FACULTY OF ENGINEERING AND SUSTAINABLE DEVELOPMENT
Department of Building, Energy and Environmental Engineering
Energy Losses Study on District Cooling Pipes
Steady-state Modeling and Simulation
Marius Alexandru Calance
2014
Master’s Degree Thesis, D Level, 30 Credits Energy Systems
Master Program in Energy Systems
Supervised by Jan Akander and Mathias Cehlin Examiner: Taghi Karimipanah
1
Abstract
Distribution losses are a very important factor in district energy systems. By optimizing the losses in such a system, both economical and environmental aspects can be fulfilled.
Unfortunately, there is few information regarding losses for district cooling systems. This
study focuses on losses in district cooling networks by using both R-network and FEM
simulation models. A R-network model composed of thermal conductances has been
developed through analytical equations and simulations have been performed for valida-
tion. Afterwards, an in-progress construction project of a district cooling network from
the city of G¨avle, Sweden, is analyzed. The assessment consists of 15 pipe diameters in
three configurations (two symmetric cases and one asymmetric), at three ground laying
depths (0.8, 2 and 4 meters) for a duration of 7 months (April to October). A particular
case in which the main distribution pipes from and to the plant are submerged in the city’s
river for a distance of 1 km is investigated in order to estimate the temperature increase of
the supply water. A maximum cooling loss below 2% of the total delivered energy dur-
ing the season for any network configuration resulted from the calculation. Finally, the
mixed pipes array seems to be a feasible investment both economically and technically
but it cannot be used for the entire network spread since a part of the network has been
already built with the non-insulated plastic pipes. The R-network model proved to be ef-
fective and reliable in the analysis which provides confidence that it can serve as a solid
foundation for a calculation tool - primarily for design purposes and also for estimating
energy loss.
Sammanfattning
Distributionsf¨orluster ¨ar en viktig faktor i fj¨arrenergisystem. Genom att optimera f¨orluster i s˚adana system, kan b˚ade ekonomiska och milj¨om¨assiga aspekter uppfyllas.
Tyv¨arr finns det ringa information om r¨orf¨orluster i fj¨arrkylasystem. F¨oreliggande studie
fokuserar p˚a f¨orluster i ett fj¨arrkylan¨at genom att b˚ade anv¨anda ett R-n¨atverk och FEM
simuleringsmodeller. Ett R-n¨atverksmodell best˚aende av termiska konduktanser har utveck-
lats genom analytiska ekvationer och simuleringar med FEM har utf¨ort f¨or validering av
modellen. D¨arefter har ett fj¨arrkylan¨atverk som konstrueras i G¨avle, analyserats. Un-
ders¨okningen omfattar 15 olika r¨ordiametrar i tre utf¨oranden (dubbelr¨or med tv˚a sym-
metriska och en osymmetrisk v¨armeisolering) och i tre f¨orl¨aggningsdjup (0,8; 2 och 4 me-
ter) f¨or en s¨asong om 7 m˚anader (April t o m Oktober). S¨arskilt utreds ¨okningen av tem-
peraturen hos framledningsmediet, d¨ar matningsr¨oren f¨orlagts i en ˚a mitt i staden om en
str¨acka av 1 km. Den maximala f¨orlusten under s¨asongen, bland alla r¨orkonfigurationer,
motsvarar 2% av den totala levererade energin. Slutligen konstateras att kombinationen
av isolerade framledningsr¨or och oisolerade returr¨or verkar som en g˚angbar investering,
ekonomiskt och tekniskt, men kan inte anv¨andas i hela n¨atet eftersom stora delar har
redan byggts med oisolerade plastr¨or. R-n¨atverksmodellen, som visades vara effektiv
och p˚alitlig i unders¨okningen, kan som ber¨akningsverktyg, framf¨orallt f¨or dimensioner-
ing och f¨or att uppskatta energif¨orluster.
Acknowledgments
This work has been done for FVB Sverige AB and G¨avle Energi AB in the purpose of discovering new methods and/or ways of improving the piping networks in order to have a more efficient distribution of the coolant in district cooling networks.
I would like to thank Stefan Jonsson from FVB AB for the opportunity, Jan Akander for
the solid analytical input, Mathias Cehlin for the theoretical support, Roland Forsberg for
putting me in touch with the company, as well as Bengt Rinne from G¨avle Energi AB for
the technical guidance.
Contents
1 Introduction 15
1.1 Energy use . . . 15
1.2 Solutions for cooling . . . 17
1.2.1 Vapour-Compression Chillers . . . 17
1.2.2 Absorption Chillers . . . 17
1.2.3 Deep Lake Water Cooling . . . 18
1.2.4 Ice Slurry . . . 18
1.2.5 Thermal storage . . . 19
1.2.6 Distribution . . . 19
1.3 G¨avle Energy and FVB . . . 20
2 Aim and scope 23 3 Theory 25 3.1 District heating and cooling pipes . . . 25
3.1.1 Types of pipes for district energy . . . 25
3.1.2 Standards . . . 27
3.2 Models and methods . . . 28
3.2.1 Steady-state and dynamic calculations . . . 28
3.2.2 Models from literature . . . 28
3.2.3 Finite element method . . . 29
3.3 District Cooling in G¨avle . . . 29
3.3.1 System layout . . . 29
3.3.2 Pipes used . . . 30
3.3.3 G¨avle climate and river data . . . 32
4 Method 35 4.1 Building COMSOL Multiphysics r model . . . 35
4.2 Calculation and COMSOL Multiphysics r . . . 37
4.2.1 Case 1: Non-insulated plastic pipes . . . 37
4.2.2 Case 2: Insulated plastic pipes . . . 42
4.2.3 Case 3: Insulated supply pipe and non-insulated return pipe . . . 43
4.2.4 Cooling loss calculation . . . 45
4.3 R-network . . . 46
4.3.1 Motivation why - design purposes . . . 47
4.3.2 Equations . . . 48
4.3.3 Validation of R-network . . . 52
4.4 Temperature change over distance . . . 52
5 Results 57 5.1 Results from use of the models . . . 57
5.2 COMSOL vs R-network . . . 60
5.3 Insulated/non-insulated/mixed pipes . . . 61
5.4 Pipes in the river . . . 70
6 Discussion 71 6.1 Models . . . 71
6.1.1 Validity . . . 71
6.1.2 Limitations . . . 71
6.2 Insulated/non-insulated/mixed pipes . . . 72
6.3 Do we need insulation? . . . 72
6.4 Future research . . . 72
7 References 75 8 Appendix 79 8.1 Figures . . . 79
8.2 Plots . . . 99
List of Figures
1 District cooling delivery in Sweden, 1992-2013 (from Svensk Fj¨arrv¨arme) 15 2 Cooling delivery and total network length in Sweden, 1996-2013 (from
Svensk Fj¨arrv¨arme) . . . 16
3 Elements of a district cooling system . . . 19
4 District heating pipe system . . . 25
5 Triple service pipe . . . 26
6 Network array and branches lengths (used with FVB permission) . . . 30
7 Network array and sections dimensions (used with FVB permission) . . . 32
8 Model boundary conditions in COMSOL . . . 36
9 Heat source input . . . 38
10 Internal boundaries settings . . . 38
11 External boundaries settings . . . 39
12 Model after solving . . . 40
13 Boundary integration . . . 40
14 Point evaluation . . . 42
15 Boundary integration by quadrants . . . 44
16 Thermal network illustration of the heat paths through the model . . . 46
17 An example of calculations made to determine the conductances (the up- per half of the figure) and simulation with chosen temperatures. . . 48
18 500 mm diameter plastic pipe installed in the river - picture 1 (used with FVB permission) . . . 52
19 500 mm diameter plastic pipe installed in the river - picture 2 (used with FVB permission) . . . 53
20 Convective heat transfer coefficient for water (derived from equations [18]) 54 21 Losses by monthly average external temperature at 0.8m . . . 61
22 Losses by monthly average external temperature at 2m . . . 62
23 Losses by monthly average external temperature at 4m . . . 63
24 Ratio between pipe diameter and insulation thickness . . . 64
25 Losses at 0.8m depth for all three cases . . . 64
26 Losses at 2m depth for all three cases . . . 65
27 Losses at 4m depth for all three cases . . . 65
28 Losses by depth for non-insulated pipes . . . 65
29 Losses by depth for insulated series 1 pipes . . . 66
30 Losses by depth for mixed-pipes array . . . 66
31 Losses by external temperature variation for φ110 mm non-insulated plastic pipes at three different depths . . . 67
32 Losses by external temperature variation for φ110 mm insulated series 1 plastic pipes at three different depths . . . 67
33 Losses by external temperature variation for φ110 mm mixed plastic pipes at three different depths . . . 67
34 Temperature gradient for each of the three cases . . . 68
35 Conductances variation in all three cases at 2m depth for φ110mm . . . . 69
36 Temperature in the supply pipe related to river temperature . . . 70
37 Temperature in the return pipe related to river temperature . . . 70
38 Dimensions for insulated plastic pipes used in the network (From KWH - Wehoarctic catalogue) . . . 79
39 Dimensions for plastic pipes used in the network (From Uponor catalogue) 80 40 Instructions for ground pipe installation - distances (used with FVB per- mission) . . . 81
41 500 mm diameter plastic pipe along the river, starting from the plant - picture 1 (used with FVB permission) . . . 82
42 500 mm diameter plastic pipe along the river - picture 2 (used with FVB permission) . . . 83
43 Water temperature of G¨avle river for one year (image from Capital Cool-
ing Technical Study) . . . 91
List of Tables
1 Pipe lengths by diameter in the network . . . 31
2 Already built sections of the network . . . 31
3 Monthly outdoor average temperature . . . 33
4 Monthly average water temperature . . . 33
5 Thermal conductivities and other parameters . . . 36
6 Calculation parameters . . . 55
7 Average seasonal cooling losses classed per pipe diameter in [W/m] . . . 57
8 Seasonal cooling losses in different configurations of the network in MWh 58 9 Seasonal cooling losses in different configurations of the network in MWh 59 10 Percentage of losses in different network configurations compared to en- ergy delivery . . . 59
11 Differences between models for several diameters of non-insulated pipes
at 0.8m depth . . . 60
12 Variation of the conductances in all three cases for φ100 mm at 2m depth 69
Nomenclature
Φ e – External heat flow [W/m]
Φ g – Ground heat flow [W/m]
Φ s – Supply pipe heat flow [W/m]
Φ r – Return pipe heat flow [W/m]
Φ sm – Supply to mean heat flow [W/m]
Φ rm – Return to mean heat flow [W/m]
Φ sr – Supply to return heat flow [W/m]
Φ esm – Heat flow for the supply side, external to mean temperature point [W/m]
Φ smg – Heat flow for the supply side, mean temperature point to ground [W/m]
Φ erm – Heat flow for the return side, external to mean temperature point [W/m]
Φ rmg – Heat flow for the return side, mean temperature point to ground [W/m]
Λ s – Supply pipe conductance [W/m·K]
Λ r – Return pipe conductance [W/m·K]
Λ sm – Conductance of the supply pipe to mean point [W/m·K]
Λ rm – Conductance of the return pipe to mean point [W/m·K]
Λ sr – Supply to return pipe conductance [W/m·K]
Λ es – External point to supply pipe conductance [W/m·K]
Λ gs – Supply pipe to ground conductance [W/m·K]
Λ gr – Return pipe to ground conductance [W/m·K]
Λ esm – External to mean point on the supply side conductance [W/m·K]
Λ smg – Mean point to ground on the supply side conductance [W/m·K]
Λ erm – External to mean point conductance on the return side [W/m·K]
Λ rmg – Mean point to ground conductance on the return side [W/m·K]
Λ pipe – Supply plastic pipe conductance [W/m·K]
T w – Temperature of the water from the river [ o C]
T g – Temperature in the ground (at 10m depth) [ o C]
T e – Outdoor temperature [ o C]
T s – Temperature of the fluid in the supply pipe [ o C]
T r – Temperature of the fluid in the return pipe [ o C]
T sm – Temperature of the mean point on the supply side [ o C]
T rm – Temperature of the mean point on the return side [ o C]
D – Outer diameter of the pipe [m]
d – Inner diameter of the pipe [m]
d y – Outer diameter of the pipe [m]
d i – Inner diameter of the pipe [m]
Q – Heat source inside the pipe [W/m 3 ]
˙
m – Mass flow rate of fluid [kg/s]
L – Pipe length [m]
k g – Thermal conductivity of the ground [W/m·K]
k i – Thermal conductivity of the insulation [W/m·K]
k p – Thermal conductivity of the plastic [W/m·K]
α i – Convective heat transfer coefficient inside the pipe [W/m 2 ·K]
α y – Convective heat transfer coefficient outside the pipe [W/m 2 ·K]
v i – Flow velocity of the fluid inside the pipe [m/s]
v y – Flow velocity of the river outside the pipe [m/s]
A – Cross-sectional area of the pipe [m 2 ]
ρ – Mass density of the fluid [kg/m 3 ]
x – Distance/length [m]
1 Introduction
1.1 Energy use
A way of facing the environmental and energy challenges is the smart and efficient use of energy, that includes reusing energy waste and using low-carbon fuels [1]. District heating and cooling or also called district energy can provide efficiency, environmental and economic advantages both to the communities and energy consumers [1] [2]. It is very important to have an efficient way of tranportation of heating and cooling in urban settlements. In this way, a lower use of resources can be met in analogy with a conven- tional heat and cold supply. like boilers and air conditioners [2].
In a district cooling network the cold is delivered to the consumer by a distribution grid constituted from pipes (which are the carriers). Usually the distribution system has two pipes laying side by side which then serve through connections, the buildings/consumers.
District energy systems have been used in Europe since the 14th century, with one of the very first district heating systems still operating today in France (Chaudes-Aigues thermal station). The main users of the district energy systems in Europe are the North- ern European countries but this type of system has been increasingly used in Germany, Netherlands, Belgium and several other countries as well in the last decade [1] [3].
0 100 200 300 400 500 600 700 800 900 1000
1992 1993 1994 1995
1996 1997 1998
1999
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
GWh
During the past few years the big demand of district cooling increased rapidly in Eu- rope, even in Sweden where a colder climate is present given the country’s upper northern latitude [4]. Stockholm’s district cooling network (operated by Fortum V¨arme) for exam- ple, is by far the largest in Sweden in terms of number of consumers and delivery (cca.
426 GWh) [5]. There are several other cities that are currently using district cooling in Sweden and this pursued to a considerable increase during the last two decades in both cooling delivery and network length across the country (Figure 1 and Figure 2).
-‐50 50 150 250 350 450 550
0 100 200 300 400 500 600 700 800 900 1000
1996 1997
1998 1999
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
km
GWh
Delivery Network Length
Figure 2: Cooling delivery and total network length in Sweden, 1996-2013 (from Svensk Fj¨arrv¨arme)
Energy losses are a consequence of circulating the cooling through pipes. Hence, by determining the losses for district cooling pipes, a view upon the performance of the system will be given as mentioned in [6], though for district heating applications. While for district heating networks the temperature difference between supply and return is normally between 40 to 50 o C, in district cooling networks the difference is much lower (around 10 o C). Consequently, a larger pipe section is needed for the same amount of energy distributed, a thing that increases the cost of the investment when compared to a district heating network [7].
16
1.2 Solutions for cooling
In district cooling plants the chilled water/coolant can be produced through different machinery which the majority of them are described next.
1.2.1 Vapour-Compression Chillers
Vapour-compression chillers are driven by turbines, electricity and alternative engines.
The most usual chiller used in central chilled water stations is the centrifugal compressor (driven by electricity). Most mechanical chillers use ammonia, R22, R-123 or R134a.
Because of their high global warming potential, R22 and R134a could be phased out in the future. At the moment, R22 has a limit of time use set for the year 2015 [8].
1.2.2 Absorption Chillers
By the source of energy used, absorption chillers can be divided in two major categories:
indirect fired and direct fired. When this type of chiller is used as an integrated part of a chilled water production system, in general, indirect fire units are adopted because of their capacity of utilize waste and excess heat available.
The absorption chillers have few advantages over the vapour-compression machines:
- ability to use recovered heat and convert it to cooling energy;
- lower electrical requirements for the unit’s operation;
- reduced vibration and sound levels when operating;
- the solutions used as refrigerant do not affect the ozone layer.
Two of the most used absorption systems available in commercial chillers are Aqueous
Ammonia and LiBr (Lithium Bromide) - Water solutions. For the latter one, water is the
refrigerant and for the Ammonia - Water, ammonia is the refrigerant. The minimum water
temperature a LiBr machine can deliver is 4 o C and the ammonia water-based solution
below 0 o C, depending on the heat input temperature level [8].
1.2.3 Deep Lake Water Cooling
It is also named ”free cooling” and defines the ability of a large physical body to natu- rally behave as a heat sink or a source of low temperature. This occurs in areas where the climatic conditions are favorable and this allows the water temperature to drop to a somewhat low level. At this point the water can be extracted and it’s cooling energy used, after which, the water would be returned to the source. The chilled water from the lakes can be used directly in cooling systems for buildings and indirectly by supplying cooling energy via heat exchangers to chilled water systems.
In the Stockholm area, Sweden, there are several already built projects that use both salt water and fresh water lakes. The systems are indirectly connected through heat exchang- ers to the district cooling networks.
It is obvious the major advantage this solution brings because of the capacity to re- duce many kWh of electricity consumed in the machinery operation and minimizing the amount of refrigerant used. However, the impact of the warmer return water on the ecosystem in the area must be taken into consideration [8].
1.2.4 Ice Slurry
An ice slurry cooling system is a rather new cooling method that requires ice slush pro- duction at a plant. Ice slurry is a mixture of a liquid (that can be pure water or a water- based solution that prevents the mixture from freezing) and ice crystals that is pumped into the network. There are few different ways to produce ice for cooling systems and such devices are producing it like so, according to [9]: - water spraying into cold gas or other fluid medium; - cyclic freezing and thawing of an evaporator surface; - evap- oration of the freezing point depressing alcohol; - super cooling of water and sudden bulk nucleation of ice crystals. The most common solutes used in industry are propylene glycol, sodium chloride, ethanol and ethylene glycol which are used in different percent- ages [8] [9].
The main advantage of this type of cooling system is the high energy transport and stor-
18
age density of the ice slurry; its large number of particles creates a big heat transfer surface area. When used for thermal storage, an ice slurry system can use a tank as small as 1/10 of an equivalent chilled water system, with the same cooling capacity [9].
1.2.5 Thermal storage
Thermal storage systems are used in district cooling configurations for reducing the chillers’ requirements and operating costs. This can be achieved by producing the chilled water/mixture during the night when the electricity is cheaper (off-peak hours), store it and then using it to partly shift the cooling load during daytime when peak hours occur.
In district cooling systems, both water and ice storage solutions are common. The chilled water storage system is limited to a 4 o C temperature while the ice mixture system to 0.5 - 1 o C, but special refrigeration equipment is necessary (for operating below 0 o C) [8] [9].
1.2.6 Distribution
The cooling network combines the needs of the all the consumers, aggregates the loads
and then is serving the customers with chilled water from a central plant (Figure 3). The
cooling energy that can come from a variety of sources is delivered to customers through
a dedicated pipe network to cool the spaces in demand. The consumers are connected to
the distribution system via a heat exchanger or a direct connection.
Usually the pipe network is laying in the ground, but depending on its spread and layout it can also have branches mounted at the surface - having direct contact with the outdoor conditions - or in the water of a river or lake. The chilled water is commonly delivered through pairs of single pipes and twin pipes (insulated or not), depending on the energy need.
There are two main motivations for minimizing distribution losses.
• The first is the temperature increase in the supply; an increased temperature will affect the designed cooling capacity for the consumers. In other words, the cooling potential is reduced when the temperature increases. Another problem is the influence of the outdoor temperature variation on the supply temperature. In order to compensate for the increased supply temperature, more chilled water has to be supplied to meet the demand, therefore more energy for circulating the water (i.e pump energy) is required.
• The second is that more cooling energy has to be supplied to the system to maintain the desired system temperatures. This translates into a higher primary energy consumption.
Altogether, the type of pipes used, installation environment along with external factors and pipe dimensions are affecting the losses in the distribution system of a district cool- ing network.
1.3 G¨avle Energy and FVB
G¨avle Energi AB is the producer and supplier of energy (district heating and cooling, electricity) in the G¨avle area as well as the maintainer of the networks. G¨avle Energi pro- duces energy from biomass and wood waste which reduces the carbon footprint and has a reduced impact on the environment [10]. The role of G¨avle Energi in this project is the production and delivery of the chilled water to the consumers at the designed parameters and the maintenance of the system.
FVB Sverige AB is an international Swedish company which offers professional energy consultancy to their clients. With offices in countries like Canada, Bahrain, United States
20
and Sweden, FVB is involved in projects of Heating, Cooling, Combined Heat and Power and Processes [11]. In this particular project the office in G¨avle is closely involved in the building stages of the network, having its input in both technological and economic docu- mentation. Both FVB and G¨avle Energi are deeply involved in this particular project and the partnership is based on great collaboration and communication between the teams.
The cooling plant in the project is located near to the bay, in the East side of the G¨avle
city. Given the location of the cooling plant, the main pipes that connect it with the rest
of the network had to be submerged in the water of G¨avle river. While the chilled water
is delivered through a system very similar with the one shown in Figure 3, the submerged
pipes are a concern for cooling loss during summer due to high temperature of the river,
which makes one of the points of interest of this paper.
2 Aim and scope
The main focus of this study was to analyze the influence of different parameters such as external temperature, pipe material and ground properties upon district cooling networks as well as determining the cooling loss. A numerical model based on thermal conduc- tances has been developed along with simulations for verification. Fifteen pipe diameters were evaluated with range between 75 and 500 mm in three different cases: non-insulated plastic pipes, insulated series 1 plastic pipes and insulated supply with non-insulated re- turn plastic pipes. Also a particular case for the water submerged 500 mm plastic pipes has been assessed.
A numerical method has been developed and simulations were performed in order to de-
termine the cooling losses in the distribution network. Formulas have been used in the
analytical part for quantification of its parameters, while the simulations were conducted
with a finite element program for verification. In this paper only single pipes that are
designed for the existing network were considered. The total length of the network is
about 5.9 km which consists of the 15 pipe diameters mentioned above. The case studied
is a real project in progress in the city of G¨avle, Sweden, which is intended to serve both
commercial and residential customers.
3 Theory
3.1 District heating and cooling pipes
3.1.1 Types of pipes for district energy
In district energy networks there are used different types of pipes, based on diameter, area served, delivery or medium of installation. Pipes with typical usage in distribution systems for district energy networks are: pairs of single pipes, twin horizontal pipes side by side integrated in a circular insulation case and twin vertical pipes which can be depicted in Figure 4. Also, triple pipes are used as service pipes which are shown in Figure 5. Due to hydraulics advantages of circulating fluids in circular pipes, the common pipes have annular geometry. The outer casing of the pipes however - for the insulated ones - can have other geometry than the one of the inner pipe, such as the egg-shape (Figure 4D). This type of pipe is used more often in district heating applications due to a higher efficiency when compared to single or twin pipes [12]. For district cooling applications pairs of single pipes and twin pipes are the frequent choice, the latter one being used in situations in which the diameter permits.
Figure 4: District heating pipe systems 1 : a) Pair of single pipes; b) Horizontal twin pipe;
c) Vertical twin pipe; d) Egg-shaped twin pipe. The boxes around the pipes indicate the
size of the trench
Figure 5: Triple service pipe in 4 versions: 2 a) even forward pipe dimensions, b) dis- similar forward pipe dimensions, c) ... also asymmetrical placement of forward pipes, d) super insulation on first priority forward pipe (future). F1: First priority forward pipe, F2: second priority forward pipe, closed most of the time, R: return pipe
1 images from Danfoss Technical Paper. Advanced and Traditional Pipe Systems. Optimum Design of Distribution and Service Pipes by Mr. Halldor Kristjansson, Danfoss a/s and Mr. Benny Bøhm, Technical University of Denmark. Presented at 10th international Symposium District Heating and Cooling 2006, Hanover - and based on [12]
2 See footnote 1
26
3.1.2 Standards
The industry is usually very adaptable and responsive to the demand and therefore, among the standard pipes, in terms of dimensions and insulation layer thickness, customizable versions of pipe media can be built at request. For district heating applications in general, the pipes are made from shot-blasted carbon steel (for normal operating temperatures) which offers mechanical stability and high velocity limit or high density polyethylene (for low-temperature district heating) but can be used in district cooling as well. A large applicability for cooling is the PEHD (high-density polyethylene) pipe. The pipes are manufactured through the extrusion process by special machinery.
The insulated pipes have a low thermal conductivity polyurethane insulation of different thicknesses which defines the series of the pipes; a higher number represents a larger insulation area around the pipe. Common series are from 0 to 4, with 0 representing the thinnest insulation layer available and 4 the thickest. Usually, the low series (0 or 1) are used for cooling applications and higher series for heating, when the insulation is crucial and must prevent the water of losing temperature while the pipe is exposed to extreme temperatures.
Both the inner pipe and insulation are enclosed in a high density polyethylene outer cas- ing which is strong against indentations, is leak-tight against water when at liquid phase and offers high resistance against diffusion. The diffusion is the permeability of the polyethylene material against fluids in gaseous state (water vapor). Some manufactur- ers (like LOGSTOR) have made such calculations for verifying the permeability of their outer casings. In order to protect the pipe and insulation against diffusion, a special foil called diffusion barrier can be inserted in the pipe’s structure in the manufacturing pro- cess and is available as an option at purchase, both for cooling and heating pipes.
Some pipe suppliers might suggest installation environments (e.g. ground buried or sus-
pended - air exposed) or laying depths and techniques based on soil properties and other
factors.
3.2 Models and methods
3.2.1 Steady-state and dynamic calculations
In general, there is one big difference between the two calculations. In the steady-state calculations the model is assumed not to have any variation in its boundaries and/or they are not affected by any changes over time. The calculation is performed with conditions at a specific moment (e.g. yearly average outside temperature), without looking over the changes that occur in short periods of time. For the dynamic (transient) calculations how- ever, time-dependent variations (also called dynamic effects) are a necessary condition in the model development. Some boundary conditions (e.g. external temperature) must be inputed as time-dependent function which is described by different variation curves (e.g. sinusoidal). In dynamic calculations short periods of time can be simulated for very precise assessment of the transient effects upon the model [13] [15].
3.2.2 Models from literature
In literature there are different methods adopted in order to calculate distribution losses, but the majority of them are for district heating networks. In [12] the thermal perfor- mance of several types of pipes (pair of single pipes, horizontal twin pipe, vertical twin pipe and egg-shaped twin pipe) for distribution and service is assessed. In [13] can be found steady-state calculations for heat losses in district heating networks for circular in- sulated pipes based on the heat conduction formulas from [14]. Usually the pipes studied for heat losses are circular (single, twin, triple) and steady-state calculations are per- formed due to a more accessible and easier way to apply the method in comparison to dynamical calculations [15].
28
3.2.3 Finite element method
The finite element method (FEM) analysis is defined as numerical mathematical calcula- tions that are performed in order to get an approximate value of the final solution by using smaller and simpler components called sub-domains. A number of sub-domains forms the model. The sub-domains are divided into small cells. In heat transfer applications, heat is modeled as being transferred between the cells by means of thermal conduction.
Then, calculations for each cell are performed by means of iteration. The error in this type of modeling is rather small and it depends on the model size; a smaller model in- volves smaller errors.
This type of modeling can be performed in 1-D, 2-D and 3-D as well for steady-state and dynamic conditions. FEM is used in different applications in engineering given it’s accuracy and adaptability in managing highly complex geometries and materials within the model [16]. It has been also used in a couple of studies mentioned in this paper, such as in [12] and [17].
3.3 District Cooling in G¨avle
3.3.1 System layout
The network is designed to provide chilled water both to residential and commercial
customers in the central area of G¨avle city. Total length of the piping system is ≈ 5.9 km,
among which 1 km is submerged in the G¨avle River and are the only connection of the
plant with rest of the network. A schematic view with the entire network spread can be
depicted from Figure 6 and the submerged pipes in Figure 41 and Figure 42 in Appendix.
Figure 6: Network array and branches lengths (used with FVB permission)
3.3.2 Pipes used
In the network, pairs of single pipes both non-insulated and insulated series 1 plastic pipes are used. There are dimensions between 75 and 500 mm and in Table 1 each diameter and its length is presented. Also a schematic view of the network and its diameters is shown in Figure 7. There are some sections from the network that are already built using non-insulated plastic pipes. According to FVB, at the moment of the calculation those diameters and their lengths were as in the Table 2 below. It must be mentioned that 75 mm, 90 mm and 500 mm diameters are available only as non-insulated plastic pipes.
The geometrical properties of the non-insulated and insulated pipes can be checked in Figure 38 and Figure 39 from Appendix.
30
Table 1: Pipe lengths by diameter in the network Diameter (mm) Length (m)
75 12
90 283
110 780.5
125 309
140 1017.5
160 125
180 524
200 137
225 62
250 273
280 103
315 525
355 329
400 435
500 1002
Total 5917
Table 2: Already built sections of the network
Diameter [mm] Length [m]
110 111
140 154
160 113
180 49
200 127
315 73
400 435
Figure 7: Network array and sections dimensions (used with FVB permission)
3.3.3 G¨avle climate and river data
The monthly average temperature is according to SMHI (Swedish Meteorological and Hydrological Institute) and it is valid for the year 2013. The SMHI temperatures for each month of the cooling season (April to October) are available in section 7.2 in the Appendix and below in Table 3. As boundary condition in the ground, at 10 m depth, the average annual temperature of 5 o C was set and is supposed to be constant during the year. [17]. For the case in which the pipes are submerged in the river, the monthly water temperatures were used in the calculation and they are shown in Table 4. This can be depicted also in the study paper made by Capital Cooling Energy Services AB and which was provided by FVB (Figure 43 from Appendix).
32
Table 3: Monthly outdoor average temperature Month SMHI temperature Input temperature
April 3.6 o C 3 o C
May 11 o C 11 o C
June 14.6 o C 15 o C
July 16.5 o C 17 o C
August 16 o C 16 o C
September 11.1 o C 11 o C
October 6.3 o C 6 o C
Table 4: Monthly average water temperature
Month Temperature April 5.3 o C
May 13.1 o C
June 18.4 o C
July 20.1 o C
August 17.9 o C
September 11 o C
October 8.9 o C
4 Method
This section provides details upon the build, calculation and validation of the models, together with the equations that are the foundation of the R-network and the boundary conditions used in the simulations. Also, the procedure for the case in which pipes are submerged in water is described.
4.1 Building COMSOL Multiphysics r model
In this section the model construction is detailed. The model itself was created in a Class Kit License of COMSOL Multiphysics v3.5 software available on the G¨avle University’s on-line accessed server, Citrix. It is a 2D model built in the Heat Transfer module→
Steady-state. This is a detailed model that can be used for steady-state heat losses. The soil is represented by a 20 m in length and 10 m in height rectangle and it is the most frequently used geometry when modeling the ground for heat loss calculations [17].
It was known that the network uses a pair of single pipes for supply and return, so this
was the layout that had to be represented in the model. The pipes were ”buried” in the
ground at depths of 0.8 m, 2m and 4m from the surface; the distance is measured from the
center of the pipe. All elements of the pipes were represented by circles and according
to the dimensions and thicknesses presented in the KWH [20] and Uponor [21] pipe
catalogs (Figure 38 and Figure 39). Also two ”evaluation points” were represented in
the center of the pipes (one for supply and one for return) for convenient measurement in
the conditions implementation stage that is described in the next section. The mounting
distances between the pipes - which varies by diameter, according to standards - were also
respected and they can be depicted in Figure 40 (Appendix). Some parameters needed in
the computation are seen below in Table 5.
Table 5: Thermal conductivities and other parameters
Polyurethane Insulation 0.025 [W/m·K]
PEHD 0.4 [W/m·K]
Soil 1.5 [W/m·K]
Air heat transfer coefficient at the ground surface 25 [W/m 2 ·K]
Supply temperature (T s ) 5.5 o C
Return temperature (T r ) 13 o C
Laying depth 0.8; 2; 4 m
Boundary Conditions
In the analytical model the boundary conditions for the external surface and ground have been 0 o C and 1 o C depending on the case and the conditions imposed. In the simulation model on the other hand, the boundary conditions for the upper surface were the real temperature variation that is shown in Table 3. A view of the model and its boundaries is given in Figure 8. For computational convenience the approximated temperatures were used in the model as in Table 3.
Figure 8: Model boundary conditions in COMSOL
36
4.2 Calculation and COMSOL Multiphysics r
The calculation consists of two models, one in COMSOL Multiphysics r software and Excel r , with the latter one based on the equations written in the theory section above. In COMSOL the model simulates different conditions based on the input given (boundary conditions), such as the properties of the ground, pipes, insulation and external temper- ature and/or solar radiation. Together with COMSOL the conditions mentioned in this section were used for obtaining the values needed as input in the analytical model from Excel r file for obtaining the losses. The total length of the network is 5917 m and is shown in Table 4 for each section individually. A detailed description of the procedure and conditions for all three cases are presented next.
4.2.1 Case 1: Non-insulated plastic pipes
For the first considered case, when it was assumed that we have plastic pipes both on the supply and return, a set of conditions were imposed as follows in order to get the needed output from COMSOL Multiphysics r . The conditions were the ones that follow next.
Condition 1
Adidabatic pipes both on the supply and return; Φ s = Φ r = 0 W/m and T e = 1 o C, T g = 0 o C.
In this first condition there is no heat flow through any of the pipes, therefore the value
of Q, as heat source, in the dialog box is 0 [W/m 3 ]. This can be checked from Physics
menu button→ Subdomain Settings and by clicking the space from inside the internal
circle that must become highlighted (Figure 9).
Figure 9: Heat source input
The inner wall boundaries of the pipes must be set to ”Continuity” (Physics menu button→ Boundary Settings and choosing the inner walls) as in Figure 10.
Figure 10: Internal boundaries settings
Temperature boundaries, both at the surface and in the ground can be set in the same manner as for the pipes’ walls (from the Physics menu button→ Boundary Settings and then choosing the upper and down surface of the model). The upper surface is set as ”Heat
38
Flux” with the temperature value inserted in the T inf box. while the ground boundary as ”Temperature” (Figure 11). It must be mentioned that a selected boundary turns into color red to be more visible through the whole model, as shown in Figure 11.
Figure 11: External boundaries settings
This condition provides gives the value for the downward heat flux (Φ 1∗ g ) 2 that is needed in the R-network model. To obtain it, the model must be meshed, refined once and then integrated. Here are the steps: Mesh menu button→ Initialize Mesh, refining mesh once (Mesh menu button→ Refine Mesh) and solving (Solve menu button→ Solve Problem) Figure 12, after which boundary integration is chosen (Postprocessing menu button→ Boundary Integration) and select the upper surface (as in Figure 13) and click on ”Apply”; the value of the integration will appear in the log box in the bottom of the screen.
2 Φ ...∗ e , Φ ...∗ g , T r ...∗ and T s ...∗ are values that are provided by COMSOL Multiphysics r and the 1... , 2...
Figure 12: Model after solving
Figure 13: Boundary integration
Condition 2
T s = T r = 1 o C and T e = T g = 0 o C.
Here the temperature in the supply and return pipes can be set from Physics menu button→ Boundary Settings and by choosing the inner walls of both pipes. From the
”Boundary Condition:” box, ”Temperature” should be selected and the value inserted in
40
”T 0 ” box. ”Continuity” condition has to be set for the outer surface of the pipe. From the same menu button as for the pipes’ case (Physics menu → Boundary Settings) the external and ground temperatures must be set as the condition imposes.
From here the values for the upward heat flow (Φ 2∗ e ) 3 and downward heat flow (Φ 2∗ g ) are found. 4 . The procedure of getting the values follows the same steps of meshing, refining and integration of the boundaries of interest as for the condition 1.
Condition 3
T e = T g = 0 o C and 10 W/m extraction from the supply pipe (Φ s ) and 20 W/m injection in the return pipe (Φ r ).
The temperature is the same on both upper and lower ground boundaries (0 o C), a heat flow of -10 W/m is extracted from the supply pipe and one of 20 W/m is injected in the return pipe. The -10 and 20 W/m heat flows values for the supply and return pipe respectively are given by the formulas
Q = −10/(π · r 2 )[W/m 3 ] and
Q = 20/(π · r 2 )[W/m 3 ] where:
Q - total heat flow per cubic meter;
r - the inner radius of the pipe in meters.
The resulted values must be inserted accordingly in the supply and return pipe as Q, heat sources in the dialog box from the Subdomain Settings sub-menu.
By running the simulation for this condition (mesh, refine, integrate) the temperature both
in the supply (T s 3∗ ) and return pipe (T r 3∗ ) is given. This can be done from Postprocess-
ing menu button→ Point Evaluation and choosing the center of both pipes, individually
(Figure 14); the reading values must be in Kelvin. It must be specified that the points of
evaluation must be pre-built in the model, in the drawing stage (see sub-chapter 4.1.2 -
Building COMSOL Multiphysics r model).
Figure 14: Point evaluation
4.2.2 Case 2: Insulated plastic pipes
In this case insulated pipes were assumed, series 1 for district cooling respectively. The same procedure has been followed as in the previous case, with three conditions imposed that are written below:
Condition 1
Adiabatic pipes both on the supply and return; Φ s = Φ r = 0 W/m and T e = 0 o C, T g = 1 o C.
In this condition, the only difference from the case no.1, is that the temperatures are switched between outdoors (T e ) and in the ground (T g ); the entire procedure is the same, and the value to look for is also the upward heat flow (Φ 1∗ e ). and downward heat flow (Φ 2∗ g ).
Condition 2
T s = T r = 1 o C and T e = T g = 0 o C.
This condition is identical with the one described in the condition 2, case 1 and the method used was identical. ”Continuity” must be set for the rest of outer diameters/layers of the pipe. The values to find after the boundary integration are the upward heat flow
42
(Φ 2∗ e ) and downward heat flow (Φ 2∗ g ).
Condition 3
T e = T g = 0 o C, 100 W/m injection in the supply pipe (Φ s ) and an adiabatic return pipe (Φ r ).
After setting the upper and ground temperatures in the boundary conditions, the calcula- tion for heat injection in the supply pipe has to be made; this is realized with the formula
Q = 100/(π · r 2 )[W/m 3 ]
where Q and r have the same meaning as in condition 3, case 1. Q value must be inserted in the material properties section as Heat Source. After all the data has been introduced in the model, a simulation has been performed following the same order of meshing, refining and solving, succeeded by a point evaluation for getting the temperature values on the supply (T s 3∗ ) and return pipes (T r 3∗ ).
4.2.3 Case 3: Insulated supply pipe and non-insulated return pipe
In this case, in terms of calculations - because of the non-symmetry - also three conditions have been developed, as in the first two cases. The conditions are as follows:
Condition 1
T e = T g = 0 o C and T s = T r = 1 o C.
At first, the condition boundaries must be inserted in the software (Physics menu button→
Boundary Settings) by choosing the inner surface of the pipes as well as the upper and
lower extremities of the model. After setting the boundaries of the model in COMSOL
Multiphysics r according to this first condition, the values to be found were the heat flux
from the supply pipe (Φ s condition 1), the heat flux from the return pipe (Φ r condition 1)
and upwards heat flow from the upper boundary (Φ e condition 1). To find the heat flow
from each pipe, the integration must be done separately for the quadrants of the same
sign/direction as in Figure 15; the total heat flow for one pipe must have the absolute
Figure 15: Boundary integration by quadrants
Condition 2
T e = 1 o C, T g = 0 o C and adiabatic supply and return pipes (Φ s = Φ r = 0 W/m).
The boundaries for the second condition have to be updated in the COMSOL model.
No heat flow for the return and supply pipe (but the boundary condition for the inner surface of the pipes should be set to ”Continuity”. The outside temperature has been set to 1 o C and the ground to 0 o C respectively (Physics menu button→ Boundary Settings and choosing the boundaries of interest). Here the value to be found is the upward heat flow (Φ e condition 2) which is obtained by following the same steps described in the first two cases.
44
Condition 3
T g = T e = 0 o C, and Φ s = 100 W/m, Φ r = 0 W/m.
This last condition lets us get the final necessary values that are needed in the Excel r analytical model as input for obtaining the conductances. While the temperature is the same on both upper and lower ground boundaries (0 o C), an heat flow of 100 W/m is injected in the supply pipe and none for the return pipe. ”Continuity” should be set at the inner surface of both pipes as previously, from ”Boundary Settings”. The 100 W/m injection is calculated by the same formula used in condition 3, case 2. By having all the new settings made in the model, a solver can be run in the same manner as for all the conditions above. The values of interest are the temperatures from the center of the pipes after the heat injection in the supply was made. For getting the temperatures, the same procedure must be followed as in the cases above, since it’s identical.
4.2.4 Cooling loss calculation
In the calculation of cooling loss, average seasonal values were used. The average sea- sonal loss is the sum of the average supply and return loss and such values are shown in the Results section and more detailed in Appendix.
The total loss in the network was calculated in four configurations and two situations:
first, the real case when the φ500 mm pipes are submerged in the river and second, an hypothetical case with the φ500 mm pipes buried in the ground, for comparison. The four configurations are: full non-insulated plastic pipes, mixed pipes (insulated supply and non-insulated return) network, and another two mixed and insulated configurations in which the already built branches with non-insulated pipes are included. It must be mentioned that φ75 mm and φ90 mm pipes are not available as insulated, hence plastic non-insulated pipes were used and are included in all configurations.
For the seasonal cooling loss, the 214 days from April to October were considered as
100% operating time. Given the lower demand in colder months and overnight time,
both 50% and 70% from the total operating time were included in the calculation. The
4.3 R-network
The R-network used is a model composed of conductances determined by analytical equations, which solved, provide the values for thermal conductivities. This type of method is used as a simplified model to determine the thermal performance of the district cooling piping system. In the case studied here, the purpose of this type of modeling in terms of thermal performance of the pipes is associated with cooling losses, though it can be used for heating losses as well.
Figure 16: Thermal network illustration of the heat paths through the model
46
4.3.1 Motivation why - design purposes
The main reason to use this type of modeling is the high accuracy, which, by increasing the number of components in the model, increases. Another advantages are:
-the boundary conditions within the network can be enhanced for particular ranges, there- fore, providing a precise analytical solution;
-the boundary conditions are not material layer thickness dependent;
-even if the R-networks are optimized for a constant number of nodes, calculation can be performed for a variable number of nodes also [19].
-the results of the calculations are instant in the Excel tool after inserting the input when compared to COMSOL.
The R-network development started from the premise that the model uses steady-state conditions, the monthly average external temperature, internal for the ground and the temperatures on the supply and return are all constant. This model can be implemented in any calculation program, such as Excel. With the conductances determined for a cer- tain pipe type and configuration, the program makes extremely fast calculations on losses for any conditions given by the user.
The tool can be used in the design work or for simulations purposes and it is an im- provement of simpler models [12] where only one external temperature is dealt with. In this work, the model considers a ground temperature and another temperature above the ground. However, in this model, the temperature dependency and aging of the pipe insu- lation have not been considered - the thermal conductivity of the insulation is constant.
The conductances are calculated for a standardized set of parameters like pipe dimen- sions, insulation levels, spacing between pipes and depth in the ground. Conductances have to be pre-calculated, preferably with a FEM-tool or by measurements.
In the model (Figure 16), which is based on a thermal conductances circuit, temperatures,
heat flows and conductances are represented. In order for the model to provide results
there is an input required for each condition, such as in Figure 17 (upward, downward,
the ground). The determination of conductances (above the line) and the simulation itself (below the line) are shown in this case, primarily to check if conductances give reliable results against COMSOL with ”actual” temperatures.
Figure 17: An example of calculations made to determine the conductances (the upper half of the figure) and simulation with chosen temperatures (lower).
4.3.2 Equations
A set of equations has been developed [Jan Akander] for each considered case to deter- mine the conductances, which are the base of the calculation. The purpose of the model is that of being able to provide reliable results through conductances. The latter ones are used together with some values from COMSOL in finding the losses for each pipe diameter.
Symmetrical/non-symmetrical cases
The study has been performed for different cases as mentioned above in the equations
48
defining part. While the pipe properties are the same both for the supply and return pipe in the first two cases (non-insulated plastic pipes and insulated plastic pipes) the sym- metry occurs between the two above-mentioned. This translates into a more convenient calculation in terms of the difficulty of the equations since we get the values for both sides - return and supply - by solving the equations for only one side. Hence, Λ esm = Λ erm , Λ smg = Λ rmg and Λ sm = Λ rm .
On the other hand, in the asymmetric case, when we have mixed pipes (insulated plastic pipe on the supply side and non-insulated plastic pipe on the return side) the things get more complicated since the process requires solving the entire set of equations for both supply and return pipes.
Symmetrical case (pairs of non-insulated and insulated series 1 pipes)
Due to symmetry, the other conductances on the other side of the model have the same values as those derived below. The digit placed as exponent shows which condition the value has been obtain from and the star shows that the value is a COMSOL output.
Λ smg = Φ 1∗ e 2
1 − Φ 2∗ g Φ 2∗ e
(1)
Λ esm = Φ 1∗ e 2
1 − Φ 2∗ e Φ 2∗ g
(2)
Λ sm = Φ 2∗ g − Φ 2∗ e 2 ·
1 + 2·Λ Φ
2∗eesm
(3)
for non-insulated pipes
Λ sr =
Φ 3∗ s − T s 3∗ · Λ sm
Λ
smg+Λ
esmΛ
smg+Λ
esm+Λ
smT s 3∗ − T r 3∗ (4)
and for insulated pipes
[100 −
Λ sm − Λ Λ
2smsmg
+Λ
sm+Λ
esm· T s 3∗ ]
Asymmetrical case (insulated series 1 supply pipe and non-insulated plastic re- turn)
The ”efficiency” of the pipe η
0is introduced in order to facilitate the calculations. It indi- cates how much of the heat supplied to the pipes is conducted to the outdoor environment and it’s calculated by the formula:
η
0= Φ 1 e
Φ
0s + Φ
0r (6)
Λ smg = Λ sem · 1 − η
0η
0(7)
Λ sem = 1
2 Φ
3e− 1
Λ smg (8)
Λ smg = Φ 3 e
2 · η
0(9)
Λ sem = Φ 3 e
2 · (1 − η
0) (10)
Λ sem + Λ smg = Φ 3 e 2 ·
1
η
0· (1 − η
0)
(11)
Λ sm =
Φ
0sT
s0· Φ 2
3e·
1 η
0· ( 1−η
0)
Φ
3e2 ·
1 η
0· ( 1−η
0)
− Φ T
0s0 s(12)
50
Λ sr =
[Φ s −
Λ sm − Λ Λ
2smsmg
+Λ
sm+Λ
sem· T s 2∗ ]
T s 2∗ − T r 2∗ (13)
Pipes in water. Temperature increase with length.
dΦ
dx = T s (x) − T w
Λ pipe (14)
Λ pipe = 1
π · d i · α i + 1
π · λ · ln d y d i
+ · · · + 1
π · d y · α y = constant (15) [18]
and for losses
dΦ
dx = T s (x) − T w
1
π· d
i· α
i+ π· λ 1 · ln
d
yd
i+ π· d 1
y
· α
y(16)
[18]
dΦ = −M · cp · dT s (17)
Z T
sLT
s0dT s T s (x) − T w =
Z L 0
dx
−M · cp · Λ pipe (18)
T s (x) = T w + (T sL − T w ) · e −
x
M · cp·Λpipe
