Improved performance of hydronic heating systems connected to … · 2011-04-08 · ISRN LUTMDN/TMHP—11/3048—SE Kkk ISSN 0282-1990 Improved performance of hydronic heating systems

ISRN LUTMDN/TMHP—11/3048—SE Kkk ISSN 0282-1990

Improved performance of hydronic heating systems connected to district heating

R.P.M.M. van der Wijst (Roy)

Division of Efficient Energy Systems Department of Energy Sciences Faculty of Engineering, LTH Lund University P.O. Box 118 SE-221 00 Lund Sweden

Improved performance of hydronic heating systems connected to district heating

R.P.M.M. van der Wijst (Roy) July 2010

Lund University, Lund, Sweden: Department of Energy Sciences, Faculty of Engineering

Division of Efficient Energy Systems J. Wollerstrand PhD, Associate professor

P-O. Johansson MSc, PhD student

Eindhoven University of Technology, Eindhoven, The Netherlands: Department of mechanical engineering

Section energy technology prof.dr.ir. A.A. van Steenhoven

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Table of Contents 1. Introduction .......................................................................................................................... 5

1.1 Background ...................................................................................................................... 5

1.2 Objectives ........................................................................................................................10

1.3 Outline of the report .........................................................................................................10

2. Case study on hydronic heating system ...........................................................................11

2.1 Method ............................................................................................................................12

2.2 Theory .............................................................................................................................12

2.2.1 Nusselt correlations .................................................................................................................... 13

2.2.2 Physical model ........................................................................................................................... 17

2.2.3 Heat transfer in a space heating system with add-on-fans ........................................................ 18

2.2.4 Fan differential pressure experiments ........................................................................................ 21

2.3 Modeling setup ................................................................................................................21

2.3.1 Heated vertical plate .................................................................................................................. 21

2.3.2 Extended model of the radiator with an add-on-fan. .................................................................. 23

3. Results .................................................................................................................................27

3.1 Heated vertical plate ........................................................................................................27

3.1.1 Heated vertical plate model validation ....................................................................................... 27

3.1.2 Isotropic diffusion ....................................................................................................................... 27

3.1.3 Anisotropic diffusion ................................................................................................................... 31

3.1.4 Weak constraints and scaling .................................................................................................... 32

3.2 Extended radiator model ..................................................................................................32

3.2.1 With temperature profile and radiation ....................................................................................... 32

3.2.2. With temperature profile and without radiation ......................................................................... 32

3.2.3. With temperature profile, without radiation, with add-on-fan .................................................... 33

3.3 Fan measurements ..........................................................................................................37

4. Discussion ...........................................................................................................................39

Acknowledgements ................................................................................................................41

Bibliography ............................................................................................................................43

Appendix A. COMSOL™ Simulation data ..............................................................................45

A.1 Isotropic diffusion ............................................................................................................45

A.2 Anisotropic diffusion ........................................................................................................47

A.3 With and without radiation ...............................................................................................47

A.4 With and without add-on-fans ..........................................................................................48

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Appendix B. Fan measurement data .....................................................................................51

Appendix C. Manufacturer’s data ..........................................................................................53

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1. Introduction This report focuses on hydronic heating systems connected to a district heating network. The background section deals with the important features of district heating, including a district heating network and distribution, customer interface, heat exchange, power generation and characteristics for district heating in Sweden. Furthermore, the chapter continues with presenting objectives for this project and concludes with an outline of this report.

1.1 Background In Sweden district heating is the dominant heating source according to (Johansson, et al., 2009). The heat market share for district heating is over 75% for multi-residence buildings, almost 60% for non-residential buildings, but only 10% for detached houses where electric heating is the most common heat source. District heating is a network of buildings or dwellings consuming heat from a central heat source (Skagestad, et al., 1999), as depicted in a simplified manner in Figure 1. District heating systems often cover large areas (e.g. entire cities) and are very complex plants involving many stations and thousands of consumers.

Figure 1. Simplified district heating network. Picture retrieved from (Johansson, et al., 2009) with permission.

In a district heating system, heat is produced centrally. Centralized and large-scale heat production has several advantages over decentralized production. Some of the advantages are high efficiency in large production units, low specific construction costs, possibility of establishing combined heat and power production (will be treated with more detail later on), possibility of using waste heat, flexibility of energy supply by changing energy sources, high degree of reliability in heat supply (Persson, 2005). In a district heating system, heat is distributed to the customer via a piping system with water as the heat carrier. Water is very suitable as heat carrier since there is an ample supply, it is non-toxic, clean, cheap and has a relatively high heat capacity. District heating water is distributed from the heat source through supply pipes to the customer’s interface and is returned via pipes after heat has been extracted. Delivery is achieved by circulating pumps, creating a pressure differential between the supply and return pipes. Pumps are selected carefully to overcome the flow resistance in the supply and return pipes and the use of variable speed drives to control the

Production unit

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pumps ensures that consumed power is minimized. Basically, district heating systems are controlled by two different principles. Either the temperature is kept constant while the flow is varied in order to respond to the changing demand, or the flow is fixed and the temperature varies. In reality, different combinations of the two systems are found. Generally, the variation of flow responds much quicker to changes of demand than changes of temperature do. Therefore, variable speed pumps are important elements of modern district heating systems besides the costs aspects mentioned before. In practice, district heating flow follows a general control strategy. An example of a control strategy based on external air temperature is presented in Figure 2.

Figure 2. District heating (primary) flow temperature as function of external air temperature. Limitations on the district

heating flow temperature are given by pipe mechanics at low external temperature and factors such as legionella at high external air temperatures. Picture retrieved from (Skagestad, et al., 1999).

Another important topic to address is the distribution in a district heating system. A number of different types of pipe material is available on the market, however the vast majority of systems are based on pre-insulated steel pipes, depicted in Figure 3. The core of the pipes consists of a corrugated carrier pipe, covered with poly-urethane (PUR) foam, which is in total covered by a corrugated sheath pipe of steel, finished with two layers of rubber with an outer polyethylene sheathing. Many pipe systems also include a detection system that continuously monitors the presence of moisture, indicating a leakage. The detection system consists of two wires within the insulation foam, able to indicate a leakage spot within a meter accuracy. Leakage monitoring provides an early warning to the district heating operator to carry out preventive corrections. Unchecked pipes can quickly deteriorate requiring emergency action and potential temporarily loss of heat to customers. The district heating supply water temperature is often limited by the type of pipes used. Most systems use piping

Figure 3. Detailed view of district heating pipe (Skagestad, et al., 1999).

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that have a maximum operating temperature of 140°C. It is common to operate at lower temperature, below 120°C, and even operation below 80°C is not unusual (almost always during low heating load and during summer conditions). Pressures can go up to 25 bar but the majority operates with a maximum pressure of 16 bar or even lower. Heat losses in modern district heating distribution depend on a number of factors such as the length of the system in relation to the heat load, insulation and temperature level. Heat losses basically account for 5% - 20% annually according (Skagestad, et al., 1999). Once the district heating distribution system has transported heat energy to the customer, it has to be transferred to the internal distribution system of the house or building. The (internal) space heating circuit can be connected either indirectly or directly to the district heating system (Persson, 2005). In the former case, circuits are separated hydraulically by a heat exchanger. With a direct connection, the district heating water is distributed within the building to directly provide heat to space heating equipment. Benefits of indirect systems are that those provide better protection against pressure oscillations and corrosion in the space heating system, due to the more limited risk of oxygen continuously being supplied to the hydronic system of the building. In addition, the amount of water that can potentially leak into the building is much smaller if the primary water is not led into the internal system of the house. A drawback for indirect connection is the higher installation costs required compared to a direct connection. From a thermodynamic point of view, a direct connection is preferred since the primary return temperature at an indirect connection is substantially higher compared to a direct connection. Since in Sweden most indirect connections are used and given a few advantages over direct connections, the indirect connection variant is regarded in this project. Several types of heat exchangers exist for use with district heating systems. In this introduction the two most important types will be highlighted: plate heat exchangers and shell and tube heat exchangers. The plate heat exchanger generally has a cost advantage and significantly less surface area is required compared to shell and tube units, for the same operating conditions, because the latter have much higher heat transfer rates. With plate heat exchangers the approach temperature between the primary return and the secondary return is closer, generally 1-2°C compared with 6-7°C for most shell and tube heat exchangers. For this reason, the plate heat exchanger is attractive to district heating operators.

Figure 4. Gasket plate heat exchanger. Picture retrieved from

http://www.apiheattransfer.com/us/Products/HeatExchangers/PlateHeatExchanger/GasketedPHE.htm

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Plate heat exchangers come in two options: brazed plates or with gaskets between plates. The brazed plate heat exchangers are sealed units that cannot be disassembled and, hence, cleaned like a gasket plate heat exchanger. Brazed units tend to be smaller than gasketed heat exchangers since a larger surface area is devoted to the actual heat exchange. In addition brazed heat exchangers do not require the level of maintenance required by the gasketed version. The gasket material often degrades losing its flexibility and hence its ability to seal. The result of this is water leaks. Gasketed heat exchangers especially tend to suffer in systems where the heating is frequently switched on and off. Shell and tube heat exchangers are still being used in some district heating systems, but are gradually being phased out as they do not provide sufficiently low approach temperatures between primary and secondary side water and require a lot of space. For both types of heat exchangers the size and number of heat exchangers to suit the building load should be carefully selected.

Figure 5. Shell and tube heat exchanger. Picture retrieved from http://commons.wikimedia.org/wiki/File:Straight-

tube_heat_exchanger_1-pass.PNG

The internal distribution system of a house or building mainly consists of pipes connected to hydronic radiators around the entire building. Hydronic heating is referred to as using water as a medium for heat transfer in a conventional space heating system, comprising metal tubes connected to radiators. A district heating system includes mainly a combined heat and power (CHP) plant, generating both electricity and heat at a greater efficiency than separate plants could. If the CHP station is fueled by bio-mass the electricity produced will contribute to reduce the emissions of unwanted greenhouse gas compared to a coal-based power plant. In Figure 6 a biomass-fueled CHP plant is depicted graphically indicating the main processes involved. As a first step biomass is inserted into the combustion chamber via a conveyor belt. A heat exchanger provides high pressure steam, which is fed to a steam turbine. In the steam turbine, the high pressure steam condensates driving the generator to generate electricity. The residual heat from the steam turbine is fed through a second heat exchanger to extract heat, which can be used for district heating for example. The cooled feedwater is fed to the heat exchanger in the combustion

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chamber to repeat the cycle. In addition, a number of heat only producing plants, covering peak load and for stand-by, are connected in order to assure the heat production in all load cases.

Figure 6. Biomass-fueled combined heat and power station in a graphical representation, demonstrating the main processes involved. First biomass is inserted into the combustion chamber via a conveyor belt. A heat exchanger provides high pressure steam, which is fed to a steam turbine. In the steam turbine, the high pressure steam condensates driving the generator to generate electricity. The residual heat from the steam turbine is fed through a second heat exchanger to extract heat, which can be used for district heating for example. The cooled feedwater is fed to the heat exchanger in the combustion chamber to repeat the loop. Picture retrieved from http://www.unendlich-viel-energie.de/uploads/media/Biomass_CHP.jpg [10-11-2010].

(Johansson, et al., 2009) argue that a reduction of the district heating system (primary) supply temperature has a greater impact on the electric power-to-heat ratio than a reduction of the primary return temperature. However, there is a larger potential of reducing the primary return temperature in a district heating network. A reduced primary return temperature results in a decreased flow rate in contradistinction to a reduction of the primary supply temperature that will increase the flow rate. If the reduced temperature level is used to increase the heat load in the district heating network the annual operation hours of the CHP station will increase and more electricity can be produced. Since the taxes for electricity produced in a CHP station are very favourable, the electric power-to-heat ratio is of great interest. Since this project deals with district heating in Sweden, this background section concludes with district heating in Sweden and its history and features. In Sweden, the 2-pipe system is by far the most common solution, with temperature levels typically varying between 70°C and 110°C in the supply pipes and between 40°C and 65°C in the return pipes. The first Swedish district heating system was built in 1948 as a municipal system in the town of Karlstad (Persson, 2005). In the period 1950 to 1960 district heating expanded due to extensive building of houses, where during the period 1975 to 1985 district heating expanded considerably in order to achieve fuel flexibility (given the oil crises). According to (Persson, 2005), the shift from an almost exclusive use of oil as heat source in the district heating production in 1970 to a very low use of oil by the

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end of 1980s is dramatic. Rising costs of fossil fuel and increased environmental concern has led to an increased use of biofuels in Swedish district heat production, making up for more than 60% of the supplied energy source in 2003 (Persson, 2005). Due to the introduction of the green electricity certificate system as a regulatory instrument in Sweden in 2003, biomass-fueled CHP generation is in general the most profitable alternative for district heating companies. According to (Swedish energy agency, 2007) more than 30% of the district heating heat is produced in CHP stations in Sweden nowadays. District heating is an isolated system, which allows for different fuel mixes in different district heating networks mainly due to local conditions, e.g. access to waste heat from industries.

1.2 Objectives As mentioned afore, (Johansson, et al., 2009) have argued that the temperature level of a district heating system influences the performance of a combined heat and power (CHP) station. A reduction of either the primary supply temperature or the primary return temperature influences the electric power-to-heat ratio . This ratio will rise. In order to decrease the primary return temperature, the heat output of the houses connected to the system could be increased (e.g. more heat should be extracted by the heating system of customers, resulting in a lower district heating return temperature). A method to achieve a higher heat output of a hydronic heating system is to add fans to existing radiators, introducing forced convection in addition to the natural convection (Buoancy). Field studies (Johansson, et al., 2010) have proven that by installing add-on-fan blowers on existing radiators the temperature level in the heating system can be substantially reduced. Field studies have also shown that the heat output, with constant supply temperature and mass flow through the radiator, can increase with more than 50%. Since the air flow has not been measured separately in the field study, this project aims to investigate the influence of air velocities introduced by add-on-fans on the heat output of hydronic heating systems. Different from the approach in the field study, this influence is to be investigated via simulation models instead of performing actual field studies. In order to fulfill this objective, within this project approach attention is to be paid to the accuracy of the simulation model first, then with an extended model the add-on-fans will be modeled in a more reality-like context. The problem is assumed to be a stationary, two-dimensional problem. The heating system is assumed to be operating at a temperature program 60°C/45°C.

1.3 Outline of the report This report continues with introducing the case study in chapter two. Furthermore, the second part of chapter two focuses on the method, theory and modeling setup for this project. In chapter three the results of this project are presented and interpreted in line with the afore presented method and modeling setup. Regarding the objectives presented in this chapter and the results in chapter 3, conclusions are drawn and recommendations for future research are given in chapter 4. The remainder of this report is devoted to acknowledgements, bibliography and appendices.

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2. Case study on hydronic heating system In this chapter the case study is introduced. Furthermore this chapter includes a description of the used method to achieve the objectives of this project. After the method quite a substantial part of this chapter is devoted to theoretical backgrounds of the physical model. This chapter concludes with the description of the used simulation models. The add-on-fan to be applied on existing radiators consists of several DC motor driven fans, originally used for cooling electronic devices (i.e. personal computers) with dimension 0.09 x 0.09 x 0.045 m (height x width x depth). The fans are mounted in an array with an enclosure, see Figure 7. A schematic representation of a radiator equipped with add-on-fans is given in Figure 8.

Figure 7. Fans mounted in an array with enclosure. Picture retrieved from http://elementflakten.jetshop.se [20-06-2010].

Figure 8. Schematic view of an add-on-fan mounted to an existing panel space heating radiator. Picture retrieved from

(Johansson, et al., 2010) with permission.

ms

Tss

Tsr

Add-on-fan

Increased air flow

Space heatingradiator

Out

er w

all

Floor

12

The fans are distributed by a Swedish company called A-energi AB1. This company describes the features of the add-on-fan blower as a possibility to reduce the temperature program without changing the radiators2

.

In this case study the radiator is assumed to be a panel radiator with length 1L m and height 0.59h m, approximated by a vertical plate. The indoor temperature

infT is assumed to be

constant at 21°C. In the following analyses at each analysis the temperature of the radiator is indicated, being either a temperature profile or a fixed temperature.

2.1 Method In this case study use has been made of finite element method to simulate heat transfer on a hydronic heating system. The commercial finite element package COMSOL™ Multiphysics 3.5a with the Heat Transfer module is used for this project. In order to get familiar with the finite element package and its accuracy first focus is placed on a heated vertical plate as a benchmark problem, since it is possible to compare numerical results with analytical work. In order to compare results obtained from COMSOL™ to theoretical values, a literature study about Nusselt correlations is required as well as an investigation in the way COMSOL™ deals with heat transfer. A next step when the heated vertical plate is under investigation is the influence of stability parameters like isotropic and anisotropic diffusion on the accuracy of COMSOL™. Subsequently, focus is placed on a more extended radiator model, with realistic dimensions and composition. Therefore a concrete wall is added to the surroundings and the radiator is modeled with a core of cast-iron covered with iron plates. With this extended model, validations are performed. When heat transfer by radiation is taken into account in the model, it is possible to compare the simulation results to manufacturer’s data of a radiator. Thereafter focus is placed on a case where add-on-fans are applied in the model. In order to achieve a proper modeling of fans in COMSOL™, actual fan measurements are to be performed.

2.2 Theory In this section relevant topics will be highlighted, discussed and compared to literature. Being part of a literature study first of all several Nusselt correlations are treated, then the way COMSOL™ deals with heat transfer is discussed. After this part, the physical model is explained and this subsection ends with the heat transfer of radiator systems. The section ends with the modeling setup.

1 http://elementflakten.jetshop.se 2 http://elementflakten.jetshop.se/om-elementflakten-i-54.aspx

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2.2.1 Nusselt correlations As the heat transfer coefficient h is determined by using correlations in the form of the Nusselt number, reading (Incropera, et al., 1996):

L

hLNu

k , (2.1)

the heat transfer coefficient is a function of the Rayleigh number and the Prandtl number, since L L

Nu C Ra , (2.2) and

3

2

( )Pr Prs

L L

g T T LRa Gr

(2.3)

With g the gravity constant, the expansion factor, s

T the temperature of the surface, T the ambient temperature, L the length of the plate and the kinematic viscosity. Since all parameters in (2.3) are assumed constant, except the temperature difference, the Rayleigh number is assumed to be dependent on the temperature difference only. The relation between the Rayleigh number and the temperature difference is visualized in Figure 9. In literature, many correlations have been established for specific cases, which will be discussed here. The onset of turbulence, affecting the heat transfer inevitably, is assumed to

start at 910Ra .

Laminar regime For the laminar regime, the Nusselt number is given by(Churchill, et al., 1975):

1 9 44 16 90.670 / [1 (0.492 Pr) ]Nu Ra . (2.4)

Equation (2.4) represents the various computed values within 1 percent from Pr 0 to Pr and is in general agreement for 5 910 10Ra . For 910Ra deviations owing to the onset of turbulence become dominant and for 0Ra deviations owing to thickening of the boundary layer relative to the distance from the starting edge of the plate are present. Another correlation for the Nusselt number, established for the laminar regime is given by (Churchill, et al., 1975):

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9 416 9

0.6700.68

[1 (0.492 Pr) ]

RaNu

(2.5)

Equation (2.5) provides a good representation for all 910Ra with slightly better accuracy for laminar flow than equation (2.4), although this equation is suitable for most engineering calculations(Incropera, et al., 1996).

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For a uniformly heated plate, the following correlation is established by(Churchill, et al., 1975):

14

9 416 9

0.6700.68

[1 (0.437 Pr) ]

RaNu

. (2.6)

Laminar plus turbulent regime For the laminar plus turbulent regime, similar correlations are established by(Churchill, et al., 1975):

1

1 62

892716

0.3870.825

[1 (0.492 / Pr) ]

RaNu

. (2.7)

This correlation provides a smooth transition from the laminar to the turbulent regime, whereas the actual transition is known to be essentially discrete. For a uniformly heated plate, the following correlation is established by(Churchill, et al., 1975):

1

1 62

892716

0.3870.825

[1 (0.437 / Pr) ]

RaNu

, (2.8)

Which is quite similar to equation (2.7), whereas this equation is also an adequate representation for this boundary condition. According to (Churchill, et al., 1975), more accurate representations for the laminar regime are provided by equation (2.5) and (2.6) and these simpler expressions should be used rather than equations (2.7) and (2.8) for 910Ra . Equation (2.7) provides a good representation for the mean heat transfer for free convection from an isothermal vertical plate over a complete range of Ra and Pr even though it fails to indicate a discrete transition from laminar to turbulent flow. Another Nusselt correlation is established by (Holman, 1997), reading: ( Pr )m

f f fNu C Gr , (2.9)

where the subscript f indicates that the properties in the dimensionless groups are evaluated at

the film temperature 12( )

f wT T T . For a vertical plate and a certain interval of the product

Prf f f

Gr Ra are given in Table 1.

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Figure 9. Rayleigh number as function of the temperature difference for free convection along a vertical plate with

1 1 294.15 [-]T , 0.59 mL and 5 21.83 10 m s .

Table 1. Coefficient for specific interval of Rayleigh number.

fRa C m

4 910 10 0.59 14

9 1310 10 0.021 25

9 1310 10 0.10 13

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COMSOL™ heat transfer theoretical background COMSOL™ uses built-in equations to calculate the value of the heat transfer coefficient. If the option ‘external natural convection for a vertical wall’ is chosen, COMSOL™ uses the following theoretical framework to determine the heat transfer coefficient(Comsol2, 2009). For laminar flow in external natural convection for a vertical wall:

0.25

avg lam0.56

Th F

L

(2.10)

3 Preferred case according to (Holman, 1997).

0 20 40 60 80 100 120 140 160 180 200 2200

0.5

1

1.5

2

2.5

3

3.5x 10

9

Temperature difference [degC]

Ray

leig

h nu

mbe

r [-]

Rayleigh number as function of temperature difference

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For turbulent flow in external natural convection for a vertical wall: 0.33

avg turb0.12h F T (2.11)

Where

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lam 3

RaF k

L T

(2.12)

and

13

turb

RakF

L T

(2.13)

For medium air, these are given by:

lam6.3126 1.4322 logF T (2.14)

2turb121.9 69.518 log 10.255 logF T T (2.15)

10.058 4.4449 log3Ra 10T

TL (2.16)

2Pr 2.8469 1.3494 log 0.1949 logT T (2.17) With both knowledge about literature and COMSOL™ a comparison is possible. In order to compare the theoretical framework of COMSOL™ with the previously discussed correlations from literature, Figure 10 is included. Since (Churchill, et al., 1975) recommend equation [5] for all 9Ra 10 , COMSOL™ seems to overestimate the heat transfer coefficient by roughly 30% and therefore the heat output for laminar flow. For 9Ra>10 (turbulent flow) COMSOL™ seems to overestimate the heat transfer coefficient as well, but in a lower degree concluded according Figure 10. The other equations included in this figure are adapted from (Myhren, et al., 2009) and (Sundén, 2001).

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Figure 10. Heat transfer coefficient as function of temperature difference for different correlations. Compare the graphs for Churchill [5] with COMSOL™ for a laminar regime and compare the graphs for Churchill [9] with COMSOL™ for the turbulent regime.

2.2.2 Physical model The general governing equations in 3-dimensional Cartesian coordinates, where ( , , )u v wu , are given below (Bejan, 1993). Mass conservation

0t

u

(2.18)

Navier Stokes equations (x,y,z components)

pt

uu u f I T f , (2.19)

where a constitutive law is needed to determine T . Energy equation

0 20 40 60 80 100 120 140 160 180 200 2200

1

2

3

4

5

6

7

8

Temperature difference [degC]

Hea

t trn

sfer

coe

ffici

ent [

W/m

2 K]

Heat transfer coefficient as function of temperature difference

ComsolMyhren (paper)Holman [7-25]Holman (prefered +) [7-25]Sundén (10-32,33)Churchill [3]Churchill [5]Churchill [9]Churchill [14]

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2 2 2

2 2 2p

T T T T T T Tc u v w k q

t x y z x y z

(2.20)

where 2 2 2 2 2 2

2u v w u v v w w ux y z y x z y x z

Equation of state pV mRT p RT (2.21) The model is introduced in COMSOL™ for the stationary case in 2-dimensional Cartesian coordinates with Newtonian fluid and without internal heat production. Applying these assumptions to equations (2.18)-(2.20) yields the following partial differential equations to be solved by COMSOL™: Mass conservation

0 u Navier Stokes equations

dvtensor

tensor tensor scalar

tensor

vector

23

Tp k

u u I u u u I F

(2.22)

Where dvk is the dilatational viscosity which equals zero for air (Comsol2, 2009).

Energy equation

s pk T Q q T c T u , (2.23)

Where Q is a heat source and sq the production/absorption coefficient (Comsol2, 2009) .

2.2.3 Heat transfer in a space heating system with add-on-fans The heat output from a radiator to the room occurs by convection and radiation. Heat transfer from warm water through a radiator is summarized by(Johansson, et al., 2010): ( )

p ss srQ mc T T kA , (2.24)

with m the mass flow rate,

pc the heat capacity at constant pressure,

ssT the secondary supply

temperature, sr

T the secondary return temperature and the logarithmic mean temperature difference.

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The latter is given by:

inf

inf

ln

ss sr

ss

sr

T T

T T

T T

, (2.25)

with

infT the room temperature.

In equation (2.24) the k represents the heat transfer from the hot water to the metal surrounding the water, conduction through the metal and convection from the outside of the radiator to the room. Under the assumption that the convection and radiation between the radiator and the room are the dominating parameters, k is given by:

conv radk (2.26)

Rewriting equation (2.24) with substitution of equation (2.26) yields for the heat output: conv conv rad radconv rad

Q Q Q A A (2.27) Elaborating on radiation yields the following relation for the heat output from radiation,

3 3

rad4

1

radm rad m

radrad rad

radiator

Q T A C TA

A

(2.28)

under the assumption that rad radiator

1A A and rad and

radA are constant for a specific

radiator. For convection a more sophisticated approach should be established. Convection arises due to temperature difference between the radiator surface and the surrounding air and appears to be a function of the Nusselt number as mentioned before in subsection 2.2.1 Nusselt correlations. The heat output due to convection can be divided into three regimes: natural convection, mixed convection and forced convection. The three regimes will be briefly discussed in order to establish a theoretical framework for the entire flow regime. Natural convection In the natural convection regime the Nusselt number depends on the Rayleigh number (Ra), see equation (2.3). The Prandtl number for air is considered as constant Pr 0.71 , which will be used in this framework. The Nusselt relations for natural convection are already mentioned in subsection 2.2.1 Nusselt correlations, see equations (2.5) and (2.7). Forced convection For forced convection the Nusselt number is calculated by (Holman, 1997): For 5Re 5 10 0.5 1/30.664 Re PrNu (2.29)

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For 5 75 10 Re 10 1/3 0.8Pr 0.037 Re 871Nu (2.30)

where the Reynolds number Re is defined as:

ReuL

(2.31)

Mixed convection An intermediate regime when convection is neither dominated by natural convection nor by forced convection, mixed convection appears. In this case the Nusselt number is calculated according (Johansson, et al., 2010): 3 3

natural forcedNu Nu N (2.32)

Evaluating equation (2.27) for the three regimes as function of the air velocity and interpolating between the Rayleigh-limits yields Figure 11.

Figure 11. Heat output as function of air velocity for the theoretical framework of the radiator. Between the Rayleigh-limits the heat output has been interpolated.

0 1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

350

400

450

Air velocity [m/s]

Hea

t out

put [

W]

Convective heat output as function of air velocity

Convective heat outputInterpolation

21

Since the assumptions of the above equations are actually not valid for comparing with add-on-fans (e.g. no wall-effects are incorporated etc.), only the value of this theoretical framework where no additional air velocity is introduced is compared to the case where no add-on-fan is applied. The value from the theoretical framework visualized in Figure 11 is 160 W. Furthermore, (Johansson, et al., 2010) have shown that the additional heat output from the radiator is increasing rapidly when the air flow is increased. With radiation taken into account the additional heat output is increasing, but at a lower rate since the mean temperature is reduced. These conclusions are in accordance with what is observed in Figure 11: heat output tends to increase when the air flow is increased. As mentioned previously, since no wall-effects are taken into account for this framework, the actual increased heat output will be lower than depicted in Figure 11.

2.2.4 Fan differential pressure experiments In order to achieve a proper modeling of add-on-fans in COMSOL™, experiments should be carried out to measure air velocities introduced by the fan. Actually the fan introduces a pressure differential causing the air to flow with increased velocity. The goal of this experiment is to establish a relation between the applied voltage of the fan and the generated air velocities close to the fan. In order to measure air velocities, a pitot tube is installed near an operating fan, see Figure 12. The pitot tube is connected to a measurement device, being able to measure pressure differences. According to the principle of a Pitot tube, the velocity follows from:

2 p

v

(2.33)

In order to get a good impression about the characteristic magnitude of velocities over the radius of the fan, the velocity profile, the pitot tube is moved in radial direction with a fixed increment in radial direction.

2.3 Modeling setup

2.3.1 Heated vertical plate According to the presented method, first a heated vertical plate is modeled, see Figure 13. For symmetry reasons only half of the plate is modeled. Height )b represents the heated vertical plate surrounded by air.

Figure 12. Schematic view of experimental setup.

Fan

Measurement device

Pitot tube

22

Table 2. Parameters and its value corresponding with the heated vertical plate.

Parameter Value Dimension (a) 0.26 [m] (b) 0.59 [m] (c) 0.15 [m] (d) 0.1 [m]

T 21 [°C]

radT Varies [°C]

Radiator material Cast iron Radiator thickness 0.02 [m] Surroundings Air Element type Lagrange Discretization Galerkin Analysis type Stationary The radiator is modeled in COMSOL™ Multiphysics 3.5a as 2-dimensional, with the options general heat transfer (GHT) and weakly compressible Navier-Stokes (NS) enabled. The reader is referred to Figure 13 in combination with Table 2 for dimensions and other parameter values. Applied boundary conditions: GHT: - left boundary of radiator: radiator temperature is prescribed - right boundary of radiator: convective surface condition boundary condition - on the right boundary of the model a temperature is the ambient temperature prescribed. - bottom, top and left pieces above and under the plate are insulation/symmetry boundaries. - in the middle of the half-plate a temperature is prescribed, either 30°C, 40°C and 60°C respectively.

b

d

a

c

Figure 13. Heated vertical plated with dimensions. For symmetry reasons only half of the plate is modeled. Height b) represents the heated vertical plate surrounded by air.

23

NS: - right boundary: open boundary, no normal stress - bottom and radiator boundaries: wall, no slip - pieces below and above radiator: symmetry boundary - top boundary: outlet; no normal stress Stability parameters: Numerical solutions of transport equations can sometimes exhibit oscillations even when the exact solutions are smooth. These spurious oscillations are caused by numerical instabilities. COMSOL™ provides a set of stabilization techniques (Comsol1, 2009) i.e. isotropic diffusion and streamline diffusion, including anisotropic diffusion, streamline upwind Petrov-Galerkin (SUPG) and Galerkin least-squares (GLS). The added diffusion definitely dampens the effects of oscillations and impedes their propagation to other parts of the system. Isotropic diffusion: isotropic diffusion is equivalent to adding a term to the physical equation. The new term is a tuning parameter

id with recommended values less than 0.5

id (Dillon, et

al., 2009). The effect of isotropic diffusion is to dampen oscillations and impede propagation of oscillations. Anisotropic diffusion: anisotropic diffusion is similar to isotropic diffusion method but occurs only in the direction of the streamline. Like isotropic diffusion, anisotropic diffusion modifies the equation with an additional term. The COMSOL documentation suggests values for anisotropic diffusion

sd should be less than

sd0.25 (Dillon, et al., 2009).

It is not always necessary to set the value of isotropic diffusion as high as 0.5 to get a smooth solution, and it should be chosen smaller if possible. For the modeling of this case the stability techniques adding isotropic diffusion and anisotropic diffusion are used.

2.3.2 Extended model of the radiator with an add-on-fan.

Figure 14. Radiator in more realistic context. Now the radiator is modeled with a copper core, covered with iron plating and surrounded with air.

b

d

a

c

24

Table 3. Parameters and its value for the extended radiator model.

Parameter Value Dimension (a) 0.26 [m] (b) 0.59 [m] (c) 0.15 [m] (d) 0.1 [m]

T 21 [°C]

radT Profile, see

eqn. (2.34) [°C]

Radiator material Copper core Iron plating

Fan height 0.025 [m] Fan width 0.09 [m] Wall emissivity (concrete)

0.94 [-]

Radiator emissivity 0.954 [-] The radiator is modeled in COMSOL™ Multiphysics 3.5a as 2-dimensional, with the options general heat transfer (GHT) and weakly compressible Navier-Stokes (NS) enabled. The reader is referred to Figure 14 in combination with Table 3 for dimensions and other parameter values. The applied temperature profile is determined by computational estimation of the temperature profile over the height of a radiator, reading rad offset offset

0.8795 24.904 45 [ C]T y y y y

, (2.34)

which gives for an offset

offset0.15y m a temperature of 60°C at the top of the radiator (

0.59 0.15 0.74y m) and a temperature of 45°C at the bottom of the radiator ( 0.15y m). In order to obtain the extra heat output from the radiator by using add-on-fans the mass flow through the radiator is assumed to be constant. Boundary conditions: - on the right boundary of the model a temperature is the ambient temperature prescribed. - bottom, top and left pieces above and under the plate are insulation/symmetry boundaries. - in the middle of the half-plate a temperature is prescribed, either 30°C, 40°C and 60°C respectively. Modelling add-on-fans. The approach within this project to include add-on-fans in the model is by applying a volume force on a rectangular subdomain with dimensions similar to fan dimensions (0.09 x 0.045 m), see chapter 2. Case study on hydronic heating system. The volume force is chosen such that the product of the volume force with the height of the fan yields a pressure (difference) on the

4 http://www.infrared-thermography.com/material-1.htm

25

cross-sectional area 3 2N m m N m Pa . This pressure difference should be equal

to the differential fan pressure obtained from fan measurements. For example, if a fan with height 0.09 m typically generates air with average velocity 3 m/s at a certain voltage over it, a volume force of 3/0.09 = 33.33 N/m3 should be entered in COMSOL™ as a volume force acting on the subdomain representing the fan. Isotropic diffusion is used as a stability technique in these simulation series.

26

27

3. Results In this chapter the results of the case study as explained in chapter 2 are presented. This chapter starts with the results from simulations with a heated vertical plate, including model validation with literature, stability parameter investigation in relation to accuracy and continues with results from simulations with an extended radiator model in the subsequent section. The latter case includes a comparison with manufacturer’s data for a typical type of radiator when radiation is taken into account in the model, the influence on the heat output with and without radiation taken into account in the model and the influence of add-on-fans on the heat output. Ultimately the last section of this chapter is about measurements carried out with a real fan.

3.1 Heated vertical plate

3.1.1 Heated vertical plate model validation As mentioned above, the first case under investigation is the heated vertical plate. Modeling this case without taking convection into account, COMSOL™ yields the following results: Table 4. Results for a heated vertical plate without convection taken into account. Literature values are compared to simulation results.

Temperature 30⁰C Temperature 40⁰C Temperature 60⁰C Source Heat output [W/m] Heat output [W/m] Heat output [W/m] Literature 12.856 31.7243 77.95788 COMSOL 16.60355 41.639315 101.044285 Difference 29.15% 35.53% 29.61% In subsection 2.2.2 Physical model is argued that COMSOL™ seems to overestimate the heat transfer coefficient by roughly 30% and therefore the heat output. This statement is in agreement with the results obtained from simulations with a heated vertical plate, see Table 4. The difference between COMSOL and literature values is close to 30%.

3.1.2 Isotropic diffusion According to the presented modeling setup for the heated vertical plate, for three distinct plate temperatures, 30°C, 40°C and 60°C respectively, the influence of the mesh size and isotropic diffusion parameter

id on the accuracy investigated. The results are displayed in Figure 15,

Figure 16 and Figure 17 for the three temperatures respectively. For more information about simulation data, the reader is referred to appendix A.1 Isotropic diffusion.

28

Figure 15. The error made by introducing different levels of isotropic diffusion for different mesh sizes at constant plate temperature of 30⁰C.

0 0.05 0.1 0.15 0.2 0.25 0.3-20

0

20

40

60

80

100

120

140

160

180

isotropic diffusion, delta value

erro

r (%

)

Error versus isotropic diffusion, Trad=30 degC

Mesh size 0,1Mesh size 0,01Mesh size 0,005Mesh size 0,002Mesh size 0,001Mesh size 0,0005Mesh size 0,0001

29


0 0.05 0.1 0.15 0.2 0.25 0.3-20

0

20

40

60

80

100

120

140

160

180


erro

r (%

)

Error versus isotropic diffusion, Trad=40 degC


30


In general, for all temperatures hold that the error originating from simulations tends to be smaller at smaller mesh sizes. Furthermore, the error tends to decrease at decreasing value of isotropic diffusion, however the error changes sign for very small value of isotropic diffusion for mesh sizes below 0.002 m and is up to -10% off. This smaller error, or higher accuracy, comes at a cost: increased computational time. The computational time required to calculate the heat output tends to increase with decreasing value of isotropic diffusion. Furthermore, the computational time tends to increase dramatically with decreasing mesh size. A detailed optimalization study regarding times is not possible, since COMSOL™ shows some non-reproducible behavior with outliers on computational time. However, the afore mentioned general trend is clearly observed. For more information on computational time, please see appendix A.1 Isotropic diffusion. The error for mesh sizes 0.002 m and smaller tends to converge, whereas the errors at mesh sizes 0.1; 0.01 and 0.05 m seem to be off to a large extend especially for isotropic values above

id = 0.05. The slopes of all lines generally tend to increase for higher temperatures. So, for higher values of

id it is important to choose a sufficient small mesh size in order to reduce the error made.

Since the lines tend to converge, for smaller values of id the error is less dependent on mesh

0 0.05 0.1 0.15 0.2 0.25 0.3-20

0

20

40

60

80

100

120

140

160

180


erro

r (%

)

Error versus isotropic diffusion, Trad = 60 degC


31

size. With this benchmark problem data insight is acquired about the behavior and typical errors made by introducing isotropic diffusion as stabilization technique at different mesh sizes.

3.1.3 Anisotropic diffusion According to the presented modeling setup for the heated vertical plate, for 40°C plate temperature, the influence of the mesh size and anisotropic diffusion parameter

sd on accuracy

is investigated. The results are graphically displayed in Figure 18. For more information about simulation data, the reader is referred to appendix A.2 Anisotropic diffusion.

Figure 18. The error made by introducing different levels of anisotropic diffusion for different mesh sizes at constant plate temperature of 40⁰C.

The error made by introducing different levels of anisotropic diffusion sd seems to be

independent for the extent to which anisotropic diffusion is introduced in the model. Moreover, the absolute error is larger compared to the case when isotropic diffusion is introduced in the model, therefore anisotropic diffusion is not used in further simulations as stabilization technique. The general trends observed for isotropic diffusion seems to be present in this case as well: the error tends to decrease for decreasing mesh size and the computational time tends to rise with decreasing mesh size and decreasing anisotropic diffusion.

0 0.05 0.1 0.15 0.2 0.25-14

-13.8

-13.6

-13.4

-13.2

-13

-12.8

-12.6

-12.4

-12.2

-12

anisotropic diffusion, delta value

erro

r (%

)

Error versus anisotropic diffusion, Trad=40 degC

Mesh size 0,001Mesh size 0,0005Mesh size 0,0001

32

3.1.4 Weak constraints and scaling Applying weak constraints and scaling independently seems to have no influence on the results from simulations for the benchmark case, since exactly the same results were obtained when these options were either enabled or disabled. Therefore, these options are not investigated nor used further in this project. Weak constraints is disabled and automatic scaling of COMSOL™ is accepted.

3.2 Extended radiator model

3.2.1 With temperature profile and radiation The radiator is modeled as a copper plate covered with iron plates as outlined in the modeling setup. A concrete wall, radiator temperature profile and radiation is applied in the model, in order to compare the outcome with manufacturer data (Len10). Manufacturer: Lenhovda Radiator type: Panelradiator MP Number of channels: 25 Length: 1000 mm Heat output: 330 W Temperature: radiator temperature profile (supply 60°C, return 45°C) Room temperature: 21°C The manufacturer’s data is included in Appendix C. Manufacturer’s data. The heat output obtained from the radiator model in COMSOL is compared to manufacturer’s data in Table 5. Table 5. Heat output Q from radiator model with radiation for different values of isotropic diffusion compared with the manufacturer’s data. Delta is the isotropic diffusion parameter.

delta = 0.5 delta = 0.4 delta = 0.3 delta = 0.2 delta = 0.1 delta = 0.05 delta = 0.01

Side Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Left 258.323 254.357 246.322 231.591 203.849 178.91 144.019 Right 332.943 310.162 286.104 260.233 231.28 214.605 199.129

Total model

591.266 564.519 532.426 491.824 435.129 393.515 343.148

Error 79.17% 71.07% 61.34% 49.04% 31.86% 19.25% 3.98% Table 5 shows a decreasing error with decreasing value of the isotropic diffusion parameter

id ,

reaching a minimum error of roughly 4% at id =0.01. The model seems to be very accurate in

modeling the radiator compared to manufacturer’s data. Moreover, the influence of radiation as heat transfer mechanism is clearly observed as the heat output from both sides of the radiator is not equal.

3.2.2. With temperature profile and without radiation The radiator heat output is investigated with and without radiation taken into account. The results are displayed in Figure 19.

33

Figure 19. The radiator heat output as function of the isotropic diffusion parameter with and without radiation taken into account.

Both curves show the same shape, independent whether radiation is included or not. The heat output seems to be independent of isotropic diffusion, since the distance between the graphs is almost equal for every value of isotropic diffusion. The extra heat output from radiation ranges from double heat output at lowest values of isotropic diffusion to 45% at the maximum value of isotropic diffusion in this graph. The share of radiation in heat output from a hydronic radiator typically makes up for 50-60%, which is obtained at isotropic values above 0.2. A plausible explanation for this result is not yet found, however the results seems to be realistic according (Trüschel, 1999).

3.2.3. With temperature profile, without radiation, with add-on-fan The radiator heat output for add-on-fans applied is investigated without radiation taken into account for different mesh sizes at different values of isotropic diffusion. The add-on-fan is modeled by the application of a volume force on the subdomain representing the fan as outlined in the modeling setup section. The magnitude of the volume force is 10 N/m3, which followed from the fan measurements. The reader is referred to subsection 3.3 Fan measurements for more details. The numerical solution is shown in Figure 20. The left panel shows the pressure distribution and velocity field without add-on-fans. The pressure distribution and velocity field

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5150

200

250

300

350

400

450

500

550

600


Hea

t out

put f

rom

radi

ator

(W)

Heat output as function of the isotropic diffusion parameter

RadiationNo radiation

34

with add-on-fans are shown in the right panel, showing an increased air velocity especially along the radiator plate and above.

Figure 20. COMSOL™ solution. The surface indicates pressure and the arrows indicate the velocity field. Left: without fan

included in the model. Right: with fan included in the model.

The numerical results are given in Table 6, Table 7 and Table 8, from which the data is displayed in Figure 21.

35

Figure 21. The radiator heat output as function of the isotropic diffusion parameter without radiation taken into account and for different mesh sizes with and without add-on-fans applied.

Table 6. Total radiator heat output without and with add-on-fan applied for a mesh size of 0.001m at different values of the isotropic diffusion parameter. HO means heat output and delta is the isotropic diffusion parameter.

Mesh 0.001m

delta = 0.2 delta = 0.1 delta = 0.05 delta = 0.015 delta = 0.01

Side Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Without fan

Left - 128.2663 104.5105 82,699715 79,31032 Right - 111.0808 94.32942 80,417132 78,1482 Total - 239.347 198.84 163.117 157.459

With fan Left 221,139508 175,698032 141,719691 107,463074 - Right 197,330534 154,34792 126,625949 102,056963 - Total 418.47 330.046 268.346 209.52

Extra HO Total % - 37.88% 34.96% 28.45% -

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11150

200

250

300

350

400

450

500

550

Isotropic diffusion, delta value

Hea

t out

put f

rom

radi

ator

(W)

Heat output as function of the isotropic diffusion parameter with and without fan

Mesh 0,001m no fanMesh 0,001m fanMesh 0,002m no fanMesh 0,002m fanMesh 0,005m no fanMesh 0,005m fan

36

Table 7. Total radiator heat output without and with add-on-fan applied for a mesh size of 0.002 m at different values of the isotropic diffusion parameter. HO means heat output and delta is the isotropic diffusion parameter.

Mesh 0,002m



Left - 149,082986 117,894 88,3328 83,5938 Right - 129,201613 105,592 85,2379 81,8248 Total - 278.2846 223.486 173.5707 165.4186

With fan Left - 207,512594 163,517 117,233 108,517 Right - 186,452113 147,71 112,548 106,221 Total - 393.9647 311.227 229.781 214.738

Extra HO Total % - 41.57% 39.26% 32.38% 29.81% Table 8. Total radiator heat output without and with add-on-fan applied for a mesh size of 0.005 m at different values of the isotropic diffusion parameter. HO means heat output and delta is the isotropic diffusion parameter.

Mesh 0,005m


Side Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Without Fan

Left - 199,35 153,16 103,605 95,1049 Right - 173,47 135,951 100,703 94,0917 Total - 372.82 289.111 204.308 189.197


Extra HO Total % - 42.63% 43.98% 40.80% 41.42% As being part of the theoretical framework, from Figure 11 a heat output of 160 W is calculated without fans. In Table 6 is given that for a mesh size 0,001 m and isotropic diffusion value

id =

0.01 the heat output equals 157 W, which means -1.9% off compared to the theoretical framework. In Table 7 and Table 8 the heat output equals 165 W and 189 W for mesh size 0,002 and 0,005 m respectively. In the latter cases the error is somewhat larger, due to inaccuracies introduced by a using a courser grid according to what the benchmark problem has learned in this context. The simulated values are in accordance with the theoretical framework for heat output without fans. Another result is that the heat output from both sides of the radiator appears to be almost equal. This could be explained by the fact that radiation is not taken into account in this model. To this end, compare for instance the values for the left and right heat output without fan at mesh size 0.001 m at isotropic diffusion 0.01 in Table 6. This shows that the assumptions in the theoretical framework are valid, since here is assumed that the total heat output is the sum of the heat output from both sides. With the application of add-on-fans Table 6 and Table 7 show that the heat output is increased in the order of 30% for low values of isotropic diffusion, which is in the same order of magnitude as field studies have shown (Johansson, et al., 2010).

37

3.3 Fan measurements The fan measurements have been carried out in a laboratory environment with a Pitot tube as explained in section 2.2.4 Fan differential pressure experiments. The results are displayed in Figure 22.

Figure 22. Pressure difference as function of radial coordinate of the fan at 7.502 V. Half of the fan is displayed here.

As visualized in Figure 22 the differential pressure varies over the radius of the fan, since in the center (x=4 cm) the fan is mounted to the frame with bearings, affecting the flow obviously. From this data, an average pressure difference of 1,01 Pa is computed at 7.502 V. Computing the corresponding velocity with equation (2.33) yields 1.3v m/s. In order to model this fan in COMSOL™ the following volume force should be applied on the subdomain: FY = 1.01 / 0.09 = 11.22 N/m3. A remark should be made here: fans are usually mounted in an array with two, three or even more fans, dependent on the length of the radiator. Local velocities may vary due to air gaps between two subsequent fans, resulting in likely a lower average velocity. As an approximation, a volume force of 10 N/m3 is applied on the subdomain in COMSOL™. At the spot where the pressure difference equals the average value, as a chosen representative point for the differential pressure of a fan, an investigation is carried out about the relation between applied fan voltage and pressure difference. The results are displayed in Figure 23.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Radial coordinate [m]

Pre

ssur

e di

ffere

nce

[Pa]

Pressure difference as function of radial coordinate

[cm]

38

Figure 23. Pressure difference as function of applied fan voltage.

Figure 23 shows that the pressure difference increases when the voltage over the fan is increased. The voltage range indicated in Figure 23 corresponds to the range indicated by the manufacturer of the fan. Below 3 V the fan is apparently not able to overcome friction, resulting in a non-rotating device. The aim of this result is to characterize the behavior of a fan with a certain voltage over it. Moreover, this result can be used for comparing simulations with real life situations.

2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

3

3.5

Fan voltage [V]

Pre

ssur

e di

ffere

nce

[Pa]

Pressure difference as function of fan voltage

39

4. Discussion Regarding the objectives of this project and the presented results in chapter 3, conclusions are drawn in this chapter. Furthermore, recommendations for future research are given. Benchmark problem According to the literature study, COMSOL™ seems to overestimate the heat transfer coefficient by roughly 30% and therefore the heat output for laminar flow. For 9Ra>10 (turbulent flow) COMSOL™ seems to overestimate the heat transfer coefficient as well, but to a lower extent as is concluded from Figure 6. This conclusions are in agreement with the results obtained from simulations with a heated vertical plate, see Table 3. The difference between COMSOL™ results and literature values is close to 30% off. Isotropic seems to be a good choice for obtaining numerical stability in the solution at the expense of introducing a slight error in the results. The results for the benchmark problem have given insight in the behavior of COMSOL™ connecting either the influence of mesh size or the value of isotropic diffusion introduced in the model on the accuracy. In general, for three different temperatures hold that the error originating from simulations tends to be smaller at smaller mesh sizes. Furthermore, the error tends to decrease at decreasing value of isotropic diffusion. A maximum absolute error of 10% is observed for very small values of isotropic diffusion at mesh sizes below 0.002 m. Moreover, the computational time required to calculate the heat output tends to increase with decreasing value of isotropic diffusion. In addition, the computational time tends to increase dramatically with decreasing mesh size. Results for three different temperature levels show a trend that the slopes of all lines generally tend to increase for higher temperatures. So, for higher values of

id it is important to choose a

sufficient small mesh size in order to reduce the error made. Since the lines tend to converge, for smaller values of

id the error is less dependent on mesh size.

Since the results have shown a quite high accuracy at low values of isotropic diffusion, this stability technique is used for the remainder of this project in order to obtain stable solutions. Simulations with anisotropic diffusion as stabilization technique have shown that the error made by introducing different levels of anisotropic diffusion

sd seems to be independent for the extent

to which anisotropic diffusion is introduced in the model. Moreover, the error is larger compared to the case when isotropic diffusion is introduced in the model. Therefore, anisotropic diffusion is not used in further simulations as stabilization technique. Extended model A series of simulation with and without radiation taken into account have shown that the heat output seems to be independent of isotropic diffusion, since the distance between the graphs is almost equal for every value of isotropic diffusion. From this results one may conclude that the difference in heat output modeled with and without radiation is a realistic result for a wide range of isotropic diffusion present in the model. The share of radiation typically makes up for 50-60% of the heat output. A plausible explanation for this behavior is not yet found, however the results seems to be realistic according (Trüschel, 1999). In order to validate the extended radiator model with available analytical data, manufacturer’s data has been used to compare COMSOL’s results. Incorporating important properties learnt from the benchmark problem resulted in modeling the extended radiator with a maximum

40

absolute error of 4% compared to manufacturer’s data. Therefore one may conclude that the extended radiator model seems to give realistic results. Once the extended model has been verified, it can be used to model add-on-fans. In order to model the fans in a realistic way, measurements have been carried out on a fan, resulting in an average pressure difference 1,01 Pa when operating at 7.502 V. This pressure difference corresponds to a velocity of 1.3v m/s. In order to model this fan in a correct way in COMSOL™ a volume force of 10 N/m3 is applied on a subdomain with dimensions equal to fan dimensions. It should be noted that fans are usually mounted in an array with multiple fans, causing likely a non-uniform velocity field with lower average air velocity induced by the differential pressure of the fan. With add-on-fans included in the model, it appears that the heat output without fan on both sides of the extended model is comparable. Therefore, the results are in agreement with the theoretical framework, since uniform temperature on both sides is assumed. With the application of add-on-fans Table 6 and Table 7 show that the heat output is increased in the order of 30% for a specific fan operation point, which is in the same order of magnitude as field studies have shown (Johansson, et al., 2010). This project does not entirely fulfill its objectives and, as a result, future research is recommended for this case study. Since this project aims to investigate the influence of air velocities introduced by add-on-fans on the heat output of hydronic heating systems and in this project extra heat output for one value of air velocity is calculated, different air velocities should be modeled in order to meet the objectives entirely. Especially Figure 23 could be helpful for this purpose, i.e. modeling add-on-fans under different conditions. Another improvement of the model could be realized by taking into account radiation in combination with the add-on-fans. With these improvements, a model will resemble to reality to a larger extent. In line with this improvements, one may think of enlarging the spatial dimensions of the model in order to allow for circulation in the room. Another improvement to achieve a more realistic model could be made by modeling physical heat losses (i.e. window). Ample changes could be proposed here, however this chapter concludes with the recommendation to investigate the influence of other temperature profiles on the extra heat output by add-on-fans.

41

Acknowledgements This work has been carried out at the Department of Energy Sciences from the Faculty of Engineering, Division of Efficient Energy Systems at Lund University. I would like to thank my direct supervisors Associate Professor Janusz Wollerstrand and PhD student Per-Olof Johansson for the opportunities, guidance, support and valuable comments they have given me during my project. I am grateful to PhD-students Patrick Lauenburg, Hedvig Paradis, Farhad D. Rad and people from other departmens in the M-house for the good ambiance in the coffee room and nice discussions about virtually everything. The kindness of all people involved in the second and fourth floor of the M-house made me feel very welcome and comfortable. Furthermore, I would like to thank my professor at Eindhoven University of Technology, prof. dr.ir. A.A. van Steenhoven for giving me the opportunity to do my internship abroad in such a nice environment. Finally, I would like to thank Rickard Solsjö, Henning Karlsson and Ali Alsam for their support, the good ambiance in our room and the numerous moments we had a good fresh coffee or at least a discussion about it. All people mentioned here have contributed to making my time in Lund one of the most memorable periods in my life.

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Persson, Tommy. 2005. District Heating for Residential Areas with Single-Family Housing. Lund : s.n., 2005. Doctoral thesis.

Skagestad, Bard and Mildenstein, Peter. 1999. District heating and cooling connection handbook. 1999. International energy agency.

Sundén, prof. B. 2001. Kompendium i värmeöverföring. Lund University : Lunds Tekniska Högskola, 2001. Publikation 2001/1.

Swedish energy agency. 2007. Energy in Sweden. 2007.

Trüschel, A. 1999. Värmesystem med luftvärmare och radiatorer - en analys av funktion och prestanda (Heating systems consisting of air heating coils and hot water radiators - an analysis of operation and performance). Gothenburg, Sweden : Licentiate thesis, Chalmers, 1999.

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Appendix A. COMSOL™ Simulation data In this appendix the data for the isotropic diffusion investigation is included.

A.1 Isotropic diffusion In this case the isotropic diffusion as stability parameter is investigated. (All files are in the folder \Isotropic_diff) Procedure: - mesh size on subdomain air = 0.01 m - stabilization parameters: HT: streamline diffusion (GLS) + isotropic diffusion NS: streamline diffusion (GLS) + isotropic diffusion T_rad = 30°C delta = 0,3 delta = 0,2 delta = 0,1 delta = 0,05 delta = 0,01 Mesh size (on boundary 8)

Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m]

0,1 46.002 38.4664 29.2268 23.2678 16.752 0,01 46.002 38.4664 29.2268 23.2678 16.752 0,005 42.45239 35.3026 26.7898 21.5451 16.155 0,002 33.443 28.2076 22.2051 18.6808 15.3368 0,001 29.3295 25.0919 20.3251 17.5907 15.0732 0,0005 26.6512 23.1503 19.2193 16.9748 14.9297 0,0001 24.5896 21.6594 18.3739 16.5072 14.8228 delta = 0,3 delta = 0,2 delta = 0,1 delta = 0,05 delta = 0,01 Mesh size (on boundary 8)

Time [s] Time [s] Time [s] Time [s] Time [s]

0,1 26.625 28.749 31.609 31.171 38.984 0,01 16.515 26.063 29.297 26.094 29.343 0,005 17.328 27.875 31.141 27.547 31.188 0,002 23.984 38.156 38.218 38.14 42.734 0,001 48.968 71.468 56.625 57.218 81.905 0,0005 71.952 125.201 149.091 146.857 151.788 0,0001 735.725 538.04 578.102 459.369 582.758 Literature: h_ave = 2.421 W/m^2K Q = 12.856 W COMSOL: Q = 16.60355 W/m T_rad = 40°C delta = 0,3 delta = 0,2 delta = 0,1 delta = 0,05 delta = 0,01 Mesh size (on boundary 8)


0,1 133.728 110.99 82.929 64.6059 44.0681

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0,01 133.728 110.99 82.929 64.6059 44.0681 0,005 122.554 100.988 75.1842 59.1108 42.1183 0,002 94.5943 78.7958 60.56 49.7188 39.2312 0,001 81.502 68.7882 54.4143 46.0957 38.3255 0,0005 72.7132 62.3621 50.710 44.0106 37.831 0,0001 65.7605 57.3535 47.8779 42.4399 37.4687 delta = 0,3 delta = 0,2 delta = 0,1 delta = 0,05 delta = 0,01 Mesh size (on boundary 8)


0,1 16.5 29.328 29.438 32.968 32.234 0,01 30.124 44.703 39.484 31.25 34.016 0,005 92.719 61.406 60.094 61.765 61.906 0,002 29.203 57.016 62.625 52.188 42.437 0,001 35.452 87.609 90.608 90.093 84.296 0,0005 77.093 158.404 174.341 162.326 171.67 0,0001 285.903 449.635 506.728 452.338 452.603 Literature: h_ave = 2.83 W/m^2K Q = 31.7243 W COMSOL Q = 41.639315 W/m T_rad = 60°C delta = 0,3 delta = 0,2 delta = 0,1 delta = 0,05 delta = 0,01 Mesh size (on boundary 8)


0,1 371.498 306.62 226.116 173.042 112.475 0,01 371.498 306.62 226.116 173.042 112.475 0,005 338.781 277.265 203.359 156.956 106.825 0,002 257.674 212.523 160.128 128.649 97.6111 0,001 218.922 182.668 141.49 117.462 94.6996 0,0005 192.178 162.95 129.983 110.915 93.1178 0,0001 170.507 147.369 121.174 106.01 91.9732 delta = 0,3 delta = 0,2 delta = 0,1 delta = 0,05 delta = 0,01 Mesh size (on boundary 8)


0,1 34.155 43.28 62.218 65.639 44.937 0,01 22.64 48.843 42.655 52.843 55.889 0,005 59.454 60.688 69.781 63.5 62.531 0,002 76.156 44.406 46.578 42.453 46.937 0,001 61.281 92.374 67.999 88.108 103.405 0,0005 82.406 166.592 176.029 167.841 188.545 0,0001 294.809 517.384 510.963 504.384 503.478 Literature: h_ave = 3.388 W/m^2K Q = 77.95788 W

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COMSOL: Q = 101.044285 W/m

A.2 Anisotropic diffusion Procedure: - T_rad = 40°C - mesh size on subdomain air = 0.01 m - results retrieved from control line (see model figure) - run the model with isotropic diffusion gradually decreased from 0,5 to 0,01 in order to get proper starting values. HT: streamline diffusion enabled NS: streamline diffusion (GLS) + isotropic diffusion 0.1 - HT: change streamline diffusion from GLS in anisotropic diffusion (default is

sd =0.25), run

- HT: untick isotropic diffusion, run - NS: untick streamline diffusion (GLS), run - NS: choose non-isothermal flow with T as variable, run (gives the same result as previous line) Delta = 0.25 delta = 0.2 delta = 0.1 delta = 0.05 delta = 0.01 Mesh size (on boundary 8)


0,1 - - - - - 0,01 - - - - - 0,001 -35.823456 -35.812157 -35.789691 -35.778546 -35.769665 0,0005 -35.91078 -35.90147 -35.882991 -35.873843 -35.866566 0,0001 -35.973085 -35.963942 -35.945855 -35.936943 -35.929877

Delta = 0.25 delta = 0.2 delta = 0.1 delta = 0.05 delta = 0.01 Mesh size (on boundary 8)


0,1 - - - - - 0,01 - - - - - 0,001 31.453 37.796 37.828 37.796 37.781 0,0005 56.234 67.483 67.484 67.077 67.062 0,0001 260.809 312.558 322.183 323.684 313.043

A.3 With and without radiation Complete model with GHT and NS (\Radiator_model2\Radiator_ns_wall_rad_tprofile_ewall09-parsw.mph): - T_rad = profile - mesh size on subdomain air: max 0.01 m - mesh size on middle line radiator (boundary 10): max 0.001 m - stabilization parameters HT: streamline diffusion (GLS) + isotropic diffusion NS: isotropic diffusion

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- wall emissivity 0.9 [-] - emissivity radiator 0.95 [-] Parsweep (values are in file \Radiator_model2\isodiff_parsweep_ewall09.txt) delta = 0.5 delta = 0.4 delta = 0.3 delta = 0.2 delta = 0.1 Delta = 0.05 Delta = 0.01

Side Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Left (b.10)

258.323 254.357 246.322 231.591 203.849 178.91 144.019

Right (b16)

332.943 310.162 286.104 260.233 231.28 214.605 199.129

Total 591.266 564.519 532.426 491.824 435.129 393.515 343.148

delta = 0.5 delta = 0.4 delta = 0.3 delta = 0.2 delta = 0.1 Delta = 0.05 Delta = 0.01

Mesh size Time [s] Time [s] Time [s] Time [s] Time [s] Time [s] Time [s] 0,001 169.452 215.295 245.311 345.466 1987.456 2751.779 3554.883 Without radiation Folder: \Different_grid_and_iso\grid_001\NO_fan\no_fan_isoxx delta = 0.5 delta = 0.4 delta = 0.3 delta = 0.2 delta = 0.1 Delta = 0.05 Delta = 0.01

Side Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Q [W/m] Left (b.10)

210.113454 199.704724 184.279943 161.732232 128.2663 104.5105 79.31032

Right (b16)

212.502803 189.834329 165.851465 140.016531 111.0808 94.32942 78.1482

Total 422.616257 389.539053 350.131408 301.748763 239.3471 198.83992 157.45852

A.4 With and without add-on-fans Mesh 0,001m



Left - 128.2663 104.5105 82,699715 79,31032 Right - 111.0808 94.32942 80,417132 78,1482 Total - 239.347 198.84 163.117 157.459

With fan Left 221,139508 175,698032 141,719691 107,463074 - Right 197,330534 154,34792 126,625949 102,056963 - Total 418.47 330.046 268.346 209.52

Extra HO Total % - 37.88% 34.96% 28.45% -

Mesh 0,002m



Left - 149,082986 117,894 88,3328 83,5938 Right - 129,201613 105,592 85,2379 81,8248 Total - 278.2846 223.486 173.5707 165.4186

With fan Left - 207,512594 163,517 117,233 108,517 Right - 186,452113 147,71 112,548 106,221

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Total - 393.9647 311.227 229.781 214.738

Extra HO Total % - 41.57% 39.26% 32.38% 29.81%

Mesh 0,005m



Left - 199,35 153,16 103,605 95,1049 Right - 173,47 135,951 100,703 94,0917 Total - 372.82 289.111 204.308 189.197


Extra HO Total % - 42.63% 43.98% 40.80% 41.42%

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Appendix B. Fan measurement data Fan measurement data to be included. Radial position [m] Pressure difference [Pa] 0 0.7 0.5 1.0 1.0 1.45 1.5 1.6 2.0 1.45 2.5 1.05 3.0 0.6 3.5 0.35 4.0 0.2 Voltage U [V] Pressure difference [Pa] 3.018 0.2 3.508 0.25 3.999 0.3 4.501 0.4 5.003 0.45 5.500 0.5 6.004 0.65 6.507 0.75 7.008 0.85 7.502 1.05 8.00 1.1 8.51 1.3 9.01 1.55 9.50 1.6 10.00 1.9 10.50 2.05 10.99 2.15 11.51 2.2 12.01 2.3 12.52 2.65 13.00 2.7 13.51 3.25

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Appendix C. Manufacturer’s data In the table below, manufacturer’s data of the radiator is given(Len10). The radiator under unvestigation in this project is with height (Swedish: höjd) 590 mm and length (Swedish: längd) 1000 mm and according to the table below yields 330 W.

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