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An Ice Rink Refrigeration System based on CO2 as Secondary Fluid in Copper Tubes

by

Khuram Shahzad

Master of Science Thesis Master Program of Sustainable Energy Engineering

2006

Department of Energy Technology Royal Institute of Technology

Stockholm, Sweden

CO2 as Secondary Fluid in a Copper Tube System

ABSTRACT This report is a study of the use of copper tubes with CO2 as heat transfer fluid in ice rink applications. Copper tubes can be rolled rather easily up to the required length which decreases installation cost and simplifies the procedure. A test ice rink was built at IUC Ref Centre, Katrineholm with copper tubes. FEMLAB and EES are two softwares that were used for analysis. The comparison between 12.7 mm diameter copper tubes with and without plastic foil cover, 9.5 mm diameter copper tubes with and without plastic foil cover, 21.3 mm diameter steel pipes and 25 mm diameter plastic pipes is presented in the report. The reason to have plastic foil over copper tubes is to avoid the minor risk of chemical corrosion. Furthermore the foil serves as mechanical wear protection as well, which in this case could appear if rubbing would occur due to thermal expansion and contraction. It is found that 12.7 mm copper tube with plastic foil is good choice in terms of heat transfer. At rated heat flux of 100 W/m2 and with a pitch of 100 mm, it is 0.18 oC better than 9.5 mm copper tube with plastic foil. This report includes the investigation which shows that there is no danger of movement of copper tubes inside the rink bed due to thermal expansion and contraction during operation. It also includes the comparison of average Friedel pressure drop model and average homogeneous pressure drop model with experimental results. Average Friedel pressure drop method gave good results. It predicted 20 to 25 % higher pressure drop at lower CR and about 60 % at higher CR than the experimental results for 120 meter long and 12.7 mm diameter copper tubes. 120 meter long copper tubes are good choice; as header can be placed on short side of the ice rink. It will reduce the header length and connections to half. FEMLAB modelling for conduction heat transfer gave good results and can be used as a tool for design and optimization. The optimization of the pitch of the copper tubes and circulation rate of CO2 is also analyzed. This analysis reveals that practically, absolute cost per year does not change much with the change of pitch. It will depend on the interest and conditions to go for smaller pitch than 100 mm. The analysis for optimum circulation rate reveals that there is no practically optimum circulation rate since it is very small degree that we can optimize for. The circulation rate that we should operate at is the one that gives circulation rate more than one at the highest cooling load to avoid dry evaporation It also includes the investigation which shows that thermal conductivities of plastic foil and concrete can be improved to rise to evaporation temperature.

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ACKNOWLEDGEMENTS I would like to express my gratitude to my supervisors Björn Palm and Samer Sawalha at KTH, Royal Institute of Technology, Stockholm and Jörgen Rogstam at IUC Ref Centre, Katrineholm for their invaluable help during my thesis work. All of them gave me full support when I needed and gave me push in the right direction. I would also like to thank Per-Olof Nilsson at IUC Ref Centre who helped me in measurements and lab work and also David Sharp and Bengt Julin from Outokumpu Copper Products AB who helped me for the economical statistics of copper tubes. I would also like to say special thanks to the financiers of the project; Katrineholms Kommun, Outokumpu Copper Products AB, Sörmlands Sparbank/Tillväxtbanken and The Swedish Energy Agency. At last I must say thanks to all who did not bother to sacrifice their presence during my thesis work.

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CONTENTS

1 INTRODUCTION 6

2 ICE RINK TECHNOLOGY 8

2.1 Types of Ice Rinks 8 2.2 Applications of Ice Rinks 9

2.2.1 Ice Hockey Rink 10 2.2.2 Curling Rink 10 2.2.3 Figure Skating Rink 11 2.2.4 Speed Skating Rink 11 2.2.5 Recreational Skating Rink 12

2.3 Ice Rink Floor Design 12 2.3.1 Preparation of Rink Floor 14 2.3.2 Open or Sand Fill Type Rink Floor 14 2.3.3 Permanent General-Purpose Rink Floor 14 2.3.4 All-Purpose Rink Floor 15 2.3.5 Portable Rink Floor 15

2.4 Refrigeration Systems in Ice Rinks 16 2.4.1 Direct Refrigeration System 17 2.4.2 Indirect Refrigeration System 17

2.5 Heat Loads 17 2.5.1 Conductive Loads 18 2.5.2 Heat Gain to the Piping 18 2.5.3 Heat Gain from Coolant Circulating Pump 18 2.5.4 Ice Surfacing 18 2.5.5 Convective Loads 18 2.5.6 Radiant Loads 19

3 MINIATURE ICE RINK AT IUC REF CENTRE 20

3.1 Miniature Ice Rink Geometry and Layout 20 3.2 Structural Design Analysis 22

3.2.1 Stress Calculation 22 3.2.2 Fatigue Evaluation 24 3.2.3 Conclusion 25

3.3 Experimental Equipment 25

4 THEORETICAL MODELLING AND SIMULATION 28

4.1 Heat Transfer Analysis 28 4.1.1 Conduction Heat Transfer-FEMLAB Modelling 28 4.1.2 Convective Heat Transfer-EES 31 4.1.3 Results and Remarks 31

4.2 Pressure Drop Analysis 37

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5 EXPERIMENTATION 39

5.1 Analysis of Movement of Copper Tubes inside Ice Rink Bed 39 5.1.1 Comparison and Conclusion 40

5.2 Cooling Load of the Ice Rink 41 5.2.1 First Test 42 5.2.2 Second Test 42 5.2.3 Third Test 44 5.2.4 Conclusion 44

5.3 Pressure Drop in 60 Meter Copper Tubes 45 5.3.1 12.7 mm Copper Tubes 45 5.3.2 9.5 mm Copper Tubes 46 5.3.3 Conclusion 48

5.4 Heat Transfer in 60 Meter Copper Tubes 48 5.5 Pressure Drop in 120 Meter Copper Tubes 49

5.5.1 Conclusion 50 5.6 Heat Transfer in 120 Meter Copper Tubes 50 5.7 Conclusion for Pressure Drop and Heat Transfer Analysis 54

6 VERIFICATION OF FEMLAB MODEL 55

7 OPTIMIZATION 56

7.1 Economical Optimization 56 7.1.1 Conclusion 60

7.2 Optimization of Circulation Rate (CR) 61 7.2.1 Conclusion 64

8 POTENTIAL IMPROVEMENTS 65

8.1 Plastic Foil 65 8.2 Concrete 66

9 CONCLUSION 69

10 REFERENCES 71 APPENDIX I 73 Analysis for Movement of Each Copper Tube inside Rink Bed 73 APPENDIX II 77 EES Model for Convective Heat Transfer inside Copper Tubes 77 EES Model for Average Friedel Pressure Drop 78 EES Model for Average Homogeneous Pressure Drop 79

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1. INTRODUCTION Sustainable energy system is an important topic these days around the world. Sustainability is not being considered only in technical but also in economical aspect. The majority of the energy being used is from non-renewable fossil fuel sources and very small percentage comes from renewable sources. It is not easy task to make an energy system, which is based on non-renewable fossil fuel sources, as a sustainable one because these non-renewable fossil fuel sources may last for few decades. Any system produces or consumes energy must be sustainable in both technical and economical aspect. Ice rinks systems consume a lot of energy and it is a rapidly increasing application. The ice rink refrigeration technology must be optimized technically and economically in such a way that it may become more sustainable. Research and investigations are going on for in this direction. Ice rink refrigeration systems have been working in two ways: first solution is direct expansion system with ammonia or R-22 as refrigerant and second solution is indirect system with calcium chloride, glycol or CO2 as secondary fluid. Direct expansion ammonia system is not allowed for indoor ice rinks because of risk of leakage while R-22 is practically phased out. Indoor ice rinks are now common due to weather condition, hence indirect system is necessary. The most common heat transfer fluid for indirect system is calcium chloride solution which is pumped in plastic pipe system. Pumping power for such system in full scale is 12 to 15 kW; hence a significant amount of pumping energy is required on a yearly basis. Many ice rinks remain operational 10 to 11 months per year which means that the required annual pumping power is significant [Jörgen Rogstam; 2005]. CO2 is a phase changing fluid and now being used in some ice rink installations in indirect system solutions. Because of its phase changing property, pumping power can be reduced by 90 to 95% compared to the traditional calcium chloride solution [Jörgen Rogstam; 2005]. Due to high pressure, CO2 requires metal pipes instead of plastic. Direct ammonia systems have been made with steel pipes because it has favourable properties which are strength, corrosion resistance and compatibility with concrete. Steel pipes are also used for the systems with CO2 as heat transfer fluid in indirect systems. There are about 15 indirect ice rink systems based on CO2 as heat transfer fluid in Europe. Most of them are in Switzerland but few are in Austria, Germany and Holland [Jörgen Rogstam; 2005]. One big disadvantage of using steel pipes is cost factor. Steel pipes are available in 12 meter length and 19000 meter steel pipes are required in ice rink. Hence this installation requires round about 1700 licensed wildings, which is expensive solution and main factor in cost [Jörgen Rogstam; 2005]. The purpose of this project is to study the use of copper tubes, instead of steel pipes, with CO2 as heat transfer fluid. Copper tubes can be rolled easily up to length up to 120m which decreases installation cost and simplifies the procedure. The installation of copper tubes will not be much more work intensive than plastic pipes but material cost will be higher than plastic. Refrigeration system and distribution system will be more

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expensive than traditional indirect heat transfer fluid system, but it will be equal to the steel pipe solution (excluding labour costs). This study includes investigation about thermal expansion and contraction of copper tubes inside the ice rink bed during operation. It also includes heat transfer analysis of the smaller size copper tubes to compare with larger size steel and plastic pipes. It also includes pressure drop calculations to have an estimate of pressure drop and therefore pumping power. There is a need to develop a tool to optimize the system by developing thermal model, pressure drop model and a calculation procedure for the economical optimization.

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2. ICE RINK TECHNOLOGY A heat transfer fluid is circulated through network of pipes or tubes to produce required thickness of ice sheet. These pipes or tubes are located under the ice sheet. In direct expansion systems, this heat transfer fluid is ammonia or R-22 but R-22 is being phased out while ammonia is not allowed for indoor applications of direct expansion systems. For indoor applications, indirect systems are suitable in which calcium chloride, or glycol is used predominantly as heat transfer fluid but CO2 being phase changing fluid becomes more important for indirect ice rink applications. 2.1 Types of Ice Rinks Ice rinks can be divided into three types. When ice rink is going to be used for longer period during a year and also environment is not suitable then rink must be build indoor. Most of the ice rinks are now constructed indoor. An indoor ice rink is shown in Figure 1.

Figure 1: Indoor ice rink at Dallas’ Galleria [Travelocity; 1996-2005] Under suitable weather conditions, rink is constructed outdoor. But limitation for outdoor rink is that it can not be in operation during warm outdoor conditions. Outdoor rinks only operate during winter season. An outdoor ice rink is shown in Figure 2.

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Figure 2: Europe’s largest outdoor ice skating rink in City Park [PBase; 1999-2005] These rinks can be laid down where it is needed. Only requirement is to prepare the ground and level it carefully. Portable ice rinks can be transferred anywhere. A portable ice rink is shown in Figure 3.

Figure 3: Portable ice rink for exhibition games in Tokyo, Japan [Los Tres Papagayos; 1999-2005]

2.2 Applications of Ice Rinks Ice sheet can be used for different kind of ice sports but it needs specific dimensions for specific kind of sports. For different sports, following are the dimensions:

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2.2.1 Ice Hockey Rink There are different standards for hockey rink. The North American hockey rink size is 26 m by 61 m while rink must have radius corners of 8.5 m. Hockey rink size of 30 m by 60 m having 6 m radius corners is accepted in Olympic and International hockey. This hockey rink size is also used in Europe. There are also some substandard rinks with different dimensions and in those rinks, a radius corner not less than 6 m should be provided to facilitate the resurfacing of ice with mechanical resurfacing machines [ASHRAE; 1998].

Figure 4: Midwest wireless civic centre ice hockey rink [MSU Mavericks; 2005] 2.2.2 Curling Rink Standard size for curling rink, which is accepted, is 4.3 m by 45 m and important point in this rink is that space is provided by increasing width of ice sheet for installation and dividers between the sheets, particularly at the circles [ASHRAE; 1998].

Figure 5: Curling rink at Town of Melita [CAP; 2005]

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2.2.3 Figure Skating Rink A 5 m by 12 m ice surface is enough for school or compulsory figures while freestyle and dance routines generally requires much larger area than school or compulsory figures which is 18 m by 36 m or it can be more [ASHRAE; 1998].

Figure 6: Tony kent arena for figure skating [Masscot Interactive; 2000-2005] 2.2.4 Speed Skating Rink Hockey-size rink has been used traditionally for indoor speed skating. Outdoor speed skating track accepted for Olympic is different. It is oval shape track having total length of 400 m. This track is 10 m wide with 112 m straight ways and curves with inner radius of 25 m. Outdoor speed skating rinks are more common but full size indoor speed skating are constructed recently [ASHRAE; 1998].

Figure 7: Speed skating track in the Yucatan region of Mexico [Kathie Fry; 1999-2003]

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2.2.5 Recreational Skating Rink Any kind and shape of nice resurfaced ice surface can be used for recreational skating and recreational skating can be done on that surface until an efficient resurfacing of that surface is kept. Each person, who is actually skating, generally needs 2.8 m2 but 2.3 m2

per skater is also acceptable for those rinks where there is not large number of pre-teens skaters. The area of a ice hockey rink is 1517 m2 which has 26 m by 61 m dimensions with 8.5 m radius corners and almost 650 skaters of mixed groups can skate easily [ASHRAE; 1998].

Figure 8: Malaysia’s first recreational ice skating rink [Sunway City Berhad; 1997-2005] 2.3 Ice Rink Floor Design Generally, there are five types of rink floor designs which are being used:

a) Open or sand fill type, for plastic or metal piping or tubing b) Permanent, General-purpose type, with piping or tubing embedded in concrete

on grade c) All-purpose type, with piping or tubing embedded in concrete with floor slab

insulated on grade d) All-purpose floors, supported on piers or walls e) All-purpose floor with reheat; use this type when water table and moisture are

severe problems or when the rink is to operate for more than six months

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Figure 9: Ice Rink Floors [ASHRAE; 1998]

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2.3.1 Preparation of Rink Floor Preparation of rink bed is important when natural ground is going to be used, regardless of whether a sand fill or a permanent general-purpose floor is needed. Natural ground needs proper preparation while elevated sand and gravel subsoil is better than natural ground for preparation of rink bed. Water is hot issue for rink and there should be proper prevention of collecting water in low areas in case of clay, part clay or rock subsoil. In case of clay or rock, it must be cleaned carefully otherwise crushed stone and gravel must be added to increase the level of rink round about 1200 mm [ASHRAE; 1998]. These crushed stones and gravel need to be rolled perfectly and water must be avoided for the settlement of fill. To ensure the rapid drying of sand and rink piping, quick drain of melted ice at the end of skating season must be applied in case of sand fill rinks. This leads to longer life of steel piping. Damp cinders can corrode steel piping easily because cinders can have sulphur. So cinders should never be used to fill open sand fill rinks. Level of the rink is really important issue and it needs careful attention. Level surface over the entire rink must be in the range of ± 3 mm in any 1 m2 and ± 6 mm overall [ASHRAE; 1998]. 2.3.2 Open or Sand Fill Type Rink Floor This type of floor is the least expensive rink floor in all. The bed is prepared with crushed stone or other fill over which wood sleepers are placed to support the cooling pipes. The clean washed sand is filled around the cooling pipes. The rinks, where initial cost is important factor and also rink is going to be used only for one purpose like curling rinks as well as hockey and skating rinks, then this type of floor is build. Clay or cinders should not be used in the bed or for fill around the pipes. Sand level must be accurate and tubing rinks are laid on sand with out any support or sleepers. Plastic pipes are used in this type of floor which is 25 mm plastic pipe and these pipes are covered with sand to a depth 13 to 25 mm [ASHRAE; 1998]. This sand provides additional strength to the ice surface and it also reduces the cracking. This arrangement for laying the plastic pipes or tubing mats on top of black top or concrete is also used in many portable outdoor rinks. Recreational skating rinks also use this arrangement but they consist of steel pipes supported on notched steel sleepers, which in turn are supported on concrete piers down to solid ground. 2.3.3 Permanent General-Purpose Rink Floor Most indoor rinks that operate with an ice surface for only a portion of the year have permanent general-purpose concrete floor to obtain a better return on investment. This type of floor has sub floor insulation and heat pipes so that floor may be used for other purposes after skating season is over. The floor should withstand average street load and 25 or 30 mm steel or plastic pipes are used which are embedded in a 100 to 150 mm thick steel-reinforced concrete slab [ASHRAE; 1998].

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The ice floor must be constructed to withstand the frequent change from hot to cold in those sports arenas, where ice is removed from the floor for other use of floor like other sports and entertainment. The refrigerant machinery must have enough capacity to freeze a 16 mm thick ice sheet in 12 hours [ASHRAE; 1998]. In case of quick changeovers required or high moisture content in the subsoil or when floor is elevated or when rink is in continuous use for more than 9 months then sub floor insulation is necessary [ASHRAE; 1998]. This sub floor insulation reduces the cooling load. The same subsoil precaution must be taken as for a sand fill rink to construct permanent general-purpose floor. The concrete floor should withstand, at a minimum, the average road pavement load. Insulation must be applied according to the local conditions which may be laid on a level concrete or sand base. The concrete mixture should have 28-day strength of 140 to 240 kPa and be put in the place in quality manner [ASHRAE; 1998]. It is advised that frequent defrosting must be avoided in case of general-purpose floors. When rink constructed with general-purpose floor is to be used during ice season for the purposes that require an ice-free floor, it is preferable to place an insulated portable-section wood floor over the ice for each occasion. 2.3.4 All-Purpose Rink Floors All-purpose floors are same as permanent general-purpose floor but they need extra precautions in their construction such as provisions for the free movement of the freezing slab with respect to the sub floor because all-purpose floors have to withstand both expansion and contraction of frequent frosting and defrosting and thermal shocks because of the circulation of very low-temperature coolant. A well- constructed header trench of sufficient size to house the headers and connections and the sub floor heating system, if applicable, is essential unless the steel distribution headers are cast into the concrete slab as part of the rink. Thermal expansion and contraction is important issue so there must be provision into the design for the movement of the pipes. This trench should be equipped with removable covers and be well-drained to facilitate drying out. The headers and piping in the trench are not usually insulated, which allows for the periodic inspection and painting of the piping. However, unless a large trench is provided, consideration should be given to insulating the headers on rinks that operate year-round because of the massive build-up of the frost. There must be provision for purging air from the rink piping and header system. 2.3.5 Portable Rink Floor Portable rink floor has come into existence for large size outdoor rinks with the introduction of plastic pipes in ice rink technology. This floor is almost similar to the sand fill floor except that plastic piping is used instead of steel. Special steel pipe spacer bars

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are used in place of sleepers and pipe clips. These are 50.8 mm wide bars which are punched to lock the plastic pipes from bottom and hence making centre-to-centre distance of 88.9 mm as shown in Figure 10 [C. V. Bengle; 1956]. These bars are laid directly on the levelled natural ground or fill. Vapour barrier is laid over the ground or fill and sealed, if it is necessary. These are required in case of tennis courts and playing fields. The spacer bars are then set on the insulating material, spaced 1.8 to 2.4 m on centres and levelled to within 6.35 mm with wooden shims [C. V. Bengle; 1956].

Figure 10: Plastic pipe arrangement on spacer bars showing shields [C. V. Bengle;

1956] The plastic pipe is virgin black polyethylene 25.4 mm IPS [C. V. Bengle; 1956]. It can be extruded in any length, so it is better to extrude in same length as the length of the rink to avoid joints or cuts. The plastic pipe is uncoiled and laid directly into the interlocking jaws of spacer bars. High impact polyethylene return bends are used with integral adapters. These bends are placed into two pipe ends and secured by the special worm wheel type stainless steel hose clamps. When rink floor has been laid, then washed sand is filled between plastic pipes but top of the pipe surface is not covered with sand. Galvanized steel is slipped over the pipe which form protective shield for the pipe and prevent the possible cutting of plastic pipe bye the sharp edges of the skate blades. Steel pipe nipples are inserted into supply and return pipe ends to weld supply and return pipe into steel headers. Hose clamps hold the pipe end to these nipples. Supply and return headers are in a trench at the end of the rink and run along its width. 2.4 Refrigeration Systems in Ice Rinks There are two kinds of refrigeration systems in ice rinks i.e. direct refrigeration system and indirect system.

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2.4.1 Direct Refrigeration System In direct refrigeration system, refrigerant is directly pumped into rink piping for cooling which is then returned into a large storage tank. Vapour is then sucked by compressors from the top of the storage tank and then they are fed into condenser. Liquid refrigerant from condenser is returned to storage tank. There are pumps which pump refrigerant from tank to rink piping. Purpose of large storage tank is that a huge quantity of cold refrigerant is stored which can be pumped into rink piping when load is increased suddenly or when there is need of full capacity at the start to convert water into ice sheet. Ammonia is used as refrigerant in most the case in this system. R-22 has been also used as refrigerant but it is being phased out while Ammonia is not allowed in direct expansion systems for indoor ice rinks due to risk of leakage. 2.4.2 Indirect Refrigeration System Indirect system is most common these days for ice rink applications in which heat transfer fluid is pumped into rink piping from a large storage tank. This heat transfer fluid is cooled by mechanical refrigeration system. Calcium chloride is the most common heat transfer fluids for this application. CO2 has been used in about 15 installations as the secondary fluid in the indirect system instead of the brine [Jörgen Rogstam; 2005]. Calcium chloride solution has -20 oC freezing point. The maximum rise in brine temperature is 3 oC, which means that rise of 0.5 oC in supply main, rise of 2 oC in rink piping and rise of 0.5 oC in return line [C. V. Bengle; 1956]. A significant pumping power i.e. 108000 kWh/yr is required to pump brine into rink piping [Jörgen Rogstam; 2005]. For brine, plastic or steel piping can be used in rink bed. CO2 is phase changing fluid so it requires much less pumping power than brine. Liquid CO2 is pumped into metal piping because of high pressure of CO2. In return line, CO2 is in two phase where liquid and vapour are separated in a large storage tank. CO2 vapour is condensed into liquid by mechanical refrigeration system and come back to storage tank to be ready to be pumped again into rink piping. Due to boiling mechanism, evaporation temperature is same throughout the rink but there is minor drop in evaporation temperature due to pressure drop in piping. Due to relatively high operating pressure of CO2, steel pipes have been used in all the CO2 installations. 2.5 Heat Loads Operating and energy costs for ice rinks are significant, and these costs should be analyzed during design. Heat load components at design operating conditions must be added for good estimation of required refrigeration. Effective design and operation can reduce the amount of each heat load.

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2.5.1 Conductive Loads If the rink is not insulated then heat gain from the ground below the rink and at the edges is in the range of 2 to 4% for the total heat load [ASHRAE; 1998]. In such rinks, frost heaving may result due to accumulation of permafrost. Frost heaving is really dangerous to both the rink and the piping. Heaving also makes it more difficult to maintain a usable ice surface. When system is run first time then this heat gain is highest; however, it decreases as the temperature below the rink decreases and permafrost accumulates. Good insulation reduces the heat gain from ground. 2.5.2 Heat Gain to the Piping Heat gain to the piping is totally dependent on length of the piping, surface area and ambient temperature, which is normally 2 to 4% of the total heat load [ASHRAE; 1998]. This heat gain reduces when frost accumulates naturally on the headers. Insulation can also be applied to the rink piping to reduce this heat gain. 2.5.3 Heat Gain from Coolant Circulating Pump The coolant circulating pumps normally operates 24 hour per day which can add maximum 24% of the total refrigerant load [ASHRAE; 1998]. This estimation of heat gain is for brine based ice rink systems. The pumping heat load is the pumping power plus adjustment for the pump and motor operating efficiency. Energy consumption from pump operation can be reduced by using pump cycling, two-speed motors, multiple pumps, or variable-speed motors with the appropriate controls which in turn will reduce the heat gain from pump. 2.5.4 Ice Surfacing Ice surface condition is restored by flooding hot water onto the ice surface having temperature in the range of 55 to 80 oC which is significant operating load [ASHRAE; 1998]. The temperature of flooded water affects the load and time required to freeze this water. Maintaining good water quality through water treatment may permit the use of lower flood water temperature and less volume. 2.5.5 Convective Loads The convective load from air to ice surface may represent 28% or more of the total heat load to the ice [ASHRAE; 1998]. Convective load is dependent on the air temperature, air velocity and relative humidity. Rink should be design in such a way that air movement across the ice surface should be avoided. Smoking must be banned in the arena to reduce ventilation because if you have more ventilation, it means you have pulled more humidity in.

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2.5.6 Radiant Loads Indoor ice rinks produce perfect geometry for radiation in which a large and cold plane i.e. ice sheet is maintained under an equally warm plane i.e. the ceiling. For outdoor rinks, radiant sources are sun or warm cloud cover. Radiant heat load is round about 35% of the total heat load [ASHRAE; 1998]. Radiation from ceiling is dependent on the coefficient of surface emissivity of the ceiling’s material. Every material like paint, asbestos, glass, wood, oxidized iron, plaster, paper, gypsum, brick etc has a coefficient of 80 to 95%. Even white lacquer paint is 80%. However, aluminium foil is only 5%. Energy consumption can be dropped up to 30%, if aluminium foil on ceiling surface is used [MacCracken; 1974]. Lighting is also a major source of radiation and heat to the ice surface for indoor rinks which depends on quantity of lighting and how the lighting is applied. If light is applied directly on ice surface then direct radiant heat component can be as much as 60% of the kilowatt ratting of the luminaries [ASHRAE; 1998]. Heating system based on radiators can be another source of radiant heat load. Radiators should be located and directed to avoid direct radiation to the ice surface.

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3. MINIATURE ICE RINK AT IUC REF CENTRE As mentioned earlier, using CO2 as heat transfer fluid instead of brine, 90 to 95% of pumping energy can be saved. This is a considerable saving because ice rinks generally operate 10 to 11 months per year and pumps work all time. Steel pipes are used with CO2 because of high pressure of CO2. Steel pipes are available in 12 meter length and need to be weld which is a huge investment. Copper tubes can be a cheap solution instead of steel pipes because copper tubes are available up to 100 meter length. Copper tubes can be rolled out due to which building process is really fast and huge welding cost can be saved. There might be a danger of movement of copper tubes inside rink bed due to thermal expansion and contraction of copper. An ice hockey rink is decided to be built at Katrineholm, Sweden using the concept to use copper tubes instead of steel tubes to save the investment cost. A miniature ice rink was made to test the copper tubes technology to be applied afterward in a real size ice hockey rink at Katrineholm. (See Figure 16) 3.1 Miniature Ice Rink Geometry and Layout FEMLAB and EES tools were used to analyze the thermal design the miniature ice rink at IUC Ref Centre. FEMLAB was used for conductive heat transfer in bed which was from inside surface of copper tube to the ice surface while convective heat transfer inside copper tubes and pressure drop analysis was done in EES. Ice rink bed design was very much similar to existing ice rink bed design which can be seen in Figure 11.

Figure 11: Design of miniature ice rink bed at IUC Ref Centre

Ground was prepared and then 100 mm layer of insulation was laid down. Above insulation, a layer of 100 mm of concrete was poured. On the surface of concrete, plastic supports for copper tubes were placed with centre-to-centre distance of 1200 mm. Copper tubes were fixed on these plastic supports with a pitch of 100 mm then 50 mm layer of concrete was poured by keeping tubes in the centre of the concrete. The top layer was the ice sheet having 25 mm thickness approximately.

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Figure 12: Rink tubing layout The surface area of the rink was 10mx5.5m as shown in the Figure 12. The length of copper tube was 60 m which means that there were total 6 turns of each copper tube inside rink bed because length of the rink was 10 m. There were total 9 circuits of copper tubes out of which 4 circuits of 12.7 mm copper tube with plastic foil over it, 1 circuit was 12.7 mm copper tube without plastic foil, 1 circuit of 9.5 mm copper tube without plastic foil and 3 circuits of 9.5 mm copper tube with plastic foil over it. Based on the analysis of the prototype described above, a new optimized prototype was built. Rink bed design for prototype 2 was exactly same as prototype 1 in which only 12.7 mm copper tubes with plastic foil were used having 120 meter length. The headers can be placed on short side of ice hockey rink in case of 120 meter long copper tubes. The reason to have plastic foil over copper tubes is that there is a minor risk of chemical aggressive pollution close the tubes in the ice rink application. It is advised [Outokumpu; 2005] for safety reasons to apply a plastic foil to the copper tubes when copper tubes are installed inside the concrete. Furthermore the foil serves as mechanical wear protection as well, which in this case could appear if rubbing would occur due to thermal expansion and contraction. The total circuits were 4.5 which can be seen in Figure 13.

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Thermocouples around Copper Tubes and above

Concrete Surface

Pressure Transducer at Exit Pressure Transducers at

Inlet of Tubes

Figure 13: Layout of new rink

In new rink, there were total 12 turns of each copper tube inside rink bed with a pitch of 100 mm. The surface area of new rink was also exactly the same as before. 3.2 Structural Design Analysis-Stress Calculation and Fatigue Evaluation of Copper Tube Piping in an Ice Rink Application [Fred Nilsson; 2005] 3.2.1 Stress Calculation In order to perform the stress calculations as a consequence of the thermal expansion the following assumptions are made.

a) The tube is free of stress at the installation (1) CT oo 15+=

b) The tube will follow the expansion of the concrete which is αb (T-To), where αb is the coefficient of thermal expansion for concrete. No slip is assumed between the

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tube and the concrete. This will over estimate the stress but as discussed below this is a reasonable assumption.

c) The concrete is assumed to be stiff. This over estimates the stress but is reasonable since the amount of concrete is by far more than the tubes.

d) The temperature changes are slow so the tubes and the concrete could be assumed to have the same temperature.

With Hooks Law the elongation is given as

( )omx TT

E−+= σ

σε (2)

Where xα is the thermal expansion coefficient of the metal and E is the coefficient of elasticity. Combining (1) and (2) will give the thermal stress of the tube in the longitudinal direction.

( )( ombx TTE −−= )αασ (3) The following data is available for copper and iron:

MPaxE 51018.1= , Kx om 1108.16 6−=α , Kx o

b 11012 6−=α With these values introduced the following stress figures are obtained:

MPax 0.17−=α , At -15 oC MPax 3.11−=α , At -5 oC

If the corresponding calculation for steel is performed with data for steel , MPaxE 51006.2= Kx o

m 11014 6−=α Hence

MPax 4.12−=α , At -15 oC MPax 2.8−=α , At -5 oC

The inner pressure also yields stress. The copper tube has dimensions (do= 12.7 mm and di=11.1 mm). The pressure is 31 bars = 3.1 MPa at –5 oC. The circumferential stress, ϕα and axial stress, xα is then

MPax 238.0

95.51.3==ϕα , and MPax 5.11=α

Corresponding at –15 oC: MPa1.17=ϕα , and MPax 6.8=α

23


If thermal and pressure related stress is added up the following result is obtained for copper tubes: MPa1.17=ϕα , MPax 4.8−=α At -15 oC MPa23=ϕα , MPax 3.0−=α At -5 oC If the average stress and amplitude stress is calculated for copper tubes MPaa 95.2=ϕα , MPaxa 1.4=α MPam 20=ϕα , MPaxm 1.4−=α The corresponding for steel pipes are (do= 21 mm and di=17.2 mm). MPa1.11=ϕα , MPax 9.6−=α At -15 oC MPa15=ϕα , MPax 7.0−=α At -5 oC If the average stress and amplitude stress is calculated for steel tubes MPaa 95.2=ϕα , MPaxa 1.3=α MPam 1.13=ϕα , MPaxm 8.3−=α The possibility of slip between the tube and the concrete could lead to lower stress levels than indicated above. The friction forces are difficult to estimate. Assume that the friction force per unit length is F N/m. The total axial force is the FL, where L is the slipping distance. This implies an elongation which is opposite to the thermal elongation of the size EAFL where A is the cross sectional area of the tube. The friction force will exceed the axial movement if σΔ≥AFL where xax σσ 2=Δ . Assume that the slip distance is 10m. For the larger tube the area is A=29.9 mm2. Friction force of F= 24 N/m is required to avoid slip. Most likely the friction force will be larger than indicated and consequently the analysis above is not unnecessarily conservative. In general it can be said that the stress situation in the steel tube is more favourable. The stress amplitude in both directions is approximately 2/3 of the corresponding for the copper tube 3.2.2 Fatigue Evaluation In the MNC handbook no. 8 (Metallnormcentralen 1980), there are fatigue data available for copper. For the studied material it is given a fatigue limit of ±75 MPa for rotational bending. For the actual tension load in this case it could be assumed that the fatigue limit is σu=±70 MPa. For steel pipes the fatigue limit is somewhat higher σu=±100 MPa.

24


For the biaxial state of stress the Sines criterion is used. Consequently effective stress amplitude and an average stress are given according to:

axaaxaeffa ϕϕ σσσσσ −+= 22 , and

mxmeffa ϕσσσ +=

For copper tube: , Mpaeff

a 7.3=σ Mpaeffm 9.15=σ

For steel pipe: , Mpaeff

a 9.2=σ Mpaeffm 3.9=σ

In both cases the average stress is so low in comparison to the flexural strength at break so that only the fatigue stress is relevant to look at. Consequently a safety factor can be calculated as 70/3.7=19 for copper tubes and 100/2.9=34 for steel pipes. 3.2.3 Conclusion For both types of tubes the fatigue safety factor is very high. For copper it is 19 and for steel, it is almost double. 3.3 Experimental Equipment The experimental system i.e. miniature ice rink was built next to the IUC Ref Centre laboratory using the chilling capacity for the laboratory machines. This chiller was supplying cold brine to the CO2 condenser. The CO2 refrigerant system along with miniature ice rink can be seen in Figure 14. The CO2 condenser can be seen to the top left of the Figure 14 and green lines are showing the brine loop. The CO2 condenser was special copper soldered plate heat exchanger from SWEP to bear 40 bars pressure and was connected to the tank and worked on self circulation (thermosyphon loop). Tank was made from steel for maximum pressure of 40 bars having 230 litres capacity. The CO2 pump was hermetic pump with four wings. System was small so it needed less CO2 flow and CO2 pump was the smallest pump available and yet it had much higher pumping capacity than required. For this reason, most of the CO2 was pumping back to the tank. There was a return line after the pump to ensure a minimum flow through the pump to cool the motor. The CO2 refrigerant unit had filter dryer, relief valves and security valves. The brine temperature was controlled by a three way mixing valve.

25


Figure 14: CO2 refrigerant system along with miniature ice rink

Figure 15: CO2 refrigerant system at IUC Ref Centre

26


There was a turbine flow meter after the CO2 condenser to measure the condensed CO2 with a range of 1 to 10 litres per min. A turbine flow meter with a range of 2 to 20 litres per min was installed after the pump to measure the flow of CO2 to the ice rink. Flow of CO2 to the rink was controlled by the flow control valve which was located after the CO2 pump. Circulation rate for CO2 was changed by changing flow of CO2 with the help of this valve. Brine pump was from Wilo and type of the pump was Strats 80/12-1. An inductive flow meter was used to measure the flow of brine. The range of flow meter was 0 to 250 litres per min.

Figure 16: Miniature ice rink at IUC Ref Centre There were pt-1000 sensor probes to measure the temperature of brine at the inlet and outlet of the CO2 condenser. Copper tubes were equipped with T-type thermocouples to record the temperatures. There were also T-type thermocouples on the concrete surface. Thermocouples can be seen in Figure 13. An infrared sensor was installed to record the temperature of ice surface. System was equipped with 0 to 35 bars pressure transducers to measure the pressure at desired place which are shown in Figure 13.

27


4. THEORETICAL MODELLING AND SIMULATION FEMLAB and EES were the two tools which were dominantly used to design and simulate the ice rink system for heat transfer and pressure drop. FEMLAB was used only for conduction heat transfer i.e. conduction heat transfer from inner surface of refrigerant tube to the ice surface in the rink bed while convection heat transfer inside refrigerant tube and pressure drop analysis was done with EES. 4.1 Heat Transfer Analysis Heat transfer analysis can easily be divided into two parts i.e. conduction heat transfer and convective heat transfer. 4.1.1 Conduction Heat Transfer-FEMLAB Modelling FEMLAB has powerful module of heat transfer. There were few assumptions made in FEMLAB model which were:

a) Ground was assumed to be perfectly insulated. b) Plastic around the copper tubes was assumed to be high density polyethylene. c) Thickness of concrete above refrigerant tubes and thickness of ice was assumed

to be same at every part of rink bed. d) Density of concrete as well as ice was assumed to be constant along the

geometry. For modelling, 12.7 mm copper tube with and without plastic and 9.5 mm copper tube with and without plastic were taken. For comparison, 21.3 mm steel pipe and 25 mm plastic pipe were also taken for modelling. The thickness of concrete taken was 50 mm having 21.3 mm steel pipes in middle. Hence thickness of the concrete above steel pipes was 14.35 mm. The same thickness of concrete above plastic pipe and copper tubes was taken. The pitch was taken 100 mm for steel, plastic and copper tubes to compare with each other. The pitch is the centre-to-centre distance between two rink pipes or tubes. Average heat flux was increased from 50 W/m2 to 300 W/m2 with the increment of 50 W/m2. Inner tube surface temperature was calculated using FEMLAB modelling which was giving -4 oC ice surface temperatures for each case. For copper tubes, pitch was also decreased from 100 mm to 75 mm with the decrement of 5 mm for each case which was used later to optimize the system. There were total 156 FEMLAB simulations for comprehensive analysis. The following is a sample of the calculations that has been performed using FEMLAB. Calculations for 12.7 mm copper tube with plastic foil are shown in Figure 17. In this model, ground was taken perfectly insulated then a layer of 100 mm concrete was applied which was same in all other cases. Then there was 42.3 mm layer concrete and 12.7 mm copper tube with plastic foil was in the middle of this concrete layer to give 14.35 thick layer of concrete above the tube. Thickness of plastic foil was 0.45 mm. The top layer was a 25 mm ice sheet.

28


The surface colour showing the temperature distribution and isothermal lines can also be seen in Figure 17. Flow of heat flux is shown by red arrows. Markers of maximum and minimum temperature can also be seen.

1 2

3

Figure 17: FEMLAB model of 12.7 mm copper tube with plastic foil

Figure 18 is the plot of vertical cross section for heat flux which is the cross section 1 in Figure 17. It is clear from the plot that the heat flux at the bottom of the concrete ground (point zero at the x scale in Figure 18) is zero while the heat flux at the top of the ice surface is 100 W/m2. The decrease in heat flux is exponential with the increase in depth and finally it drops to zero.

Figure 18: Vertical cross section for heat flux in FEMLAB model, line 1 in figure 17

29


Figure 19 is the plot of vertical cross section for temperature distribution which is the cross section 2 in Figure 17; point zero at the x scale is at the top of the ice surface. It is seen in the plot that the inner tube surface temperature that gives -4 oC at the surface of 25 mm thick ice with heat flux of 100 W/m2 is -7.47 oC. The temperature drop across copper tube is 0.001 oC. This is negligible temperature drop which can not be seen in Figure 19. The temperature drop across plastic foil is 0.41 oC. It is shown as bend of the right part of the temperature line in Figure 19.

Figure 19: Vertical cross section for temperature distribution in FEMLAB model, line 2

in figure 17

Figure 20: Horizontal cross section for temperature distribution at ice surface, line 3 in

figure 17

30


Figure 20 is the cross section 3 which is the horizontal cross section for temperature distribution at the ice surface. Ideally temperature should be constant at the ice surface but it is not possible. There is variation of 0.18 oC with an average surface temperature of -4.09 oC. It is clear from the plot that the coldest temperature is just over the tube surface and the hottest is over the pitch centre. The method described above has been used with all the cases of different geometries and heat fluxes. 4.1.2 Convective Heat Transfer-EES Convective heat transfer analysis was done in EES using inner tube surface temperature obtained from FEMLAB modelling. A model was made to calculate the bulk CO2 or brine temperature. The circulation rate i.e. CR was assumed to be 2 for CO2 while a temperature difference of 2 oC for brine. The rest of the input data was the same as a range of 50 to 300 W/m2 heat flux and a range of 75 mm to 100 mm pitch for copper tubes was taken. Since an accepted correlation for the convective heat transfer coefficient for boiling CO2 in large tubes could not be found, hence a correlation for R12, R22 and R502 proposed by Pierre (1953) [Eric Granryd; 2005] for incomplete evaporation in horizontal copper tubes, heated by flowing water in a concentric tube, was used. EES model for convective heat transfer in given in Appendix II. 5.03 .Re).85.0.(1010.1 KfxNum

−=Where, λα dNu meanm .= ( )μπ ...4Re dm&= gLhKf .Δ= Where Num is mean Nusselt number, Re is Reynolds number, Kf is Pierre boiling number, αmean is convective heat transfer coefficient (W/m2.oC), d is diameter of tube (m), λ is thermal conductivity (W/m.oC), is mass flow rate of refrigerant (kg/s), μ is dynamic viscosity (m.s/kg), ∆h is change in enthalpy between inlet and outlet (J/kg), g is acceleration due to gravity (m/s

m&

2) and L is the length of tube (m). 4.1.3 Results and Remarks The inner tube surface temperature that gives -4 oC ice surface temperature is obtained by the conduction model in FEMLAB, while the additional temperature drop due to convection was calculated by using EES; accordingly the bulk/evaporating temperature was calculated and presented in Table 1.

31


Table 1: Bulk/evaporation temperature in oC that gives -4 oC ice surface temperature for each case

Bulk Temperature at Heat Flux Tube or

Pipe

Pitch

mm 50

W/m2100

W/m2150

W/m2200

W/m2250

W/m2300

W/m2

75 -5.77 -7.33 -8.89 -10.46 -12.02 -13.59 80 -5.83 -7.45 -9.06 -10.69 -12.30 -13.93 85 -5.87 -7.57 -9.24 -10.93 -12.60 -14.29 90 -5.95 -7.69 -9.44 -11.17 -12.91 -14.66 95 -6.02 -7.82 -9.62 -11.43 -13.23 -15.04

9.5 mm Copper

Tube With Plastic Foil 100 -6.08 -7.95 -9.82 -11.69 -13.57 -15.43

75 -5.62 -7.03 -8.43 -9.85 -11.25 -12.66 80 -5.67 -7.12 -8.58 -10.04 -11.50 -12.95 85 -5.72 -7.23 -8.73 -10.25 -11.76 -13.26 90 -5.77 -7.33 -8.89 -10.46 -12.02 -13.59 95 -5.83 -7.44 -9.06 -10.68 -12.30 -13.92

9.5 mm Copper Tube

Without Plastic

Foil 100 -5.89 -7.56 -9.23 -10.91 -12.58 -14.27 75 -5.76 -7.23 -8.70 -10.17 -11.65 -13.11 80 -5.81 -7.32 -8.85 -10.38 -11.89 -13.42 85 -5.86 -7.44 -9.00 -10.58 -12.14 -13.72 90 -5.91 -7.54 -9.16 -10.79 -12.41 -14.04 95 -5.97 -7.65 -9.33 -11.01 -12.68 -14.37

12.7 mm Copper

Tube With Plastic Foil

100 -6.03 -7.77 -9.50 -11.24 -12.97 -14.71 75 -5.64 -6.98 -8.33 -9.68 -11.03 -12.37 80 -5.68 -7.07 -8.46 -9.85 -11.24 -12.63 85 -5.73 -7.16 -8.60 -10.03 -11.47 -12.90 90 -5.77 -7.25 -8.74 -10.22 -11.70 -13.22 95 -5.82 -7.36 -8.88 -10.42 -11.95 -13.48

12.7 mm Copper Tube

Without Plastic Foil 100 -5.87 -7.46 -9.04 -10.62 -12.20 -13.79

21.3 mm Steel Pipe

100

-5.89

-7.34

-8.78

-10.22

-11.67

-13.11

25 mm Plastic

Pipe

100

-7.83

-9.65

-11.47

-13.29

-15.11

-16.93

Evaporating temperature decreases with the increase of heat flux because temperature difference between evaporating temperature and ice surface temperature increases with the increase of heat flux. Ice surface temperature is constant i.e. -4 oC; evaporating temperature has to be decrease which can be seen in Table 1. Evaporating temperature increases with the increase of pitch of copper tubes. With the increase of pitch, thermal resistance increases between tubes due to which evaporating temperature increases.

32


Different plots were made to analyze the results obtained from these simulations. Figure 21 is the plot for comparison of all 6 kinds of tubes having 100 mm pitch. Heat flux is on x-axis while temperature difference between bulk evaporation temperature and ice surface temperature (-4 oC) is on y-axis. It is obvious from the plot that plastic pipe is worse than all other tubes or pipe while steel is the best. Copper tubes are in between both. At rated heat flux of 100 W/m2, the plastic pipe is 2.31 oC worse than steel pipe. 12.7 mm copper tube without plastic foil is close to steel pipe but yet it is worse by 0.12 oC than steel pipe. Other copper tubes are showing expected trend in the plot. There is one clear indication for copper tubes that if there is desire to get closer to steel pipe then pitch of copper tubes must be decreased. It must be pointed out that diameter of the largest copper tube is almost half than the diameter of the steel pipe; this means that for the same pitch, the copper tube will have more concrete in between which is an additional thermal resistance.

Comparison of the different Tubes having 100 mm Pitch

1.87

3.46

5.04

6.62

8.2

9.79

2.03

3.77

5.5

7.24

8.97

10.71

1.89

3.56

5.23

6.91

8.58

10.27

2.08

3.95

5.82

7.69

9.57

11.43

1.89

3.34

4.78

6.22

7.67

9.11

3.83

5.65

7.47

9.29

11.11

12.93

1

3

5

7

9

11

13

50 100 150 200 250 300

Heat Flux, W/m2

Tem

pera

ture

Diff

eren

ce, d

eg C

Cu 12.7 mm Cu+Foil 12.7 mm Cu 9.5 mm Cu+Foil 9.5 mm Steel 21.3 mm Plastic 25 mm

Figure 21: Comparison of the different tubes having 100 mm pitch Figure 22 is the plot of comparison of 12.7 mm copper tubes having plastic foil with steel and plastic pipes. Plastic pipe is worst while 12.7 mm copper tube with plastic foil having 75 mm pitch is better. At 100 W/m2 of heat flux, 12.7 mm copper tube having plastic foil with pitch of 75 mm is 0.11 oC better than the steel pipe. At 300 W/m2 of heat flux, both steel and 12.7 mm copper tube with plastic having 75 mm pitch are same. It is clear from plotting that with the increase of pitch, copper tube is becoming worst than steel pipe.

33


Comparison of 12.7 mm Copper Tubes having Plastic Foil with Steel and Plastic Pipe

1.76

3.23

4.7

6.17

7.65

9.11

1.86

3.44

5

6.58

8.14

9.72

2.03

3.77

5.5

7.24

8.97

10.71

1.89

3.34

4.78

6.22

7.67

9.11

3.83

5.65

7.47

9.29

11.11

12.93

1

3

5

7

9

11

13

50 100 150 200 250 300

Heat Flux, W/m2

Tem

pera

ture

Diff

eren

ce, d

eg C

Copper-75 mm Pitch Copper-85 mm Pitch Copper-100 mm Pitch Steel-100 mm Pitch Plastic-100 mm Pitch

Figure 22: Comparison of 12.7 mm Copper Tubes having Plastic Foil with Steel and Plastic Pipe

Another plot is made to compare the 12.7 mm copper tubes without plastic foil with steel and plastic pipes which is shown in Figure 23. In this comparison, the situation is bit different for steel pipe. Plastic pipe is still worst than all but 12.7 mm copper tube without plastic foil having 75 mm pitch is best. If we take average heat flux of 100 W/m2, then 12.7 mm copper tube without plastic foil having 75 mm pitch is 0.36 oC better than steel pipe. If we keep increasing the pitch of copper tubes without plastic foil from 75 to 90 mm, it remains better than steel pipe at 100 W/m2 of heat flux but it becomes 0.02 oC worse than steel pipe at 95 mm pitch.

34


Comparison of 12.7 mm Copper Tubes without Plastic Foil with Steel and Plastic Pipes

1.64

2.98

4.33

5.68

7.03

8.37

1.82

3.36

4.88

6.42

7.95

9.48

1.87

3.46

5.04

6.62

8.2

9.79

1.89

3.34

4.78

6.22

7.67

9.11

3.83

5.65

7.47

9.29

11.11

12.93

1

3

5

7

9

11

13

50 100 150 200 250 300

Heat Flux, W/m2

Tem

pera

ture

Diff

eren

ce, d

eg C

Copper-75 mm Pitch Copper-95 mm Pitch Copper-100 mm Pitch Steel-100 mm Pitch Plastic-100 mm Pitch

Figure 23: Comparison of 12.7 mm copper tubes without plastic foil with steel and plastic pipes

Plastic foil is an added resistance around copper tube and it has its effect on heat transfer which can be seen in Figure 24 which is a plot for 100 mm pitch copper tubes. At heat flux of 100 W/m2, 12.7 mm copper tube with plastic foil is 0.31 oC worse than 12.7 mm copper tube without plastic foil. This temperature drop is across plastic foil. It becomes worse at higher heat flux because temperature across plastic foil increases due to constant thermal resistance. Another plot is made to compare the 12.7 mm copper tube having plastic foil with 9.5 mm copper tube having plastic foil which is shown in Figure 25. The pitch is 100 mm for both tubes. At rated heat flux of 100 W/m2, 12.7 mm copper tube having plastic foil is 0.18 oC better than 9.5 mm copper tube having plastic foil. Since the pitch is same for both; 9.5 mm copper tube having plastic foil has more thermal resistance in between than 12.7 mm copper tube having plastic foil.

35


Analysis of 100 mm Pitch for 12.7 mm Copper Tubes

1.87

3.46

5.04

6.62

8.2

9.79

2.03

3.77

5.5

7.24

8.97

10.71

1

2

3

4

5

6

7

8

9

10

11

50 100 150 200 250 300

Heat Flux, W/m2

Tem

pera

ture

Diff

eren

ce, d

eg C

Cu 12.7mm Cu+Foil 12.7 mm

Figure 24: Comparison of 12.7 mm copper tubes with and without plastic foil having 100 mm pitch

Comparison of 12.7 mm Copper Tube having Foil with 9.5 mm Copper Tube having Foil (100 mm Pitch)

2.03

3.77

5.5

7.24

8.97

10.71

2.08

3.95

5.82

7.69

9.57

11.43

1

3

5

7

9

11

13

50 100 150 200 250 300

Heat Flux, W/m2

Tem

pera

ture

Diff

eren

ce, d

eg C

Cu+Foil 12.7 mm Cu+Foil 9.5 mm

Figure 25: Comparison of 12.7 mm copper tube having foil with 9.5 mm copper tube having foil (100 mm Pitch)

36


4.2 Pressure Drop Analysis Pressure drop was calculated using EES. CO2 runs in two-phase condition inside the rink pipes. Programs were made in EES and correlations were used to calculate two phase pressure drop. There were two type of correlations used for the analysis and comparison i.e. Friedel pressure drop correlation and homogeneous pressure drop correlation. The Friedel correlation of two-phase multiplier (Hewitt, 1998) is used to calculate the pressure drop in the two-phase flow in the CO2 line. Reiberer (1998) compared a few correlations and concluded that the Friedel correlation gives the best approximation for CO2 pressure drop in two-phase flow in 7 mm diameter tube. CO2 enters the rink pipes in liquid phase and starts to boil until it reaches a certain quality at the exit which depends on the cooling load and the mass flow of refrigerant. The Friedel correlation is given below.

Iliqtp PP φ*Δ=Δ

( )( )0335.0045.0 *

**23.2WeFr

HFEI +=φ

( ) ( )( )liqliq

vapvap

ff

xxE**

*1 22

ρρ

+−=

( )( )264.1Reln*79.05.0

−=

vapvapf

( )( )vap

rvap d

mμπ **

*4Re&

=

( ) 224.078.0 1* xxF −= 7.019.091..0

1** ⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

liq

vap

liq

vap

vap

liqHμμ

μμ

ρρ

( )2

2

**81.9 H

tube

r

dAm

Frρ

⎟⎟⎠

⎞⎜⎜⎝

⎛

=

&

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+⎟

⎟⎠

⎞⎜⎜⎝

⎛=

liqvap

Hxx

ρρ

ρ1

1

σρ *

*2

H

tube

r dAm

We⎟⎟⎠

⎞⎜⎜⎝

⎛

=

&

Where ρvap is density of vapour (kg/m3), ρliq is density of liquid in (kg/m3), fvap is friction factor of vapour, fliq is friction factor of liquid, Revap is Reynolds number of vapour, μvap is

37


dynamic viscosity of vapour (m.s/kg), μliq is dynamic viscosity of liquid (m.s/kg), is mass flow of refrigerant (kg/s), d is diameter of tube (m), x is vapour fraction, A

rm&tube is the

area of tube (m2) and ρH is homogeneous density of fluid (kg/m3). To calculate the pressure drop, the tube must be divided into several parts. A vapour fraction is estimated for each part assuming that the change in quality is uniform along the pipe, and then pressure drop is calculated for each part. Pressure drops are added to obtain total pressure drop in the tube. This method should give a good approximate of the real pressure drop. In order to simplify the calculations, the Friedel correlation is used to calculate the pressure drop for whole tube assuming that the CO2 is in two-phase from start till end. In second step, it is also assumed that CO2 is only in liquid phase from start till end and liquid pressure drop is calculated. The average of two-phase pressure drop and liquid pressure drop is taken. In this thesis report, it is denoted as average Friedel pressure drop and used to calculate the pressure drop in this project to optimize the system. EES model for average Friedel pressure drop is given in Appendix II. Homogeneous pressure drop model is also used for the comparison with Friedel correlation. Both the liquid and the vapour phases are mixed with each other as homogeneous fluid. The average homogeneous pressure drop is also calculated in same way as in average Friedel pressure drop. Correlation for homogeneous pressure drop is given below.

( )1000**** 2

.1 dL

wfP pipeHHHhm ρ=Δ

( )( )2.1 64.1Reln*79.05.0

−=

HHf

( )( )H

rH d

mμπ **

*4Re&

=

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+⎟

⎟⎠

⎞⎜⎜⎝

⎛=

liqvap

Hxx

ρρ

ρ1

1

HtubeHr Awm ρ**=&

Where f1.H is friction factor of homogeneous fluid, ρH is homogeneous density of fluid (kg/m3), wH is velocity of homogeneous fluid (m/s), Lpipe is the length of the tube (m), d is the diameter of the tube (m), ReH is the Reynolds number of homogeneous fluid, is mass flow of refrigerant (kg/s), μ

rm&H is dynamic viscosity of homogeneous fluid (m.s/kg), x

is the quality, ρvap is density of vapour (kg/m3), ρliq is density of liquid in (kg/m3) and Atube is the area of tube in (m2). EES model for average homogeneous pressure drop is given in Appendix II.

38


5. EXPERIMENTATION 5.1 Analysis of Movement of Copper Tubes inside Ice Rink Bed One potential risk that needed to be investigated is the thermal expansion and contraction of tubes inside the rink bed. Coefficient of thermal expansion of steel is comparable with concrete so there is almost no risk of movement of steel tubes inside rink bed. This solution is working well in terms of thermal expansion and contraction. But in case of copper tubes, the coefficient of thermal expansion of copper and concrete is different and there is danger of movement of copper tubes inside the rink bed. A careful experimental study has been made to analyze this issue. All four tubes (as mentioned earlier) were selected for this analysis. A reference point was fixed at the ground and other reference point was fixed on the tube as shown in the Figure 26 and Figure 27.

Figure 26: Schematic diagram of ice rink bed with two reference points for analysis

Ice Copper Tube

Concrete Concrete

Reference Points

Figure 27: Two reference points for 12.7 mm copper tube with plastic foil

39


The length of the tube under observation was 10 meters. One end of the tube was inside of the concrete which was assumed to be fixed while the other end was outside the concrete. If there was movement of the tube inside the bed then it could be possible to measure this movement on the free side because in that case, the whole tube would move in the bed. The idea to have these two reference point was that if tube will move then reference point on the tube will move and this movement can be measured with respect to fixed point on the ground. Vernier Callipers was used to measure the distance between two reference points. This analysis was started from ambient conditions and system was not working while the first observation was made. After the first observation, CO2 was pumped into rink with flow rate of 9-10 litres per min. The system was stable after 26 hours when the second observation was taken. After the second observation had been produced, the supply of CO2 to the rink was cut off. The system was allowed to warm up for almost 66 hours. Then the third observation was executed. Again supply of CO2 to the rink was opened to cool it and the system took almost 24 hours to get fully stable. At last, the fourth and final observation was carried out. First observation is the reference for the remaining observations. This scheme applied to all 4 types of copper tubes. The analysis for individual tube is given in Appendix I. 5.1.1 Comparison and Conclusion The principal intention for this analysis was to examine that whether copper tubes will move inside the rink bed with the change of evaporation temperature inside the copper tubes or not. This analysis revealed that tubes were moving inside the rink bed with the change of temperature. Comparison between all tubes can be seen in Table 2. For the comparison, temperature and pressure of all tubes have been considered the same as the 12.7 mm copper tube with plastic foil had during the analysis period because these values were close to each other.

Table 2: Comparison of all tubes

No. of

Obs.

Time

hours

Tube Temp.

oC

Pressure

bar

Movement of 12.7

mm Tube with Foil

mm

Movement of 9.5 mm Tube with

Foil

mm

Movement of 12.7

mm Tube without

Foil mm

Movement of 9.5 mm

Tube without

Foil mm

1 0 10.90 24.90 0.0 0.0 0.0 0.0 2 26 -9.28 27.03 -0.70 -0.65 -0.10 -0.05 3 92 12.10 25.68 -0.60 -0.35 +0.05 +0.05 4 116 -9.73 26.69 -0.65 -0.50 0.0 0.0

If we compare the copper tubes with plastic foil and copper tubes without plastic foil, then it is a clear indication that they were moving with same pattern. Copper tubes with plastic foil moved 0.55 mm to 0.65 mm more than copper tubes without plastic foil. The

40


reason behind seems to be the frictional stress. The frictional stress between copper and concrete might be stronger than the frictional stress between concrete and plastic due to which tubes with plastic foil moved more than tubes without plastic foil. There might be possibility of movement of copper tubes inside the plastic foil. Another important point in this analysis disclosed that when tubes were allowed to warm up, then copper tubes with plastic foil did not expand much to get back to their original position while copper tubes without plastic foil expanded as they were expected. The reason behind the less expansion of copper tubes with plastic foil might be that copper tubes were already in the state of over expansion. The rink was exposed to high ambient temperature for long time before this analysis has been started. So tubes contracted more than they would if tubes were not exposed for this high ambient temperature for long time. Due to these conditions, tubes were not expanded to their original position during heating period of the analysis. Another explanation can be the expansion of these tubes on the fixed end. It was an assumption in the analysis that the tubes were fixed on the end which was inside the concrete. So it was possibility that during cooling period, these copper tubes were not contracting or moving on the fixed end as much as they expanded or moved during heating period. It is also clear from results that copper tubes without plastic foil expanded a bit more than the reference position but this is really small which can be the error during measurement, hence can be ignored. This analysis reveals that there will be no danger of movement of copper tubes inside the rink bed during operation of the ice rink whether the copper tube is with or without plastic foil. The maximum movement has been recorded 0.7 mm for 12.7 mm copper tube with plastic foil. This movement is not critical for a temperature change of 20.42 oC for 10 m length of tube. 5.2 Cooling Load of the Ice Rink CO2 has certain quality at the exit of the ice rink which was difficult to measure. Consequently it was not possible to measure the cooling load from the CO2 side. A heat balance across the heat exchanger i.e. CO2 condenser was the only option left to find the cooling load of the rink. Brine was used to condense the CO2 in the heat exchanger as shown in the Figure 28. There were flow meters, one on the brine side and one on the CO2 side. One problem with flow meter on CO2 side was that it stopped measuring below 2 litres per min. During normal operation of the rink, CO2 was condensing below 2 litres per min most of the time so it was difficult to measure the condensed CO2 to find the cooling load of the ice rink. Under these circumstances, the brine load was the only choice left to take as cooling load. It was necessary to be sure that brine load can be trusted as cooling load of the rink. Few tests were planned for this purpose. During these tests, the system was forced to run under such conditions that CO2 came out of the ice rink as super heated vapour which was confirmed by thermocouple installed at the exit of the ice rink. One flow meter was installed at the inlet of ice rink to measure CO2 supply to the rink bed. Under these circumstances, the inlet and outlet conditions of the CO2 were well known to make heat balance with brine side.

41


Figure 28: CO2 Condenser 5.2.1 First Test The first test was run for almost 4 hours in which average CO2 supply was 2.43 litres per min and average brine flow through heat exchanger was 126.73 litres per min. Comparison was made between CO2 and brine which can be seen in Figure 26. Cooling load is on y-axis and time is on x-axis. Brine load was oscillating much more than CO2 load. The reason was the chillers; they were not running all the time during the test. The brine inlet temperature was changing all the time with same pattern giving oscillations. The average brine load for this 4 hour test was found to be 12.42 kW and average CO2 load was 10.67 kW giving a difference of giving an average difference of 1.75 kW. 5.2.2 Second Test The second test ran almost 3 hours giving interesting results. Average CO2 supply was 2.92 litres per min and average brine flow through heat exchanger was 128.44 litres per min. Results for this test can be seen in Figure 30. This test can be divided into three parts based on results obtained, which is clear in the Figure 6.5. Oscillation of brine load in the first part was almost the same as found in first test with average difference of 1.2 kW approximately. Second part of the test had almost negligible oscillations in brine load. The reason was the chillers since they were running continuously during that period supplying brine at same temperature. This part had almost same average difference between brine load and CO2 load as in first part of this test. In third part, average CO2 load increased because this was time when the CO2 supply was increased from 2.7 litres / min to 3.2 litters per min. The fact behind this was that the accuracy of CO2 flow meter improved with higher flow. The average difference between brine load and CO2 load was almost 0.6 kW. The average brine load for this 3 hour test was found to be 13.70 kW and average CO2 load was 12.64 kW giving an average difference of 1.06 kW.

42


Brine Load vs CO2 Load

-5

0

5

10

15

20

11:02:24 11:31:12 12:00:00 12:28:48 12:57:36 13:26:24 13:55:12 14:24:00 14:52:48

Time

Coo

ling

Load

, kW

Brine Load CO2 Load Difference Poly. (Brine Load) Poly. (CO2 Load) Poly. (Difference)

Figure 29: Results of first test on cooling load


-5

0

5

10

15

20

25

12:11:31 12:40:19 13:09:07 13:37:55 14:06:43 14:35:31 15:04:19

Time

Coo

ling

Load

, kW


Figure 30: Results of second test on cooling load

43


5.2.3 Third Test The third and final test took 1 hour and 30 min to give results with 3.15 litres per min average CO2 supply and 115.44 litres per min average brine flow. Results are shown in Figure 31. Brine load showed different oscillation in this test than previous two tests because scan rate was different in this test than previous ones. The scan rate was 5 seconds for this test while it was 30 seconds for first two tests. The purpose of reducing the scanning time was to analyze the pattern of the oscillations and whether it was possible to reduce these oscillations in brine load by shortening the scan rate or not. But it was obvious after third test that oscillations were independent of scan rate and totally dependent on the chillers. The average brine load for this third test was 13.4 kW which was almost same as CO2 load.


-10

-5

0

5

10

15

20

9:41:46 9:56:10 10:10:34 10:24:58 10:39:22 10:53:46

Time

Coo

ling

Load

, kW


Figure 31: Results of third test on cooling load 5.2.4 Conclusion The results obtained from these three tests showed that average brine load was giving approximately exact cooling load of the ice rink and pump power and heat loss to ambient has to be deducted from the brine load. Heat loss was found to be 1 to 4% of the brine load which was dependent on the ambient conditions. Further analysis was based on this conclusion.

44


This was the time when further tests were planned for heat transfer and pressure drop analysis. There were two basic inputs which were important for analysis i.e. heat flux and circulation rate (CR). Ideally there should be a facility to control the heat flux and the CR according to the requirement of the test but it was impossible to control the heat flux. Heat flux was changing each day depending on the ambient conditions which was also affecting the CR. So these tests were difficult to control. 5.3 Pressure Drop in 60 Meter Copper Tubes As mentioned earlier, there were two diameter copper tubes in first test rink i.e. 12.7 mm copper tubes and 9.5 mm copper tubes. These tests were executed separately for both diameter tubes by closing circuits of one diameter tubes at one time and running test for other diameter tubes. Pressure transducers were installed at the inlet and outlet of copper tubes as shown in Figure 13. It is suggested that the reader must read the section 4.2 first in order to completely understand the pressure drop analysis. 5.3.1 12.7 mm Copper Tubes There were total 5 tests conducted for 12.7 mm copper tubes. During these tests, 5 circuits of 12.5 mm copper tubes were fully opened and 4 circuits of 9.5 mm copper tubes were fully closed. Each test took more than 4 hours. Results are shown in Table 3. Ideally the heat flux should be constant while the CR can be changed in each test but it was impossible here. Heat flux was not constant in each test due to which only 3 tests, out of 5, could be taken for the analysis and comparison with pressure drop models. Flow of CO2 was changed through flow control valve for each test to change the CR.

Table 3: Experimental and Theoretical Pressure Drop in 12.7 mm Copper Tube (60 meter Long)

CR Heat Flux

W/m2

Average Homogeneous Pressure Drop

kPa

Average Friedel Pressure Drop

kPa

Experimental Pressure Drop

kPa

1.18 338 3.41 4.33 4.01 1.84 318 5.14 7.72 4.62 2.60 355 9.49 14.19 6.46

The tests, which are taken for the analysis and comparison with pressure drop models, have almost same heat flux which can be seen in Table 3. With the increase of CR, pressure drop increases; pressure drop is directly proportional to velocity of the fluid. The comparison of experimental and theoretical results for pressure drop can be seen in Figure 32. On x-axis, CR is plotted while on y-axis; pressure drop in kPa is plotted. Average homogeneous pressure drop model predicted almost 15% less pressure drop at low CR and almost 45% higher pressure drop at high CR than the experimental

45


pressure drop. This model can not be trusted as it under predicts at low CR. The average Friedel pressure drop model predicted bit higher pressure drop at each point. It over predicts 20 to 25 % at low CR and even 90 to100% at high CR. Since low CR is region is appropriate to work with in real ice rink operation; average Friedel pressure drop model is suitable. There are only 3 teats to analyze and compare which sound that there are less data points but range of CR is enough to see the trend of pressure drop models.

Experimental and Theoretical Pressure Drop in 12.7 mm Copper Tubes (60 meter)

3.41

5.14

9.49

4.33

7.72

14.19

4.014.62

6.46

2

4

6

8

10

12

14

16

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

CR

Pres

sure

Dro

p, k

Pa

Av. Homogeneous Pressure Drop Av. Friedel Pressure Drop Experimental Pressure DropPoly. (Av. Friedel Pressure Drop) Poly. (Av. Homogeneous Pressure Drop) Poly. (Experimental Pressure Drop)

Figure 32: Experimental and theoretical pressure drop in 12.7 mm copper tubes (60

meter) 5.3.2 9.5 mm Copper Tubes There were 4 tests for 9.5 mm copper tubes by keeping the 4 circuits of 9.5 mm copper tubes fully open and 5 circuits of 12.7 mm copper tube fully closed. Each test had different heat flux and ran for more than 4 hours. There were 3, out of 4, tests which could be taken for analysis and comparison. The results of these tests are shown in Table 4.

46


Table 4: Experimental and Theoretical Pressure Drop in 9.5 mm Copper Tubes (60 meter Long)

CR Heat Flux

W/m2


kPa


kPa


kPa

1.06 453 25.79 22.98 22.74 1.7 476 48.63 60.44 37.34

2.22 462 63.57 81.98 43.70 The tests, which are taken for the analysis and comparison with pressure drop models, have almost same heat flux which can be seen in Table 4. With the increase of CR, pressure drop increases; pressure drop is directly proportional to velocity of the fluid. Figure 33 is showing the comparison of experimental and theoretical pressure drop in 9.5 mm copper tube. On x-axis, CR is plotted while on y-axis; pressure drop in kPa is plotted.


25.79

48.63

63.57

22.98

60.44

81.98

22.74

37.34

43.7

20

30

40

50

60

70

80

90

1 1.2 1.4 1.6 1.8 2 2.2 2.4

CR

Pres

sure

Dro

p, k

Pa



meter) Average homogeneous pressure drop model predicted almost 20% higher pressure drop at low CR and almost 45% higher pressure drop at high CR than the experimental pressure drop. The average Friedel pressure drop model predicted 25 to 30 % at low CR and about 90% at high CR. There are only 3 teats to analyze and compare which

47


sound that there are less data points but range of CR is enough to see the trend of pressure drop models. 5.3.3 Conclusion The aim of these tests was to compare the experimental pressure drop in both 12.7 mm copper tube and 9.5 mm copper tubes. The experimental results were also checked with correlations to see that which correlation can be used to calculate the pressure drop in ice rink application. Since the CO2 pump used for this system was of much higher capacity and it was pumping more than 80 % CO2 back to the tank so pumping power could not be recorded experimentally. Due to this reason, it was very important to find the appropriate correlation to calculate the pressure drop in such application and hence to calculate the pump power and pump size. The average homogeneous model predicted good results for 9.5 mm copper tubes but not for 12.7 mm copper tubes. It under predicted 15% pressure drop than the experimental pressure drop at low CR. This model can not be trusted. Average Friedel pressure drop model gave good approximation of pressure drop for CO2. This model over predicted at each value of CR which is good. It predicted 20 to 25 % higher pressure drop than the experimental pressure drop at lower CR. At higher CR, it over predicted almost 90 to100 % than the experimental pressure drop. Since low CR region is the appropriate to work with to reduce the pump work as much as possible; the Friedel pressure drop model predicts closer to the experimental results at low CR. It was also found that pressure drop in 9.5 mm copper tubes was almost 4 to 5 times higher than the pressure drop in 12.7 mm copper tubes at same CR and heat flux. If this pressure drop is converted into pump work then there is not big difference between both tubes. But at rated heat flux of 100 W/m2, 12.7 mm copper tube with plastic foil is 0.18 oC better than 9.5 mm copper tube with plastic foil in terms of heat transfer. There is also a natural trend to remain closer to steel pipe in terms of evaporating temperature; as steel pipe has been used with CO2 in ice rink applications. Due to these reason, 12.7 mm copper tube is better choice than 9.7 mm copper tube. It was also interesting to analyze the 120 meter long copper tubes to reduce the header to half size by putting it on short size of the rink. A decision was made to make prototype 2 of 12.7 mm copper tubes with plastic foil only having 120 meter length for further analysis. 5.4 Heat Transfer in 60 Meter Copper Tubes There were 4 different kinds of copper tubes in the rink bed for the analysis, so it was difficult to perform tests for heat transfer for each kind of tube at same time. It was also not possible to analyze each tube separately. To analyze the tubes at same time, it was important to have same mass flow in both 12.7 mm and 9.5 mm copper tubes. At specific pressure drop ratio, both tubes can have same mass flow rate which was found to be 4.5 theoretically which means pressure drop in 9.5 mm copper tube must be 4.5 times higher than pressure drop in 12.7 mm copper tubes. Then 12.7 mm copper tubes

48


circuits were partially closed in such a way that a pressure drop ratio of 4.5 was obtained. When tests for heat transfer analysis were conducted, satisfactory temperature distribution was not obtained. The reason might be that the uniform distribution of CO2 was not obtained in each circuit due to partial closing of 12.7 mm copper tubes circuits. 5.5 Pressure Drop in 120 Meter Copper Tubes Tests were planned to analyze both pressure drop and heat transfer for the new rink simultaneously, because there were only 12.7 mm copper tubes with plastic foil having 120 meter length in the bed. There were total 5 pressure drop tests conducted for 12.7 mm copper tubes. Each test ran for more than 20 hours. The heat flux was not constant in each test; 3 tests out of 5 could be taken for analysis and comparison with pressure drop models. There Results for experimental and theoretical pressure drop obtained from 3 tests are shown in Table 5. Table 5: Experimental and Theoretical Pressure Drop in 12.7 mm Copper Tubes (120

meter Long)

CR

Heat Flux

W/m2


kPa


kPa


kPa

1.67 136 6.84 10.44 8.57 1.90 135 7.86 12.20 8.98 2.18 138 9.65 15.01 9.57

The tests, which are taken for the analysis and comparison with pressure drop models, have almost same heat flux which can be seen in Table 5. With the increase of CR, pressure drop increases; pressure drop is directly proportional to velocity of the fluid. The results obtained from experiments and correlations are shown in Figure 34. On x-axis, CR is plotted while on y-axis; pressure drop in kPa is plotted. Average homogeneous pressure drop model under predicted the pressure drop than the experimental pressure drop. It under predicted 20 % at low CR and at high CR, it predicted almost same as experimental pressure drop. This model can not be trusted as it under predicts. The average Friedel pressure drop model predicted bit higher pressure drop at each point. It over predicted 20 to 25 % pressure drop at low CR and even 60% pressure drop at high CR than the experimental pressure drop. Since low CR is region is appropriate to work with in real ice rink operation; average Friedel pressure drop model is suitable. There are only 3 teats to analyze and compare which sound that there are less data points but range of CR is enough to see the trend of pressure drop models.

49



7.86

6.84

9.65

12.2

10.44

15.01

8.988.57

9.57

6

7

8

9

10

11

12

13

14

15

16

1.6 1.7 1.8 1.9 2 2.1 2.2 2.3

CR

Pres

sure

Dro

p, k

Pa



meter) 5.5.1 Conclusion These tests on 12.7 mm copper tubes having 120 meter length gave expected results. The results showed that the average Friedel pressure drop method can be used in ice rink applications. This pressure drop method predicted 20 to 25 % higher pressure drop than the experimental pressure drop at lower CR for both 60 meter and 120 meter long copper tubes. At higher CR, it over predicted 90 to 100 % for 60 meter long copper tubes and about 60 % for 120 meter long copper tubes than the experimental pressure drop. These tests also revealed that 120 meter long copper tubes are good choice. Pressure drop for 120 meter long copper tubes will not be high. The pump work will not be much in case of 120 meter long copper tubes. The benefit to have 120 meter long copper tubes will be that the header can be placed along the short side of the ice hockey rink. It will reduce the length of header to half as it would be in case of putting header along the long side of the ice hockey rink selecting 60 meter long copper tubes. 5.6 Heat Transfer in 120 Meter Copper Tubes These tests were planned for both heat transfer and pressure drop analysis to make a trade off between heat transfer and pressure drop and hence finally optimize the CR.

50


There were T-type thermocouples on copper tubes by scratching the plastic off at four different places when rink bed was being constructed as shown in Figure 13. At same places, there were thermocouples on plastic foil also. On the surface of concrete, thermocouples were installed and an arrangement was made to measure the concrete thickness at those places. The holes were drilled into the ice sheet to measure the thickness of the ice at same points. The Infrared sensor to record the ice surface temperature was fixed above same area. Hence a reasonable area was instrumented to study the heat transfer. There were total 5 tests conducted and each test ran for more than 20 hours. The heat flux was not constant in each test; 3 tests out of 5 could be taken for analysis and comparison with FEMLAB results. Results of 3 tests are shown in Table 6. Table 6: Experimental and theoretical temperature difference in oC across each section

of ice rink bed

CR=1.67 CR=1.9 CR=2.18 Temp. Difference

across

Type of Result q=136

W/m2q=135 W/m2

q=138 W/m2

Convection Theo. 0.33 0.31 0.29 Convection Exp. 0.60 0.65 0.60

Foil Theo. 0.58 0.58 0.59 Foil Exp 0.45 0.45 0.41

Concrete Theo. 3.05 3.01 3.05 Concrete Exp 2.24 2.22 2.35

Ice Theo. 1.81 1.79 1.84 Ice Exp. 2.40 2.51 2.51

Theoretical results were obtained from FEMLAB and EES models. Experimental data i.e. CR, evaporation temperature and heat flux was used in the EES model to calculate inner tube surface temperature. Then, that inner tube surface temperature and heat flux was used in FEMLAB model which was built by taking average concrete and ice thickness. With the change of CR, only convective heat transfer coefficient increased due to which convective heat transfer became more and temperature difference due to convection became less which can be seen in Table 6. The improved heat transfer is very small and the convective temperature difference is reduced by only 0.04 oC which is insignificant and does not justify the increasing CR to improve the heat transfer. Experimental temperature difference inside the copper tube was more than the theoretical temperature difference as shown in Figure 35. The temperature difference is on y-axis and CR is on x-axis in Figure 35. Theoretical calculation was done in the EES model. There was an average temperature difference of 0.3 oC between both results. There might be two reasons for this difference. One reason can be convective heat transfer correlation which is used for calculations is not for boiling CO2. The other reason for this difference could be the thermocouples. These thermocouples were recording temperature with an error of ± 0.2 oC and here thermocouples were compared with bulk CO2 temperature obtained from pressure of CO2. It is also clear from Figure 35

51


that the convective temperature difference became decreased with the increase of the CR.

Theoretical and Experimental Temperature Difference (Convection)

0.310.33

0.29

0.65

0.6 0.6

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

1.6 1.7 1.8 1.9 2 2.1 2.2

CR

Tem

pera

ture

Diff

eren

ce, o

C

Theoretical Temperature Difference (Convection) Experimental Temperature Difference (Convection)Poly. (Theoretical Temperature Difference (Convection)) Poly. (Experimental Temperature Difference (Convection))

Figure 35: Experimental and theoretical temperature difference (Convection)

Theoretical temperature difference across plastic foil was round about 0.13 oC more than experimental temperature difference which can be seen in Figure 36. The reason could be the thermal conductivity of the plastic foil which was taken from ASHRAE for high density polyethylene to use in FEMLAB modelling. The thermal conductivity of foil taken was 0.33 W/m.oC for the simulations while the actual thermal conductivity of the foil could be bit higher than this value; there was no data available for the plastic foil. Experimental results for temperature difference across concrete were giving less difference than the theoretical results as shown in Figure 37. The average difference between both results was found to be 0.8 oC. There could be two possibilities for this difference. One possibility could be conductivity of the concrete taken for the FEMLAB analysis which was 1.8 W/m.oC. This value was taken directly from the FEMLAB. In ice rink applications, there can be presence of ice in concrete due to which thermal conductivity of concrete can be bit high. The other possibility of difference between theoretical and experimental results could be thickness of the concrete taken for the FEMLAB model. An average concrete thickness of 24.8 mm above the tubes was taken in FEMLAB model. It is also possible that the actual average thickness of the concrete above copper tubes was less than that value. It was noticed that the concrete did not have an even surface where an approximate average was taken based on measurements from different points on the rink surface.

52


Theoretical and Experimental Temperature Difference across Plastic Foil

0.580.580.59

0.450.45

0.41

0.35

0.4

0.45

0.5

0.55

0.6

0.65

1.6 1.7 1.8 1.9 2 2.1 2.2

CR

Tem

pera

ture

Diff

eren

ce, o

C

Theoretical Temp. Difference across Foil Experimental Temperature Difference across FoilPoly. (Experimental Temperature Difference across Foil) Poly. (Theoretical Temp. Difference across Foil)

Figure 36: Experimental and theoretical temperature difference across plastic foil

Theoretical and Experimental Temperature Difference across Concrete

3.013.05 3.05

2.222.24

2.35

2

2.2

2.4

2.6

2.8

3

3.2

1.6 1.7 1.8 1.9 2 2.1 2.2

CR

Tem

pera

ture

Diff

eren

ce, o

C

Theoretical Temperature Difference across Concrete Experimental Temperature Difference across ConcretePoly. (Experimental Temperature Difference across Concrete) Poly. (Theoretical Temperature Difference across Concrete)

Figure 37: Experimental and theoretical temperature difference across concrete

53


Theoretical temperature difference across ice was less than the experimental temperature difference as shown in Figure 38. This average difference was found to be 0.8 to 0.9 oC. The reason could only be the thickness of the ice taken for the FEMLAB analysis. The actual average thickness of the ice could be more than the thickness taken for FEMLAB models. The average thickness taken was 27.4 mm. It was found that at some places, thickness of ice was 40 mm and at few places, it was even 8 mm. There was big variation in concrete and ice surface level due to which it was difficult to find the actual average thickness of concrete and ice.

Theoretical and Experimental Temperature Difference across Ice

1.791.811.84

2.51

2.4

2.51

1.5

1.7

1.9

2.1

2.3

2.5

2.7

1.6 1.7 1.8 1.9 2 2.1 2.2

CR

Tem

pera

ture

Diff

eren

ce, o

C

Theoretical Temperature Difference across Ice Experimental Tenperature Difference across IcePoly. (Theoretical Temperature Difference across Ice) Poly. (Experimental Tenperature Difference across Ice)

Figure 38: Experimental and theoretical temperature difference across ice 5.7 Conclusion for Pressure Drop and Heat Transfer Analysis The major goal of these tests was to verify the FEMLAB results with experimental results and to find the optimum CR by making a trade off between pressure drop and heat transfer. FEMLAB results were the basis to optimize the system technically and economically; it was very important to verify the FEMLAB that it gives good results. Verification of the FEMLAB results will be discussed in section 6. These pressure drop tests provided the base to optimize the CR theoretically, as it was found that Friedel pressure drop model gives good approximation of pressure drop. There is a separate section for optimization.

54


6. VERIFICATION OF FEMLAB MODEL It was very important to verify the results of the FEMLAB models with experimental results because design and optimization was going to be based on FEMLAB modelling and simulations. FEMLAB models with average thickness of concrete and ice have been discussed in section 5.6 with their results. In that section, theoretical and experimental results for each section of the ice rink bed has been given in Table 6 and reasons for those results have also been discussed. The ultimate goal for refrigeration in ice rinks is the desired ice surface temperature at certain ice thickness. Ice surface temperature obtained experimentally and theoretically is discussed here. Experimental and theoretical ice surface temperature with inputs is given in Table 7.

Table 7: Theoretical and experimental ice surface temperature to compare FEMLAB results with experimental results

CO2

Temp. oC

Heat Flux W/m2

CR

Alpha

W/m.oC

Inner Tube Surf. Temp.

oC

Exp. Ice Surf. Temp.

oC

Th. Ice Surf. Temp.

oC -8.86 136 1.67 1180 -8.53 -3.17 -3.00 -8.85 135 1.90 1250 -8.54 -3.02 -3.05 -8.83 138 2.18 1369 -8.54 -2.96 -2.93

Experimental values i.e. CR, heat flux and CO2 temperature were used in EES model to calculate the inner tube surface temperatures which were then used in FEMLAB models to calculate ice surface temperatures. It can be seen in Table 7 that FEMLAB was predicting ice surface temperatures which were close to the ice surface temperatures obtained from experiments. There was a difference in experimental and theoretical temperature drop across concrete and ice but the ultimate goal i.e. ice surface temperatures were really close in experiments and FEMLAB models. The big difference in experimental and theoretical results is in concrete and ice layers. The reason behind this might be that the actual average thickness of concrete might be less and the actual average thickness of ice might be more than the average thickness taken for FEMLAB simulations. The thermal conductivity of concrete taken was 1.8 W/m.oC and thermal conductivity taken for ice was 2.2 W/m.oC. Both values are close and it can be assumed that there is only one single layer above copper tubes of approximately same thermal conductivity. The average thickness of this layer will be exactly the sum of average thickness of concrete and average thickness of ice taken for FEMLAB. This can be good explanation of FEMLAB results that for whole geometry, FEMLAB gave results which were close to experimental results while for concrete and ice layers, there was difference between FEMLAB results and experimental results. After this exercise, it was decided to optimize the system on the basis of FEMLAB results.

55


7. OPTIMIZATION 7.1 Economical Optimization A main aim of this project is to analyze the copper tubes in ice rink applications to reduce the initial investment and also to reduce the operational cost to a minimum level. Hence economical optimization is important issue to work out. If the pitch of the copper tubes in the rink bed is reduced then investment will increase. This reduced pitch will lower the evaporation temperature which in turn lowers the operational cost. There is an optimum pitch, which will give a trade off between investment and operational cost. For this analysis, initial cost for rink bed tubing is taken. It is assumed that remaining equipment i.e. headers, refrigeration unit, main supply line, return line, CO2 storage tank, CO2 pump etc will remain same and cost for the remaining equipment will not change with the change of pitch. First initial cost including material and labour cost of one circuit of copper tubes is calculated. Headers are located on the short side of the ice rink and both supply and return headers are at one side of the rink. The size of the ice rink is 60x30 m; hence one circuit is 120 meter long. Since copper tube with plastic foil is not available in 120 meter length yet, it was decided to use a pair of 60 meter long copper tubes which will be soldered at one end of ice rink, which is on the opposite side of the headers. First labour cost for one circuit is calculated for which time must be known to make ready one circuit. A rough estimation of time is taken including 5 min for rolling down the whole circuit on its place, 5 min for soldering the two ends of tube to both supply and return headers and 10 min for soldering the both 60 meter copper tubes with each other. One tube will be expanded and the other tube will be inserted into it, then this joint will be soldered. Therefore; Total Time for One Circuit = 20 min The Swedish labour rate for such work is 480 SEK/hr; hence Labour Cost for One Circuit = 160 SEK Now material cost for one circuit is calculated. The material cost of 12.7 mm copper tube with plastic foil is 18.3 SEK/m and length of one circuit is 120 meter; hence Material Cost for One Circuit = 2196 SEK Total Cost for One Circuit = 2356 SEK Now investment for the whole rink is calculated in Table 8. With the decrease of the pitch, number of circuits of copper tubes increases. The depreciation time of 10 years is taken which gives investment per year. Investment per year increases with the decrease of pitch of the copper tubes inside the rink bed.

56


Table 8: Investment per year of 12.7 mm copper tubes with plastic foil having different pitch

Pitch mm

No. of Circuits InvestmentSEK

Depreciation TimeYr

Investment per Year SEK/Yr

100 150 353400 10 35340.0 95 158 372248 10 37224.8 90 166 391096 10 39109.6 85 176 414656 10 41465.6 80 188 442928 10 44292.8 75 200 471200 10 47120.0

Operational cost per year is calculated for different pitches in which only cost for compressor energy is taken. It is assumed that pressure drop will remain same with the change of pitch and hence pump power will remain same for each pitch that’s why cost for pump energy is not included in this analysis. The average heat flux is 50 W/m2 and area of the ice rink is 1800 m2. The cooling load for the ice rink is 90 kW. The operational cost per year is calculated in Table 9 for each pitch.

Table 9: Operational cost per year at heat flux of 50 W/m2

Pitch

mm

CO2 Temp.

oC

Ammonia Temp.

oC

COP

Comp. Power

kW

Running Time Per

Year hr

Annual Consumption

kWh/yr

Operational Cost per

year SEK/yr

100 -6.03 -9.03 3.65 24.658 8000 197260 197260 95 -5.97 -8.97 3.66 24.590 8000 196721 196721 90 -5.91 -8.91 3.67 24.523 8000 196185 196185 85 -5.86 -8.86 3.68 24.457 8000 195652 195652 80 -5.81 -8.81 3.69 24.390 8000 195122 195122 75 -5.76 -8.76 3.70 24.324 8000 194595 194595

CO2 temperature is calculated from FEMLAB and EES simulations. This CO2 is cooled by Ammonia refrigeration unit. A temperature difference of 3 oC between CO2 temperature and Ammonia evaporation temperature is assumed. COP of the Ammonia refrigeration system is calculated from BOCK Selection Program VAP 2005 b made by BOCK Compressors. For the calculation COP, a condensing temperature of 30 oC is assumed and corresponding Ammonia evaporation temperature is used. Since cooling load is known which is 90 kW; hence compressor power is calculated. Compressors of ice rink refrigeration do not run all time throughout the year, so an average running time of 8000 hours is assumed to calculate the annual consumption of energy. Swedish electricity rate is 1 SEK/kWh which gives the operational cost per year. With the increase of average heat flux, CO2 evaporation temperature will increase resulting increase of Ammonia evaporation temperature. This increase of Ammonia evaporation temperature will lower the COP of the refrigeration unit which in turn

57


increases the compressor power and finally operational cost per year. Operational cost per year at different average heat flux is given in Table 10.

Table 10: Operational cost per year at different heat flux

Operational Cost Per Year SEK/yr

Pitch

mm

q=50 W/m2

q=100 W/m2

q=150 W/m2

q=200 W/m2

100 197260 0 426036 0 690096 0 993103 0 95 196721 1.003% 423529 1.006% 683544 1.010% 982935 1.010%90 196185 1.005% 421053 1.012% 679245 1.016% 972973 1.021%85 195652 1.008% 419825 1.015% 675000 1.022% 966443 1.028%80 195122 1.011% 417391 1.021% 670807 1.029% 956811 1.038%75 194595 1.014% 416185 1.024% 664615 1.038% 947368 1.048%

If we take 100 mm pitch as reference, then 1.014% of operational cost will reduce by reducing the pitch from 100 to 75 mm at average heat flux of 50 W/m2. At average flux of 200 W/m2, 1.048% of operational cost will reduce by going down from 100 mm to 75 mm pitch. The investment cost per year and the operational cost per year are plotted in Figure 39 along with absolute cost per year. The absolute cost per year is the sum of the investment cost per year and the operational cost per year. This analysis is for the heat flux of 50 W/m2. The pitch is plotted on x-axis while cost in SEK/year is plotted on y-axis. The absolute cost per year and operational cost per year are plotted on primary y-axis while investment per year is plotted on secondary y-axis. It is seen in the Figure 39 the absolute cost per year is minimum at 100 mm pitch. As the pitch decreases from 100 mm, the absolute cost per year increases. With the decrease of the pitch from 100 mm to 75 mm, operational cots per year decreases by 2665 SEK and investment cost per year increases by 11780 SEK. At 50 W/m2 of heat flux, it is better to have the pitch as much large as possible i.e. 100 mm. The analysis for 100 W/m2 of heat flux is plotted in Figure 40. The pitch is plotted on x-axis while cost in SEK/year is plotted on y-axis. The absolute cost per year and operational cost per year are plotted on primary y-axis while investment per year is plotted on secondary y-axis. It can be seen in the Figure 40 that the absolute cost per year is minimum at 90 mm pitch. As the pitch decreases from 100 mm to 90 mm, the absolute cost per year decreases. The absolute cost per year increases with further decrease of the pitch from 90 mm to 75 mm. At 100 W/m2 of heat flux, 90 mm pitch is found to be most suitable.

58


Optimization for 50 W/m2 of Heat Flux

194595 195122 195652 196185 196721 197260

241715239415

237118235295

233946232600

47120

44292.8

41465.6

39109.6

37224.8

35340

190000

200000

210000

220000

230000

240000

250000

70 75 80 85 90 95 100 105

Pitch, mm

Cos

t, SE

K/y

ear

30000

32000

34000

36000

38000

40000

42000

44000

46000

48000

50000

Operational Cost per Year Absolute Cost per Year Investment per YearPoly. (Investment per Year) Poly. (Operational Cost per Year) Poly. (Absolute Cost per Year)

Figure 39: Absolute cost per year at average heat flux of 50 W/m2


416185 417391419825 421053

423529426036

463305461684 461291 460162 460754 46137647120

44292.8

41465.6

39109.6

37224.8

35340

410000

420000

430000

440000

450000

460000

470000

70 75 80 85 90 95 100 105

Pitch, mm

Cos

t, SE

K/y

ear

30000

32000

34000

36000

38000

40000

42000

44000

46000

48000

50000

Operational Cost per Year Absolute Cost per Year Total Investment per YearPoly. (Total Investment per Year) Poly. (Operational Cost per Year) Poly. (Absolute Cost per Year)


59


The analysis for 150 W/m2 of heat flux is plotted in Figure 41. The pitch is plotted on x-axis while cost in SEK/year is plotted on y-axis. The absolute cost per year and operational cost per year are plotted on primary y-axis while investment per year is plotted on secondary y-axis. It is seen in the Figure 41 the absolute cost per year is minimum at 75 mm pitch. As the pitch decreases from 100 mm, the absolute cost per year decreases. With the decrease of the pitch from 100 mm to 75 mm, operational cots per year decreases by 25481 SEK and investment cost per year increases by 11780 SEK. At 150 W/m2 of heat flux, it is better to have the pitch as much smaller as possible i.e. 75 mm.


664615

670807

675000

679245

683544

690096

711735715100 716466

718355720769

725436

47120

44292.8

41465.6

39109.6

37224.8

35340

660000

670000

680000

690000

700000

710000

720000

730000

70 75 80 85 90 95 100 105

Pitch, mm

Cos

t, SE

K/y

ear

30000

32000

34000

36000

38000

40000

42000

44000

46000

48000

50000

Operational Cost per Year Absolute Cost per Year Total Investment per YearPoly. (Total Investment per Year) Poly. (Operational Cost per Year) Poly. (Absolute Cost per Year)


7.1.1 Conclusion This analysis reveals that average heat flux is the driving force for the pitch. Theoretically, at low average heat flux, the pitch must be as large as possible to keep good temperature distribution on the surface of the ice. Similarly, at high average heat flux, the pitch must be as much smaller as possible. Practically, absolute cost per year does not change much with the change of pitch. It will depend on the interest and conditions to go for smaller pitch than 100 mm.

60


7.2 Optimization of Circulation Rate (CR) It has been shown earlier that convective heat transfer increases with the increase in circulation rate (CR) of CO2 resulting higher pressure drop, but this increase in heat transfer due to CR was very small so it is not a factor really. There is an optimum circulation rate at which there is a trade off between heat transfer and pressure drop. Therefore tests were planned to find optimum circulation rate. Unfortunately tests did not conclude for optimum circulation rate but correlations for convective heat transfer and pressure drop were used for this purpose. 120 meter length and 12.7 mm diameter copper tubes with plastic foil having 100 mm pitch were analyzed. Since it was very complicated and difficult to analyze whole system i.e. main supply line, headers, return line etc so analysis was restricted only for rink bed. Correlation proposed by Pierre (1953) was used for convective heat transfer analysis and average Friedel model for pressure drop calculations was used. To convert pressure drop into equivalent change in saturation temperature (temperature drop), Clapeyron equation was used which is given below [Eric Granryd; 2005]. It is assumed that this temperature drop due to pressure drop is even along the pipe.

( ) pr

vvTt Δ′−′′

=′′Δ **

Where T is the absolute temperature of the fluid (oK), r is the latent heat of vaporization (J/kg), ∆p is pressure drop (Pa), v” and v’ are the specific volumes for saturated vapour and liquid, respectively (m3/kg).

Table 11: Temperature drop due to convection, pressure drop and temperature drop due to pressure drop at different CR and heat flux in 12.7 mm copper tubes (120 meter)

Heat Flux CR 50

W/m2100

W/m2150

W/m2200

W/m2250

W/m2300

W/m2

1.1 0.392 0.400 0.408 0.417 0.425 0.433 1.5 0.336 0.343 0.350 0.357 0.364 0.371 2.0 0.291 0.297 0.303 0.309 0.315 0.321 2.5 0.260 0.266 0.271 0.276 0.282 0.287

Temp. Drop due to

Convection oC

3.0 0.238 0.242 0.247 0.252 0.257 0.262 1.1 1.06 3.13 5.98 9.55 13.82 18.78 1.5 1.86 5.51 10.59 16.96 24.60 33.50 2.0 2.67 8.03 15.49 24.88 36.14 49.26 2.5 3.48 10.55 20.42 32.87 47.79 65.17

Pressure Drop kPa

3.0 4.31 13.14 25.51 41.12 59.83 81.61

1.1 0.013 0.04 0.079 0.13 0.196 0.276 1.5 0.023 0.07 0.139 0.231 0.348 0.492 2.0 0.033 0.102 0.204 0.339 0.511 0.723 2.5 0.043 0.134 0.268 0.448 0.676 0.957

Temp. Drop due to Press.

Drop oC

3.0 0.053 0.167 0.335 0.561 0.846 1.198

61


Results obtained from correlations are given in Table 11. It is clear from Table 11 that temperature drop due to convection increases with the increase of heat flux while it decreases with the increase of CR. Temperature drop due to pressure drop increases with the increase of CR and heat flux. One important observation can be seen from Table 11 that temperature drop due to pressure drop at low heat flux is much less than the temperature drop due to convection while it becomes more at higher heat flux. At 50 W/m2 and circulation rate of 3, temperature drop due to pressure drop is 0.053 oC and temperature drop due to convection is 0.238 oC while at 300 W/m2 and circulation rate of 3, temperature drop due to pressure drop is 1.198 oC and temperature drop due to convection is 0.262 oC. Results obtained from correlations are plotted for different heat flux. An interesting conclusion is drawn at different heat flux. Figure 42 is the plot for an average heat flux of 50 W/m2. CR is plotted on x-axis and temperature drop is plotted on y-axis. With the increase of CR, temperature drop due to convections is decreasing while temperature drop due to pressure drop is increasing which is clear from plot. Absolute temperature drop is also plotted to see optimum CR. The minimum absolute temperature drop is 0.291 oC at CR of 3 showing that higher CR is better at low heat flux.

Optimum CR at Heat Flux of 50 W/m2

0.392

0.336

0.291

0.260.238

0.0130.023

0.0330.043

0.053

0.405

0.359

0.3240.303

0.291

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1 1.5 2 2.5

CR

Tem

pera

ture

Dro

p, d

eg C

3

Temp. Drop due to Conv. Temp. Drop due to Press. Drop Absolute Temp. DropPoly. (Temp. Drop due to Press. Drop) Poly. (Temp. Drop due to Conv.) Poly. (Absolute Temp. Drop)

Figure 42: Optimum CR at heat flux of 50 W/m2

62



0.4

0.343

0.297

0.2660.242

0.04

0.07

0.102

0.134

0.167

0.44

0.4130.399 0.4 0.409

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1 1.5 2 2.5

CR

Tem

pera

ture

Dro

p, d

eg C

3




0.408

0.35

0.3030.271

0.247

0.079

0.139

0.204

0.268

0.335

0.487 0.4890.507

0.539

0.582

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 1.5 2 2.5

CR

Tem

pera

ture

Dro

p, d

eg C

3



63


Figure 43 is the plot for an average heat flux of 100 W/m2. It is clear from the plot that temperature drops due to pressure drop is getting close to the temperature drop due to convection at higher CR. The minimum absolute temperature drop is 0.399 oC giving the optimum CR of 2 at 100 W/m2 of heat flux. Results for 150 W/m2 of heat flux are plotted in Figure 44. Temperature drop due to pressure drop exceeds temperature drop due to convection at higher CR at heat flux of 150 W/m2. The optimum CR is found to be 1.1 at this heat flux at which minimum absolute temperature drop i.e. 0.487 oC is obtained. 7.2.1 Conclusion This analysis reveals that the optimization only gains a small fraction of a degree and practically it is not something that we need to strive for and this is why it was not observed in experiments. There is no practically optimum circulation rate since it is very small degree that we can optimize for. The circulation rate that we should operate at is the one that gives circulation rate more than one at the highest cooling load to avoid dry evaporation.

64


8. POTENTIAL IMPROVEMENTS In ice rink bed, heat is transferred from the top surface of the ice to the cold heat transfer fluid running in rink tubing. In case of copper tubes having plastic foil over it as rink tubing, there are four resistances in conduction heat transfer i.e. copper, plastic foil, concrete and ice. There are two possibilities to increase the heat transfer by reducing these resistances, one is to reduce the thickness of each resistance which is not possible due to technical reasons and other is to increase the thermal conductivities of each resistance material. Copper and ice are out of scope but it is possible to improve the thermal conductivities of plastic and concrete to reduce the resistance. It is shown below that how much benefit can be obtained in this regard. 8.1 Plastic Foil The plastic foil (polyethylene) around the copper tubes is 0.45 mm thick and it is not possible in manufacturing to decrease this thickness further. But thermal conductivity of the plastics can be boosted by incorporating some highly thermal conductive filler material into the plastic moulding compound. It has been shown that for polyethylene, thermal conductivities of 8.5 to 14 W/m.oC have been obtained, corresponding to temperatures of 120 to 320 oC respectively [Choy C.L., Luk W.H., and Chen F.C.; 1978]. The thermal conductivity of plastic foil used for the FEMLAB modelling was 0.33 W/m.oC and if this can be improved from 0.33 to 2 W/m.oC then there will be benefit which is shown Table 12.

Table 12: Effect of improvement in thermal conductivity of plastic foil

No. of Obs.

Thermal Conductivity of Foil

W/m.oC

Ice Surface Temperature

oC

Inner Tube Surface Temperature

oC

Bulk CO2 Temperature

oC 1 0.33 -4 -7.47 -7.77 2 1.00 -4 -7.23 -7.53 3 1.50 -4 -7.20 -7.50 4 2.00 -4 -7.18 -7.48

This analysis has done for 12.7 mm copper tube having plastic foil around it with a pitch of 100 mm for average heat flux of 100 W/m2. Circulation rate of 2 has been taken for convection heat transfer. It is obvious from the table 8 that if thermal conductivity of plastic foil is increased from 0.33 to 2 W/m.oC, then bulk CO2 temperature can be increased from -7.77 to -7.48 oC. At 100 W/m2, -7.48 oC of CO2 temperature is required to keep ice surface at -4 oC if thermal conductivity of plastic foil would be 2 W/m.oC. The effect of improvement in thermal conductivity of plastic foil is shown in Figure 45. It is clear from Figure 45 that there is big advantage in the region of 0.33 to 1 W/m.oC of thermal conductivity while from 1 to 2 W/m.oC of thermal conductivity range; only slight benefit can be obtained.

65


Effect of Improvement in Thermal Conductivity of Plastic Foil

-7.47

-7.23-7.2

-7.18

-7.77

-7.53-7.5

-7.48

-7.8

-7.7

-7.6

-7.5

-7.4

-7.3

-7.2

-7.10 0.5 1 1.5 2 2

Thermal Conductivity of Plastic Foil, W/m.oC

Tem

pera

ture

, oC

.5

Inner Tube Surface Temperature Bulk CO2 Temperature Poly. (Bulk CO2 Temperature) Poly. (Inner Tube Surface Temperature)

Figure 45: Effect of improvement in thermal conductivity of plastic foil Since it is not big gain hence there is need to look into analysis of the investment for improving thermal conductivity of the plastic foil from 0.33 to 2 W/m.oC that how much can be saved in regard to operational cost with the increase of evaporation temperature of 0.29 oC. 8.2 Concrete The thickness of the concrete above the copper tubes is 14.35 mm and there must be sufficient thickness of concrete above rink tubing to give strength to rink tubing against heavy resurfacing machines. Hence it is not possible to decrease thickness of concrete leaving the option to improve the conductivity of the concrete. In a research conducted in Material Laboratory of Institute for Research in Construction, National Research Council Canada to develop a new conductive concrete with both superior electrical and mechanical conductivity and mechanical properties. The principle behind it is the use of cement to bind together conductive materials such as carbon fibber, graphite and 'coke breeze' to make a continuous network of conducting pathway. These conductive materials are cheap by-product of steel production. The benefit of that conductive concrete is that it can be produced easily, without special equipment which has excellent mechanical and electrical conductivity properties [Emerging Construction Technologies; 2004].

66


The thermal conductivity of the concrete used for FEMLAB modelling was 1.8 W/m.oC. Let’s assume that conductive concrete has thermal conductivity of 4 W/m.oC then a range of 1.8 to 4 W/m.oC of thermal conductivity can give following benefit shown in Table 13.

Table 13: Effect of improvement in thermal conductivity of concrete No. of

Obs.

Thermal Conductivity of Concrete

W/m.oC


oC


oC


oC 1 1.80 -4 -7.47 -7.77 2 2.50 -4 -6.93 -7.22 3 3.25 -4 -6.61 -6.90 4 4.00 -4 -6.40 -6.69

This analysis has done for 12.7 mm copper tube having plastic foil around it with a pitch of 100 mm for average heat flux of 100 W/m2. Circulation rate of 2 has been taken for convection heat transfer. It is obvious from table 9 that by increasing thermal conductivity of concrete from 1.8 to 4 W/m.oC, bulk evaporation temperature can be increased from -7.77 to -6.69 oC which is a big gain. At 100 W/m2, -6.69 oC of CO2 temperature is required to keep ice surface at -4 oC if thermal conductivity of concrete would be 4 W/m.oC. The effect of improvement in thermal conductivity of concrete is shown in Figure 46.

Effect of Improvement in Thermal Conductivity of Concrete

-7.47

-6.93

-6.61

-6.4

-7.77

-7.22

-6.9

-6.69

-8

-7.8

-7.6

-7.4

-7.2

-7

-6.8

-6.6

-6.4

-6.2

-61.5 2 2.5 3 3.5 4 4.5

Thermal Conductivity of Concrete, W/m.oC

Tem

pera

ture

, oC

Inner Tube Surface Temperature Bulk CO2 Temperature Poly. (Bulk CO2 Temperature) Poly. (Inner Tube Surface Temperature)

Figure 46: Effect of improvement in thermal conductivity of concrete

67


On x-axis, there is thermal conductivity of concrete and on y-axis, there is bulk evaporation temperature. Both inner tube surface temperature and bulk evaporation temperature are increasing in same manner and magnitude with the increase of thermal conductivity of concrete. There is a gain of 1.08 oC of evaporation temperature if thermal conductivity of concrete is increased from 1.8 to 4 W/m.oC There is need to look into analysis of the investment for improving thermal conductivity of the concrete from 1.8 to 4 W/m.oC that how much can be saved in regard to operational cost with the increase of evaporation temperature of 1.08 oC. The thickness of concrete above copper tubes taken for this analysis is 14.35 mm which might be the minimum thickness of concrete above tubes. If thickness of the concrete can be maximum 25 mm above the tubes, then this gain will be more by improving the thermal conductivity of the concrete. The results for the analysis are shown in Table 14.

Table 14: Effect of improvement in thermal conductivity of thick concrete No. of

Obs.

Thermal Conductivity of Concrete

W/m.oC


oC


oC


oC 1 1.80 -4 -8.02 -8.32 2 2.50 -4 -7.32 -7.62 3 3.25 -4 -6.90 -7.19 4 4.00 -4 -6.63 -6.92

It is clear from Table 14 that there is a gain of 1.4 oC of evaporation temperature if thermal conductivity of concrete is increased from 1.8 to 4 W/m.oC

68


9. CONCLUSION This study reveals interesting results about use of copper tubes in ice rink applications. FEMLAB and EES are two computer tools found to be good for the design and analysis of such applications. The analysis, done on these two tools, shows that 21.3 mm steel pipe is better than 12.7mm copper tube with same pitch of 100 mm. The plastic pipe of 25 mm diameter is the worse. It is also important to keep in mind that the diameter of the copper tube is almost half the diameter of the steel pipe. The copper tube becomes better that steel pipe, if pitch of the copper tubes is reduced from 100 mm to 75mm. At rated heat flux of 100 W/m2, 12.7 mm copper tube having plastic foil with a pitch of 75 mm becomes 0.11 oC better than the 21.3 mm steel pipe. The analysis for thermal expansion and contraction of the copper tubes inside the concrete rink bed during operation is also conducted. This analysis reveals that there will be no danger of movement of copper tubes inside the rink bed during operation of the ice rink. The maximum movement has been recorded 0.7 mm for 12.7 mm copper tube with plastic foil. This movement is not critical for a temperature change of 20.42 oC for 10 m length of tube. The pressure drop analysis reveals that pressure drop in 9.5 mm copper tubes was almost 4 to 5 times higher than the pressure drop in 12.7 mm copper tubes at same CR and heat flux. If this pressure drop is converted into pump work then there is not big difference between both tubes. But at rated heat flux of 100 W/m2, 12.7 mm copper tube with plastic foil is 0.18 oC better than 9.5 mm copper tube with plastic foil in terms of heat transfer. There is also a natural trend to remain closer to steel pipe in terms of evaporating temperature; as steel pipe has been used with CO2 in ice rink applications. Due to these reason, 12.7 mm copper tube is better choice than 9.7 mm copper tube. !20 meter long copper tubes is a good choice. The pressure drop in 120 meter long tubes is not much. The temperature drop due to pressure drop in 120 meter long tubes is also not much. By selecting 120 meter long copper tubes instead of 60 meter long, it will reduce the header length to half as header can be placed on short side of the ice rink. It is also found that the average Friedel pressure drop model gave good approximation of pressure drop for CO2. It over predicted 20 to 25 % at lower CR and about 60 % at higher CR for 120 meter long and 12.7 mm diameter copper tubes. Heat transfer analysis shows that FEMLAB tool can be used for ice rink design. It gave ice surface temperature close to the real value. The calculated total temperature difference across the geometry was very close to the experimental one. It is also found that theoretically, the average heat flux is the driving force for the optimum pitch and the optimum circulation rate. Theoretically, at low average heat flux, the pitch must be as large as possible and at high average heat flux; the pitch must be as smaller as possible. Practically, absolute cost per year does not change much with the change of pitch. It will depend on the interest and conditions to go for smaller pitch than 100 mm. Within the tested range of CR values, its influence on heat transfer was found to be very small and the theoretical optimum value has insignificant practical importance. Therefore, CR should be kept constant at value that assures wet evaporation at the highest cooling load.

69


Thermal conductivity of plastic foil and concrete can be improved which will increase the evaporation temperature of CO2. There is need to look into analysis of the investment for improving thermal conductivity of the plastic foil and the concrete that how much can be saved in regard to operational cost with the increase of evaporation temperature of CO2.

70


10. REFERENCES Jörgen Rogstam; Samer Sawalha, Per-Olof Nilsson; 2005 ”Ice rink refrigeration system with CO2 as secondary fluid” IUC, Katrineholm, Sweden Travelocity; 1996-2005 “Dallas indoor ice rink” Available at dest.travelocity.com, as accessed 09-12-2005 PBase; 1999-2005 “Ice skating in City Park” Available at www.pbase.com, as accessed 09-12-2005 Los Tres Papagayos; 1999-2002 “Exhibition games, Tokyo, Japan, 1999” Available at www.portable-ice-rink.com, as accessed 09-12-2005 MSU Mavericks; 2005 “Midwest wireless civic centre opened in 1995” Available at www.msumavericks.com, last modified 06-12-2005, as accessed 09-12-2005 CAP; 2005 “Curling rink” Available at www.melitamb.ca, last modified 01-08-2005, as accessed 09-12-2005 Kathie Fry; 1999-2003 “A Yucatan roller rink and speed skating track” Available at www.skatelog.com, as accessed 09-12-2005 Sunway City Berhad; 1997-2005 “Malaysia’s first themed open atrium ice-skating rink” Available at www.sunway.com.my, as accessed 09-12-2005 ASHRAE; 1998 “ASHRAE Refrigeration Handbook” USA C. V. Bengle; 1956 ”Design of ice skating rink” Air Conditioning, Heating and Ventilation 53 (10), pp. 86-100 MacCracken, Clavin D.; 1974 “Engineering contributions to the ice rink industry” ASHRAE journal 16 (11), pp. 36-40 Fred Nilsson; 2005 Professor at Department of Solid Mechanics, KTH, Stockholm, Sweden Choy C.L., Luk W.H., and Chen F.C.; 1978 “Thermal Conductivity of Highly Oriented Polyethylene, Polymer” Vol. 19, pp. 155-162 Emerging Construction Technologies; 2004 “Conductive Concrete” Available at http://www.new-technologies.org, last modified 06-12-2004, as accessed 23-01-2006 Hewitt, G.F; 1998 “Heat Exchanger Design Handbook, Part 2” Begell House, Inc., NY, ISBN: 1-56700-094-0

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Reiberer, R.; 1998 “CO2 as Working Fluid for Heat Pumps” Doctoral Thesis at faculty of Mechanical Engineering, Graz University of Technology, Graz, December Eric Granryd, Björn Palm; 2005 “Refrigerating Engineering” Department of Energy Technology, Division of Applied Thermodynamics and Refrigeration, Royal Institute of Technology, KTH, Sweden Outokumpu Copper Products AB; 2005 Västrås, Sweden

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APPENDIX I Analysis for Movement of Each Copper Tube inside Rink Bed 12.7 mm Copper Tubes with Plastic Foil Following is the analysis for 12.7 mm copper tube having plastic foil over it.

Table 15: Results for 12.7 mm copper tube with plastic foil

No. of Obs.

Time

hours

Tube Temperature

oC

Pressure in the Tube bar

Distance Between Two

Reference Points mm

Movement of the Tube

mm

1 0 10.90 24.90 75.00 0.0 2 26 -9.28 27.03 74.30 -0.70 3 92 12.10 25.68 74.40 -0.60 4 116 -9.73 26.69 74.35 -0.65

If we analyze the Table 15, then it is clear that maximum contraction in 12.7 mm copper tube with plastic foil was 0.7 mm during this period of analysis. The theoretical contraction in this tube must be more if the tube is free and is not covered by concrete.

mL 10=CT 042.20=Δ 18.16 −= Coα

The change in length can be calculated by the relation of thermal expansion:

TLL Δ∗∗=Δ α

42.2010108.16 6 ∗∗×=Δ −L mmmL 4.30034.0 ==Δ Theoretically, copper tube must contract 3.4 mm but it was contracted 0.7 mm due to fully covered in the concrete. Here one correction must be made. If we carefully look at the Figure 27, then it will be clear that small length of the tube was outside of the concrete which was included in this analysis. Concrete was not effecting on this small length of tube so contraction in this part must be deduced from the measured value. mmmL 6.1651656.0 ==

CT o42.20=Δ 18.16 −= Coα

Hence, TLL Δ∗∗=Δ α 42.201656.0108.16 6 ∗∗×=Δ −L

73


mmL 057.0=Δ Finally, the maximum movement of 12.7 mm copper tube with plastic foil was found 0.643 mm inside the ice rink bed. 12.7 mm Copper Tubes without Plastic Foil Following is the analysis for 12.7 mm copper tube without plastic foil.

Table 16: Results for 12.7 mm copper tube without plastic foil

No. of Obs.

Time

hours

Tube Temperature

oC



Reference Points mm


mm

1 0 9.80 25.03 71.55 0.0 2 26 -9.35 26.98 71.45 -0.10 3 92 12.50 25.44 71.60 +0.05 4 116 -10.02 26.47 71.55 0.0

If we analyze the Table 16, then it will be evident that maximum contraction in 12.7 mm copper tube without plastic foil was 0.1 mm during this period of analysis. Theoretically, contraction in this tube should be:

CT o35.19=Δ This temperature difference produces:

mmmL 25.300325.0 ==Δ

But copper tube did not contract as much because it was fixed in the concrete. Now the effect of free length of copper tube must be deduced from the observed value. The length of this small part of tube is: mmmL 15.15715715.0 == This gives, mmL 051.0=Δ Finally, the maximum movement of 12.7 mm copper tube without plastic foil was found 0.049 mm inside the ice rink bed. 9.5 mm Copper Tubes with Plastic Foil Following is the analysis for 9.5 mm copper tube having plastic foil over it.

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Table 17: Results for 9.5 mm copper tube with plastic foil

No. of Obs.

Time

hours

Tube Temperature

oC


Distance between Two

Reference Points mm


mm

1 0 9.70 25.30 109.95 0.0 2 26 -9.20 27.11 109.30 -0.65 3 92 12.40 25.15 109.60 -0.35 4 116 -9.45 26.90 109.45 -0.50

Form Table 17, it is obvious that maximum contraction in 9.5 mm copper tube with plastic foil was 0.65 mm during this period of analysis. Theoretically, contraction in this tube should be:

CT o50.19=Δ This temperature difference causes, mmmL 28.300328.0 ==Δ But copper tube did not contract as much because it was fixed in the concrete. Now the effect of free length of copper tube must be deduced from the observed value. The length of this small part of tube is: mmmL 3.1721723.0 == This yield, mmL 056.0=Δ Finally, the maximum movement of 9.5 mm copper tube with plastic was found 0.594 mm inside the ice rink bed. 9.5 mm Copper Tubes without Plastic Foil Following is the analysis for 9.5 mm copper tube without plastic foil.

Table 18: Results for 9.5 mm copper tube without plastic foil

No. of Obs.

Time

hours

Tube Temperature

oC



Reference Points mm


mm

1 0 9.80 25.24 79.40 0.0 2 26 -8.44 27.68 79.35 -0.05 3 92 12.50 25.54 79.45 +0.05 4 116 -9.58 26.80 79.40 0.0

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Form Table 18, it is obvious that maximum contraction in 9.5 mm copper tube without plastic foil was 0.05 mm during this period of analysis. Theoretically, contraction in this tube should be:

CT o49.19=Δ This temperature difference produces, mmmL 27.300327.0 ==Δ But copper tube did not contract as much because it was fixed in the concrete. Now the effect of free length of copper tube must be deduced from the observed value. The length of this small part of tube is mmL 65.152= This yield, mmL 049.0=Δ Finally, the maximum movement of 9.5 mm copper tube with plastic was found 0.001 mm inside the ice rink bed.

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APPENDIX II Programs Written in EES EES Model for Convective Heat Transfer inside Copper Tubes q_flux=100 T_tube_surf=-12.62 L_loop_tube=120 W_loop=0.1 A_loop=L_loop_tube*W_loop L_tube=120 L_curves=0.5 L_pipe=L_tube+L_curves L_rink=10 W_rink=5.5 A_tot=L_rink*W_rink d_tube_mm=12.7 d_tube=d_tube_mm*convert(millimeter, meter) d_conv_mm=11.1 d_conv=d_conv_mm*convert(millimeter, meter) Q_dot_tot=q_flux*A_tot*convert(W, kW) P_sat=P_sat(CarbonDioxide,T=T_tube_surf) CR=2 Q=q_flux*A_loop*convert(W, kW) q_flux_tube*convert(W/m^2, kW/m^2)=Q/A_tube_surf A_tube_surf=pi*d_tube*L_pipe A_tube_inner=pi*d_conv*L_pipe m_dot_ce=Q/(h_sat_vap-h_sat_liq) h_sat_liq=ENTHALPY(carbondioxide,P=P_sat,x=0) h_sat_vap=ENTHALPY(carbondioxide,P=P_sat,x=1) m_dot_r=CR*m_dot_ce V_dot_r=m_dot_r/rho_liq rho_liq=DENSITY(carbondioxide,x=0,P=P_sat) w_liq=V_dot_r/A_tube A_tube=(pi*d_tube^2)/4 h_latent=h_sat_vap-h_sat_liq

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Q=CR*m_dot_ce*(h_out-h_sat_liq) x=(h_out-h_sat_liq)/(h_sat_vap-h_sat_liq) Nus=1.1e-3*Re_liq*Kf^0.5*0.85 Kf=(dx*h_latent*convert(kJ/kg, j/kg))/(L_pipe*a_ga) a_ga=9.81 Re_liq=(4*m_dot_r)/(pi*d_conv*mu_liq) mu_liq=VISCOSITY(carbondioxide,P=P_sat,x=0) dx=x Nus=alpha*d_conv/k k=CONDUCTIVITY(carbondioxide,P=P_sat,x=0) Q*convert(kW, W)=alpha*A_tube_inner*(T_tube_surf-T_evap) DELTAT=T_tube_surf-T_evap EES Model for Average Friedel Pressure Drop q_flux=300 T_evap=-14.83 L_loop=120 W_loop=0.1 A_loop=L_loop*W_loop L_tube=120 L_curves=0.5 L_connect=1 L_pipe=L_tube+L_curves+L_connect L_rink=10 W_rink=5.5 A_tot=L_rink*W_rink d_mm=11.1 d=d_mm*convert(millimeter, meter) Q_dot_tot=q_flux*A_tot*convert(W, kW) P_sat=P_sat(carbondioxide,T=T_evap) CR=1.5 Q=q_flux*A_loop*convert(W, kW) m_dot_ce=Q/(h_sat_vap-h_sat_liq) h_sat_liq=ENTHALPY(carbondioxide,T=T_evap,x=0) h_sat_vap=ENTHALPY(carbondioxide,T=T_evap,x=1) m_dot_r=CR*m_dot_ce

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V_dot_r=m_dot_r/rho_liq w_liq=V_dot_r/A_tube A_tube=(pi*d^2)/4 Q=CR*m_dot_ce*(h_out-h_sat_liq) x=(h_out-h_sat_liq)/(h_sat_vap-h_sat_liq) DELTAP_liq=f_liq*rho_liq*w_liq^2*(L_pipe/d)/1000 f_liq=0.5/(0.79*ln(Re_liq)-1.64)^2 Re_liq=(4*m_dot_r)/(pi*d*mu_liq) Turb=Re_liq/2300 mu_liq=VISCOSITY(carbondioxide,T=T_evap,x=0) rho_liq=DENSITY(carbondioxide,T=T_evap,x=0) mu_vap=VISCOSITY(carbondioxide,T=T_evap,x=1) rho_vap=DENSITY(carbondioxide,T=T_evap,x=1) DELTAP_tp=DELTAP_liq*phi_l phi_l=E+((3.23*F*H)/(Fr^0.045*We^0.0335)) E=(1-x)^2+x^2*((rho_vap*f_vap)/(rho_liq*f_liq)) f_vap=0.5/(0.79*ln(Re_vap)-1.64)^2 Re_vap=(4*m_dot_r)/(pi*d*mu_vap) F=x^0.78*(1-x)^0.224 H=(rho_liq/rho_vap)^0.91*(mu_vap/mu_liq)^0.19*(1-(mu_vap/mu_liq))^0.7 Fr=(m_dot_r/A_tube)^2/(9.81*d*rho_H^2) rho_H=1/((x/rho_vap)+((1-x)/rho_liq)) We=((m_dot_r/A_tube)^2*d)/(rho_H*segma) segma=SURFACETENSION(carbondioxide,T=T_evap) DELTAP_av_Fr=(DELTAP_tp+DELTAP_liq)/2 EES Model for Average Homogeneous Pressure Drop q_flux=136 T_evap=-8.86 L_loop=120 W_loop=0.1 A_loop=L_loop*W_loop L_tube=120 L_curves=0.5 L_connect=1 L_pipe=L_tube+L_curves+L_connect L_rink=10 W_rink=5.5 A_tot=L_rink*W_rink

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d_mm=11.1 d=d_mm*convert(millimeter, meter) Q_dot_tot=q_flux*A_tot*convert(W, kW) P_sat=P_sat(carbondioxide,T=T_evap) CR=1.67 Q=q_flux*A_loop*convert(W, kW) m_dot_ce=Q/(h_sat_vap-h_sat_liq) h_sat_liq=ENTHALPY(carbondioxide,T=T_evap,x=0) h_sat_vap=ENTHALPY(carbondioxide,T=T_evap,x=1) m_dot_r=CR*m_dot_ce V_dot_r=m_dot_r/rho_liq w_liq=V_dot_r/A_tube A_tube=(pi*d^2)/4 Q=CR*m_dot_ce*(h_out-h_sat_liq) x=(h_out-h_sat_liq)/(h_sat_vap-h_sat_liq) DELTAP_liq=f_liq*rho_liq*w_liq^2*(L_pipe/d)/1000 f_liq=0.5/(0.79*ln(Re_liq)-1.64)^2 Re_liq=(4*m_dot_r)/(pi*d*mu_liq) Turb=Re_liq/2300 mu_vap=VISCOSITY(carbondioxide,T=t_evap,x=1) rho_vap=DENSITY(carbondioxide,T=t_evap,x=1) mu_liq=VISCOSITY(carbondioxide,T=t_evap,x=0) rho_liq=DENSITY(carbondioxide,T=t_evap,x=0) DELTAP_hm=f_1_H*rho_H*w_H^2*(L_pipe/d)/1000 f_1_H=0.5/(0.79*ln(Re_H)-1.64)^2 Re_H=(4*m_dot_r)/(pi*d*mu_H) mu_H=1/((x/mu_vap)+((1-x)/mu_liq)) rho_H=1/((x/rho_vap)+((1-x)/rho_liq)) m_dot_r=w_H*A_tube*rho_H DELTAP_av_hm=(DELTAP_hm+DELTAP_liq)/2

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an ice rink refrigeration system based on co as … rink co2+cu_tube thesis... · an ice rink...

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