. Many t hanks to Haitham Seada for the several discussion s on the m ulti - objective o ptimization . T hanks to Younis Najim for his guidance during the early stage of this work. Special thanks to Prof. Craig Gunn for his time in revising my technical writing documents. vii I would also like to extend my sincere appreciation to Michigan State University for making all the needed resources available and for the constant support, learning activities, and guidance to be a better researcher. Many thanks to all my Egyptian friends in the East Lansing area for the help and support the y provided whenever I needed. Finally, my deepest gratitude goes to my father Ali, my mother Mona, and my brother Mohammed for all the sincere love, tremendous patience, and unlimited support they offered me. viii TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ .......................... x LIST OF FIGURES ................................ ................................ ................................ ....................... xi KEY TO ABBREVIATIO NS ................................ ................................ ................................ ..... xvii KEY TO SYMBOLS ................................ ................................ ................................ ................... xix Chapter 1: Introduction ................................ ................................ ................................ ................... 1 1.1 Background ................................ ................................ ................................ ...................... 1 1.2 Global Warming Potential ................................ ................................ ................................ 3 1.3 Mo tivation behind using CO 2 as a refrigerant ................................ ................................ .. 5 1.3.1 Unity GWP ................................ ................................ ................................ ................ 5 1.3.2 Heating Mode for Electric Vehicles ................................ ................................ ......... 6 1.3.3 Smaller Component Weight ................................ ................................ ...................... 7 1.4 Thesis Structure ................................ ................................ ................................ ................ 8 Chapter 2: Literature Review ................................ ................................ ................................ ........ 10 2.1 Rise - Decline - Revival of CO 2 as a Refrigerant ................................ ........................... 10 2.2 Thermophysical Properties ................................ ................................ ............................. 11 2.3 Transcritical Cycle ................................ ................................ ................................ ......... 16 2.4 Related Studies ................................ ................................ ................................ ............... 18 2.5 Summary an d Thesis Contributions ................................ ................................ ............... 32 Chapter 3: Thermodynamic Modeling and Analysis ................................ ................................ .... 36 3.1 Compressor Modeling ................................ ................................ ................................ .... 36 3.2 Cycle Modeling ................................ ................................ ................................ .............. 39 3.3 Analysis ................................ ................................ ................................ .......................... 41 3.4 Optimization Correlation ................................ ................................ ................................ 45 Chapter 4: Multi - Objective Optimization ................................ ................................ ..................... 48 4.1 Bi - objective Optimization ................................ ................................ .............................. 55 4.1.1 Problem Formulation ................................ ................................ .............................. 55 4.1.2 Evolutionary Multi - objective Optimization Algorithm ................................ .......... 56 4.2 Best Trade - off Solutions ................................ ................................ ................................ 57 4.2. 1 Obtained Pareto Front ................................ ................................ ............................. 57 4.2.2 Gain to Loss Ratio for moving from one solution to another ................................ . 59 4.3 Optimization Variables Effect on the Pareto Front ................................ ........................ 63 4.3.1 Effect of GC Outlet Temperature Change ................................ .............................. 63 4.3.2 Effect of Evaporation Temperature Change ................................ ........................... 65 4.3.3 Effect of Useful Superheat ................................ ................................ ...................... 67 4.3.4 Effect of Compressor Speed ................................ ................................ ................... 69 4.3.5 Effect of Compressor Performance ................................ ................................ ......... 70 ix 4.4 Operation Contour Maps and Cycle Control Strategy ................................ ................... 71 Chapter 5: Experimental Apparatus ................................ ................................ .............................. 74 5.1 CO 2 Loops ................................ ................................ ................................ ...................... 74 5.1.1 Schematics ................................ ................................ ................................ .............. 74 5.1.2 Compressor ................................ ................................ ................................ ............. 78 5.1.3 Oil Management ................................ ................................ ................................ ...... 80 5.1.4 Heat Exchangers ................................ ................................ ................................ ..... 82 5.1.5 Suction Line Accumulator ................................ ................................ ...................... 83 5.1.6 Expansion Device ................................ ................................ ................................ ... 84 5.1.7 Pressure Drop ................................ ................................ ................................ .......... 85 5.1.8 Valves, Tubing, and Fittings ................................ ................................ ................... 92 5.2 HTF loops ................................ ................................ ................................ ....................... 94 5.2.1 Steady - state Capacities ................................ ................................ ........................... 94 5.2.2 Tanks Sizing ................................ ................................ ................................ ............ 96 5.2.3 Transient Capacities ................................ ................................ ................................ 97 5.2.4 Chillers and pumps Selection ................................ ................................ ................ 100 5.2.5 Schematics ................................ ................................ ................................ ............ 102 5.3 Instrumentation ................................ ................................ ................................ ............. 102 5.4 Test - Rig Layout & 3D CAD Modeling ................................ ................................ ........ 106 5.5 System Build & Photos ................................ ................................ ................................ 110 Chapter 6: Experimental Testing and Results ................................ ................................ ............. 119 6.1 Test Method and Validation ................................ ................................ ......................... 119 6.2 Uncertainty and Repeatability ................................ ................................ ...................... 121 6.3 Results and Discussion ................................ ................................ ................................ . 123 Chapter 7: Conclusions and Future work ................................ ................................ .................... 127 7.1 Conclusions ................................ ................................ ................................ .................. 127 7.2 Future Work ................................ ................................ ................................ ................. 128 APPENDIX ................................ ................................ ................................ ................................ . 130 BIBLIOGRAPHY ................................ ................................ ................................ ....................... 133 x LIST OF TABLES Table 1 - 1. Environmental impact characteristic of common refrigerants ................................ ...... 6 Table 2 - 1. Thermodynamic properties & refrigeration capacity of common refrigerants ........... 12 Table 3 - 1. Developed volumetric and isentropic efficiency correlations at different evaporation temperatures ................................ ................................ ................................ ................................ .. 39 Table 4 - 1. Pareto Front variable and objective values for five selected solutions: maximum COP, maximum c , and three trade - off solutions ................................ ................................ .................. 57 Table 4 - 2. Gain to loss ratios for five solutions obtained from the normalized Pareto Front ...... 61 Table 4 - 3 . Gain to loss ratios for five solutions using absolute values from the Pareto Front (Eqn. ( 4.12)) ................................ ................................ ................................ ................................ ............ 61 Table 5 - 1. Compressor specifications ................................ ................................ ........................... 79 Table 5 - 2. Estimated HTF heater on - time for different heat exchangers in a cold day lab environment for preparation of the cooling mode ................................ ................................ ........ 99 Table 5 - 3. Estimated HTF Chiller on - time for different HEXs in a hot day lab environment for preparation of the heating mode ................................ ................................ ................................ ... 99 Table 6 - 1. Test Matrix showing the operating conditions for each test point ............................ 119 Table 6 - 2. Repeatability test results for Measurement M5 ................................ ......................... 122 Table A - 1 . Bill of material for the CO 2 transcritical heat pump system built at the MSU Turbo Machinery Lab ................................ ................................ ................................ ............................ 131 xi LIST OF FIGURES Figure 1 - 1. Heat pump cycle and its main components for the refrigeration, cooling, or air conditioning mode ................................ ................................ ................................ .......................... 2 Figure 1 - 2. The greenhouse effect. Credit: climatecentral.org. ................................ ...................... 4 Figure 1 - 3. The average annual global temperatures sinc e 1880. Credit: www.climate.gov ......... 5 Figure 1 - 4. Two compressor photographs of R134a and CO 2 / R744 showing the reduction in volume and space required. Credit: Kim, et al. [2004] ................................ ................................ ... 8 Figure 2 - 1. CO 2 pressure enthalpy diagram ................................ ................................ .................. 12 Figure 2 - 2. CO 2 p - T or phase diagram ................................ ................................ .......................... 13 Figure 2 - 3. Saturation pressure of R744 compared to selected refrigerants ................................ . 13 Figure 2 - 4. Vapor density of R744 compared to selected refrigerants ................................ ......... 14 Figure 2 - 5. Latent heat of vaporization of R744 compared to selected refrigerant ...................... 15 Figure 2 - 6. Refrigeration capacity of R744 compared to selected refrigerants ............................ 15 Figure 2 - 7. Vapor thermal conductivity of R744 compared to selected refrigerants ................... 16 Figure 2 - 8. Liquid thermal conductivity of R744 compared to selected refrigerants ................... 17 Figure 2 - 9. p - h diagram for a subcritical and transcritical cycles ................................ ................. 18 Figure 3 - 1. Basic CO 2 Transcritical system with the corresponding T - s and p - h diagrams ......... 36 Figure 3 - 2. Dorin CD200 - CD180H Compressor Envelope ................................ .......................... 38 Figure 3 - 3. Compressor developed volumetric efficiency correlations compared to correlations from the literature ................................ ................................ ................................ ......................... 40 Figure 3 - 4. Compressor developed isentropic efficiency correlations; compared to correlations from the literature ................................ ................................ ................................ ......................... 41 Figure 3 - 5. The effect of varying the GC pressure on the COP at different GC outlet temperatures and at 15 °C evaporation temperature ................................ ................................ ..... 42 Figure 3 - 6. The influence of varying the GC pressure on the COP at different evaporation temperatures and at 35 °C GC outlet temperature ................................ ................................ ........ 43 xii Figure 3 - 7. The impact of varying the GC outlet temperature on the COP at different GC pressures and at 15 °C evaporation temperature ................................ ................................ ........... 43 Figure 3 - 8. The effect of changing the evaporation temperature on the COP at different GC pressures and at 35 °C GC outlet temperature ................................ ................................ .............. 44 Figure 3 - 9. The influence of the superheating on the COP at 15 °C evaporation temperature; 35 °C GC outlet temperature ................................ ................................ ................................ ............. 45 Figure 3 - 10. The influence of the superheating on the COP at 15 °C evaporation temperature; 45 °C GC outlet temperature ................................ ................................ ................................ ............. 46 Figure 3 - 11: Developed correlation for optimized GC pressure shown in thick green curve compared to correlations available in the literat ure ................................ ................................ ...... 46 Figure 4 - 1. p - h diagram for CO 2 with simple transcritical cycle at T 3 =32 °C, p GC =85 bar, and T 1 =15 °C ................................ ................................ ................................ ................................ ....... 49 Figure 4 - 2. Effect of varying p GC at T 3 =32 °C, T 1 =15 °C, RPM, T sh =1 K, and with four different compressor efficiency correlations on COP ................................ ................................ ... 51 Figure 4 - 3. Effect of varying p GC at T 3 =32 °C, T 1 =15 °C, RPM, and T sh =1 K, and with four different compressor efficiency correlations on c ................................ ............................... 53 Figure 4 - 4. The COP gain for transitioning from a subcritical cycle with close to T cr to a transcritical cycle, keeping T 1 sh =1 K, and is = v = 0.7. Optimum pressures are in bar ................................ ................................ ................................ ........................ 54 Figure 4 - 5. The c gain for transitioning from a subcritical cycle with close to T cr to a transcritical cycle, keeping T 1 sh =1 K, and is = v = 0.7. Optimum pressures are in bar ................................ ................................ ................................ ........................ 54 Figure 4 - 6. Schematic of NSGA - II maximizing both objectives COP and c ............................. 58 Figure 4 - 7. Pareto Front for maximizing both COP and c with corresponding GC pressures. Solutions labeled with k=0 and k=1 are the maximum COP an d c solutions respectively. Solutions with k=0.25, 0.25, and 0.75 are labeled as example trade - off solutions. ...................... 58 Figure 4 - 8. p - h diagram indicating the cycles for the five solutions labeled on the Pareto Front in Figure 4 - 7. The green cycle produces the maximum COP, the purple cycle the maximum c , and the grey cycles represent the th ree example trade - off solutions. ................................ .................. 59 Figure 4 - 9. Normalized Pareto Front for maximizing both COP, c and G/L for moving to right an d left with k =0.25 ................................ ................................ ................................ ................... 62 Figure 4 - 10. Pareto Front for maximizing both COP, c and G/L based on absolute values for moving to right and left with k =0.25 ................................ ................................ ......................... 62 xiii Figure 4 - 11. Pareto Fronts maximizing both COP and c at T 1 =15 °C, T sh =1 K, and RPM, for different T 3 . The grey lines connect the solutions corresponding to k=0, 0.25, 0.5, 0.75, and 1 ................................ ................................ ................................ ................................ .............. 64 Figure 4 - 12. p - h diagram with cycles for four different T 3 and T 1 =15 °C, T sh =1 K, RPM, k=0.5 from Figure 4 - 11 . The circle markers on each isotherm represent the corresponding Pareto Front in Figure 4 - 11 ................................ ................................ ................................ ...................... 65 Figure 4 - 13. Pareto Fronts maximizing both COP and c at T 3 =32 °C, T sh =1 K, and RPM, for different T 1 . The grey lines connect the solutions corresponding to k=0, 0.25, 0.5, 0.75, and 1 ................................ ................................ ................................ ................................ .............. 66 Figure 4 - 14. p - h diagram with cycles for five different T 1 at T 3 =32 °C, T sh =1 K, 1800 RPM, and k=0.5 from Figure 4 - 13 ................................ ................................ ................................ .......... 67 Figure 4 - 15. Pareto Fronts for maximizing COP and c at T 3 =32 °C, T 1 =15 °C, and RPM, for different T sh . The grey lines connect the solutions corresponding to k=0, 0.25, 0.5, 0.75, and 1 ................................ ................................ ................................ ................................ ..... 68 Figure 4 - 16. Pa reto Fronts for maximizing COP and c at T 3 =45 °C, T 1 =15 °C, and RPM, for different T sh . The grey lines connect the solutions corresponding to k=0, 0.25, 0.5, 0.75, and 1 ................................ ................................ ................................ ................................ ..... 69 Figure 4 - 17. Pareto Fronts for maximizing both COP and c at T 3 =32 °C, T 1 =15 °C, and T sh =1 1 ................................ ................................ ................................ ................................ ..................... 70 Figure 4 - 18. Pareto Fronts for maximizing both COP and c at T 3 =32 °C, T 1 =15 °C, T sh =1 K, compressors efficiencies ................................ ....................... 71 Figure 4 - 19. Operation Maps that show the contour lines of the GC pressures for T 1 : - 25 C to 15 °C , T 3 : 32 °C to 45 °C, and k=0 maximum COP (first row), k=0.5 trade - off (middle row), and k=1 maximum c (last row) ................................ ................................ ................................ .......... 72 Figure 4 - 20. Tran scritical cycle control block diagram for operating at the maximum COP, c , or a desired best trade - off both represented by Pareto Fronts ................................ ........................... 73 Figure 5 - 1. Cooling mode schematic ................................ ................................ ............................ 75 Figure 5 - 2. Heating mode schematic ................................ ................................ ............................ 76 Figure 5 - 3. Series dehumidification mode schematic ................................ ................................ ... 77 Figure 5 - 4. Parallel dehumidification mode schematic ................................ ................................ 77 Figure 5 - 5. Cooling, heating, dehumidification series mode, and dehumidification parallel mode ................................ ................................ ................................ ................................ ....................... 78 xiv Figure 5 - 6. D orin CO 2 CD180H compressor detailed drawing and photo (Credit: Dorin) .......... 80 Figure 5 - 7. Oil separator photo and schematic (Credit: Temprite) ................................ ............... 81 Figure 5 - 8. (a) HBOC (b) Installation on the compressor sight glass. (c) Solenoid valve V150 (Credit: HB Products Company) ................................ ................................ ................................ ... 81 Figure 5 - 9. Schematic of the oil return line ................................ ................................ .................. 81 Figure 5 - 10. AXP10 Pressure ratings (Left) and AXP10 Photo and Schematic (right) ............... 82 Figure 5 - 11. Horizontal accumulator design drew by Temprite ................................ ................... 84 Figure 5 - 12. Schematic of SWAGELOK 31 series valve and it Cv graph ................................ ... 85 Figure 5 - 13. Suction line Pressure drop, equivalent temperature change, and the flow velocity for different tube OD ................................ ................................ ................................ .......................... 91 Figure 5 - 14. Discharge line Pressure drop, equivalent temperature change, and the flow velocity for different tube OD ................................ ................................ ................................ .................... 91 Figure 5 - 15. Liquid line Pressure drop, equivalent temperature change, and the flow velocity for different tube OD ................................ ................................ ................................ .......................... 91 Figure 5 - 16. The First Law of Thermodynamics applied to the cooling mode to estimate the needed chilling and heating capacities ................................ ................................ .......................... 95 Figure 5 - 17. The First Law of thermodynamics applied to the heating mode to estimate the needed chilling and heating capacities ................................ ................................ .......................... 96 Figure 5 - 18. A photo of ALT - 2 Mokon chiller ................................ ................................ ........... 101 Figure 19. The pump curve vs one, two, and three heat exchanger system Curves ................... 102 Figure 5 - 20. HTF Schematics ................................ ................................ ................................ ..... 103 Figure 5 - 21. Various Instrumentation used in the CO 2 transcritical heat pump test rig facility . 105 Figure 5 - 22. Test - rig layout that shows the location of different sensors ................................ .. 107 Figure 5 - 23. 3D CAD of the test - rig within the Turbomachinery Lab space at MSU ............... 108 Figure 5 - 24. CO 2 Liquid cylinder connector/adapter setup ................................ ........................ 109 Figure 5 - 25. CO 2 test rig frame on the start of the build at the Turbomachinery Lab showing the F - series flow sensor and few tubing connected to the flow sensor ................................ ............. 110 Figure 5 - 26. The Dorin CD200 - CD180H Compressor mounted on its frame within the test rig ................................ ................................ ................................ ................................ ..................... 111 xv Figure 5 - 27. The Tempri te oil separator and its relative size with respect to a keyboard. The tubing is connected to the oil return line. The two black caps are covering the sight glasses. ... 111 Figure 5 - 28. A photo schematic showing the addition of the suction line, discharge line, and the lines around the accumulator. The photo also shows the integration of four pressure relief valves. ................................ ................................ ................................ ................................ ..................... 112 Figure 5 - 29. A photograph shows the integration of pressure gauges connected to different points in the system. The pressure ga uges are only for quick monitoring of the system pressure. The system is equipped with pressure sensors to provide thermodynamic property calculations during the system run on LabVIEW and for postprocessing on MATLAB. ................................ ......... 112 Figure 5 - 30. A photo showing the accumulator that has been manufactured by Temprite and its relative size with respect to a keyboard ................................ ................................ ...................... 113 Figure 5 - 31. A photo showing the accumulator and a 3D - printed enclosure (left), the accumulator assembled in the enclosure (middle), and the accumulator integr ated with the test rig (right) ................................ ................................ ................................ ................................ .......... 113 Figure 5 - 32. Photos show the initial build of the HTF test rig. The mounting of the two tanks to the HTF frame (left), the soldering of the HTF copper tubes at the MSU machine shop (middle), and the integration of the copper tubes to the test rig (right). ................................ ..................... 113 Figure 5 - 33. Photo shows the Mokon Chiller at the Turbomachinery lab ................................ .. 114 Figure 5 - 34. A Ph oto shows the HTF test rig after connecting most of the copper tubing and the three Rosemount Magnetic flowmeters ................................ ................................ ...................... 114 Figure 5 - 35. A Photo shows the CO 2 test rig after fixing a clear polycarbonate glass sheet from the test rig back side ................................ ................................ ................................ .................... 115 Figure 5 - 36. Photos showing the progress of connecting the three cylinders; Nitrogen, liquid CO 2 , and Gas CO 2 (left) to the system through a wall mounted charg ing panel (right) ............. 115 Figure 5 - 37. Photo shows the CO 2 test rig after the tubing integration completion and fully enclosed by clear polycarbonate glass ................................ ................................ ........................ 116 Figure 5 - 38. Photo shows the HTF test rig after copper pipes integration completion and connecting the Rose mont transmitters to the flowmeter ................................ ............................. 11 7 Figure 5 - 39. Photos shows the progress of insulating different parts of the CO 2 test rig tubing 117 Figure 5 - 40. Complete photos of the experimental test rig. The left photo shows the CO 2 test rig with the data acquisition and PC. The right photo shows the HTF test rig connected to both the chiller and the CO 2 test rig from the right and the left respectively. ................................ .......... 118 Figure 5 - 41. A Screenshot showing the developed LabVIEW Test Program that monitor the system temperatures, pressure, and flow in real time and plots the p - h, T - s, and T - d diagrams 118 xvi Figure 6 - 1. The energy balance across the heat exchangers capacities M1 measurement case . 120 Figure 6 - 2. The energy balance actual and moving average signals for M1 measurement case 121 Figure 6 - 3. The CO 2 mass flow rate signal for M1 measurement case ................................ ...... 122 Figure 6 - 4. The Cooling COP measurements at different HTF inlet temperatures .................... 123 Figure 6 - 5. The Hea ting COP measurements at different HTF inlet temperatures .................... 124 Figure 6 - 6. The CO 2 mass flow rate for different HTF GC and evaporato r inlet temperatures at different pressures ................................ ................................ ................................ ....................... 125 Figure 6 - 7. The superheat taking place inside the evaporator for different HTF GC a nd evaporator inlet temperatures at different pressures ................................ ................................ ... 126 xvii KEY TO ABBREVIATIONS BPHE Brazed plate heat exchangers COP C oefficient of performance d Distance EPA E nvironmental protection agency EXV E lectronic expansion valve G Gain GC G as cooler GWP G lobal warming potential HEX Heat Exchanger HTF H eat transfer fluid IHX I nternal heat exchanger ISO I nternational organization for standardization L L oss N Number of population O O ffspring population Obj Objective ODP O zone depletion potential OHEX O utside heat exchanger OS Oil Separator P Parent population PAG P olyalkylene Glycol xviii PI P roportional - integral POE P olyolester R L umped parent and offspring population ref reference RTD R esistance temperature detector SG S pecific gravity sub Subcritical sup Supercritical VFD V ariable frequency drive VG V iscosity grade xix KEY TO SYMBOLS 1,2, etc. T hermodynamic state points, [ - ] A Tube/pipe cross sectional area, [ m 2 ] c p I sobaric specific heat capacity, [ J/ ( kgK )] C v V alve flow coefficient, [ - ] D i I nner tube diameter, [ m ] D o O uter tube diameter, [ m ] f D Darcy friction factor, [ - ] g G ravitational constant, [ m 2 /s ] h S pecific enthalpy, [ J/kg ] h fg L atent heat of vaporization, [ J/kg ] k Bi - Objective optimization index, [ - ] K F actor for the 3K pressure drop calculation method, [ - ] K 1 , K d , and C onstants extracted from tables for the 3K method, [ - ] m R efrigerant charge, [ kg ] Nu Nusselt number, [ - ] p P ressure, [ bar or psi] P P ower, [ W ] Pr P randtl number, [ - ] q V olumetric flow rate, [ GPM or m 3 /s ] V olumetric refrigeration capacity, [ kJ/m 3 ] Re Reynolds number, [ - ] xx r p Compressor pressure ratio, [ - ] s S pecific entropy, [ kJ/ ( kgK )] T T emperature, [ °C or K ] S pecific volume, [ m 3 /kg ] V V olume, [ m 3 or gallon ] V d C ompressor displacement (swept volume), [ m 3 ] x V apor quality, [ - ] y Energy balance variable, [ - ] Y C onstant which collects fixed parameters related to the geometry and operating conditions [ kW 2 /m 4 ] R efrigerant mass flow rate, [ kg/s ] C apacity, [k W ] Work per unit time (Power) , [k W ] Difference, [ - ] G reek C onstant of the compressor isentropic efficiency [ - ] S lope of the compressor isentropic efficiency [ - ] E fficiency, [ - ] D ynamic viscosity, [ N.s/m 2 ] D ensity, [ kg/m 3 ] F low speed, [ m/s ] C ompressor speed, [ rpm ] xxi Subscripts amb A mbient avg Av erage C C ooling comp C ompressor cr C ritical dis D ischarge Evp E vaporation GCo Gas cooler outlet temperature H H eating i Index in I nlet is I sentropic opt O ptimum o ut O utlet r R efrigerant ref Reference sat S aturation sh Superheat sp S et - point sub Subcritical sup Supercritical xxii t C urrent generation v V olumetric 1 Chapter 1: Introduction 1.1 Background No matter where we live on earth , heat pumps form an essential and central part of our daily lives. A heat pump is a device that uses energy to move heat from one place to another using a refrigerant. Heat pump is a broad term that involves cooling or heating depending on the cy cle's desired objective. For refrigeration , cooling, or air conditioning applications , the refrigerant pulls the heat from the cold refrigerated space (For example: a room or a passenger compartment ) and rejects the heat to an outside warm environment . In the heating mode, the refrigerant pick s up and transfer s the heat from the outside environment to the heat ed space . Heat pumps are used widely in residential and commercial building s , automotive, hospitals, theaters, restaurants , industrial processes, vending machines , and many other applications . H eat pump operation is based on a typical vapor compression cycle that is shown in Figure 1 - 1 . The main components of a heat pump system f or either cooling or heating applications consist of a compressor, a condenser, an expansion device, and an evaporator . For the cooling mode cycle, the refrigerant enters on the suction side of the compressor at state 1 as a low temperature, low pressure, and saturated vapor and goes under isentropic compress ion to the condenser pressure. Vapor refrigerant exits the compressor at a temperature well above the outside environment or the surrounding medium. Refrigerant then enters the condenser as a superheated vapor at state 2, rejecting heat to the environment at a constant pressure, and leaves the condenser as saturated liquid at state 3. The expansion dev ice then throttles the refrigerant, reducing its pressure to the evaporator pressure as well as dropping the temperature below the refrigerated space temperature. The expansion device can be a fixed area such as a capillary tube or an orifice, manually adj ustable by a needle valve or metering valve, thermostatic, or electronically adjustable one by a 2 stepper/servo motor. The refrigerant then enters the evaporator at state 4 as a mixture and evaporates while absorbing heat from the refrigerated space. The r e frigerant leaves the evaporator as a saturated vapor at state 1 and the cycle repeats. For a heating mode, the cycle is similar ; however , the refrigerant will reject heat from the condenser to the heated space and picks up heat through the evaporator from the outside environment. There are several kinds of refrigerants, the selection of which depends on aspects such their thermodynamic and transport properties; their environmental impact, which includes their influence on global warming and the ozone layer ; and properties such as toxicity and flammability. Figure 1 - 1 . Heat pump cycle and its main components for the refrigeration, cooling, or air conditioning mode 3 Refrigerants can be categorized into two m ain types: synthetic and natural. Chlorofluorocarbons (CFCs), Hydrochlorofluorocarbons (HCFCs), and Hydrofluorocarbons (HFCs) are examples of synthetic refrigerants; while common natural refrigerants include air , water (R718), ammonia (R717), and carbon di oxide , CO 2 ( R744 ). Chlorofluorocarbons (CFCs) refrigerants were developed in the 1930s and contain Chlorine, Fluorine, and Carbon, such as R12 (brand name Freon 12). CFCs are non - toxic and non - flammable and were used in various industrial, commercial, and automotive applications. In 1973, it was revealed that when CFCs reach the upper atmospher e and get exposed to ultraviolet rays, they break down into base substances. The chlorine reacts with the oxygen atoms in the ozone and break apart the ozone molecule. Molina & Rowland [1] revealed that the ch lorine emissions damage the ozone layer ; and since then , governments and industrial firms began to phase out CFC refrigerants . One atom of chlorine can destroy more than a hundred thousand ozone molecules according to the U.S. EPA . Destruction of the ozone leads to what is known as the "Ozone Hole." Ozone is naturally formed in the atmosphere and it absorbs the sun's harmful ultraviolet rays. The ozone hole increases the risk of skin cancer and weakens the human immune system leading to diseases and other e nvironmental effects. Ozone depletion potential (ODP) is a term introduced in 1983 that defines the relative amount of degradation to the ozone layer it can cause, with R11 refrigerant being fixed at an ODP of 1.0. Montreal Protocol [2] placed a regulation to phase out the production of numerous substances that were responsible for ozone depletion. 1.2 Global Warming Potential Hydrochlorofluorocarbons (HCFCs) ( which contain Hydrogen, Chlorine, Fluorine, and Carbon ) , pose only 10 % of the ODP compared to CFCs. However, HCFCs are among the greenhouse gasses that have h igh global warming concerns. T he energy from the sun reaches the earth as solar 4 radiation. While some of the radiation is reflected by the earth and the at mosphere, most of the radiation is absorbed by the earth. The earth emits infrared radiation, some passes through the atmosphere, but a portion get trapped by the greenhouse gases making the earth's surface warmer than it would be. This destroys the energy balance of the earth and causes climate changes. The global warming potential (GWP) is an index that measures how much energy the emissions of 1 ton of a gas will absorb over a given period of time relative to the emissions of 1 ton of carbon dioxide ( CO 2 ) over 100 - year period [3] . Figure 1 - 2 . The greenhouse effect . Credit: climatecentral.org. Hydrofluorocarbons (HFCs) that contain Hydrogen, Fluorine, and Carbon do not have any ODP ; and although they have lower GWP than HCFCs , their GWP is still relatively large in the range 1300 - 1900. According to the Intergovernmental Panel on Climate Change (IPCC) [4] , which includes more than 1,300 scientists, a forecast of a temperature rise of 2.5 to 10 degrees F ( over the next century is predicted due to greenhouse gases. Figure 1 - 3 shows the increase in the average annual global temperatures since 1880 . NASA [5] projects the long - term effects associated with climate change to be (1) Tempera tures will continue to rise , (2) Hurricanes will become stronger and more intense , (3) Increas ed droughts and heat waves , (4) Sea level will rise 1 - 4 feet by 2100 5 and (5) The Arctic Ocean is expected to become essentially ice free in summer before mid - century. As a matter of fact, some of these effects have been more obvious in the past few years. The intensity, frequency , and duration of North Atlantic hurricanes, as well as the frequency of Category 4 and 5 hurricanes have all increased in the las t decade . Hurricane Irma in 2017 was a Category 5 storm peaked with 180 mph winds, caused widespread and devastating damage throughout the Caribbean and the Florida Keys . In southern Texas, Hurricane Harvey barreled down as a Category 4 storm and caused ex tensive flooding in the Houston metro area. Figure 1 - 3 . The average annual global temperatures since 1880 . Credit: www.climate.gov 1.3 Motivation behind using CO 2 as a refrigerant 1.3.1 Unity GWP Under Kyoto protocol regulations [6] (adopted in 1997 and entered into force in 2005), the phasing out of HFC refrigerants is underway due to their global warming concerns. In 2015, t he US EPA listed R134a as unacce ptable refrigerant for newly manufactured light - duty vehicles manufactured or sold in the United States as of m odel y ear 2021. The regulations are pushing to actively look for a long - term, environmentally friendly alternative refrigerant. Ammonia (R717), a lthough it has zero ODP and GWP , is highly flammable and toxic. Water (R718 ) has two main disadvantages: 6 f irst i t s high freezing point limits the evaporation temperature to be above 0 C , and secondly it requires compressors to be able to handle large volu me flows and high pressure ratios due to its low operating pressures and vapor density [7] . Hydrocarbons such as propane (R290) are highly flammable and can be explosive. Carbon dioxide ( CO 2 or R744) on the other hand is a non - flammable, non - toxic fluid that has zero ODP and GWP of unity, which is negligible compared to 1300 of R134a . Table 1 - 1 summarizes environmental impact characteristics of CO 2 and other common refrigerants. Table 1 - 1 . Environmental impact characteristic of common refrigerants Refrigerant Type Chemical Formula ODP GWP Flammab le Toxic R12 CFC CCl2F2 1 2400 No No R22 HCFC CHClF2 0.05 1700 No No R134a HFC CF3CH2F 0 1300 No No R410a HFC blend 50%CH 2 F 2 /50%C HF 2 CF 3 0 2000 No No R1234yf HFO C3H2F4 0 4 Yes No R717 (Ammonia) Natural ref. NH3 0 0 Yes Yes R774 Natural ref. CO 2 0 1 No No 1.3.2 Heating M ode for Electric Vehicles Vehicles powered by internal combustion engines use the waste heat from the coolant to heat the passenger compartment. They also use the engine to run the air conditioning compressor. Modern cars with fuel - injection engines often have insufficient waste heat for heating of the passenger compartment in the winter sea son. The long heating - up period and slow defroster action is unacceptable both in terms of safety and comfort. Supplementary heating is therefore necessary, and one attractive solution may be to operate the heat pump in the heating mode . On the other hand, e lectric vehicles r ely exclusively on the energy stored in their batteries for heating and cooling since there is no engine to power the AC . The more efficient those systems are, the longer 7 the mileage range the vehicle can make . Many electric vehicles rely on old fashioned resistance heaters to warm the passenger compartment. It is effective but uses a lot of electricity to meet the desired heating capacity or the desired temperature set point . To illustrate, electric heaters prov ide heating energy output equal to the electric energy input. For example, if the cabin heating demand is ~3 kW, the electric heater will consume 3 kW ( or more due to the losses ) regardless of the ambient and set point operating conditions ; hence the effic iency is ideally 1 . On the other hand, for a CO 2 air conditioning system running in the heating mode and to meet a heating demand of 3 kW for a system running at - 20 °C ambient temperature , the system will have COP of ~3 , t hus, consuming only 1 kW of power compared to 3 kW which is one third the energy demand. Although similar COP can be achieved with other refrigerant s , CO 2 systems have other benefits in the heating mode due to the compression high discharge pressure and temperature, high capacity and COP can be achieved also at low ambient temperature s and the high outlet temperature will allow instant defrosting of automobile windshields . 1.3.3 Smaller C omponent W eight T he ope rating pressure encounter ed in CO 2 air conditioning systems is significantly higher than other traditional refrigerants, up to around 10 rimes . High pressure means higher density for any fluid , w hich leads to higher refrigeration capacity (which is the pro duct of the vapor density times the latent heat of vaporization) . Therefore, a volume amount of CO 2 refrigerant can transport much more heat compared to traditional refrigerant with the same volume. I t also means that CO 2 can transport the same amount of heat with much less volume ; and , hence , we can use smaller and more compact components , therefore , allowing miniaturization of the systems for the same heat pumping power requirements. 8 1.4 Thesis Structure This thesis is structured as follows . In Chapter 2 , we explore the history of using CO 2 as a refrigerant, highlight the important CO 2 thermophysical properties, and then introduce the transcritical cycle and emphasize the main differences compared to the conventional subcritical heat pump cy cle . Afterwards, we detail the state - of - the - art CO 2 transcritical systems and mention the main contribution (s) of previous works; and most importantly, critically assesses their methods and strategies . We conclude the chapter by pointing out the open issue s and presenting the thesis work contributions. Chapter 3 presents the transcritical cycle thermodynamic modeling and evaluates the effects of the several system parameters on the cycle performance . We present the developed volumetric and isentropic effic iency correlations for the commercial compressor used in the experimental test rig. We also present the d eveloped offline control correlation to optimize the COP for the cycle that relates the GC pressure to the GC outlet temperature , which is the most dom inant factor. Figure 1 - 4 . Two compressor photographs of R134a and CO 2 / R744 showing the reduction in volume and space required. Credit: Kim, et al . [2004] Chapter 4 introduces the new developed optimization and control technique for the CO 2 transcritical cycle based on the Non - dominated Sorting Genetic Algorithm II . The algorithm is used to study the trade - off between the COP and the cooling capacity , generat ing for different Smaller Components R134a compressor CO 2 /R744 compressor 9 operating conditions the best non - dominated solutions or the Pareto Front . The effect on the Pareto Front of each optimization variable is shown and discussed separately . A c ontrol methodology is proposed where according to a pre - defined preference, steady - state or transient operation, an optimization parameter is set to either maximize cooling or heating capacity (for obtaining comfort as soon as possible in transient operati on ), maximize COP (for minim um energy consumption) or operate at a trade - off point as desired. Chapter 5 details the experimental apparatus by presenting the schematics for the CO 2 and the HTF for cooling, heating, and two dehumidification modes . We also describe the simulations and the selection criteria for the different components including the compressor, plate heat exchangers, expansion device, suction line accumulator, oil separator, valve s , and tubing components. We show the sizing of the HTF loops based on steady - state and transient capacities. The instrumentation and various sensors used for acquiring the systems measurement signals are also presented . Chapter 6 presents the testing method, validation, and experimental results . We investigate the effect of various parameters on the COP including HTF GC outlet and evaporator inlet temperatures , the CO 2 mass flow rate, and the useful superheat. Chapter 7 contains the conclusions from the thesis findings and discuss several future research pathw ays . 10 Chapter 2: Literature Review 2.1 Rise - Decline - Revival of CO 2 as a R efrigerant CO 2 was first presented as a refrigerant for vapor - compression systems through a British patent in 1850 by Alexander Twining [8] . In 1867, Thaddeus Lowe earned a patent after conducting experiments and confirming the possibility of using CO 2 as a refrigerant. Carl Linde designed a CO 2 machine for a German company in 1882. W. Raydt received a patent in 1884 for a compression CO 2 ice - making machine. Significant progress was made when Franz Windhausen invented a CO 2 compressor, which was patented in 1886. The patent was acquired by the J&E Hall Company in Great Britain and a CO 2 - based marine plant was built in 1890, which received broa d attention. In the United States, CO 2 started to be used in the 1890s in refrigeration systems such as supermarkets, kitchen s , and small cold storage systems; and since the 1900s it has been used in comfort cooling applications such as hospitals, theaters , and restaurants [3] . In the 1940s, the marketing for CFC refrigerants led to phasing out the existing refrigerants , including CO 2 . By 1960, CO 2 had been almost completely replaced in marine - based systems. There are several reported reasons for why CO 2 has been phased out at that time as reported in [3] The c apacity and COP loss at high temperatures ( Most likely because CO 2 transcrit i cal c ycle was not studied and optimize d sufficiently at that time) The high working pressure s and the need to redesign the system The unsuccessful trials of CO 2 system manufacturers to improve and modernize the design of machinery and equipment The aggressive marketing of CFC products The revival of CO 2 was initiated in the late 1980s when Lorentzen [9] introduced a brea kthrough patent that showed that the high - side pressure in the CO 2 transcritical cycle can be controlled by a 11 throttling valve. Lorentzen & Pettersen [10] cr eated a prototype CO 2 automotive AC for comparison with an R12 - based system with equivalent capacity. Since then, the automotive industry become actively engaged in conducting further studies on CO 2 systems. As reported by [11] , the European RACE project that included car manufact urers (BMW, Daimler - Benz, Rover, Volvo, and Volkswagen), along with system suppliers (Behr and Valeo), and the compressor manufacturer (Danfoss) developed and tested from 1994 to 1997 a car - installed prototype system, with results confirming the potential for CO 2 - based car air conditioning. BMW, Audi, and DaimlerChrysler showed consist ent results through independent studies . 2.2 Thermophysical P roperties Besides the refrigerant environmental aspects , the cycle - efficient operation and component design are among the other criteria for the refrigerant selection . Understanding refrigerant thermophysical properties including thermodynamic properties (vapor pressure, enthalpy, etc.), and transport properties (thermal conductivity and viscosity) are importan t for design analysis and optimization. Most of the upcoming discussion and analysis is inspired from [3] and [12] . All the properties and plots are calculated in MATLAB usin g NIST REFPROP database [13] . Table 2 - 1 shows comparison of selected thermodynamic properties for various refrigerants. CO 2 distinguishe s itself from common refrigerants by its relatively low critical temperature and high critical pressure of 31 .1 °C and 73.8 bar respectively. Hence, for a CO 2 heat pump cycle, the heat rejection process at the high - pressure side will take place above the critical point for high ambient/sink temperatures. This area is called the "supercritical" region where there is no clear distinction between gas/vapor and liquid. This area is highlighted in red in the p - h diagram in red in Figure 2 - 1 . 12 Table 2 - 1 . Thermodynamic properties & refrigeration capacity of common refrigerants Refrigerant Critical pressure (bar) Critical temperat ure (°C) Triple point temperature (°C) Vapor density at 20 C (kg/m3) R12 41.4 112.00 - 157.05 17.9 R22 51.0 96.15 - 157.42 21.2 R134a 40.6 101.06 - 103.30 14.4 R410a 49.0 71.34 - 73.15 30.6 R1234yf 33.8 94.7 - 53.15 17.6 R717(Ammonia) 113.3 132.25 - 77.66 3.5 R774 ( CO 2 ) 73.8 31.1 - 56.56 97.6 Figure 2 - 1 . CO 2 pressure enthalpy diagram Figure 2 - 2 shows the p - T or phase diagram of CO 2 . The triple point temperature of CO 2 is - 57 C , below which solid CO 2 will be formed. 13 Figure 2 - 2 . CO 2 p - T or phase diagram CO 2 has relatively higher vapor pressure than other common refrigerants as shown in Figure 2 - 3 . At 20 C , CO 2 and R134a saturation pressure are 57.3 bar and 5.71 bar , respectively, forming a ratio of ~10. While at - 40 C , this ratio increases to 20. As a clear consequence of the high vap or pressure, CO 2 vapor density is higher compared to other refrigerants at the same temperature as shown in Figure 2 - 4 . Figure 2 - 3 . Saturation pressure of R744 compared to selected refrigerants 14 Figure 2 - 4 . Vapor density of R744 compared to selected refrigerants The heat of vaporization of CO 2 is in the same range of other refrigerants except for Ammonia (R717) , which has relatively higher values as shown in Figure 2 - 5 . The volumetric refrigeration capacity is the product of the vapor density and the heat of vaporization. Figure 2 - 6 shows the volumetric refrigeration c apacity for CO 2 and other selected refrigerants. Clearly, CO 2 has a higher refrigeration capacity than the other refrigerants. For instance, at 20 C , the ratio of the refrigeration capacity of CO 2 to R134a is 5.8. While at - 40 C , this ratio increases to 13.5. Higher volumetric refrigeration capacity means that a volume of CO 2 can absorb more heat than same volume of R134a. This implies that less CO 2 volume flow rate is required to obtain the same cooling effect [12] . T he higher the volumetric refrigeration capacity, the smaller compressor displacement. This enables CO 2 systems to have smaller and more compact compressors, which makes CO 2 systems suitable for mobile air conditioning systems where reducing the component space size is desirable . 15 Figure 2 - 5 . L atent heat of vaporization of R744 compared to selected refrigerant Figure 2 - 6 . Refrigeration capacity of R744 compared to selected refrigerants Thermal conductivity as a transport property is an important parameter for heat transfer coefficient computation in both single - phase an d two - phase flow [3] . Figure 2 - 7 and Figure 2 - 8 show the thermal conductivity of CO 2 and selected refrigerants for vapor and liquid respectively. T he thermal conductivities of saturated CO 2 vapor at 20 °C is 2.5 times higher than that of R134a vapor , w hile thermal conductivities are similar for saturated liquids at 20 °C . 16 In conclusion, CO 2 is a natural environmentally friendly strong alternative refrigerant for HFCs . CO 2 has various attractive properties , which make it a strong candidate to replace R134a . CO 2 is currently used in vending machines and supermarkets where the cycle operates subcritically as the conventional heat pump cycle. The transcritical cycle is under focus by the academic community to f urther optimize the cycle COP under steady - state and transient operating conditions. Figure 2 - 7 . Vapor thermal conductivity of R744 compared to selected refrigerants 2.3 Transcritical Cycle For vapor compression cycles operating at ambient temperature above 31.1 C , the cycle operates in the supercritical region with high - side pressure above the critical point and operates in the subcritical region with low - side press ure below the critical point . This transitioning from the subcritical to the supercritical gives the cycle its name "transcritical" . Since there is no phase change in the supercritical area, the heat exchanger that would ordinarily condense the refrigerant leaving the compressor is instead referred to as a "gas cooler" or GC . This follows the convention of referring to a supercritical fluid as a gas, recognizing that this is something of a misnomer. S ince 17 no latent heat effects (phase change) can take place above the critical point, the gas cooler exchange h eat by decreasing the gas temperature and increasing its density. Figure 2 - 8 . Liquid thermal conductivity of R 7 44 compared to selected refrigerants While in the subcritical two - phase region, pressure and temperature are coupled by the saturation curve , or in other words, the c ondenser pressure is governed by the condenser temperature ; in the supercritical region, pressure and temperature are independe nt of each other. Therefore, for a given ambient temperature that can be related to the GC outlet temperature [14] , the GC pressure (high - side pressure) can be controlled independently. The regulation of the hig h - side pressure affects the cycle COP [10] . To further illustrate how the change of the GC pressure affect s the COP, Figure 2 - 9 shows four cycle s on the p - h diagram that operate at the same evaporation temperature. The first one is a subcritical cycle shown in blue, where the high - side pressure is governed by the condensation temperature. For the three other transcritical cycles, the GC outlet temperature is the same for all of them, but they operate with different GC pressures. The first transcritical cycle shown in gray operates with a GC pressure of 78.0 bar and has a COP of 1.5. By increasing the GC pressure to 18 86.0 ba r, the specific work of compression increases ; but the increase in the cooling capacity is larger, hence the COP increases to 3.4 and th is cycle shown in green represents the optimum COP cycle . By increasing the GC pressure to 120 bar, the increase of the specific work of compression is larger than the increase of the cooling capacity; hence , COP decrease s to 2.0 for the second cycle shown in gray . The isothermal line in the supercritical region has S shape (like the shown T 3 = 35 °C) , which implies that for a given GC outlet temperature, as the high - side pressure is increased, the COP reaches a maximum above , which the added capacity no longer fully compensates for the additional work of compression [3] . Ther efore, for each GC outlet temperature, there is an optimum GC pressure that can be optimized to find the maxim um COP. Figure 2 - 9 . p - h diagram for a subcritical and transcritical cycles 2.4 Related Studies Several contributions to the CO 2 transcritical cycle analysis and understanding were carried out in [3] , [11] , [15] , and [16] . Many of these studies involved an internal heat exchanger that exchanges heat from the section of the line between the GC and the expansion valve with the s ection of the 19 line between the evaporator/accumulator and the compressor. For that reason, it is usually called a liquid - line/suction - line or just as we will refer to it here by IHX. Also, several control correlations will be reported from the literature. In all these correlations that will be presented , the pressure and temperature units are in bar and °C respectively. Inokuty [17] deduced a graphical method to determine the optimum high - side pressure of the tran scritical cycle. T he drawback of this method is that if operating conditions change, the method must be revisited to obtain a new optimal pressure value. It was not then until 1990, when Kauf [14] assessed the g raphical method developed by Inokuty [17] . He reported that "the graphical method is too time consuming and not very accurate". He was the first one to develop a control function or offline correlation that relates the optimum GC pressure to the ambient temperature. Kauf [14] reported t he difference between the ambient temperature and the GC outlet temperature to be known as the approach temperat ure. I t is written as ( 2 . 1 ) H is developed control function can be written as a function of the ambient or the GC outlet temperature ( 2 . 2 ) where 35 °C 55 °C, and consequently 37.9 °C 52.9 °C. Therefore, 91 bar 130 bar. It shall be noted, that the original paper has a sign mistake that was corrected in the equation above, thanks to Yang, et al. [18] . The maximum d eviation of COP was below 5.8 % due to the estimation of th e control function. Kauf [14] also reported that the maximum COP for a certain ambient temperature is independent of the compressor speed/frequency . Boewe et al. [19] conducted a comparative experimental study and performance investigation of CO 2 and R134a refrigeration systems . The R134a system was represented by the Ford Escort 20 mobile air conditioning system with the addition of an IHX. Their results showed that the C O 2 system has a much higher capacity and COP at lower ambient temperatures but slightly lower capacity and COP (a few percent) at very high ambient temperatures (above 45 °C). The IHX was found to improve efficiency by up to 25 % . This was especially presen t at high ambient temperatures while idling (low compressor speed). Liao at al. [20] studied the transcritical air conditioning cycle that involves an IHX. It was shown mathematically that the optimal GC pressure is dependent on the refrigerant GC outlet temperature, the evaporation temperature, the compressor performance (the isentropic efficiency) , and the amount of superheat at the c ompressor inlet. The effect of each parameter on the COP was studied; and the influence of superheat was found to be weak and , hence , was neglected. Two correlations for the optimal GC pressure were developed. The first one relates the optimal GC pressure to the GC outlet temperature, the evaporation temperature, and the compressor performance as ( 2 . 3 ) The second correlation is simplified to neglect the compressor performance effect ( 2 . 4 ) In both correlations, - 10 °C 20 °C, 30 °C 60 °C, and 0 0.3, therefore, 71 bar 120 bar. Yoshioka and Miura [21] performed an experiment on the transcritical CO 2 heat pump cycle with an IHX. Their study revealed that a COP equivalent to or higher than that of R134a can be achieved by controlling the GC pressure against the ambient temperature. Brown et al. [22] theoretically compared a CO 2 and an R134a automotive air conditioning cycle. Both cycles were similar except that the CO 2 cycle incorporated an IHX. It was found that the CO 2 21 cycle had a lower COP, and the disparity between the COP of the R134a and CO 2 cycles gets larger at higher compressor speed or higher ambient temperatures. Entropy studies showed that CO 2 had better performance in the evaporator, but the GC had poorer performance than the R134a condenser. The large CO 2 temperature glide or change in the GC is the main reason f or the high entropy generation and , hence, lowers its performance. Casson et al. [23] simulated different expansion systems for a CO 2 refrigeration transcritica l cycle. The paper introduced and explained a patented cycle design that uses two expansion devices and a liquid receiver in between. The valve after the GC is a differential one that controls the high - pressure side, and the one after the liquid receiver i s a thermostatic valve that controls the amount of superheat leaving the evaporator. The liquid receiver ensures saturation conditions at the thermostatic expansion valve entrance. The amount of refrigerant inside the liquid receiver varies as a response t o different operating conditions of the circuit. The simulation revealed that : COP decreases with the increase of water inlet temperature of the GC . The optimal GC pressure increase s with the increase of the inlet water temperature of the GC . The s ame behavior occurs for the upper pressure of the differential valve at fixed . The thermostatic expansion valve can operate only with water temperatures lower or equal to 25 °C (subcriti cal cycle), and in this case provides better COP than the using two valves ; however, it requires a larger flow rate ( five times the flow rate in the case of the transcritical cycle . ) Sarkar et al. [24] modeled and conducted an exergy analysis for the transcritical CO 2 heat pump cycle with an IHX for simultaneous cooling and heating application s . Based on the cycle analysis, the paper developed a control correlation in terms of the GC outlet temperature and evapo ration temperature. The authors concluded that to increase the COP, the system must operate at the lowest 22 possible GC outlet temperature and highest possible evaporation temperature. The exergy loss through the expansion device was estimated as 18 % , which was the highest component loss. The loss is relatively large due to the pressure difference between the high - side and low - side , and also due to the fact that near the critical point the entropy as well as other properties change rapidly, as pressure drops from supercritical to subcritical. The developed control correlation is valid for - 10 °C 20 °C and 30 °C 60 °C, and is obtained as ( 2 . 5 ) Chen and Gu [25] studied and modeled the transcritical CO 2 refrigeration cycle. The authors evaluated the effect of several parameters related to the IHX on the cycle performance. A control correlation is developed for the optimum high pressure where its coefficients are close to the one developed by Kauf [14] . Considering a 2.9 °C approach temperature, the correlation is proposed as ( 2 . 6 ) Liu et al. [26] performed an experiment on a prototype automotive CO 2 air conditioner system with an IHX. Their major findings have been : The reported COP was similar for both oil types: ISO VG 56 PAG and ISO VG 68 POE, alth ough the cooling capacity and the compressor work of POE system was higher , The COP has a maximum value at a specific CO 2 charge; undercharged CO 2 systems could result in a fast decrease of the cooling capacity and the COP . H owever, overcharged CO 2 systems could cause an abrupt increase of the compressor consumed work . The air flow rate is recommended to be high in the evaporator and the GC to increase the COP of the system . 23 The system needs a high - side pressure controller to prevent a decrease in the effic iency with the increase in the evaporator pressure. Yang et al. [27] performed a simulation of a CO 2 transcritical heat pump cycle with an IHX. It was found that the COP of the system is heavily affected by the GC pressure, which in turn influenced by the GC outlet temperature and to a lesser extent by the ambient temperature. The influence of the GC out let temperature and the ambient temperature weakens as the compressor speed increases. Several correlations were developed that relate the optimum GC pressure with the GC outlet temperature and the GC outlet temperature with the ambient temperature . The co rrelations are developed at speeds of 950, 1800, and 3000 rpm . Tamura et al. [28] carried out a theoretical study on a CO 2 transcritical automobile AC system, replacing the auxiliary electric heater (used with high efficiency automobiles where the engine heat release is low) with a heating method utilizing the heat released during dehumidification. The heat released from the refrigerant in the high - side pressure during dehumidification is transferred to the engi ne coolant through a water refrigerant heat exchanger . Thus, t he a ir is warmed using the heated engine coolant. Using this method, the cycle total work input decreased by 20 % compared to R134a system for a medium sized automobile. Another finding is that t he optimum amount of refrigerant in the heating/dehumidification mode is larger than the optimum amount in the cooling mode due to the fact that the outdoor temperature is generally less in case of the heating mo de compared to the cooling mode ; thus, the amount of refrigerant held in the outdoor heat exchanger during the heating operation is greater than the amount during the cooling operation. The paper deduced a control method using two expansion devices to adjust the refrigerant optimum charg e for cooling and heating/dehumidification modes. 24 Cho et al. [29] analyzed experimentally the cooling performance of a variable speed CO 2 transcritical cycle equipped with a scroll compressor. Parameters considered ar e the refrigerant charge, compressor frequency, EXV opening, and the length of the IHX. The optimum charge was determined by varying the charge from 1.1 to 1.5 kg and measuring the COP. The compressor frequency was swept from 30 to 60 Hz in an increment of 10 Hz. The EXV opening was varied from 35 to 56 % in an increment of 7 % . The IHX length was varied from 2 to 3 m. It was found that : Increasing the compressor frequency decreases the cooling COP because the increase of compressor power consumption was sig nificant while the increase of mass flow rate was relatively small at high frequencies . The system showed maximum COP at a specific system charge at all compressor frequencies . T herefore, the optimum refrigerant charge determined at the rated compressor fr equency can be applied at all compressor frequencies . The optimum EXV opening determined at the maximum COP at a given compressor frequency increases by increasing the frequency . Simultaneous control of the EXV opening and the compressor frequency allow th e optimal control of the GC pressure . The presence of an IHX increased the compressor power consumption by 0.8 to 2.5 % and increased the cooling capacity by 6.2 to 11.9 % ; hence , COP increased by 7.1 to 9.1 % . The COP remained nearly constant by increasing the length of the IHX beyond 2 m. Cabello et al. [30] carried out an experiment on a CO 2 transcritical refrigeration cycle that has two expansion stages with a liquid receiver in between. The first expansion device is a back - pressure valve to control the GC pressure, while the second expansion device is an EXV to control the 25 amount of superheat at the evaporator outlet. The article looked at how the cooling capacity, compressor power input, and refrigerant mass flow rate change as a function of the GC pressure in the range from 89 to 105 bar. The optimal GC pressure determined experimentally was compared to commonly used correlations in the literature namely, Kauf [14] , Liao et al. [20] , Sarkar et al. [24] , and Chen and Gu [31] . A maximum deviation of 15.7 % , 4.6 % , 1.5 % , and 7. 5 % is reported respectively. Thus, the correlation of Sarkar et al. [24] has the smallest deviation from the experimental results. It was also concluded that a small error in the estimation in the GC pressure i s more sensitive close to the critical point, meaning that it causes a bigger reduction in the COP. Also, the COP reduction is less if the GC pressure is overestimated rather than underestimated. Kim et al. [32] performed an experiment on a CO 2 transcritical air conditioning system with an IHX. The study found that increasing the compressor speed increases the cooling capacity but reduces the COP. By numbers, at idle cond itions (compressor speed of 900 rpm ), the COP was 2.7 ; while at driving conditions (compressor speed of 1800 rpm ), the COP was reduced to 1.9. The paper also proposed a control function for the optimum GC pressure to achieve maximum COP, the equation is ob tained as ( 2 . 7 ) Xiaowei et al. [33] conducted an experiment on a transcritical CO 2 heat pump water heater with an IHX and two manual expansion devices with a liquid receiver in between. The GC pressure was found to be mostly dependent on the GC outlet temperature and the evaporati on temperature. The GC pressure is regulated by adjusting the first - stage manual valve. The smaller the opening of the valve causes a higher GC pressure. The study reported that the GC pressure could not be decreased any more when the first - stage valve was at the maximum opening. Thus, the pressure is not 26 optimi zed at some operating conditions. It was also found that the superheat at the inlet of the compressor had little effect on the optim um h eat rejection pressure. Cecchinato et al. [34] analyzed the CO 2 transcriti cal refrigeration cycle. The study concludes that the control correlations obtained from the GC outlet temperature, being taken as the independent variable, behaved better than correlations with the secondary fluid inlet temperature as independent variable . Zhang et al. [35] performed simulations and experimental test ing on a transcritical CO 2 heat pump system with two expansion devices and an IHX. It was found that the optimal GC pressure mainly depends on the GC refrigerant outlet temperature, the evaporation temperature, and the performance of the compressor. The effect of superheat was found to be weak. The two - stage expansion configuration enabled the control of the high pressure and evaporating pressure , howe ver, the manual regulation of GC pressure exhibits some unsteadiness, especially for higher pressure, as the study reported. The correlation developed by Liao et al. [20] was corrected based on the experimental re sults as ( 2 . 8 ) Zhang and Zhang [36] introduced an online correlation - free or real time control method for the basic CO 2 transcritical heat pump cycle. They simulated their work to test the algorithm, but no experimental work was reported . The o ptimized GC pressure formula is obtained using the steepest descent method to track the optimal pressure set point. The formula is written in terms of the GC pressure from current and previous iteration s , cooling capacity, and compressor power consumption per unit mass flow. Therefore, measurements of the compressor suction and discharge temperatures, GC pressure, and outlet temperature are needed for the optimization formula. The authors used previously numerical models for the heat exchangers [37] . The study 27 showed few simulation test cases that evaluated the optimization technique performance. In one of the ir test cases, the algorithm adjusted the GC pressure from an initial pressure of 85 bar close to the optimal value of 100 bar, taking around 17 min. In another case, where the compressor speed changed during operation from 70 to 60 Hz , it took the algorithm around 30 min to adjust the GC pre ssure from 100 bar ini tially close to the optimal value of 104 bar. It can be noted that the time needed to optimize the COP is relatively long. Cecchinato et al. [38] proposed a real - time algorithm based on a neural network technique t o determine the optimal GC pressure for a CO 2 heat pump water heater system with an IHX. The algorithm was tested statically and dynamically. In static tests, the algorithm was trained by 240 simulation test results. This resulted in a maximum pressure dev iation of - 1.5 bar and COP deviations ranging from 0 % to 1.5 % . In dynamic testing, the operation of heat pump system was simulated over two years. The average pressure deviation was 0.9 bar. It took the system a few days for the training to adjust the op timal high pressure. A lthough the algorithm provides acceptable optimal pressure and COP deviations, it requires either large number of simulation data for training the algorithm or consistent observation to train the algorithm , which took few days in thei r dynamic testing. Qi et al. [39] experimentally studied the transcritical CO 2 heat pump water heater. The GC is cooled by water while the evaporator is cooled by air. It was found that the optimal GC pressure was largely dependent on the refrigerant GC outlet temperature. The effect of the evaporation temperature, which is dependent on the ambient temperatures, was found to be weak on the optimal GC pressure. The COP for the optimal GC pressure decreases substantially as the refrigerant GC outlet temperature increases in the temperature range from 25 °C to 45 °C. A correlation of the optimal GC pressure is obtain ed, which was found to be in a good agreement with the correlation 28 of Chen and Gu [25] . The developed correlation is valid for 25 °C 45 °C and is proposed as ( 2 . 9 ) Boccardi et al. [40] performed experiments on a CO 2 transcritical heat pump plant with two hermetic single stage reciprocating compressors and an IHX, for light commercial applications. It was found that both the CO 2 mass flow rate and the compressor absorbed power increase as the evaporation pressure increase s . At a certain evaporation pressure, increasing the GC p ressure reduces the mass flow rate, mainly due to the corresponding reduction of the volumetric efficiency, while the compressor power increases because of both the increase of discharge enthalpy and the decrease of compressor efficiency. The study showed that higher values of the GC pressure correspond to higher evaporator inlet enthalpies, which leads to reducing the cooling capacity. Baek et al. [41] conducted an experiment on a CO 2 heat pump basic cycle. The study normalized the system charge using the equation ( 2 . 10 ) where and are calculated by multiplying the system total volume by the densities of the saturated liquid and vapor at a room temperature of 25 °C . Therefore, if the system is charged with liquid refrigerant, then =1, and if the system is charged with vapo r refrigerant, then =0. Several conclusions can be made from this paper : Increasing the normalized charge results in decreasing the optimum EXV opening ; hence, the GC pressure increases by increasing the normalized charge, which therefore increases the enthalpy difference across the GC . 29 The cooling capacity increases with the increase in the normalized charge due to the increase of the enthalpy difference across the GC and the increase of the mass flow rate that increases the heat exchange in the GC . The compressor power input increases linearly with the increase in the normalized charge due to the increase in the compression ratio and therefore COP peaks at a specific normalized charge . The GC pressure decreases with the increase in the EXV opening due to the decrease in the flow restriction through the EXV, which in turn decreases the compression ratio . As the EXV opening increases, the mass flow rate inc rease; but the enthalpy difference across the GC decreases due to the decrease of the GC pressure . Because of the previous point, the cooling capacity reaches its maximum value at a specific EXV opening, due to the trade - off between the increase in the mas s flow rate and the decrease in the enthalpy difference across the GC, according to the EXV opening . The compressor power input decreases with the increase of the EXV opening due to the decrease in the compression ratio, therefore, the COP is maximized at a specific EXV opening. Kim et al. [42] utilized a previously proposed real time algorithm by the same authors to search for the optimal GC pressure and applied the algorithm to a transcritical CO 2 refrigeration cycle with an IHX. The algorithm determines the expansion valve percentage opening to obtain the corresponding optimum GC pressure. The algorithm relies on the online measured data of the refrigerant pressure and temperature at the GC outlet, pressure at compressor suction, and the compressor consumed power. This method calculates a ra tio of the expected increment cooling capacity and the compression work with the expansion valve slightly closed. This ratio is compared 30 with the current COP to determine whether the expansion valve needs to be opened or closed. The algorithm has several l imitations as reported by the authors. First, the degree of superheat change at the compressor suction can generate a decrement or increment of specific cooling capacity , which is undetectable by the real time controller. Second, the GC heat exchanger size must be sufficiently large for the controller to give acceptable results. Third, any change of the evaporation pressure will not be detected by the algorithm ; and as a result, the controller will underestimate the increment of the specific compressor work . Peñarrocha et al. [43] showed mathematically that maximizing the COP is equivalent to minimizing the compressor power consumed, which avoids the need to use several sensors. The cycle experimented in this work had two stage expansion devices with an accumulator in between. A back - pressure regulator to control the GC pressure and an electronic expansion valve to control the evaporator superheat. The paper utilized a real - time optimization method called "perturb and observe" to minimize the compressor power while measuring the evaporator secondary fluid exit temperature, the GC pressure, and the compressor consumed power. Based on these measurement signals, the controller decides the compressor speed and the position of a stepper motor that modifies the opening degree of the back - pressure valve, which are the controllable parameters. A drawback of this method is that the achievement of the optimum operating point is delayed if the environmental temperature has fast and long variations. In that case, the controller will evolve in the wrong direction during the transient time until the algorithm achieves the boundary of the max/min allowed pressure and then changes the direction towards the optimum value. The results of t his work yielded the decrease of the compressor consumed power; and, hence, the increase of the COP, however, the time the algorithm takes to reach to the optimum is long. For example , the COP took two hours to increase from 1.47 1.6, and it took 12 hours to increase from 1.47 to 1.75. 31 Hu et al. [44] applied and simulated an optimization strategy called "Extremum seeking control (ESC)" on a CO 2 transcritical heat pump water heater system with an IHX. The optimization strategy can search for the optimal input in real time without need for a system model. The control input parameter is the GC pressure, while COP is also fed back to the controller. A high - level controller based on the ESC optimization finds the opium GC pressure. Then it communicates to a low - level controller that involves an inner PI control loop to adjust the EXV opening to achieve the desired GC pressure. The simulation results s howed that for fixed operating conditions where the hot water outlet temperature and the evaporation temperature are constant, the GC pressure is adjusted from an initial value of 80 to 83.8 bar to reach the optimum COP within 2 % settling time in about 33 min. This time increased to around 93 min when the initial pressure changed to 92 bar. The authors explained that this is due to the process nonlinearity. To reflect varying operating conditions, a step input was applied on the water outlet temperature fro m 60 °C to 70 °C. The algorithm took around 83 min to reach the new optimum COP. The algorithm used has a major advantage that it is model free algorithm, although it lacks the speed of the convergence to the optimum COP value. Hazarika et al. [45] simulated a CO 2 - based air conditioning system with two expansion valves. Fin and tube heat exchangers are modeled based on a discretized approach. It was found that increasing the GC air inlet temperature reduces COP wh ile increasing the evaporator air inlet temperature increases the COP. Yang et al. [46] simulated the transcritical CO 2 refrigeration cycle with an expander and compared its performance to a throttle valve cycle. The authors referred to another study that replaced the throttling valve by an expansion turbine and could reduce the total irreversibility by 35 % and increase the system COP by 25 % . The optimal GC pressure was found to be strongly affected by 32 the GC outlet te mperature and to less extent by the evaporation temperature, as in cycles that use throttling valves. By increasing either compressor or expander efficiency, the GC pressure increases. Control correlations have been developed for the optimal GC pressure in terms of GC outlet temperature and evaporation temperature. The reported linear version of the correlation is ( 2 . 11 ) [47] theoretically compared various modifications of transcritical CO 2 heat pump systems. The relevant paper conclusions are : Systems with an IHX have COP relatively better than the basic cycle at higher ambient temperature . Systems with an IHX have a lower mass flow rate at higher ambient temperature allowing for operation with lower GC pressure . COP of systems with work recovery (expanders) is comparatively high due to work recovered . Multi - stage systems are fo und to have similar performance as the basic system for applications like refrigeration. 2.5 Summary and Thesis Contributions Summarizing the above , researchers have been focusing on understanding the effect s of the system parameters such as the refrigerant G C outlet temperature, the evaporation temperature, the compressor efficiency, the system charge and other parameters on the COP, the cooling/heating capacity, and the compressor power for the system the considered/built. M any control correlations have been developed for the GC pressure to maximize the COP either through simulations or experiments. These correlations are developed as a function of the GC outlet temperature such as [14] , [25] , [32] , and [39] ; and in a few cases as a function of both the GC outlet temperature and 33 evaporation temperature such as [24] and [20] where the last one includes a term for the compressor isentropic efficiency as well. The evaporation temperature has less effect on the COP compared to the GC outlet temper ature, while the compressor performance depends on the selected compressor isentropic efficiency. Each of these correlations is ideally v alid for the system it was simulated or experimented with including the compressor efficiency correlations and the spec ific parameter s rang es . On the other hand, few real time algorithms such as [36] , [38] , [42] , and [44 ] have been recently developed to maximize the COP online. This requires continuous pressure and temperature measurements at different locations. As highlighted in the previous subsection, in some of these methods the convergence time to the optimum v alue is relatively long. The improvement of these approaches is still in progress especially for transient operation. In addition, not all these developed methods have been verified experimentally. Therefore, the developed offline control correlations are still a good guide for the system to maximize the COP, even if they may have some deviations due to their reliance on the system model . To the best of our knowledge, a ll the developed correlations in the literature focus on optimizing the COP. However, this does not mean that the system is working at its highest cooling/heating capacity that may be desired for example in a transient start - up operation or based on the pa ssenger preference to maximize the thermal comfort (i.e. reaching the set point quicker) to cool down or heat up a space as quickly as possible to a certain condition. For that purpose, a multi - objective optimization study will be conducted to better under stand the trade - off between COP and cooling capacity ; and based on that, a control and optimization strategy will be developed that can alter the system operation to work on its optimum COP, optimum cooling/heating capacity, or a tradeoff point as desired. Since the commercial compressor we are using in our experimental apparatus has 34 no available efficiency correlations either from the manufacturer or the literature, we will model the compressor by develop ing the isentropic and volumetric efficiency correla tions for this compressor . The developed efficiency correlations are compared to several ones available in the literature. In addition, and to facilitate the multi - objective study and optimization strategy, t he CO 2 transcritical cycle performance is modele d in a MATLAB environment and analyzed to investigate the effect of the GC outlet temperature, the evaporation temperature, and the superheat on the COP for the system considered in the experimentation. Furthermore , since the offline correlations depend ma inly on the type of the compressor and the system under investigation , an optimized control correlation is generated and compared to the common ones in the literature, which relates the optimized GC pressure to the GC outlet temperature. The correlation ca n be used to maximize the COP in the specified range of operating conditions for the considered system. For further experimental investigations of the system, a CO 2 air conditioning system and its coolant system have been constructed at the MSU Turbomachi nery Lab that support cooling, heating, and dehumidification modes . Several system parameters effects on the cooling and heating COP will be analyzed and reported. The thesis contributions can be summarized a s follows : Developing the transcritical thermodynamic model, the compressor efficiency correlations, and an offline control correlation for our experimental system . Understanding the tradeoff between the COP and cooling/heating capacity and how the Pareto Fronts are affected by the GC outlet temperature, evaporation temperature, superheat, compressor speed, and compressor performance. 35 Develop ment of a bi - objective optimization and control strategy to either operate at the optimum COP , the optimum cooling/heating capacity , or a tradeoff point based on a predefined preference Proposing a hybrid offline and online control methodology for optimizing the system COP and/or the cooling/heating capacity . The hybrid approach reduce s the time to approach th e desired optimum solution compared to online methods only . Designing, building, testing, and validating a CO 2 heat pump test rig facility with plate heat exchangers that support cooling, heating, and dehumidification modes Experimentally investigating sev eral system parameters effects on the cooling and heating COP for the CO 2 transcritical system . 36 Chapter 3: Thermodynamic M odeling and A nalysis This chapter presents the thermodynamic modeling of the CO 2 transcritical cycle and a nalyzes its performance. The basic CO 2 transcritical cycle schematic that consists of a compressor, GC, expansion device, and an evaporator is shown in Figure 3 - 1 along with the p - h and T - s diagrams. The assumptions considered for the cycle simulation and analysis are as follows: the cycle is assumed to operate at steady - state, the compression process is adiabatic but non - isentropic, the heat transfer with the ambient of components other than the heat the exchangers is neglected, the evaporation and the gas cooling processes are isobaric, the pressure drop in heat exchangers and CO 2 tube lines are neglecte d, and CO 2 is considered as a pure fluid neglecting the effect of the lubricant on the properties. Figure 3 - 1 . Basic CO 2 Transcritical system with the corresponding T - s and p - h diagrams 3.1 Compressor M odeling The compressor selected for this study is a Dorin CD200 - CD180H, 3 - phase, 230 V, and 60 Hz with 1.34 kW rated input power. The compressor supports evaporation temperatures ranging from - 30 °C to 15 °C. To simulate the cycle behavior, the compressor efficiency correlations are needed to calculate the compressor discharge enthalpy and the mass flo w rate. The compressor isentropic and volumetric efficiency correlations are expressed as [19] 37 ( 3 . 1 ) ( 3 . 2 ) software was used to simulate the compressor behavior at different operating conditions. The compressor discharge pressure was swept from 75 to 140 bar at co nstant GC outlet temperature of 35 ° C and a total superheating of 1 K. The superheat can take place either inside the evaporator, which adds to the cooling capacity, and/or it can be generated outside the evaporator, which is usually due to the pressure dr op in the connecting lines between the evaporator outlet and the compressor suction and/or external heat transfer to the line. Eqns. ( 3 . 1 ) and ( 3 . 2 ) are used to calculate the isentropic and volumetric efficiency for each data point. A MATLAB code was written to determine the efficiency correlations using regression analysis. For each itera tion, the code takes the mass flow rate , and the compressor consumed power as input from the . The NIST REFPROP database ( Lemmon et al. , 2013) is used within the MATLAB code to retrieve the thermodynamic properties of CO 2 . The compressor envelope is shown in Figure 3 - 2 high - side pressure for the evapo ration temperature range from - 30 °C to 15 °C. This line can be expressed with Eqn. ( 3 . 3 ) . This equation is used to ensure that the high - side pressure in each sweep iteration is within the compressor envelope. 38 Figure 3 - 2 . Dorin CD200 - CD180H Compressor Envelope ( 3 . 3 ) M selected evaporation temperature. For the work discussed here, the efficiency correlations are developed at evaporation temperatures of - 8 °C, 0 °C, and 15 °C. Comp ared to relying on a set of correlations developed at a single evaporation temperature, this was found to provide more accurate results when the correlations are used at different evaporation temperatures in the cycle analysis. A third - order polyn omial fit that takes the form of Eqns. ( 3 . 4 ) and ( 3 . 5 ) has been adapted for the resulting efficiencies as a function of the compressor pressure ratio . Table 3 - 1 presents the polynomial coefficients for the different evaporation temperatures. Using the developed correlations, the maximum deviation of the calculated mass flow rate and the compressor power he correlations was ±0.34 %. Figure 3 - 4 shows the developed compressor volumetric and isentropic efficiency correlations represented by Eqns. (4) and (5) along with Table 3 - 1 , compared to CO 2 compressor correlations used in the literature. The correlations of Sarkar et al. (2009) , Casson et al . (2 003) , Ortiz et al. (2003) , and 39 Liao et al. (2000) are based on experimental data fitting for a semi - hermetic compressor, while no information was provided for the Robinson and Groll (1998) correlations. It can be noted that the isentropic efficiency varies considerably between different compressors ; hence , selecting the right correlations for the selected compressor is important for the cycle accurate simulations. ( 3 . 4 ) ( 3 . 5 ) Table 3 - 1 . Developed volumetric and isentropic efficiency correlations at different evaporation temperatures (°C) - 8 1.0904 - 0.1929 0.0189 - 0.0003 0.7532 - 0.1378 0.0351 - 0.0029 0 1.0829 - 0.1965 0.0202 - 0.0001 0.7191 - 0.1358 0.0455 - 0.0048 15 1.0380 - 0.2044 0.0249 0.0002 0.0561 0.5536 - 0.1961 0.0240 3.2 Cycle M odeling For the basic transcritical cycle shown in Figure 3 - 1 , and c onsidering the compressor isentropic efficiency, the enthalpy at state 2 is calculated by ( 3 . 6 ) The refrigerant mass flow rate is determined based on the compressor volumetric efficiency ( 3 . 7 ) The expansion process is considered isenthalpic, hence ( 3 . 8 ) The cooling capacity is ( 3 . 9 ) 40 The compression power is calculated by ( 3 . 10 ) The cooling coefficient of performance is calculated as ( 3 . 11 ) A parametric study is carried out to show the effect of several parameters on the cooling COP. The range of the GC pressure is varied from 75 to 140 bar, the GC outlet pressure from 32 °C to 53 °C, the evaporation temperature from - 30 °C to 15 °C, and the superheat from 0.5 K to 15 K. Figure 3 - 3 . Compressor developed volumetric efficiency correlations compared to correlations from the literature 41 Figure 3 - 4 . Compressor developed i sentropic efficiency correlations; compared to correlations from t he literature 3.3 Analysis Figure 3 - 5 shows the influence of varying GC pressure on the COP at different GC outlet temperatures at 15 °C evaporation temperature and 1K superheat. Clearly, there is an optimum GC pressure for each GC outlet temperature where the COP is maximum. This is shown by the g reen curve polynomial fit connecting those optimum points. Apparently, and as indicated by Yang et al. [18] , the accurate determination of the optimum GC pressure is much more sensitive close to the critical point than at higher pressures. At higher GC pressures, the COP curves are flatter; hence, the maximum COP becomes almost insensitive to the estimate of optimal high pressure. The effect of changing the GC pressure on the COP at different evaporation temperatur es at 35 °C GC outlet temperature is shown in Figure 3 - 6 . The evaporation temperature of - 30 °C was excluded from this simulation because of the limited a llowed high - side pressure of 82 bar at this evaporation temperature. The green curve connects the optimum pressure points. From the graph, at the two extreme evaporation temperatures, - 25 °C and 15 °C, the optimum GC pressure is 90.5 bar and 42 86.2 bar respe ctively. In fact, if 86.2 bar pressure is applied as a GC pressure for the whole evaporation temperature range, the resulting COP is no more than 1.5% (at either - 15 °C or - 25 °C) away from the optimum COP. Hence, the effect of the evaporation temperature on the optimum GC pressure is negligible compared to the more considerable effect that the GC outlet temperature has on the optimum GC pressure. Figure 3 - 5 . The effect of varying the GC pressure on the COP at different GC outlet temperatures and at 15 °C evaporation temperature The effect of changing the GC outlet temperature on the COP at different GC pressures at 15 °C evaporation temperature is shown in Figure 3 - 7 . It can be noted that the optimum GC pressure increases with the increase of the GC outlet temperature. It is also clear for the shown range that the COP is maximum at the lowest GC outlet te mperature. Hence, for the best COP the cooling process in the GC should be the best possible. 43 Figure 3 - 6 . The influence of varying the GC pressure on the COP at different evaporation temperatures and at 35 °C GC outlet temperature Figure 3 - 7 . The impact of varying the GC outlet temperature on the COP at different GC pressures and at 15 °C evaporation temperature If the pressure is fixed at 86.2 bar, the COP at is no more than 1.5% away from the optimum COP at - 15 °C or - 25 °C 44 Figure 3 - 8 shows that COP increases with the increase of the evaporation temperature as in conventional (subcritical) heat pump cycles. This graph is generated for GC outlet temperature of 35 °C where the 86.2 bar GC pressure line represents the maximum COP line neglecting the effect that the changing evaporation temperature has on the optimum GC pressure. Considering the GC pressure curves for 75, 86.2, and 100 bar, it can be noted that the under - estimatio n of the optimum GC pressure generates higher reduction in COP compared to the over - estimation of the optimum GC pressure. For instance, at 10 °C evaporation temperature, the COP is 2.85 at 86.2 bar, while the COP at 75 and 100 bar is 0.82 and 2.65 respect ively. Figure 3 - 8 . The effect of changing the evaporation temperature on the COP at different GC pressures and at 35 °C GC outlet temperature The impact of the amount of the superheating taking place inside the evaporator, which adds to the cooling capacity at various GC pressures is plotted in Figure 3 - 9 for GC outlet temperatures of 35 °C and 45 °C, both at 15 °C evaporation temperature. At 35 °C, the superheating has a negligible effect at all GC pressure except at 75 bar. At 45 °C, the superheating has a considerable effect on the COP for 75 and 100 bar GC pressures. It can be concluded that at most GC pressures, the 45 superheating has hardly an influence on the COP, especially if the GC pressure is much greater than the critical pressure. However, if the GC pressure is close to the critical pressure, COP can significantly increase with an increasing amount of superheating, and even more so if additionally, the GC outlet temperature is high. Figure 3 - 9 . The influence of the superheating on the COP at 15 °C evaporation temperature; 35 °C GC outlet temperature 3.4 Optimization Correlation Based on the above analysis, for our compressor and operating ranges, the GC outlet temperature is the most influential parameter on the optimum GC pressure. A second - order polynomial is developed based on the simulated points shown in Figure 3 - 11 , which is calculated at a 15 °C evapora tion temperature and 1K total superheat. The polynomial is plotted in thick green. ( 3 . 12 ) 46 Figure 3 - 10 . The influence of the superheating on the COP at 15 °C evaporation temperature; 45 °C GC outlet temperature Figure 3 - 11 : Developed correlation for optimized GC pressure shown in thick green curve compared to correlations available in the literature 47 This correlation is developed for the range of operating conditions of 32 °C < < 53 °C and 75 bar < < 140 bar. Figure 3 - 11 shows the developed correlation in comparison with the common ones in the literature displayed with their respective valid range. I n this chapter, the CO 2 transcritical cycle was modeled and analyzed. For the selected compressor, the isentropic and volumetric efficiency correlations are developed from simulated data points at three different evaporation temperatures. The efficiency correlat ions are compared to correlations from the literature. The isentropic efficiency varies considerably between different compressors ; hence , selecting the appropriate correlations for simulating the cycle behavior is important. The effect of the GC outlet pr essure and temperature, the evaporation temperature, and the useful superheat taking place inside the evaporator on the COP are investigated and discussed. The GC outlet temperature is the most influential parameter on the optimum GC pressure. The evaporat ion temperature has a negligible effect on the optimum GC pressure. An optimized offline control correlation is developed and compared to common ones in the literature. The correlation relates the optimized GC pressure to the GC outlet temperature , which c an be used to maximize the transcritical cycle COP for relevant range of operating conditions. 48 Chapter 4: Multi - Objective O ptimization Maximizing COP is equivalent to minimizing the work consumed by the compressor for a certain amount of cooling capacity as shown in [43] , which translates into minimizing fuel/energy consumption. However, this does not mean that the system is working at its highest cooling/heating capacity that may be desired for example in a transient start - up operation to cool down or heat up a space as quickly as possible to a certain condition or for a continuous load that is higher than at the maximum COP. In this work, the trade - off between maximizing COP and the cooling capacity ( ) is analyzed and the results are equally valid for the heating capacity. The best solutions for both objectives of maximizing COP and are presented by a Pareto Front for given operating conditions. The solutions that construct the Pareto Front are equall y good and cannot be dominated by other solutions. Each solution of the Pareto Front has a unique GC pressure and superheat that can be used as reference values for the system controller. Here, the Non - Dominated Sorting Genetic Algorithm II (NSGA - II) [48] is used to generate the Pareto Front with the best non - dominated solutions between the COP and for any set of operating conditions, based on a transcritical CO 2 thermodynamic model presented in Chapter 3 . An optimizati on parameter that ranges from 0 to 1 is introduced to easily select maximum COP, maximum , or trade - off solutions in between. The methodology can be applied for transcritical cycles in cooling and heating applications, including a simple cycle, or modi fied cycles like with an IHX, an expander, an ejector, or multi - stage compressor cycles, and for different working fluids. It is here discussed for the example of using CO 2 (R744) in a simple cycle. By referring to Figure 3 - 1 , t he simulation and analysis assumes (1) the cycle operates at steady - state, (2) CO 2 is a pure fluid neglecting the effect of a lubricant on the properties, (3) the 49 compression process is adiabatic but non - isentropic, (4) the only heat exchange occurs in the heat exchangers, hence, the superheat is useful, (5) no pressure drop occurs in t he heat exchangers and CO 2 lines, hence and and (6) The compressor volumetric and isentropic efficiencies are not affected by compressor speed. The compressor typically has a high - side pressure limit, which is set here at 140 bar. Figure 4 - 1 shows the p - h diagram for CO 2 with a simple transcritical cycle operating as an example at GC outlet temperature of 32 °C, GC pressure of 85 bar, and evaporation te mperature of 15 °C. Figure 4 - 1 . p - h diagram for CO 2 with simple transcritical cycle at T 3 =32 °C , p GC =85 bar , and T 1 =15 °C The constant temperature line for 32 °C and 45 °C and a line with constant entropy s=s 1 are shown in orange and green respectively. It can be inferred that increases with the increase of at constant and . Due to the more pronounced S - shape of the isotherms near the critical point, the increase of near the critical point is higher than far away from the critical point. With the non - conflicting conflicting 50 increase of , the compression power also increases but in an almost linea r fashion. There is a point where the relative increase in becomes less than the relative increase in the compression power. At this point, COP reaches its maximum. It can be found by equating the derivative of the COP with respect to to zero [14] ( 4 . 1 ) where is a function of and (Eqn . ( 3 . 6 ) ) , and can also depend on . The maximum COP condition is then ( 4 . 2 ) showing that at this point along the isotherm with increasing , the decrease of relative to the mass - specific cooling capacity equals the increase of relative to the mass - specific compression work. For the cycle in Figure 3 - 1 , this point is indicated on the isotherm at . At GC pressures below this point, higher COP and larger are non - conflicting objectives. Both objectives are conflicting at GC pressures above this point, where with increasing the COP decreases while increases further. Figure 4 - 2 shows how COP develops with varying at , , , and for three compressors efficiency correlations ( [49] , [50] , [51] ) and constant efficiencies of 0.7. The optimum pressure for the maximum COP varies only insignificantly by 0.7% around the mean across the presented effici encies and operating conditions. 51 Figure 4 - 2 . Effect of varying p GC at T 3 =32 °C , T 1 =15 °C, RPM , T sh =1 K , and with four different compressor efficiency correlations on COP The maximum can be found at ( 4 . 3 ) and i f the compressor volumetric efficiency is constant, i.e. , the mass flow rate is constant with chang ing , Eqn. ( 4 . 3 ) simplifies to ( 4 . 4 ) This condition occurs for CO 2 the maximum appears at the maximum allowed in the system, which is here at 140 bar. Figure 4 - 3 is generated using the same volumetric efficiencies used in Figure 4 - 2 . If the volumetric efficiency decreases with increasing compressor pressure ratio , the mass flow rate reduces (Eqn. ( 3 . 7 ) ) . With the mass flow rate reducing with higher compressor pressure ratios, can increase or decrease with increasing , depending on whether the increase of the enthalpy 52 difference across the evaporator or the mass flow reduction is dominant. This effect is observed in Figure 4 - 3 where the maximum (purple circle) occur at pressures of 97.3, 106.9, 122 bar for the efficiency correlations from [51] , [49] , and [50] respectively, and at the maximum allowed pressure in the system of 140 bar for constant volumetric efficiency, corresponding with Eqn. ( 4 . 4 ). Except the 140 bar, these pressure values mark the point, where the mass flow rate reduction due to the increase of pressure ratio starts to dominate over the increase of the enthalpy difference across the evaporator. In the pressure range from the maximum COP (green circle in Figure 4 - 2 ) to the maximum (purple circle in Figure 4 - 3 ) for each efficiency correlation, these two objectives a re conflicting, whereas in the range from the critical pressure to the with maximum COP (left of the green circle in Figure 4 - 2 ) these two objectives are non - confli cting, as also indicated in Figure 4 - 1 . Considering the above analysis, it can be of interest to exploit the feature of transcritical cycles that by adjusting the GC pressure: maximum COP, maximum , any trade - off point between these both, or lower below the point of maximum COP can be obtained. While maxim um COP can be of interest for minimal energy consumption, maximum may be of interest especially for transient operation (e.g. for quickly achieving thermal comfort at start - up or change of set - point). A trade - off point between maximum COP and maximum can be selected by a controller as a compromise between energy efficiency and thermal comfort. Working with reduced at GC pressures below the point of maximum COP can be employed at low load to avoid on - off cycling of the compressor. 53 Figure 4 - 3 . Effect of varying p GC at T 3 =32 °C , T 1 =15 °C , RPM , and T sh =1 K , and with four different compressor efficiency correlations on c Exploiting the features of transcritical cycles, it can be beneficial to transition by purpose from a subcritical cycle to a transcritical cycle by allowing T 3 to increase, especially if T 3 is already close below the critical temperature. As an example, benefits in terms of percentage increase of COP and respec tively are shown in Figure 4 - 4 and Figure 4 - 5 for a cycle operating with , and , and constant compressor efficiencies of 0.7. Figure 4 - 4 and Figure 4 - 5 indicate an increase of COP by more than 7% and simultaneously an increase of by more than 16% when transitioning from a subcritical cycle with to a transcritical cycle w ith and optimum GC pressure for maximum COP (75.7 bar), i.e. by allowing to increase by only while increasing by . Keeping then and further increasing the GC pressure to the optimum for maximum , can be further increased while then reducing COP again due to the conflicting nature of these two objectives in this range. The COP and gains of transitioning from a subcritical cycle to a transcritical cycle diminish as further away T 3 is from the critical 54 temperature as Figure 4 - 4 and Figure 4 - 5 show for the pre sented conditions. The next section describes the problem formulation for the bi - objective optimization in the range from maximum COP to maximum . Figure 4 - 4 . The COP g ain for transitioning from a subcritical cycle with close to T cr to a transcritical cycle, keeping T 1 =15 °C , , T sh =1 K , and is = v = 0.7 . Optimum pressures are in bar Figure 4 - 5 . The c g ain for transitioning from a subcritical cycle with close to T cr to a transcritical cycle, keeping T 1 , T sh =1 K , and is = v = 0.7 . Optimum pressures are in bar 55 4.1 Bi - objective Optimization 4.1.1 Problem Formulation A bi - objective trade - off Pareto Front between COP and for the transcritical vapor compression cycle and here for CO 2 as a refrigerant is generated and exploited for the control objective based on the preference whether maximum COP (minimum energy consumption), maximum (achieving maximum cooling), or working at a trade - off point between the two is desired. The optimiz ation problem considers at any point satisfying the two conflicting objectives: The optimization variables considered are , , , , and . is dependent on e.g. the ambient temperature and is independent of the GC outlet temperature. The useful superheat can be monitored and controlled for systems without compressor suction line accumulator that is to prevent otherwise liquid refrigerant from entering the compressor at low evaporator loads . The variable bounds considered for the optimization problem are: ( 4 . 5 ) ( 4 . 6 ) ( 4 . 7 ) ( 4 . 8 ) ( 4 . 9 ) For relevant solutions, the problem formulation is subject to the constraints ( 4 . 10 ) Since compressor efficiencies vary for different compressors [49] ; and to keep this analysis independent of a particular compressor, the isentropic and volumetric efficiency are both assumed to be constant ( 56 4.1.2 Evolutionary Multi - objective Optimization Algorithm Classical direct and gradient based methods may converge to a suboptimal solution instead of an optimal solution if the initial condition changes. In addition, classical methods need to run a single - objective optimizer many times to obtain a Pareto Front. Moreover, good distribution (or diversity) of the Pareto Front solutions is not guaranteed. The Non - dominated Sorting Genetic Algorithm II (NSGA - II) [48] use d here is an evolutionally algorithm that overcomes the limitations of classical methods. Figure 4 - 6 shows a schematic outline of how the NSGA - II works. The algorithm starts with a random parent population with size and creates an offspring population having the same size as the parent population. These two populations are lumped together to form with population size . The objective functions (i.e. COP & ) are calculated for the combined population . A non - dominated sorting (a hierarchical partial ordering operation) is then performed on to classify it into several fronts ( , , , ...). The solutions are sorted in an ascending level of non - domina tion. The next generation population is formed by copying fronts from the top of the hierarchical list. To maintain the fixed population size of , the copying operation is continued until no more complete fronts can be accepted. Then, the final fron t that could not be accepted completely is operated with a diversity preserving operator to select the required number of points, i.e. , preserve them and reject the rest of the final front population. NSGA - II employs a computationally fast crowding distanc e operator for this purpose. The above method works iteratively in generations to (i) emphasize non - dominated solutions in a population, (ii) emphasize diverse solutions in a population, and (iii) emphasize previously found good solutions for both COP & objectives. Along with NSGA - selection criteria help a randomly created population to progress towards the Pareto - optimal front 57 with generations. The number of population and generation have been selected after som e test runs as 200 for each. 4.2 Best Trade - off Solutions 4.2.1 Obtained Pareto Front Figure 4 - 7 shows the best non - dominated optimum solutions in blue that is the finally obtai ned Pareto Front (here referred to as Pareto Front). A parameter is introduced that ranges from zero to 1 . Zero represents the maximum COP solution and 1 the maximum solution, whilst for example represents the 40 th percentile of the sorted non - d ominated solutions that start with the maximum COP, hence being closer to the maximum COP than to the maximum solution. Each solution of the Pareto Front has a corresponding variable space solution, i.e. , a corresponding GC outlet temperature, GC pressu r e , evaporation temperature, useful superheat, and compressor speed. All the Pareto Front solutions are found at the minimum , the maximum , and the maximum . The maximum COP occurs at bar and , while the maximum occurs at bar and . Table 4 - 1 shows the variable and objective values for five selected solutions: the maximum COP ( ), the ma ximum ( ), and three trade - off solutions ( , and ). The five solutions are marked in Figure 4 - 7 . Figure 4 - 8 shows the heat pump cycles corresponding to the five marked solutions in a p - h diagram. Table 4 - 1 . Pareto Front variable and objective values for five selected solutions: maximum COP, maximum c , and three trade - off solutions k Objectives Variables COP [ - ] [kW] [°C] [bar] [°C] [K] [ rpm ] 0 5.8 4.8 32 77.5 15 10.0 1800 0.25 5.3 5.3 32 83.4 15 10.0 1800 0.5 4.5 5.7 32 93.8 15 1.0 1800 0.75 3.7 6.0 32 108.6 15 1.0 1800 1.0 2.8 6.3 32 140.0 15 1.0 1800 58 . Figure 4 - 6 . S chematic of NSGA - II maximizing both objectives COP and c Figure 4 - 7 . Pareto Front for maximizing both COP and c with corresponding GC pressures. Solutions labeled with k=0 and k=1 are the maximum COP and c solutions respectively. Solutions with k=0.25, 0.25, and 0.75 are labeled as example trade - off solutions. 59 In Figure 4 - 8 , the green cycle with presents the cycle that produces the maximum COP of 5.8. The purple cycle with = 140 bar presents the cycle that produces maximum of 6.3 kW. The three gray cycles in between present cycles for the three examples of best trade - offs between maximum COP and , where both COP and are less than their maximum achieved with the green and the purple cycles respectively. For increasing G C outlet temperatures, the green circles connected by the green dotted line show the trend of state 3 for cycles operating at maximum COP, and the purple circles connected by the purple line show the trend of state 3 for cycles operating at maximum . Be cause the volumetric compressor efficiency is constant, the maximum occurs at the maximum allowed GC pressure (Eqn. ( 4 . 4 ) .) Figure 4 - 8 . p - h diagram indicating the cycles for the five solutions labeled on the Pareto Front in Figure 4 - 7 . The green cycle produces the maximum COP, the purple cycle the maximum c , and the grey cycles represent the three example trade - off solutions. 4.2.2 Gain to Loss Ratio for moving from one soluti on to another All the Pareto Front solutions between the maximum COP and the maximum solutions represent optimized trade - off solutions. A gain to loss ratio can be defined as the ratio of the gain 60 on the objective that is to increase ( or ) over th e loss on the other objective ( or ) when moving from one solution to another by adjusting the GC pressure. Hence, it can be written as , when moving to the right to increase ( 4 . 11 ) , when moving to the left to increase COP Figure 4 - 9 shows the normalized Pareto Front for maximizing both COP and used for the G/L calculations. Table 4 - 2 contains the G/L ratio calculations for both moving from left to right and right to left between values of 0, 0.25, 0.5, 0.75, and 1. The distances through are the differences in norma lized COP and between these solutions in the Pareto Front as shown in Figure 4 - 9 . For example, if the system is operating at maximum COP with k=0, there may be a mot ivation to move to right to e.g. to increase considerably (more than double as much in its range then COP would reduce in its range) while reducing COP acceptably. Differently, if the system is operating at a pressure corresponding to , i. e ., , the motivation may be less to move to a neighboring point for the betterment of either objectives. Therefore, the G/L can be used as a determining factor for moving from one solution to another depending on the desired system performance. The G/L ratio can be calculated on a normalized basis as above, if the evaluation emphasizes on utilization of available range between the two objectives, or on an absolute basis if the ratio of percent increase over percent decrease is of relevance. For the latter, Eqn. ( 4 . 11 ) can be formulated as , when moving to the right to increase ( 4 . 12 ) , when moving to the left to increase COP 61 evaluating at the current point of operation with . Alternatively, gain and loss could be evaluated regarding e.g. , the maximum value (respective objective), keeping the basis constant. Results of Eqn. ( 4 . 12 ) for same step size like in Table 4 - 2 with are shown in Table 4 - 3 , where e.g. , moving to the right from to , increases by 10.4% from 4.8 kW to 5.3 kW and COP reduces by 8.6% from 5.8 to 5.3, resulting in G/L=1.21, which expresses that increases 21% more than COP reduces. Table 4 - 2 . Gain to loss ratios for five solutions obtained from the normalized Pareto Front G/L k 1 =0 k 2 =0.25 k 3 =0.5 k 4 =0.75 k 5 =1 Moving to the right - Moving to the left - Table 4 - 3 . Gain to loss ratios for five solutions using absolute values from the Pareto Front ( Eqn. ( 4 . 12 ) ) G/L k 1 =0 k 2 =0.25 k 3 =0.5 k 4 =0.75 k 5 =1 Moving to the right - Moving to the left - While a relative coarse step size like that presented in Table 4 - 2 , Table 4 - 3 , Figure 4 - 9 and Figure 4 - 10 may already be practical, also any smaller reasonable can be chosen instead, and G/L can also be evaluated e.g. on an absolute basis by , when moving to the right to increase ( 4 . 13 ) , when moving to the left to increase COP 62 Therefore, the trade - off for steady - state or transient can be further modulated by an additional objective function correlating thermal comfort and energy consumption, where the gain to loss ratio can be a determining factor for moving the operating point. Figure 4 - 9 . Normalized Pareto Front for maximizing both COP , c and G/L for moving to right and left with k =0.25 Figure 4 - 10 . Pareto Front for maximizing both COP , c and G/L based on absolute values for moving to right and left with k =0.25 63 4.3 Optimization Variables Effect on the Pareto Front While Table 4 - 1 , Figure 4 - 7 , Figure 4 - 9 , and Figure 4 - 10 represent the Pareto Front obtained for the entire optimization variable space bound by Equations ( 4 . 5 ) through ( 4 . 9 ) , any or all the optimization variables can for practical reasons assume v alues different than in Table 4 - 1 , altering the Pareto Front. The effect of each on the Pareto Front is discussed in this section. The effect of the compressor performa nce expressed in compressor efficiency correlations on the Pareto Front is analyzed additionally. 4.3.1 Effect of GC Outlet Temperature Change Figure 4 - 11 shows the effect of changing GC outlet temperature on the Pareto Front at , , , and on COP and at k values of 0, 0.25, 0.5, 0.75, and 1. Figure 4 - 12 shows the cycles for with their corresponding GC pressure and each in a p - h diagram, and also indicates the GC pressure range for the Pareto Front on the isotherm by coloring it with same color as the respective Pareto Front in Figure 4 - 11 . The trend of the Pareto Fronts reflects that increases with decreasing , because the GC outlet enthalpy decreases, enlarging the enthalpy difference acros s the evaporator . If is set to reflect constant k value, the enthalpy difference across the compressor decreases, and COP increases. Figure 4 - 11 shows the percentage increase in COP and if decreases from 45 °C to 40, 35, and 32 °C at and 1. For example, at , i.e. at the maximum COP solutions, if decreases from 45 °C to 35 °C, COP and increases by 83% and 14% respectively. Each Pareto Front spans a different range of GC pressures for each GC outlet temperature as reflected in both figures. The higher the GC outlet temperature, the smaller is the Pareto Front range of optimum solutions. This is due to the increase of the pres sure corresponding to the maximum COP solution (Eqn. ( 4 . 2 ) ) , while the maximum solution (Eqn. ( 4 . 4 ) ) remains 64 at the maximum allowable system pressure of 140 bar. For example, the Pareto Front minimum pressures are 77.9, 85.3, 98.4, and 112.6 bar for 32, 35, 40, and 45 °C respectively as indicated in Figure 4 - 11 . For , the Pareto Front collapses into one point presenting the maximum COP and the maximum solution at the maximum system pressure of 140 bar (Eqn. ( 4 . 6 ) ) . If the system allows a GC pressure higher than 140 bar, then there will be a Pareto Front at 54 °C. Figure 4 - 11 . Pareto Fronts maximizing both COP and c at T 1 =15 °C , T sh =1 K , and RPM , for different T 3 . The grey lines connect the solutions corresponding to k=0, 0.25, 0.5, 0.75, and 1 65 Figure 4 - 12 . p - h diagram with cycles for four different T 3 and T 1 = 15 °C, T sh =1 K , RPM , k=0.5 from Figure 4 - 11 . The circle markers on each isotherm represent the corresponding Pareto Front in Figure 4 - 11 4.3.2 Effect of Evaporation Temperature C hange Figure 4 - 13 shows the effect of varying evaporator temperature at , , and . Figure 4 - 14 shows the cycles for and each from Figure 4 - 13 in a p - h diagram. With increasing , the changing Pareto Fronts show both COP and increase for constant . increases because of increased mass flow with higher vapor density at higher evaporation pressure, overriding the reduced enthalpy difference across the evaporator with increased evaporation temperature due to the shape of the saturated vapor line of the vapor dome. While COP is independent of mass flow rate, it still increases because the relative reduction of enthalpy difference across the compressor is more than across the evap orator. This can be shown by equating the derivative of the COP with respect to to zero and rearranging to ( 4 . 14 ) 66 It is furthermore noted that for CO 2 , the compressor inlet enthalpy increases monotonically with for all , so that the enthalpy difference across the evaporator even increases while it decreases across the compressor, always increasing COP wi th increasing in that range. Figure 4 - 13 also shows the percentage increase in COP and if increases from - 25 to - 15, - 5, 5, and 15 °C at and . For example , at k=0, i.e. at the maximum COP solutions, if increases from - 25 °C to 5 °C, COP and increases by 151% and 131% respectively. As the evaporation temperature gets lower, the Pareto Front shrinks due to the reduction in both COP and ranges. This shrinking in the Pareto Front continues to just before the evaporation temperature reaches the triple point at - 56.6 °C. Figure 4 - 13 . Pareto Fronts maximizing both COP and c at T 3 =32 °C , T sh =1 K , and RPM , for different T 1 . The grey lines connect the solutions corresponding to k=0, 0.25, 0.5, 0.75, and 1 67 Figure 4 - 14 . p - h diagram with cycles for five different T 1 at T 3 =32 °C , T sh =1 K , RPM , and k=0.5 from Figure 4 - 13 4.3.3 Effect of U seful S uperhea t For constant enthalpy at the evaporator inlet, increasing useful superheat increases the enthalpy at the evaporator outlet and hence the enthalpy difference across the evaporator, which acts to increase (Eqn. ( 3 . 9 )) and CO P (Eqn. ( 3 . 11 ) ) . With increasing also the compressor inlet temperature increases causing competing effects of increased enthalpy difference across t he compressor reducing COP, and of lower density at the compressor inlet reducing mass flow rate (Eqn. ( 3 . 7 ) ) and hence . Figure 4 - 15 and Figure 4 - 16 show the effect of varying for two different cas es at and , respectively both at and , demonstrating that the competing effects can dominate, e.g. for the maximum solutions (highest ) in Figure 4 - 15 , whereas this is not the case in Figure 4 - 16 and e.g. not for the maximum COP solutions (lowest ) in Figure 4 - 15 . For the increase of from to in Figure 4 - 15 , at , COP and increase by 1.8% and 0.4% respectively, while at both COP and decrease by 1.3% 68 and 2.0% respectively and in Figure 4 - 16 , both COP and increase at by 5.5% and 1.0%, and at by 2.4% and 1.6% respectively. While the changes in COP and resulting from changing can be deemed relative small, their direction depends on the particular operating conditions, with inversions observed at closer to the critical temperature and high GC pressures, i.e. solutions for larger (higher ). Figure 4 - 15 . Pareto Fronts for maximizing COP and c at T 3 =32 °C , T 1 =15 °C, and RPM , for different T sh . The grey lines connect the solutions corresponding to k=0, 0.25, 0.5, 0.75, and 1 69 Figure 4 - 16 . Pareto Fronts for maximizing COP and c at T 3 =45 °C , T 1 =15 °C, and RPM , for different T sh . The grey lines connect the solutions corresponding to k=0, 0.25, 0.5, 0.75, and 1 4.3.4 Effect of C ompressor S peed The effect of varying the compressor speed on the Pareto Front is shown in Figure 4 - 17 for °C , , and . As expected, with increasing compressor speed, increases proportionally due to the increase of mass flow rate delivered by the compressor (Eqn. ( 3 . 7 ) ) and Eqn. ( 3 . 9 ) ) . For example , at the maximum COP solutions, if increases from to , increases by 80 %. The COP remains unaffected with speed change if the compressor volumetric and isentropic efficiency remain the same. In practice, the compressor efficiencies may change with speed. 70 Figure 4 - 17 . Pareto Fronts for maximizing both COP and c at T 3 =32 °C , T 1 =15 °C , and T sh =1 K , for differen The grey lines connect the solutions corresponding to k=0, 0.25, 0.5, 0.75, and 1 4.3.5 Effect of C ompressor P erformance Figure 4 - 18 shows for °C , °C , , and rpm the Pareto Fronts for constant isentropic and volumetric compressor efficiency ( and variable efficiencies correlated for four semi - hermitic compressors from the literature ( [23] , [49] , [50] , and [51] ). The compressor isentropic and volumetric efficiency correlations have a significant effect on the Pareto Front as shown. The isentropic efficiency affects the compressor outlet enthalpy, which in turn changes the enthalpy difference across the compressor affecting COP. The volumetric efficiency affects the mass flow rate, which changes and in turn also COP. 71 Figure 4 - 18 . Pareto Fronts for maximizing both COP and c at T 3 =32 °C , T 1 =15 °C , T sh =1 K, and , for different compressors efficiencies 4.4 Operation Contour Maps and Cycle Control Strategy A set of Pareto Fronts can be generated offline covering all the possible operating ranges of and . Each Pareto Front is generated by fixing each of these both variables to cover all possible operating condition combinations . Resulting from this, Figure 4 - 19 shows for the entire operation space of and at for three selected values of the optimization parameter ( maximum COP solution, trade - off solution, and maximum solution) the contour maps of the reference GC pressure for the controller, and the resulting , and COP . The GC pressure contour is omitted for as for such case the optimum pressure is always the maximum allowed GC pr essure of 140 bar. A sample system control block diagram is shown in Figure 4 - 20 . Based on the input of measured and , and corresponding with a predefined preference, i.e. , a value (for maximum COP, maximum , or a trade - off solution), the optimizer retrieves the P areto Front, and feeds the corresponding reference and for achieving the desired system behavior. The controller 72 compares the reference signals to the actual measured ones, calculates the error , and acts accordingly based on the implemented control approach. The control approach can include that to avoid compressor on - off cycling at low load, the GC pressure is reduced below the one for maximum COP ( ) to operate at reduced at a point where and COP are non - conflicting. As shown in Figure 4 - 20 , an optional online optimizer can be integrated in the loop e.g. before the controller, resulting in conjunction with the offline optimizer in a hybrid solution. Such a hybrid solution can reduce the time to approach the desired operating point compared to online only methods. Compared to offline only methods, this can additionally enhance COP and based on the actual system characteristics, while it is also able to adapt to changing system characteristics. Figure 4 - 19 . Operation Maps that show the contour lines of the GC pressures for T 1 : - 25 C to 15 °C , T 3 : 32 °C to 45 °C , and k=0 maximum COP (first row), k=0.5 trade - off (middle row), and k=1 maximum c (last row) Here, always maximum allowable pressure of 140 bar 73 Figure 4 - 20 . Transcritical cycle control block diagram for operating at the maximum COP, c , or a desired best trade - off both represented by Pareto Fronts This chapter investigate d the transcritical CO 2 vapor compression heat pump system from the perspective of maxim izing both the COP and the cooling or heating capacity utilizing Pareto Fronts here generated with the NSGA - II algorithm, where each solution on a Pareto Front is designated by an optimization parameter k and corresponds to a particular gas cooler pressure and superheat. A gain to loss ratio for the Pareto Front solutions is presented that can be used as a criteria for moving from one solution to another. The effect of each optimization variable on the Pareto Front is shown separately. The gas cooler outlet temperature, the evaporation temperature, the compressor speed, and the compressor performance have significant effect on the Pareto Fronts compared to the superheat. A control methodology is introduced where the reference GC pressure and superheat corres ponding to the maximum COP, cooling capacity, or a best trade - off solution between both as desired is retrieved from pre - generated Pareto Fronts that cover the expected operating condition ranges. The proposed methodology can be used for simple or modified cycle configurations, for cooling and heating application, for off - line, online, and hybrid solutions. 74 Chapter 5: Experimental Apparatus This c hapter presents the details of selecting the different components of the CO 2 transcritical experimental test - rig and prese nts the schematics, sizing equations, technical specifications, layouts, 3D CAD design of both the CO 2 , and the HTF loops . In addition, we present the experimental test - rig build details. 5.1 CO 2 Loops 5.1.1 Schematics The cycle schematics have been developed to allow investigation s of cooling, heating, and dehumidification modes. The HTF loops are not shown in these schematics for simplicity and will be presented separately in the HTF loops section. The cooling mode is shown in Figure 5 - 1 where low pressure and temperature vapor CO 2 enters the compressor and leaves as high pressure and temperature. The refrigerant enters the oil separator so that the o il is returned to the compressor through the oil charge plug. Refrigerant is then directed by a 3 - way valve to pass along the OHX coils that act as a GC or condenser depending whether the heat rejection is above or below the critical point respectively. Th e refrigerant leaves the OHX and is directed by another 3 - way valve to expand through the cooling expansion device before entering the evaporator coils. The accumulator then receives any liquid refrigerant to ensure that the compressor suction is getting v apor refrigerant only and minimal oil content. 75 Figure 5 - 1 . Cooling mode schematic Figure 5 - 2 presents the schematic of the heating mode where the vapor CO 2 , after passing by the compressor and oil separator , is directed by a 3 - way valve to pass along the interior GC HEX coils, noting th at this HEX will act as a condenser if the heat rejection occurs below the critical point. The refrigerant then expands through the heating expansion device before exchanging heat with the HTF through the OHX coils that acts as an evaporator. The liquid re frigerant is separated from the vapor refrigerant in the accumulator before the vapor flows again into the compressor. The dehumidification series mode shown in Figure 5 - 3 resembles the heating mode up to the point where the refrigerant leaves the OHX, then a 3 - way valve directs the flow to expand through the cooling expansion device; after which, CO 2 evaporates and the vapor refrigerant flow through the co mpressor. In this mode the refrigerant is sent to circulate through the three heat exchangers. Also, in this mode the refrigerant evaporates in a series fashion through the OHX and evaporator coils. In an automotive air conditioning system, and as reported in [52] , the air will be cooled and 76 dehumidified by the evaporator to the degree required for demisting the windshield before being reheated by the interior GC and blown into the cabin. Figure 5 - 2 . Heating mode schematic Figure 5 - 4 shows the dehumidification parallel mode, which resembles the heat ing mode up to the exit of the interior GC. In this mode, the shut - off valve located in the center of the schematics is fully open, while in all other previous mode, this valve was fully closed. CO 2 is divided according to the percentage opening of the coo ling and heating expansion devices. One portion expands through the heating expansion device before circulating through the OHX and being directed by a 3 - way valve to the accumulator. The other portion passes through the shut - off valve before expanding thr ough the cooling expansion device and evaporating. The two portions combine again at the intersection connection before the accumulator, and the refrigerant is sent to the compressor. A schematic that presents all the modes is shown in Figure 5 - 5 . 77 Figure 5 - 3 . Series dehumidification mode schematic Figure 5 - 4 . Parallel dehumidification mode schematic 78 Figure 5 - 5 . Cooling, heating, dehumidification series mode, and dehumidification parallel mode 5.1.2 Compressor A compressor is required that shall provide enough cooling and heating capacities for a midsize vehicle. For such a vehicle, the range of required cooling and heating capacities are from 3 to 5 kW and 5 to 8 kW respectively. Another requirement for the heat ing mode is the capability to support ambient temperatures down to - 30 °C . Thus, a compressor that supports evaporation temperature down to - 30 or even lower is required. Several manufacturers entered the market of CO 2 compressors with the most common types being semi - hermetic and rotary compressors. A survey has been carried out to find and compare different types of CO 2 semi - hermetic compressors. The compressor selected for this study is a Dorin CD200 - CD180H, 3 phas e, 230V, and 60 Hz. The compressor's rated input power is 1.34 kW . Additional specifications are shown in Table 5 - 1 . B ased on simulating different data points in Dorin software , the compressor can provide maximum cooling and heating capacities of 5.5 and 8 kW respectively . 79 Most of the other available compressors provide capacities more than this ; thus , they were oversized for our application. Table 5 - 1 . Compressor specifications Specification Value Bore 22 mm Stroke 17 mm Swept volume (V d ) 12.9/10 6 m 3 Displacement 1.35 m 3 /h @ 60 Hz Speed 1740 rpm @ 60 Hz Max low - side pressure 100 bar Max high - side pressure 150 bar The Dorin CD200 category has a splashing disc lubrication mechanism. In this lubrication method, the crankcase, which acts as an oil sump, is filled with oil to a certain level. As the crank shaft rotates, the connecting rod and cranks haft dip into the oil sump causing the oil to be splashed on the rubbing surfaces. The motor driving the compressor is an asynchronous 4 - poles motor. A small, electric heater immersed in the crankcase oil is often used to maintain adequate oil temperature s. The rated speed at 60 Hz is 1740 rpm . According to email communications with Dorin Corporation , The CD200 compressors can run from 60 down to 30 Hz. However, between 40 and 30 Hz, a resonance may appear. For this reason, Dorin recommends checking the co mpressor behavior in the whole range of speed s and in the case of a reson ance problem, it is recommending skipping the se frequencies. They also recommend always keeping the voltage to frequency ratio constant even when the speed is reduced. A Hitachi WJ20 0 variable frequency drive is attached to drive the compressor to control the frequency (and hence, the speed). The compressor schematic and photo are shown in Figure 5 - 6 . 80 Figure 5 - 6 . Dorin CO 2 CD180H compressor detailed drawing and photo ( Credit : Dorin) 5.1.3 Oil Management Since t he compressor does not have an integrated oil separator; an oil management scheme is considered . The purpose of the oil separator is ensuring that the refrigerant circulating in the system is oil free. In such a system, the measurement of the temperature and pressure determines the enthalpy at each state point. If there is oil circulating in the system, it will affec t the measurement accuracy. An oil separator from Temprite, M odel 131 coalescent filter type, is installed at the compressor discharge that returns oil to the compre ssor charge plug. The oil separator photo and schematic are shown in Figure 5 - 7 . The oil separator is rated up to 160 bar and is equipped with 3/8 - inch fema le NPT connection for the three ports: the vapor inlet, vapor outlet, and oil outlet. The oil separator has also two 3/4 - inch ports for the installation of two eye - sight glasses provided by PresSure Products Company (PPC), one at the bottom and the other o ne at the level of the oil vapor outlet port. 81 Figure 5 - 7 . Oil separator photo and schematic ( Credit : Temprite) To control the oil return line, a sensor from HB Products Company is installed just below the oil outlet of the oil separator . The sensor shown in Figure 5 - 8 communicates with a solenoid valve at the return line to open/close if there is oil accumulated seen by the sensor or not . According to Dorin, the oil injected to the compressor charge plug shall be at a pressure that is between 5 bar and 10 bar higher t han the crankcase pressure. The crank case pressure is the same as the low - side pressure. For that reason, a needle valve that can withstand high pressure is placed after the solenoid valve to reduce the oil pressure . The oil return line schematic is shown in Figure 5 - 9 . Figure 5 - 8 . (a) HBOC (b) Installation on the compressor sight glass. (c) Solenoid valve V150 ( Credit : HB Products Company) Figure 5 - 9 . Schematic of the oil return line 82 5.1.4 Heat Exchangers Three heat exchangers are needed for this study as the schematics showed: A n outside heat exchanger that will act as an evaporator in the heating mode or as a GC/condenser in the cooling mode, a GC /condenser for the heating mode, an e vaporator for the cooling mode. Brazed plate heat exchangers (B PHE) were a favored selection due to their compactness, low volume, and compatibility with CO 2 . BPHE consists of cascaded corrugated stainless - steel plates that are brazed together using materials such as copper and nickel. The standard BPHE units are built from AISI316 steel with copper as a brazing material. Nickel is used as brazing material in applications where copper presents compatibility probl ems with process fluids. Each plate has a characteristic corrugation pattern that governs the degree of thermal efficiency and hydraulic behavior of the BPHE unit. T he operating conditions of each heat exchanger were given to Alfa Laval Company which inclu d ed the maximum capacity, its associated refrigerant and HTF inlet and outlet temperatures, pressures, and flow rates. The recommended BPHE was AXP10 - 20H - F where "20" is the number of plates, "H" is the type of plate, and "F" means 316 stainless. The brazi ng material is copper. This unit has temperatures that range from - 196 °C to 225 °C. The pressure rating and a schematic showing the dimensions of the AXP unit are shown in Figure 5 - 10 . Figure 5 - 10 . AXP10 Pressure ratings (Left) and AXP10 Photo and Schematic (right) 83 5.1.5 Suction Line Accumulator As reported in [53] , the standard rotational speeds of compressors are between 1,725 and 3,400 rpm . At these speeds, if any liquid enters the compressor chamber, it can cause instantaneous mechanical failures. A condition kn own as slugging occurs when a large amount of liquid refrigerant is entrained with the vapor refrigerant. Slugging is accompanied by pounding and knocking sounds and frequently causes instantaneous compressor damage. Even if the liquid refrigerant returns to the compressor in small quantities ( but over a long period of time) , this liquid refrigerant tends to dilute the oil, reducing its lubricity and generating a condition of rapid bearing wear. Suction line accumulators help protect compressors against eit her immediate or long - range damage caused by the return of liquid refrigerant to the compressor. Accumulators are vessels that can be vertical or horizontal. Vertical accumulators use a U or J tube to draw gaseous refrigerant off the top of the vessel. Mos t accumulators have at the bottom of this tube, a small orifice to pick up a small amount of oil and liquid refrigerant and meters it back with the gaseous refrigerant. This small amount of liquid refrigerant will boil off in the suction line. The oil will be carried with the gaseous refrigerant back to the compressors. Two considerations were important while sizing the accumulator. First, the accumulator shall be able to hold the system's liquid refrigerant. Normally, the accumulator liquid - holding capacit y shall not be less than 50 % of the system charge [54] . Second, the accumulator shall perform without adding excessive pressure drop into the system. If the accumulator is sized too big to handle the system capacity (T he system capacity is smaller than the accumulator minimum capacity . ), the orifice will not meter back oil due to the reduced flow through the accumulator. The accumulator needs to be selected to ensure that the system capacity is above the minimum rating. If the accumulator is sized too small to handle the system 84 capacity (The system capacity is larger than the accumulator maximum capacity . ) , this problem will cause the orifice to meter back more refrigerant (which may contain liquid refrigerant) due to th e increased gas flow past the orifice. An accumulator volume of 2.7 L was calculated based on the estimated system volume . A horizontal design was proposed and sent to Temprite for quoting and manufacturing. Figure 5 - 11 shows the current 3D design of a horizontal accumulator , which encompasses a sight glass and oil outlet that can be utilized for oil removal that may be accumulated in the accumulator . The accumulator is designed horizontally for compactness purposes of the test - rig. The accumulator is equipped with a heat exchanger to cool down the ref rigerant coming out of the GC just prior to the expansion process. Figure 5 - 11 . Horizontal accumulator design drew by Temprite 5.1.6 Expansion D evice A Swagelok SS - 31RS4 manual metering valve is selected that has a maximum pressure of 193 bar at 454 °C and a temperature range of - 53 °C to 454 °C. A schematic photo of the manual metering valve and its C v graph is shown in Figure 5 - 12 . Since the expansion device encompass two - phase flow, calculation of the C v is involved. The calculation of C v was carried out by using Eqn. ( 5 . 1 ) , 85 which is primarily used for liquid flow. Using this equation may introduce deviations as CO 2 is in a supercritical state at the valve inlet, but the equation is st ill valid for a good approximate value as pointed and used in [22] in their CO 2 transcritical experimental facility. T he estimated C v value for the maximum capacity case (and hence maximum mass flow rate case) was less than 0.04. ( 5 . 1 ) Figure 5 - 12 . Schematic of SWAGELOK 31 series valve and it Cv graph 5.1.7 Pressure Drop For the system to operate efficiently, pressure drop calculations are considered to find the optimum refrigerant tube size that would not produce considerable pressure drop and affect the cooling/heating capacities. The tube sizing is carried out for the suction, discharge, and liquid lines. After extractin g the mass flow rate ( ) and the density ( ) from test conditions simulations for the maximum capacity cases, a code was written in MATLAB to calculate the total pressure drop , which is the sum of tubing friction losses , fitting losses , eleva tion difference pressure drop/gain , valves, and other elements pressure drops. 86 Friction losses are the losses of pressure that occur in the pipe or duct flow because of the fluid's viscosity near the surface of the pipe or duct. The Darcy Weisbach e quation [55] relates the pressure loss due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid as ( 5 . 2 ) The flow speed is determined by ( 5 . 3 ) where A is the internal cross - sectional area. Reynold number is defined by ( 5 . 4 ) The Darcy friction factor f D is usually calculated from the Moody friction factor chart [56] . The chart is made from the following equations [57] . For laminar flow with Re 2100, the Hagen - Poiseuille equation [57] gives ( 5 . 5 ) For transitional flow where the friction factor varies with both Re and K, the Colebrook equation [58] is used ( 5 . 6 ) w here the stainless - steel abs olute roughness coefficient is =0.015 [59] . The Colebrook equation is also found to cover the fully developed flow regions for smooth and rough pipes as reported in [60] . We used this equation instead of the Moody chart as it can be handled easier using a computer. However, f D is not implicitly expressed in the equation; therefore, it needs a numeric 87 calculation. We used a function written in MATLAB that calculates using the method of quadratic iteration [60] , which is valid for Re 2300. The function take s Re and th e r elative roughness coefficient ( ) as inputs and generates f D . Several methods are available to calculate the fittings pressure drop. For fittings such as 90 - degree bends, the geometry of the fitting has a greater impact o n the pressure loss than does an equivalently sized length of pipe. The best case for determining the loss in a fitting would be to use experimental data; however, this is often not available. The equivalent length method is the oldest and most common one [61] [62] , which treats the fitting as a straight pipe with a specific length that depends on the geometry of the fitting. This length is generally larger than the arc length of the bend. This met hod does not take into consideration the Reynolds number and the pipe diameter. [63] is a modification of the equivalent length method, which takes into consideration the higher degree of turbulence in valves and fittings than in a pipe with a given Reynolds number. The loss coefficient method estimates the pressure drop in a fitting thro ugh a loss coefficient, K, determined by experiments. Loss coefficients values are tabulated, but these values are constant regardless of the pipe components geometry (diameter, elbow radius, type of pipe connection, etc.) and Reynolds number [64] . [65] depends on the velocity of the fluid and pipe diameter. The calculations are independent on the roughness of pipe and type of connection elbow. The 2 - K method [62] , [66] , and [67] is based on experimental data of valves, fittings, and elbows acquired for various Reynolds numbers. The K coefficient is a function of the Reynolds number, geometry of a given component, and the type of pipe connection for elbows. But it i s not influenced 88 by roughness. Clearly, the 2 - K method is more accurate than the equivalent length method as it applies an additional constant to improve characterization of the fitting pressure drop with variation of the fluid Reynolds Number. The 3 - K me thod [67] is similar to the 2 - K method but with a higher predicative value for the broad radius of Reynolds numbers and fittings dimensions [64] . The 3 - K method is also dependent on elbow inner diameter and the value of Reynolds number. In [64] , the authors performed a simulation study comparison between the different methods listed above and the study reported that the 3 - K method [67] is recommended for a calculation of the pressure drop of 90 degree elbows because it accounts directly for the effect of both Reynolds number and fitting size on the loss coefficient and reflects more accurately the scale effect of fitting size and connection type. The 3 - K method has been followed here to find the pressure drops for bends, union Tees, branching, sensor fittings, expansion areas, and contraction areas. The 3 - K method depends on calculating the K factor according t o the equation ( 5 . 7 ) where K 1 , K , and K d are extracted from tables. For a square reduction, if Re<2500 ( 5 . 8 ) w here D 1 is the entrance diameter and D 2 is the exit diameter. A nd for Re > 2500 ( 5 . 9 ) 89 For a square expansion, if Re < 4000 ( 5 . 10 ) w here D 1 is the entrance diameter and D 2 is the exit diameter. A nd for Re > 4000 ( 5 . 11 ) The fitting losses can then be calculated by ( 5 . 12 ) As fluid flows through a piping system, where pipes rise and fall and change elevation, the pressure at a point in a pipe is also affected by the changes in elevation of the fluid that have occurred. The net change in elevation h z is calculated, for instan ce for the suction line from the evaporator outlet to the compressor inlet. The pressure drop/gain is expressed as ( 5 . 13 ) For valves, a valve has a C v of 1 when a pressure of 1 psi causes a flow of 1 US gallon per minute of water at 60 ° F (i.e. SG = 1) through the valve. Since the pressure drop through a valve is proportional to the square of the flow rate the relationship between C v , flow rate and pres sure drop can be expressed as ( 5 . 14 ) Therefore, the valve pressure drop can be expressed as ( 5 . 15 ) 90 The flow sensor used in CO 2 loop is Micro Motion F - Series Coriolis flow meter. The pressure drop across the flow meter is obtained as a function of the flow rate from Emerson . For the oil separator, our talks with Temprite revealed that the estimated pressure drop across the 131 mod el is around 1.5 psi. Apparently, this pressure drop increase s if the filter gets contaminated. A constant pressure drop of 5 psi is assumed during these calculations . For the accumulator , the nominal pressure drop across acc umulator may not exceed 0.3 bar , as reported online. Hence, for this study, that was the assumption. A MATLAB code has been developed to calculate the total pressure drop in the suction, discharge, and liquid lines of the cooling mode considering tube sizes of 1/4, 3/8 and 1/2 - inch. Aft er calculating the pressure drop, the equivalent temperature drop in Fahrenheit is calculated by assuming constant enthalpy. For such refrigeration systems, the pressure drop should not produce more than 2 °F in the suction line and 1 °F in each of the dis charge and liquid line [68] . Figure 5 - 13 , Figure 5 - 14 , and Figure 5 - 15 show the pressure drop in bar, temperature drop in Fahrenheit, and the flow velocity in m/s for the different tube OD diameters, for the suction, liquid, and discharge lines respectively. As sh own in the graphs, for 3/8 - inch OD, the temperature change due to the pressure drop is less than 2 °F in the suction line and less than 1 °F in both discharge and liquid lines. The flow velocity for this case is acceptable (not very small and not very high flow velocity). Based on this analysis, all the tubes have been selected with a 3/8 - inch OD and a wall thickness of 0.049 inch. 91 Figure 5 - 13 . Suction line Pressure drop, equivalent temperature change, a nd the flow velocity for different tube OD Figure 5 - 14 . Discharge line Pressure drop, equivalent temperature change, and the flow velocity for different tube OD Figure 5 - 15 . Liquid line Pressure drop, equivalent temperature change, and the flow velocity for different tube OD 92 5.1.8 Valves , Tubing, and Fittings Different types of valves are needed in the CO 2 loops for isolation, filling, discharging, and routing the flow. The s election of valves mainly depends on the application, temperature range, pressure range, and the valve flow coefficient, which varies with the valve size, hence, also the valve end connection size. The reported leak rate of the valves is also checked to make sure that no considerable leakage will take place in the system. Most of the available valves in the market do not cover the whole temperature range of the CO 2 in the loop from - 40 °C to 160 °C. The low end is - 40 °C because the compressor supports evaporation temperature s down to - 30 °C; hence, 10 °C is considered a good extra margin. The high - end 160 °C is estimated from running various simulated data points and observing the highest compressor discharge temperature, which was around 150 °C; and 10 °C is also considered as a safety f actor. The maximum high - side and low - side pressure is 140 and 100 bar respectively, which is rated from the compressor data sheet. Since the CO 2 loop supports cooling, heating, and dehumidification modes, the location that is identified as the high temperature and pressure for one mode may also be identified as the low temperature and pressure in another mode. Hence, for each of the four modes, valves are identified and selected according to the location into which they will be placed in the loop, i.e., that can support working in all modes. For locations that will be e xposed to high temperature, the 3 - way valve SS - 83XPS6 with PEEK seats is selected because it c overs a temperature range from - 17 °C to 232 °C. The valve has a C v value of 0.75. For locations that will be exposed to low temperature, the 2 - way and 3 - way valv es SS - 43GS6 and SS - 43GXS6 respectively, which cover from - 53 °C to 148 °C, are selected. The 2 - way valve has a C v value of 1.5, while the 3 - way valve has a C v value of 0.9. Only one location in the loop that will see both high and low temperature depending on which mode is operating, which 93 is the location just before the O HEX. This location has two 2 - way valves to control whether the flow enters the HEX from th e top or bottom. If the HEX acts as evaporator, refrigerant will enter from the bottom. If the HEX acts as condenser, refrigerant will enter from the top. These two valves are chosen as a needle valve SS - 6NBS6 that has a temperature range - 53 °C to 648 °C. The needle valve has a C v value of 0.86. Although, a needle valve is usually used as a regulating valve, it can also be used as a shut - off valve as confirmed by Swagelok. The maximum pressure rating of all valves varies with the temperature as reported in the tables in the datasheets. All the valves chosen to have been checked to have pressure rating suitable for the valve location. All the above valves as reported by Swagelok have a maximum allowable leak rate of 0.1 std cm 3 /min under tests with nitrogen at 69 bar. This leak rate, 0.1 std cm 3 /min , represent s 4 ppm (or 0.0004 % ) of our maximum expected CO 2 flow rate (150 kg/h corresponds to 24000 std cm 3 /min , at 100 kg/m 3 CO 2 vapor density ) . If we consider a 1 m/s flow speed in a 3/8" line with 0.049" wall thickness, we get 1/10 of this with 0.00004 m 3 /s for 1 m/s, putting the leakage at 40 ppm 0.004 % . Furthermore, we may consider that the leak testing is done at only 69 bar, so we could double the result (considering that our maximum pressure is 140 b ar) putting it at 0.01 % . However, 1 m/s may not be the lowest relevant flow condition. If we assume operating in the range of 10 % to 100 % capacity, this puts the leak to 0.1 % at 100 % capacity. 0.1 % leakage is still a relative low number. So, this seems t o be acceptable for practical operational tests and investigations as this leakage is within the system and not connected to the ambient. When these valves used in places that will be exposed to the ambient such as the charging valve, the valve outlet is c apped to ensure ambient outlet end leak tight. All the tubing used are S wagelok, 316/316L SSL Seamless, 3/8 - inch OD and 0.049 - inch wall thickness. The tubing and fittings are rated up to 4800 psi (330 bar) . The temperature rating 94 reported in the data sheet is from - 28 °F to 37 °F . The fittings are 316 SSL which is rated to the same temperature and pressure rating of the tubing. After several talks with Swagelok technical team , they confirmed that there are customers who used these tubing and fittings in much more extended temperature range application; hence, they confirmed that these tubing and fittings will work for our application range from - 40 °C to 200 °C. 5.2 HTF loops The purpose of the heat transfer loo ps is to provide the needed cooling and heating capacities for each HEX. T he CO 2 cycle design needs to reflect conditions where the CO 2 refrigerant temperature is at - 30 °C, which is the compressor's lowest evaporation temperature. At this operating condit ion, CO 2 will be able to pick up heat from - 30 °C temperature or less from the environment. Providing HTF with a temperature of - 30 °C or lower will enable us to reflect the environmental conditions of an automotive in the winter. For that reason, a chille r with sufficient capacity of - 30 °C is required to be able to reach that goal. 5.2.1 Steady - state C apacities As depicted from the compressor simulations, the maximum and minimum cooling capacity is 5.5 kW and 0.5 kW respectively, while the maximum and minimum h eating capacity is 8.0 kW and 1.5 kW respectively. The capacities can be translated to express the maximum capacity of each HEX in each mode as follows: t he maximum evaporator capacity is 5.5 kW, the maximum outside HEX capacity is 8.0 kW, and the maximum interior GC capacity is 8.0 kW. For the cooling mode steady - state operation, since the maximum evaporator capacity is 5.5 kW, it can be assumed that the maximum heater capacity for the evaporator in the cooling mode is 6.0 kW to account for neglected heat losses. For the OH EX that will act as a condenser/ GC mode with a maximum capacity of 8.0 kW, we can assume that the maximum needed chilling capacity for the 95 O HEX in the cooling mode is 10.0 kW (assuming 2 kW of external heater control for desired temperat ure set - point, fine tuning.) Figure 5 - 16 shows the cooling mode schematics with the first law of thermodynamics applied on the system. Similarly, for the heating mode steady - state operation, since the maximum O HEX capacity (that will a ct as an evaporator) is 5.5 kW, it can be assumed that the maximum heater capacity for the O HEX in the heating mode is 6.0 kW. For the interior GC that has a maximum capacity of 8.0 kW, we can assume that the maximum needed chilling capacity for the OH EX i n the heating mode is 10.0 kW. Figure 5 - 17 shows the heating mode schematics with the F irst L aw of T hermodynamics applied on the system. Hence, for steady - state operation a single chiller of 10 kW capacity or more is required that will cool either the interior GC or the O HEX and two heaters each of 6.0 kW capacity. Figure 5 - 16 . The First Law of T hermodynamics applied to the cooling mode to estimate the needed chilling and heating capacities 96 Figure 5 - 17 . The First Law of thermodynamics applied to the heating mode to estimate the needed chilling and heating capacities 5.2.2 Tanks S izing Before looking at the transient testing needed capacities, an estimate of the tank size for each HTF cooling loop is obtained first. Chiller manufacturers recommend that 3 - 6 gallon s is needed per ton of nominal cooling. This range extends to 6 - 10 gallons per ton for enough temperature control [69] . For the work considered here, we assume 8 gallons per ton of refrigeration. The actual system volume shall be subtracted from t he required system volume. But since the HTF piping has a small diameter (around 1 inch as will be shown later) and consequently small volume compared to the tank s size, the piping volume can be neglected. The calculation is based on the maximum capacity for each HEX , which is stated one more time here: 5.5 kW for the evaporator, 8.0 kW for the O HEX, and 8.0 kW for the interior GC . Thus, the volume calculations for each HEX line/loop can be written as 97 ( 5 . 16 ) ( 5 . 17 ) ( 5 . 18 ) For the sake of unification, all tank sizes will be considered the same size, thus ( 5 . 19 ) 5.2.3 Transient C apacities The objective of the transient testing is to prepare each HEX HTF inlet temperature to reflect various environmental conditions. The HTF is set so that the behavior and operation of the refrigerant cycle can be studied and investigated because it would ref lect the operation of the heat pump cycle in hot and cold environmental conditions. Hence, this will allow the testing of the CO 2 cycle at different transient operating conditions. The evaporator and interior GC HTF inlet temperatures reflect the vehicle c ompartment temperature in summer and winter respectively, while the O HEX reflect the environment temperature. As the testing conditions revealed, for the cooling mode, the evaporator and the OHEX are both set from 25 °C to 45 °C. While for the heating mode, the OHEX is set from - 30 °C to 10 °C, while the interior GC is set from - 30 °C to 25 °C, considering that the vehicle compartment might be warmer than the environment. Thus, for all cases, the evaporator set range is from 25 °C to 45 °C, the interior GC will be set from - 30 °C to 25 °C, while the O HEX will be set from - 30 °C to 45 °C. Since the experiment is conducted in a lab environment, the HTF temperature is steered from the lab temperature to the desired set point. We assume that a hot day (in the summer) temperature in the lab is 35 °C, while a cold day (in the winter) in the lab is 15 °C. It is important to calculate the needed time to prepare the HTF from its initial temperature to any te mperature that lies in each HEX set range. Calculating the time assures 98 that heaters and chillers capacities obtained from the steady - state calculations are enough for the transient preparation. If the time obtained is found to be relatively long, that i mpl ies that the heater/chiller capacity need to be increased to accommodate the transient test preparation. The time is calculated from ( 5 . 20 ) w here V is the tank volume and is the temperature difference between the HTF initial temperature (ideally the temperature of the lab environment) and the HTF required set point. and c p are calculated at the average temperature of the initial and set - point temperatures. Heater capaci ties are checked for the test - rig operation either in the cooling or the heating mode. Table 5 - 2 shows the computed heater on - time for the evaporator and t he OHEX for the cooling mode, if the HTF temperature is steered from 15 °C initial temperature to 45 °C set point. As shown, less than half an hour is required to reach the maximum desired temperature in a cold lab day, using the heater capacities obtained in the steady - state analysis. Thus, the heaters capacities are suitable for the transient testing as well. For the heating mode, the same procedure is followed as for the cooling mode. Since in the steady - state analysis, no heater was needed for the inter ior GC , the heater capacity of the interior GC will be assumed 6 kW as other selected heater capacities. The heater on - time needed from 15 °C to 25 °C with a heater capacity of 6 kW is only 8 min. The chillers' capacities developed at the stead - state are a lso verified for test - rig operation in either the cooling or the heating mode for the transient operation. For the cooling mode, the minimum required temperature for transient testing is 25 °C for both the evaporator and the OHEX . If we assume a hot day in the summer where the lab temperature is 35 °C , a chiller is needed with a reasonable capacity to steer the HTF from 35 °C to 25 °C . From the steady - state analysis, the OHEX chiller capacity is shown to be 10 kW. If a chiller with this capacity is obtained , the 99 maximum capacity is usually nominal at 20 °C , which means a close value to 10 kW at 25 °C . For the evaporator, the steady - state analysis did not need a chiller ; hence , a chiller with appropriate capacity can be selected for the transient preparation. We assume a 1 kW chiller for the evaporator. In Table 5 - 3 , the estimated time of coo ling the HTF from 35 °C to 25 °C is shown. It can be concluded that a chiller capacity of 10 kW is more than enough for the OHEX , and a chiller capacity of 1 kW is suitable for the evaporator. Table 5 - 2 . Estimated HTF heater on - time for different heat exchangers in a cold day lab environment for preparation of the cooling mode Heat Exchanger T i nitial (°C) T sp (°C) Heater Cap. (kW) Time (min) Evaporator 15 45 6 23 O HEX 15 45 6 23 Interior GC 15 25 6 8 Table 5 - 3 . Estimated HTF Chiller on - time for different HEXs in a hot day lab environment for preparation of the heating mode Heat Exchanger T i nit i al (°C) T sp (°C) Heater Cap. (kW) Time (min) Evaporator 35 25 3.7 @ 20 °C 12 O HEX 32 - 29 3.7 @ - 29 °C 80 Interior GC 35 - 29 3.7 @ - 29 °C 80 For the heating mode, the minimum required temperature for transient testing is - 30 °C for both the OHEX and the interior GC . Thus, a chiller is needed with a reasonable capacity to steer the HTF from 35 °C to - 30 °C . From the steady - state analysis, the in terior GC chiller capacity is shown to be 10 kW. For the OHEX , the steady - state analysis of the cooling mode needed a chiller with capacity of 10 kW. However, if a chiller with a nominal capacity of 10 kW is obtained, the capacity at the lowest set point is usually less than this. A chiller is selected that has a capacity of 3.7 kW at - 29 °C as will be discussed in the next subsection. To steer either the O HEX or the interior GC from 35 °C to - 29 °C . This needs 80 minutes as shown in Table 5 - 3 . If the pump chiller can drive 100 two HEX lines at the same time, this time is doubled to become 160 minutes (less than three hours) to cool two HEXs with the same chiller. This increase to 4 hours if the chiller will cool three HEXs at the same time. This amount of time is not very long and , hence , considered acceptable. Thus, one chiller can be used to prepare the three heat exchangers if the pump can drive them. B ased on the a bove analysis, the required heater and chiller nominal capacities to support both steady - state and transient test conditions are as follows: Each heat exchanger ne eds a heater of 6 kW capacity. T he three HEXs each needs a chiller of 10 kW nominal capacity and a capacity of around 3.5 kW at - 29 °C to ensure that the time needed to prepare the HEXs is not very long. 5.2.4 Chillers and p umps S election Different chillers that can support the steady - state requirement can also support the transient conditions but with different chilling time. Choosing a chiller does not depend solely on the nominal capacity but also on the lowest set point temperature and how much capacity is at this set point. The chiller prices increase with lower set point and with increased capacity at the lowest set point. A survey has been carried out to compare different chillers available in the market in terms of these parameters. The chiller selected a high capacity, the Mokon ALT - 2 , with a capacity of up to 12,391 BTU/hr ( 3.63 kW) at - 20 °F ( - 29 °C), and 44,976 BTU/hr ( 13.2 kW) at 20 °F ( - 6.5 °C), tested with 50/50 % water/ethylene glycol ratio. The chiller has an air - cooled condensing unit. The chiller is equipped with 2 HP pump where its characteristic curve is shown in Figure 19 by the green thick line. The chiller has 9 kW heater. The chiller operating temperature range is from - 20 °F ( - 29 °C) to 20 °F ( 93 °C). The chiller photo is shown in Figure 5 - 18 . 101 Figure 5 - 18 . A photo of ALT - 2 Mokon chiller To assure that the chiller pump is suitable for our system flow and pressure drop, a MATLAB script code is written to calculate the system pressure drop at different flow rates. The 3 - K method has also been followed here for pressure drop calculation for d ifferent fittings. The ethylene water glycol mixture thermodynamic properties are calculated based on experimental empirical data provided by Dow Chemical Company. A static head of 2 m is assumed because the HEXs are in a height above the pumps. By looking at Figure 19 , the red curve represents the system curve for 1 - inch tubing and single loop of the HTF, in other words, a loop that includes one HEX only. Th e blue curve represents the 1 - inch tubing but for two parallel lines, assuming the chiller will cool two HEXs. The black solid line shows the HEX flow limit as provided by Alfa Laval. This constrain t is possibl e since the HEX will have a relatively high pr essure drop beyond this flow limit. The dashed magenta line represents the flow limit for two parallel loops, which is double the flow rate limit for one HEX. Looking at this graph, we can conclude the selected pump is suitable for our application. It seem s clear that the operating points can move further to the left side if we incorporate valves to increase flow restriction and, hence, increase the pressure drop and reduce the flow rate. Two pumps similar to the Mokon chiller pump are selected for the two other HEX loops. 102 Figure 19 . The pump curve vs one, two, and three heat exchanger s ystem Curve s 5.2.5 Schematics The HTF cycle schematic is shown in Figure 5 - 20 . Before each HEX, an immersion electric heater is used to fine tune the temperature setting. Shut - off valves are placed at different locations to allow the flow to be directed and enable each chiller to cool one, two, or the three heat exchangers. A flow meter is placed in each HTF line to estimate the cooling/heating capacity. Temperature sensors are inserted at different locations to assist in controlling the HTF temperature. 5.3 Instrumentation A RTD, 1000 , 4 - wire, 1/8 - inch probe diameter, Omega brand is used to measure the absolute temperature at different locations of the CO 2 and HTF loops. It has an accuracy of ± (0.15 + 0.002* T) where T ranges from T= - 30 °C to 300 °C. RTD principle is based upon metals that produce a change in electrical resistivity with a change in temperature. The nominal resistance, which is 1000 is defined at 0. The NI module used for the RTD measurement, which will be highlighted in a 103 data acquisitio n subsection, has an excitation current (I) of 0.1 mA. The self - heating power I2R generated in the RTD is found to be 10 mW, where R is the RTD nominal resistance 1000 . This self - heating power is less than an RTD with 100 nominal resistance by a factor of 10. The 4 - wire is the most accurate configuration compared to the 2 - wire and the 3 - wire ones. In the 2 - wire, the lead wire resistance cannot be compensated for or canceled ; thus , their resistances are included in the RTD measurement, which affects the RTD accuracy. The 3 - wire configuration compensates for the lead wires, under the assumption that all the three lead wires have the exact same resistance. This enhances the accuracy but leaves an amount of the error in the reading. In the 4 - wire configurati on, a current source powers the circuit through two wires and the other two wires are used to read the RTD resistance value. Hence, the reading is proportional only to the RTD. Figure 5 - 20 . HTF Schematics 104 An absolute pressure measurement is conducted at the various points in the CO 2 loop by Omega MM series pressure sensor. It has a pressure range up to 175 bar. The output is 4 - 20 mA, and its accuracy is ± 0.0 5 % FS. The CO 2 mass flow rate is measured by Emerson F025 Coriolis flow meter. It has a mass flow accuracy of ± 0.5 % of rate for gases and ± 0.2 % of rate for liquids. The flow meter has a pressure rating up to 160 bar and a temperature range from - 100 °C to 204 °C. The Coriolis flow meter contains an energized vibrating tube . When the fluid passes through this tube the mass flow momentum results in a change in the tube vibration . Therefore, the tube will twist causing a phase shift. This phase shift is measured and can be correlated to the mass flow rate . An Emerson flow transmitter 1700 series is used, which carries the electronics needed in a remo te mount fashion. The flow meter unit interfaces with the transmitter through a 9 - wire cable. The HTF mass flow rate is measured by a Rosemount magnetic flow meter 8700 series, which has a 0.25 % of rate accuracy. It has a PTFE lining , which extends the fl ow meter temperature range from - 29 °C to 177 °C. It has a maximum pressure rating that depends on the fluid operating temperature. The maximum pressure is 215 psi at 177 °C and 285 psi for temperatures from - 29 °C to - 38 °C. Both F series and Rosemount fl ow sensors have the capability to generate frequency signals that are proportional to the measured mass flow rate. National Instruments data acquisition devices along with LABVIEW software are used for acquiring the measurement signals to a PC and for gen erating control signals. A Compact DAQ 9179 USB chassis with 14 slots was chosen, which supports analog I/O, digital I/O, and counter/timer measurements. Each slot can accommodate a data acquisition module that can be voltage, current, or a module dedicate d for specific type of measurements such as thermocouple or RTD. For acquiring CO 2 loops RTD signals, 3 units of NI 9226 module dedicated for RTD 105 measurement, with a nominal resistance of 1000 was chosen, each with 8 channels . The module has an accuracy of ± 0.15 °C, for a temperature range from - 200 °C to 150 °C. For pressure signals, a current module NI 9208 , which supports ± 20 mA current measurement with 16 channels , was selected. To measure the flow meter signals, a counter module NI 9361 was chosen. The module has 8 channels where each channel can be configured to read single pulse train. The variable frequency drive used to control the compressor speed is used to measure the absorbed power of the compressor; hence, no dedicated watt - meter sensor is n eeded. Figure 5 - 21 shows photos for the different instrumentation used and discussed above. Figure 5 - 21 . Various Instrumentation used in the CO 2 transcritical heat pump test rig facility 106 5.4 T est - R ig L ayout & 3D CAD Modeling Figure 5 - 22 shows the test rig detailed schematic layout showing the location of pressure, temperature, and flow sensors in the CO 2 loop. The schematic also shows the pressure relief valves and their respective cracking pressures. The 3D CAD design is shown in Figure 5 - 23 . Several considerations were made in constructing the 3D CAD. First, it enables testing with either the manual or electronic expansion valve if need to be attached in parallel. Second, it has the capability of flow reversion for the O HEX to allow effective operation. The OH EX acts as an evaporator or condenser GC, depending on the cycle mode. As advised by Alfa Laval, for an evaporator mode, the fluid shall enter from bottom and leaves from the top to ensure that no liquid leaves the evaporator. While in the condenser mode, the fluid shall enter from the top and leaves from the bottom so that any condensed liquid leaves the HEX. The test - rig is also designed such that all components drain to the accumulator d uring the off cycle. A portable frame with wheels is also considered so that the test - rig fits through a standard door for transportation. 107 Figure 5 - 22 . Test - rig layout that shows the location of different sensors 108 Figure 5 - 23 . 3D CAD of the test - rig within the Turbomachinery Lab space at MSU After the build completion, the CO 2 test rig was tested by 300 PSI Nitrogen gas to detect the points of leaks. After identifying and fixing all leaks, the test rig was left pressurized overnight under 500 PSI pressure, and no leak was detected. The HTF test rig was also tested by 50 PSI air pressure to identify and fix all sources of leaks. The CO 2 test rig was then vacuumed to 290 Micron. When the vacuum pump was shut off, the system was able to hold a vacuum level of 590 Micron for 25 minutes. To charge the system with CO 2 , this was done in two steps: first by charging gas CO 2 until the system pressure reaches 10 0 PSI , then if more charging mass is needed, a liquid CO 2 is pumped in to the system. The liquid and gas cylinders used from Airgas were CD I200S ( CARBON DIOXIDE INS TRUMENT GR 4.0 SIZE 200 CGA 320 SYPHON ), and CD I200 ( CARBON DIOXIDE INSTRUMENT GR 4.0 SIZE 200 CGA 320 ) respectively . A Concoa pressure regulator 109 is used for the CO 2 gas cylinder. No regulator was needed for the liquid cylinder, but a connector/adapter se tup that is shown in Figure 5 - 24 . Figure 5 - 24 . CO 2 L iquid cylinder connector/adapter setup As a rule of thumb, a refrigerant charge of 2 - 4 pound per ton of cooling is needed. For our system , since the maximum c ooling capacity is 5.5 kW ~ 1.56 Ton refrigeration , the r ange of charge needed is 3.12 - 6.24 pound s , that is 1.4 - 2.8 kg . We charged the system with 1.5 kg. Our estimation of the system volume tubing is not more than 1 .0 L , plus 2.7 L for the Accumulator , plus 6. 1 L for low - pressure side of the c ompressor , and 0.25 L of high - pressure side of the compressor gives ~10 L . Experimentally, this was verified by c harg ing the system with Nitrogen and applying the ideal gas law . T he system volume estimat ion was 7 - 10 L , where the volume v ariability is due to the variability in pressure sensor readings . The compressor is equipped with relief valves at the inlet and output port. Additionally, f our Parker pressure relief valves are installed at different locations with their respective crack ing pressure shown in Figure 5 - 22 . A clear polycarbonate glass is installed all around the CO 2 test rig to provide protection for the personal involved in the operation. Extension bars are fabricated and connected to the valve bodies to op erate them through the glass during the system operation. After the leak test, the CO 2 test rig is insulated. 110 5.5 S ystem Build & Photos The experimental platform consists of t wo separate but connected test rigs : o ne for CO 2 and one for the HTF connected by flexible tubes that carry the heat transfer fluid . The next series of photos shows the progress of building both test rigs with photographs of the several components used. Figure 5 - 25 . CO 2 test rig frame on the start of the build at the Turbomachinery Lab showing the F - series flow sensor and few tubing connected to the flow sensor 111 Figure 5 - 26 . The Dor in CD200 - CD180H Compressor mounted on its frame within the test rig Figure 5 - 27 . The T emprite oil separator and its relative size with respect to a keyboard . The tubing is connected to the oil return line . The two black caps are covering the sight glasses . 112 Figure 5 - 28 . A photo schematic showing the addition of the suction line, discharge line, and the line s around the accumulator . The photo also shows the integration of four pressure relief valves . Figure 5 - 29 . A photograph shows the integration of pressure gauges connected to different points in the system. The pressure gauges are only for quick monitoring of the system pressure. The system is equipped with pressure sensors to provide thermodynamic property calculations during the system run on LabVIEW and for postprocessing on MATLAB . 113 Figure 5 - 30 . A photo showing the accumulator that has been manufactured by Temprite and its relative size with respect to a keyboard Figure 5 - 31 . A photo showing the accumulator and a 3D - printed enclosure (left), the accumulator assembled in the enclosure (middle), and the accumulator integrated with the test rig (right) Figure 5 - 32 . Photos show the initial build of the HTF test rig . T he mount ing of the two tanks to the HTF frame (left), the soldering of the HTF copper tubes at the MSU machine shop (middle) , and the integration of the copper tubes to the test rig (right) . 114 Figure 5 - 33 . Photo shows the Mokon Chiller at the Turbomachinery lab Figure 5 - 34 . A Photo shows the HTF test rig after connecting most of the copper tubing and the three Rosemount Magnetic flowmeters 115 Figure 5 - 35 . A Photo shows the CO 2 test rig after fixing a clear polycarbonate glass sheet from the test r ig back side Figure 5 - 36 . Photo s showing the progress of connecting the three cylinders ; Nitrogen, liquid CO 2 , and Gas CO 2 (left) to t he system through a wall mounted charging panel (right) 116 Figure 5 - 37 . Photo shows the CO 2 test rig after the tubing integration complet ion and fully enclosed by clear polycarbonate glass 117 Figure 5 - 38 . Photo shows the HTF test rig after copper pipes integration completion and connecting the Rosemont transmitters to the flowmeter Figure 5 - 39 . Photos shows the progress of insulating different parts of the CO 2 test rig tubing 118 Figure 5 - 40 . Complete photos of the experimental test rig. The left photo shows the CO 2 test rig with the data acquisition and PC. The right photo shows the HTF test rig connected to both the chiller and the CO 2 test rig from the right and the left respectively. Figure 5 - 41 . A Screenshot showing the developed LabVIEW Test Program that monitor the system temperatures, pressure, and flow in real time and plots the p - h, T - s, and T - d diagrams CO 2 Test Rig PC & DAQ HTF Test Rig Chiller 119 Chapter 6: Experimental Testing and Results The test matrix in Table 6 - 1 was developed to experimentally investigate the performance of the cooli ng and heating cycles . Each row represents a set of four or five steady state measurements. All the measurements are conducted at a constant HTF evaporator mass flow rate of 0.22 kg/s and a constant HTF gas cooler mass flow rate of 0.07 kg/sec. The HTF loo ps inlet temperatures of both the evaporator and the gas cooler are shown in the table first and second columns. All measurements are taken at a constant compressor speed of 1740 rpm . For each measurement, when steady state is reached, the data is recorded for five minutes and the mean value of each measured variable is computed to represent the test point steady state measurement. Table 6 - 1 . Test Matrix showing the operating conditions for each test point [ °C ] [ °C ] Test point [ bar ] Max energy balance variability : y [ % ] 5 20 M1, M2, M3, M4 78.1, 79.1 81.2, 82.3 0.16, 0.20, 0.15, 0.20 10 25 M5, M6, M7, M8 78.6, 81.5, 83.2, 85.8 0.2 4 , 0. 19 , 0.1 7 , 0.10 30 M9, M10, M11, M12 87.8, 89.9, 91.4, 93.2 0.07, 0.07, 0.09, 0.16 15 30 M13, M14, M15, M16 87.7, 89.7, 91.7, 93.6 0.16, 0.1 8 , 0.1 2 , 0.0 8 35 M17, M18, M19, M20 89.3, 91.7 93.5, 95.0 0.2 2 , 0.22, 0.19, 0. 09 20 35 M21, M22, M23, M24, M25 89.9, 91.3, 92.6, 95.0, 95.5 0.40, 0.3 6 , 0.3 6 , 0.26, 0.2 6 6.1 Test Method and Validation The HTF was run first, and after reaching the desired operating temperatures and flow rates, the CO 2 loop was run. The steady state criteria was used for each test point to determine that steady state was obtained. It is based on checking the energy balance (y) across the CO 2 gas cooler, the evaporator, the compressor power, and the oil separator as show n in Eqn. ( 6 . 1 ) . The oil separator is included in the equation due to the heat loss in the transient period that gradually decreases as 120 the system approaches the steady state. The equation is normalized with respect to the HTF gas cooler capacity. The moving average is calculated for the variable y. The variable y is shown for the measurements in the last column of Table 6 - 1 . In all the measurements, th e moving average of the variable y is bounded within ±0 . 4 % . ( 6 . 1 ) Figure 6 - 1 shows the transient response of the system for the heat exchanger capacities and the compressor power, while Figure 6 - 2 shows the moving average of the energy balance variable for the same measurement case. In this measurement case, the steady state measurement is calculated from the last fi ve minutes in the 30 minutes measurement duration. Figure 6 - 1 . The energy balance across the heat exchangers capacities M1 measurement case 121 Figure 6 - 2 . The energy balance actual and moving average signals for M1 measurement case 6.2 Uncertainty and Repeatability The uncertainty in COP is computed according to [70] . The uncertainty in the calculate d enthalpy using NIST REFPROP is computed according to [71] . For the temperature and pressure range here, the uncertainty in the enthalpy calculation is less than or equal to ±1.5%. The uncertainty in the calculated cooli ng and heating COP is within below 6.5%. To assess the system measurement repeatability, the test point M5 was repeated five times on different dates as shown in Table 6 - 2 . The table shows the input conditions and several computed quantities. The mean and standard deviation values are shown in Table 6 - 2 and show the variability ranging between ~0.2% and 1. 8 % . The refrigerant mass flow rate signal for M1 is shown in Figure 6 - 3 . As mentioned in Section 2, the placement of the flow meter downstream the compressor and after the oil separator helps suppressing the compressor pulsations. This is demonstrated with the flow signal not containing any pulsation. Any oscillations left in the signal is attributed to the fluctuation in the measured 122 temperature due to the fluctuation in the HTF supplied by the chiller, therefore, this consequently affects the pressure and hence the flow rate. Table 6 - 2 . Repeatability t est results for Measurement M 5 Date Oct 21, 2019 Oct 29, 2019 Nov 11, 2019 Dec 3, 2019 Dec 16, 2019 Mean Standard Deviation [ % ] Test point M 5 _R1 M 5 _R2 M 5 _R3 M 5 _R4 M 5 _R5 (°C) 30.3 30.2 30.3 30.2 30.2 30.24 0.18 (°C) 15.3 15.2 15.1 15.1 15.1 15.16 0.59 (kg/s) 0.0171 0.0163 0.0169 0.0167 0.0167 0.0167 1.78 (kg/s) 0.0704 0.0706 0.0701 0.0694 0.0704 0.0702 0.67 (kg/s) 0.225 0.225 0.224 0.225 0.224 0.2246 0.24 (bar) 93.6 95 93.2 93.4 93.8 93.8 0.75 (kW) 4.34 4.25 4.26 4.24 4.24 4.27 0.99 (kW) 2.76 2.7 2.74 2.71 2.73 2.73 0.88 (kW) 1.8 1.78 1.75 1.76 1.75 1.77 1.23 ( - ) 1.53 1.51 1.56 1.54 1.56 1.54 1.38 ( - ) 2.41 2.38 2.43 2.41 2.43 2.41 0.85 Figure 6 - 3 . The CO 2 mass flow rate signal for M1 measurement case 123 6.3 Results and Discussion Figure 6 - 4 shows the cooling COP plot against the GC pressure all at different HTF GC and evaporator inlet temperatures. The test points M1 through M25 are shown in the test matrix in Table 6 - 1 . As shown in Figure 6 - 4 , the increase of the GC inlet temperature from 25 °C to 30 °C while the evaporator inlet temperature was set to 10 °C reduces the optimum COP from 1.87 to 1.50. Additionally, the change of the GC inlet temperature from 30 °C to 35 °C wh ile the evaporator inlet temperature was set to 15 °C reduces the optimum COP from 1.50 to 1.29. These COP changes are relatively higher compared to the effect of the increase of the evaporator inlet temperature. The increase of the evaporator inlet temper ature from 10 °C to 15 °C , while the GC inlet temperature was set to 30 °C , increases the optimum COP from 1.50 to 1.56. Similarly, the increase of the evaporator inlet temperature from 15 °C to 20 °C , while the GC inlet temperature was set to 35 °C increases the optimum COP from 1.29 to 1.33. Figure 6 - 4 . The Cooling COP measurements at different HTF inlet temperatures 124 A similar trend is shown in Figure 6 - 5 for the heating COP. These results correlate with results reported in the literature that the optimum COP occurs at the minimum GC CO 2 /secondary inlet temperature and the maximum evaporator CO 2 /secondary inlet temperature. In all the 25 measurement cases, the minimum and the maximum difference between cooling and heating COP is 0.86 and 0.92 respectively. Figure 6 - 5 . The Heating COP measurements at different HTF inlet temperatures The change of the CO 2 mass flow rate is shown in Figure 6 - 6 for the test cases in Table 6 - 1 . For each measurement set, the increase in the GC pressu re decreases the mass flow rate in almost linear fashion. This is mainly due to the compressor volumetric efficiency decrease as demonstrated for several CO 2 compressors [49] . Moreover, the increase in the HTF ev aporator inlet temperature, which results in an increase in the evaporation pressure, results in an increase in the CO 2 mass flow rate as shown in [40] and [26] . 125 Figure 6 - 6 . The CO 2 mass flow rate for different HTF GC and evaporator inlet temperatures at different pressures Figure 6 - 7 shows the useful superheat for each test point in Table 6 - 1 at the corresponding GC pressure. The useful superheat is the one taking place insid e the evaporator. For each set of test points, the effect of changing the GC pressure for the ranges shown results in no more than 1 K superheat. The increase in the HTF GC inlet temperature from 25 °C to 30 °C and from 30 °C to 35 °C , while the HTF evapor ator inlet temperature was kept constant at 10 °C and 15 °C respectively results in negligible change in the useful superheat. On the other hand, the increase in the HTF evaporator inlet temperature increases the useful superheat significantly as shown for the increase from 5 °C through 20 °C. 126 Figure 6 - 7 . The superheat taking place inside the evaporator for different HTF GC and evaporator inlet temperatures at different pressures 127 Chapter 7: Conclusions and Future work 7.1 Conclusions The COP can increase by more than 7 % if the cycle makes a transition from the subcritical to the transcritical . and COP are non - conflicting in the range from critical pressure to of maximum COP, and conflicting above this point till the isotherm becomes vertical . Maximum COP gas cooler pressure does not change significantly across different compressors , but the maximum gas cooler pressure is dependent on the compressor performance due to the difference in the volumetric efficiency . Pareto Fronts are developed that represent the tradeoff between COP and in the range of conflicting objectives . The Gain/Loss ratio can be used as a transitioning criteria from one solution to another on the Pareto Front. At =54 °C, the Pareto Front b ecomes only one point, representing the maximum COP and the maximum solution. COP and increase or decrease with increasing useful superheat depending on the operating conditions due to the competing effects of the mass flow rate and the enthalpy dif ference across the compressor and the evaporator The compressor isentropic and volumetric efficiency correlations have considerable effects on the Pareto Front . COP and contour maps can aid in predicting the COP, and in the transition from one point to another across the Pareto Fronts . 128 An offline optimization approach is developed that could enable the system to work close to its maximum COP, maximum , a tradeoff solution, or at a point where and COP are non - conflicting for lower avoidi ng ON - OFF cycling, and switch as desired . A hybrid offline/online optimization and control approach is proposed that can reduce the time to approach the desired optimum compared to online methods only. Compared to Offline methods only, it can additionally enhance COP and based on the actual system behavior/characteristics, while it is also able to adapt to changing system behavior . The experimental test results showed: The placement of the flow meter downstream the compressor and after the oil separator helps suppressing the compressor pulsations. The HTF GC inlet temperature has a significant effect on the COP compared to the HTF evaporator inlet temperature. With the increase of the GC pressure, the mass flow rate decreases approximately in a linear fashion. 7.2 Future Work Several Pathways can be explored based on this thesis research work: First, i ncluding other objectives in the optimization problem. For example, for a modified cycle with an internal heat exchanger (IHX), the length of the IHX can a be variable subject to optimization and the pressure drop, size, or cost could be a third objective Several mathematical models are available in the literature for the heat pump system components. The heat exchangers dynamics dominate the system behavior as the compressor and the expansion device have very fast dynamics ; and , hence, they are modeled as static, semi - empirical relationships. For the purpose of implementing new 129 control algorithms on the experimental test - rig, developing a mathematical model for the test rig and validating the model against experimental data could simplify the control design process by simulating the controller before experimental testing and validation. 130 APPENDI X 131 Table A - 1 . Bill of material for the CO 2 transcritical heat pump system built at the MSU Turbo Machinery Lab Category Component ( s ) Manufacturer (Distributor) Model and/or Part number Qty Compressor Compressor unit & motor Dorin (Blissfield) CD200 - CD180H 1 Variable Frequency Drive Hitachi (Williams Distributing) WJ200 - 022LF 3 Oil Separation Oil Separator Temprite Model 131: Hermetic 1 Oil sensor HB Products (Temprite) HBOC 1 Oil solenoid valve HB Products (Temprite) V150 1 Heat exchangers Heat Exchanger Alfa Laval AXP10 - 20H - F 3 Expansion Device Manual Swagelok (H.E. Lennon) SS - 31RS4 2 Electronic (EXV) Carel (United Refrigeration Inc) E2V14CS000 2 EXV Driver Carel (United Refrigeration Inc) EVD0000E50 1 Accumulator Accumulator In house design manufactured by Temprite 1 HTF loops Chiller Mokon ALT - 2 1 Pump Scott (Kerr Pump) MP231 304 SS FTD 1.25x1 NPT, EPDM/CB/SIL SEAL 5.75'' IMP DIA 2HP 3500RPM 2 Temperature Measurement Resistance Temperature Detector ( RTD ) Omega PR - 11 - 3 - 1000 - 1/8 - 6 - E - 120 20 Pressure measurement Absolute p ressure transducers Omega MMA2.5KC1B2C5T4A6CE 10 132 Table A - Bill of material for the CO 2 transcritical heat pump system built at the MSU Turbo Machinery Lab Flow Measurement F series Coriolis Flow meter for CO 2 Emerson F025PB77CRAAEZZZZ 1 F series Coriolis Flow meter transmitter for CO 2 1700C11ABAEZZZ 1 Rosemount Magnetic Flow meter for HTF 8705TSA005C1M0N5 3 Rosemount Magnetic Flow meter transmitter for HTF 8732EMR1A1N5M4 3 Data Acquisition Data Acquisition Chassis National Instrument Compact DAQ (cDAQ - 9179). 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