THE EFFECT OF A THIN FOIL ON THE HEAT LOSSES BEHIND A RADIATOR

Transcription

1 F A C U L T Y O F E N G IN E E RIN G A ND SUST A IN A B L E D E V E L OPM E N T THE EFFECT OF A THIN FOIL ON THE HEAT LOSSES BEHIND A RADIATOR Núria Barguilla Jiménez February 2013 Master s Thesis in Energy Systems Master Program in Energy Systems Examiner: Ulf Larsson Supervisor: Mathias Cehlin and Jan A kander

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3 Abstract This thesis work is the study of the effect of an aluminium foil on the losses that produced by a radiator, situated under a window, through the wall behind it. The reason behind this topic is due to the energy problem and the different goals that governments have set up to try to reduce the use of energy. For example, more specifically a Swedish national goal is to decrease the energy use of the built stock with 50% by For this purpose, an experimental set up was built in the University of Gävle, Sweden. The arrangement was composed by a radiator and a window facing a climate chamber. A total of twenty one temperatures and two heat fluxes in the exterior wall were measured in the set up. Ten different measurement scenarios with different radiator temperature, 40 C, 50 C and 60 C; two different distance between the radiator and the wall, 5 and 9 centimetres and with and without the aluminium foil, were performed. With the experimental results, a CFD model was validated. Two different models were done, first a 2D model and afterwards a 3D model. For the turbulence, the chosen model was standard k ε model. There were 54 cases simulated with the 2D model and the 3D model was used just for validation. The cases had different variables such as radiator temperature, outdoor temperature and wall insulation. With these cases, analysis of the effectiveness of the presence of an aluminium foil behind the radiator is performed to evaluate if there is a significant reduction of the losses. The results showed with both methods that the aluminium foil reduces the losses of the wall behind the radiator. The savings varied depending on the boundary conditions of the case and it were obtained a maximum of 4% and a minimum of 1,3%.

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5 Nomenclature A Area [m 2 ] D Distance de between radiator and wall [cm] K Constant of the heat power of a radiator equation n Exponent of the heat power of a radiator equation q Heat flux [W/m2] Q extra Q rad Q req Q wall R R e R i T e T i T rad Heat loss at the of the back wall associated with the type of heating system [W] Heat power of the radiator [W] Heating requirement of the room [W] Heat loss at the back wall [W] Conduction resistance of the wall [m 2 K/W] Convection outdoors resistance [m 2 K/W] Convection indoors resistance [m 2 K/W] Outdoor temperature [ C] Indoor temperature [ C] Radiator temperature [ C] U U value [W/m 2 K] y Distance from the floor [cm] ε Emissivity Sub index Al CFD Lab Presence of Aluminium Result from CFD Result from experimental set up

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7 Table of Contents Nomenclature 5 1 Introduction Background Objectives Related works Theory Aluminium foil CFD Models Boundary Conditions Method Laboratory Assembly Measurements Thermocouples Thermopile Software Methodology Conditions Limitations CFD Gambit Ansys Fluent Savings Calculation Results and discussion Experimental... 35

8 4.2 CFD D Validation D Validation Savings Calculation Comparison of the different cases Conclusion References.. 55 Appendices. 57

9 1 Introduction 1.1 Background Nowadays there is a worldwide problem that needs to be solved in a relatively short period of time. That problem is the production of energy. The consumption of energy is very high and it is going to increase in the next years due to a population growth and increased standard of living in developing countries. Also the data show that around 80% of primary energy used in the world comes from non renewable sources. [1] Because these sources are limited, it is urgent to try to find a solution. Moreover most of these non renewable sources are fossil fuels, which entail the production of CO 2. Linked to this issue there is also the problem of climate change that comes due to the emissions of CO 2. [2] To find the answer to these problems there is two ways face them. The first one is to try to find others ways to produce energy and the second one, try to reduce the consumption or try to make systems that are more efficient. During 2004, the building and service sector account for 40% of the energy use in the EU, thus using more energy than in each of the industrial and transportation sectors [1]. A majority of the consumption comes from the heating in buildings, especially regions with really cold winters such as Sweden. In the next figure, it can be seen the energy consumption divided by sectors in Sweden for the year The energy consumption for residential and services is the 41% of the total consumption. This is equivalent to 166 TWh of which 53 TWh are for heating. [3] 41% 36% Industry Transport Residential and Services 23% Source: Swedish Energy Agency Fig.1: Energy consumption in Sweden (2010) 9

10 Another factor is that a Swedish national goal is to decrease the energy use of the built stock with 50% by 2050, in comparison to energy used in [5] In order to achieve this goal, the energy use of the old building stock has to substantially be reduced, see for example [4]. This will be a costly process, which has to be commenced today and most likely continue beyond The figure number two shows the energy consumption in Sweden during the lasts decades. It can be seen that there is a growing tendency of the energy consumption. [3] The dip in 2009 is due to the global financial crisis (reduced energy use in the industry) and the increase in 2010 is due to a severely cold winter (increase in the energy use of the residential and services sector namely buildings). TWh Industry Transport Residential and Services Total Fig.2: Energy consumption evolution in Sweden Between about 1965 and 1975, the building stock in Sweden expanded immensely due to the million programme, see for example [6]. In essence, a total of one million villas and apartments were erected during this period of time. The quick building pace, in combination with testing new building technologies and to keep cost low together with an insufficient level of maintenance, have resulted in that the buildings from that time are in need of renovation or retrofitting. A characteristic of the building technology of the time is that massive materials were used in external walls, such as bricks and aerated concrete. However the radiators, normally placed under the window, were fit in line with the inner surface of the external wall; leaving the only possibility of having a thin wall 10

11 towards the external environment. Usually wood frame walls with mineral wool were mounted there, commonly with thicknesses of 45, 70 or maximum 95 mm. There is a quite amount of energy produced that is lost by the wall behind the radiator since this wall is to be regarded as being poorly insulated. During the 1980 s, this problem was recognized. One option to reduce this loss was to put an aluminium foil in the wall behind the radiator. The foil was placed on the wall surface to reflect the long wave radiation from the radiator, to minimize the heat transfer through the wall. But there were voices that said that this would not work: if the internal surface temperature of the wall is reduced, the heat transfer by convection will increase and thereby deplete the gains made by long wave radiation. Fig.3: Buildings made in 1950 Figure 3 shows a multifamily building that was erected in The external was are made of a layer of bricks (120 mm), an air cavity (25 mm), aerated concrete blocks (200 mm) and about 25 mm mortar. The wall below the windows is a thinner wood frame walls with a higher U value, which has a higher heat loss as seen in the figure. [7] One problem with actions to reduce energy is that often are expensive and this solution is very affordable and with an easy access for many people. Therefore this thesis tries to study the effect of the aluminium foil in the heat losses of a radiator. 1.2 Objectives The main objective of this thesis intends to find a way to reduce the consumption of energy by trying to make a heating system more efficient with low costs. This study will see the effect of an aluminium foil to reduce the radiator losses, since no 11

12 previous scientific studies have found. The foil is placed on the inside surface of the wall, behind the radiator. This includes the following ones: To quantify the reduction of the radiator losses due to the aluminium foil. To measure the radiator losses in an experimental set up installed in a laboratory room. Temperatures and heat fluxes are monitored. To use the CFD method to obtain the radiator losses. To compare the two methods used to get the results. To study the effect in different cases, these ones will include the outdoor temperature, the thermal insulation level of the wall behind the radiator and the temperature of the radiator. 1.3 Related works There are not a lot of studies in this field but some related works are the following: The effect of wall emissivity on radiator heat output [8]. This work studied variation of the heat output of a panel radiator altering the emissivity of the wall behind the radiator. It was done with both methods, experimental and CFD. The results indicated that the heat that the heat output could be increased by 20% with a black wall instead of a reflective one. The effect of surface roughness and emissivity on radiator output [9]. This work studied the variation of the heat output altering the emissivity and roughness of the wall behind the radiator. Also it was done experimentally and with CFD. The results indicated that high emissivity and large scale surface increased the heat output about 26%. 12

13 2 Theory 2.1 Aluminium foil The reason why the material to reduce the losses of a radiator is aluminium is because of its low emissivity. This makes that the surface with aluminium foil reflects most part of the heat and does not go through the wall. In this way the radiation is reduced and the losses through the wall behind the radiator are lower. 2.2 CFD The abbreviation CFD stands to computational fluid dynamics and it consists of a numerical method used to analyse systems that involve fluid flow, heat transfer and associated phenomena. This technique started to have a heavy use in the 1980s and until today it is known to be a very powerful method that can be used in a wide range of application areas. The CFD codes are structured around numerical algorithms. The mathematical basis is based on conservation of mass, momentum and energy. The main parts of the CFD method consists in the making the grid, defining the models and boundary conditions and afterwards the solving the model and processing data. [10] Models There are three different physical phenomena that are present in this case. These are energy, turbulence and radiation. The energy equation is derived from the first law of thermodynamics. This one states that the rate of change of energy of a fluid particle is equal to the rate of heat addition to the fluid particle plus the rate of work done on the particle. The turbulence model is used to describe the characteristics of the flow. The CFD code for the turbulence model should have a wide applicability, be accurate, simple and economical to run. There are different models to describe the phenomena. The most common are the classical based on time averaged Reynolds equations and the 13

14 large eddy simulation. In this thesis, the model used is a two equation model: the standard k ε. This model is semi empirical based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (ε). [11] The radiation model used is the discrete ordinates (DO) radiation model solves the radiative transfer equation for a finite number of discrete solid angles, each associated with a vector direction fixed in the global Cartesian system (x, y, z).! [11] Boundary Conditions In this thesis the boundary conditions were wall boundary conditions and a pressure outlet condition. In the wall boundary conditions, there were some parameters that needed to be determined such a fixed temperature, the emissivity or heat transfer coefficient for outdoor convection. To have a good mesh, it has to be evaluated the non dimensional parameter defined as the next equation where Δy & is the distance of the near wall, v the velocity, ρ the density and τ ) the wall shear stress. y * = Δy & v,τ ) ρ Depending of the used turbulence model, the y + has to take a certain value in order to resolve the laminar sublayer. The near wall treatment model in this is enchanted wall treatment that requires y + values lower than 1. 14

15 3 Method 3.1 Laboratory This chapter is about the experimental study. Here the set up will be described, how were the measurements done and which results were obtained. The experimental study took place in a laboratory room at the University of Gävle, Sweden. The laboratory room was built to look like a room with a window Assembly The laboratory assembly it is not complicated. It took place in a laboratory room which was built to look like housing. This room was situated next to a climate chamber that was used to simulate the outdoor temperature. Therefore a window was made in the wall that was facing the climate chamber. Fig.4: Assembly (left picture), Climate chamber (right picture) 15

16 The simulated window was composed of plywood and has the same U value as a double glazed window, namely about 3.0 W/m² K. After that there was a cavity made under the window where a plane electric radiator was located. The radiator was electric and was the type that was working on and off. Since the study has to be in steady state, a voltage regulator was placed with the radiator in order to have a constant temperature. Therefore the temperature could be changed selecting a voltage. With that different temperatures could be reached with a lower limit of 35 C. The whole assembly was painted black in order to have the same emissivity everywhere. This was done to try to be as close as possible of an emissivity of one, which is the emissivity of a black body. The following image shows the measures of the assembly in metres. Fig.5: Assembly measures: frontal view (left), profile view (right) 16

17 3.1.2 Measurements There were made two different types of measurements, temperatures and heat flux. The temperatures were taken from various points, a total of 21, in the different walls as well as the radiator and the floor. There was a total of twenty one different temperatures that were measured in the assembly. These temperatures were obtained with thermocouples (type T). The heat flux was measured with a heat flux sensor (type Huxeflux HFP01). There were a total of two points in the external wall were the measurements were taken. The wires of the thermocouples and the heat fluxes sensors were connected to a printed circuit board. This one transmitted the data to a computer where data could be saved and visualized. The next picture shows how were these measurements placed. Fig.6: Assembly with measurements devices Thermocouples The thermocouples are active sensors used to measure temperatures. They consist of two different conductors, usually metals, which are joined together in the point of measuring. When the junction is heated or cooled, it generates a small voltage signal based on the energy conversion principles and they don t required any external electrical generation. This electric potential is related to the temperature. Their main advantages are small size, stability, ruggedness, moderate sensibility over a 17

18 wide range of temperatures and also they are inexpensive. The main limitation with thermocouples is accuracy, system errors of less than one degree Celsius can be difficult to achieve. Fig.7: Thermocouple The thermocouples that were used were type T, also named copper constantan. This type has the electrodes made of copper (+) and an alloy of copper and nickel ( ). Their range is very wide from 270 C to +400 C. They were stuck in the wall with some duct tape, except the ones in the wall behind the radiator. For theses ones, there were slots made in the wall to put the wires of the thermocouples. This was done to prevent the thermocouples from disturbing the air flow behind the radiator. As said before, there was a total of twenty one points were the temperature was taken. Four of them were measured in the exterior wall, one in the window and the rest in the wall were the radiator was situated; all of them in the middle of the assembly. The exact positions can be seen in the next image, all the measures are in centimetres. 18

19 Fig.8: Position of the thermocouples in the external wall In the wall behind the radiator there was a total of eight different points were the temperature was measured. Five of them were right in the middle of the wall; two of them were the radiator finished and the last one, between the rests. The exact position of the thermocouples can be seen in the next picture, measures in centimetres. The radiator is showed with a discontinuous line. Fig.9: Wall behind the radiator with thermocouples 19

20 There were three thermocouples in the interior wall. Two of them were in the window and the other one, above the window. All of them were situated in the middle section. It can be seen the exact position in the next image. Distances are in centimetres. Fig.10: Internal wall with thermocouples Also there were two thermocouples that measured the temperature of the floor. All in the middle section and situated in a distance of forty cm and eighty cm from the interior wall. There were two measured temperatures of the radiator in order to know if there were differences in different points in the radiator. The last two measured temperatures were the internal and exterior air Thermopile A heat flux sensor is called thermopile. It is a transducer that generates an electrical signal proportional to the total heat rate applied to the surface of the sensor. It is composed with several thermocouples connected in series and sometimes in 20

21 parallel. The measured heat rate is divided by the surface area of the sensor to determine the heat flux. There were two points were the heat flux was measured, these ones were on the external wall behind the radiator. The exact position can be seen in the following image. The distances are in centimetres Software Fig.11: Heat flux sensor positions The software used to obtain the result is called Labview. This is only used to visualize and obtain the temperatures from the thermocouples and the heat flux. Also it was used to see when the system reached steady state. The program was designed to take a measurement every thirty minutes. The next image shows what it looks like. 21 Fig.12: Screenshot of Labview

22 3.1.3 Methodology The process of the laboratory experiments consists in setting up a tension of the voltage regulator to have a certain temperature of the radiator. Turn on the wind tunnel to simulate the exterior temperature and start the monitoring scheme in order to take the measurements. As it can be seen in the figure 12, the experiment was stopped when it reached steady state, i.e. the temperatures were stable. There were performed a total of ten different cases in the laboratory with three variables. These variables are the distance between the wall and the radiator, the temperature of the radiator and with or without the aluminium foil. There were two different positions for the radiator depending on how close it was to the wall. The two distances were five and nine centimetres. There were two temperatures with the first distance; 40 C and 50 C and three with the second one; 40 C, 50 C and 60 C. With this there are five different cases. The rest were with these exact conditions but with the aluminium foil behind the radiator. Case Temperature ( C) Distance (cm) Aluminium No No No No No Yes Yes Yes Yes Yes Table 1: Laboratory cases Every case was simulated until it reached stationary condition. This took around ten hours in every case. In order to obtain one temperature value, it was calculated the mean value with the data in steady state Conditions There were some conditions that were the same in every simulation. These are the following: The outdoor temperature was 20 ±1 C in all the different cases. This temperature was chosen to simulate in the worst of the cases in a Swedish climate. This temperature could not be entirely stable due the working of the wind tunnel. The indoor temperature was 20 C. To accomplish this temperature the door of the testing room was open in order to achieve the room temperature of 22

23 the laboratories (the heat from the radiator would otherwise give different indoor temperatures). In order to not have internal thermal loads that could influence the system, the lights were turned off in all the simulations Limitations There were some limitations that have to be taken into account. These are the following ones: In order to measure the temperature in the external wall, in the wind tunnel, there was made a hole in the window where the wires went though. This could make that part of the heat was lost though this hole, but should be negligible in comparison the heat output from the radiator. There were some extra heat loads that could not be taken from the test room. These are the computer load and heat loss from the voltage regulator. However, these are more or less constant. All the measurement devices have a margin of error. In this case the thermocouples ±1 C and the thermopiles have an error of ±5%. 3.2 CFD The process of working with CFD can be divided in three main parts: pre processor, solver and post processor. In this thesis the pre processor part has been done with two different softwares: Gambit and Ansys Fluent 14.0., while the solver and the post processor part was done just with Ansys Fluent. The pre processor is the most important part because it contains the model design and conditions. It can be divided in different parts: Definition of the geometry: draw the system of interest to study Mesh generation: divide the regions of study in small elements where the solution will be calculated Selection of physical and chemical phenomena that are needed to be modelled. Phenomena such as energy, turbulence, radiation, etc. Definition of material properties used in the studied system Definition of cell zone conditions: define the material of each region 23

24 Definition of boundary conditions: the exterior and the interior The solver is the part where the solution is calculated. The post processor is the part where the solution has been calculated and it can be showed in different plots form such as vector, lines, contour, etc Gambit The methodology in Gambit can be divided in three parts. These are the following: geometry, mesh and conditions. The first step in Gambit is to create points, after that the points are joint with lines that will create surfaces. In the 3D case the surfaces will be used to create the volumes. In this thesis, the control volume is a part of the room with the radiator. Not all the room was drawn because it would have taken a lot of time of solving and because the important part it is the wall behind the radiator. The measures of the control volume can be seen in the figure five. The next image shows the volume control in 2D. 24 Fig.13: Geometry of the 2D cases

25 At first, the idea was to only do a 2D model. Due to the results obtained with the two dimension model, it will be explained in the chapter four; it was decided to also make a 3D simulation. The control volume of the 3D model was only half of the room since it was symmetrical and the 3D simulation takes a long time to solve. The figure 14 shows this geometry in 3D. Number of cells 2D D Fig.14: Geometry of the 3D case The mesh was created using trial and error in order to fulfil the requirement that the value y + was smaller than one. That is because it was used enchanted wall treatment as explained in chapter two. The form of the mesh is rectangular since all the areas are rectangular. The mesh was sharper all around the radiator and near the walls 25

26 because there were high changes. The total number of cells in both cases can be seen in the table number two as well as the mesh in the figure 15. Number of cells 2D D Table 2: Number of cells Fig.15: Mesh of the 2D and 3D case 26

27 3.2.2 Ansys Fluent The software Ansys Fluent is used to simulate fluid dynamics. With the Gambit file opened, there are different things that need to be done in Fluent. The steps to follow consist of finishing the pre processor, solving and getting the results. The first thing in the pre processor is to set up the gravity in the y direction. Afterward set up the models, materials, cell zone conditions and boundary conditions. There are three different models used in this simulation: energy, turbulence and radiation. These are more detailed in the chapter two. The turbulence model used was Standard k ε with enchanted wall treatment and the radiation model is discrete ordinates. There are four different materials involved in this simulation. These are: Air: used with the default properties except for the density that was changed to incompressible ideal gas Wood: used with the default properties for the exterior part of the wall, both in the inside wall and the exterior Mineral wool: for the insulation inside of the wall with a thermal conductivity of 0,04 W/mK Aluminium: used for the wall behind the radiator with an emissivity of 0,1 After defining the materials, it has to be established which areas have each material. The cell zone condition is where this is done. Every region created in Gambit is attributed with the corresponding material. The following figure shows the materials of the model. 27

28 Fig.16: Materials of the control volume There are three different kinds of boundary conditions in this model. The first one is a pressure outlet since this wall it is not a real wall. The backflow temperature is the room temperature, 20 C. The external wall was set up as a convection free steam with a standard heat transfer outdoor coefficient of 25 W/m 2 K, the outdoor temperature took three different values, 20 C, 10 C and 0 C. Another boundary condition is a fixed temperature. This was set up in the floor and the ceiling with a temperature of 20 C and in the radiator where the temperature took three different 28

29 values: 30 C, 40 C and 50 C. The last one is coupled. This one takes place in the internal wall and it is a predetermined option because this wall is only used to transfer the heat. The emissivity of all the surfaces was set up as 0,9 with the exemption of 0,1 on the wall behind the radiator when the aluminium foil was set up. The boundary conditions for the 3D case are the same except that one of the faces had the condition of symmetrical wall. Fig.17: Boundary Conditions 29

30 A total of 54 cases there were performed. There were four variables that were combined: the radiator temperature, the outdoor temperature, the U value and the emissivity of the wall behind the radiator. The distance between the radiator and the wall it was always five centimetres. The value of the variables can be seen in the table three. T rad T e U ε ,36 0, ,48 0, ,62 Table 3: Values of the variables 3.3 Savings Calculation To calculate the reduction obtained with the aluminium foil, the methodology is to compare the results based on the idea of satisfying the same heat requirement of the room for both cases. The equation that involves the different heats is the equation 3.1. This one is obtained with a simple energy balance in steady state taking the simulated room as the control volume. The general equation for how much a radiator dissipates heat is: Q /01 = Q /23 + Q 256/0 (3.1) Where Q /23 is the heating requirement on basis of the transmission and ventilation losses, independent of the heating system type. Q 256/0 is the extra heat loss that is associated with the type of heat emitting system that is used, in this case the radiator that gives extra losses by heating the back wall s inner surface to higher temperatures than an ideal system would. The ideal system creates the indoor temperature without generating extra losses. For any heat emitting system, the heating requirement, Q /23, must be met and this is done at a certain temperature for the considered system. In this case, when the requirement of the room must be fulfilled, the radiator temperature with and 30

31 without the foil will not be identical. It is expected that the convective contribution to the room via the channel behind the radiator is less due to the presence of the aluminium foil. The reduction in convective heat from behind must be compensated by increasing heat emission from the front and this requires that the temperature of the radiator is increased. This will in turn increase heat loss from the wall. With the CFD software it can be directly obtained Q rad CFD and the Q extra CFD for every case, together with the radiator temperature that is associated with each Q / The procedure is as follows: When the calculations have converged to a result, the post processing allows finding the total power emitted from the radiator, Q rad CFD and the power that is totally conducted as loss through the back wall, Q wall CFD. The heat loss power Q wall CFD is composed of the heat loss that is system independent, i.e. U )0;; A )0;; T 2 ) and the extra loss that the radiator creates by heating the wall, Q extra CFD Q )0;; 789 = U )0;; A )0;; T 2 ) + Q 256/0 789 (3.2) The total heat emitted by the radiator, Q rad CFD, which is a function of temperature T rad CFD, will therefore supply Q / Cf(T / )E = Q / Q 256/0 789 (3.3) Insertion of equation 3.2 into 3.3 gives Q / Cf(T / )E = Q / Q )0;; 789 U )0;; A )0;; T 2 ) (3.4) The requirement can for the simulation be established (observe that U )0;; A )0;; T 2 ) implicitly is within Q / ) so that Q / = Q / Cf(T / )E Q )0;; U )0;; A )0;; T 2 ) (3.5) Hereby, Q / is converted to be a function of the temperature difference between the radiator and the indoor air temperature, such as defined in EN 442 [12] and for example Q / = K (T / ) G (3.6) 31

32 Giving, expressed with indexes for the case without aluminium: Q / = K (T / ) G Q )0;; U )0;; A )0;; T 2 ) (3.7) For the case with aluminium, the expression is: Q / HI = K H; (T / H; 789 ) G JK Q )0;; 789 H; + U )0;; A )0;; T 2 ) (3.8) In this way, for a given requirement, the radiator temperature can be established for the cases with and without aluminium foil. Finally, when T / without aluminium and T / H; with aluminium are known, the energy savings can be estimated when the two systems prove to fulfil the same heating requirement. It can be concluded, that the difference in heat loss through the wall, is equal to the difference in heat emission, so that Q )0;; 789 Q )0;; 789 H; = K (T / ) G K H; (T / H; 789 ) G JK (3.9) The difference can be expressed as savings with the unit percent, related to the radiators total emission without the foil. The calculus of the U value it is showed in the equation U )0;; = + R + R 2 (3.10) The value of R si and R se are the usual surface thermal resistances (inverse of the sum of the convective and radiative heat transfer coefficients), the interior takes the value of 0,13 m 2 K/W and the exterior 0,04 m 2 K/W. The R is the conduction resistance that depends of the case. This resistance is calculated with the equation R = T 2)0;; q (3.11) Once the heat requirement is obtained, it can be plotted the Q req and the Q rad versus the temperature difference between the radiator and the room in order to obtain the 32

33 equation of the power of the radiator. Therefore the constant K and n are found. In the next graphics can be seen this equations of the Q req and the Q rad. In every pack of cases, the equation is different due to the different air flow conditions around the radiator. With the equation obtained from the plots and with the same Q req, it can be calculated the radiator temperature for the case with and without aluminium. With the temperature obtained now it can be calculated the Q rad for both cases and afterwards calculate the savings with the equation % savings = Q /01 Q /01H; Q / (3.12) 33

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35 4 Results and discussion This chapter consists of the analysis of the data obtained from both methods, experimental and CFD. Also a validation of the CFD model will be made and a comparison of the different cases. 4.1 Experimental As explained in the chapter three, there were two types of measurements performed: temperatures and heat flux. In the next figures the data from the laboratory experiments will be analysed. All the data can be found in the annex. The first figure, fig.18, is a graph that shows the measured heat flux versus the temperature of the radiator. The ten different cases, shown in the table one, can be joined in four different groups. These groups are formed depending on the distance of the radiator from the wall, five or nine centimetres, and presences of an aluminium foil. As the figure shows, with a higher temperature of the radiator, the heat flux also becomes higher, as expected from the theory. The relationship between these two parameters seems to be non linear. This can only be analysed in the cases that the distance between the wall and the radiator is nine because there is not enough data in the case of five centimetres. In the case without aluminium the tendency is logarithmic while the case with aluminium the tendency is exponential. However because there is only one case to be analysed it cannot be assured that these are the real tendencies. These will be analysed with the CFD method. Regarding the differences with different distances between the wall and the radiator, the values with nine centimetres are lower but not enough to say the there is considerable difference. It can be observed that the slope is higher when the distance is nine centimetres. 35

36 q [W/m 2 ] Without Al (5cm) Without Al (9cm) With Al (5cm) With Al (9cm) T rad [ C] Fig.18: Evolution of the heat flux The next graph, fig.19, shows the evolution of the five temperatures measured of the wall behind the radiator in the middle section in relation with the distance from the floor. The first figure is without aluminium foil. It can be seen that the temperatures get higher as the distance increases. That happens until a certain point where the temperature decreases. The points on the wall can be seen on the figure nine in the chapter three. The point more close to the floor has the lowest temperature. That is because of the airflow from the room, which has a temperature of twenty degrees approximately, goes up from behind the radiator. Since the radiation is really high, the view factor makes the ends with a lower temperature. Regarding the temperature gradient, it has the biggest difference of thirteen degrees in the case of five centimetres of the wall and a radiator temperature of 50 C. With the same radiator temperature, logically, the cases with the radiator further from the wall, the temperatures are lower. The temperatures differ at maximum 3 C. With higher radiator temperatures, the temperatures of the wall differ more with the distance. 36

37 T [ C] Trad=40 (5cm) Trad=50 (5cm) Trad=40 (9cm) Trad=50 (9cm) Trad=60 (9cm) y [cm] Fig.19: Temperatures of the wall behind the radiator without aluminium The next figure shows as well the temperatures of the wall behind the radiator but with the aluminium foil. As expected, the temperatures are much lower than without aluminium due to the reduction of radiation. Here unlike without the aluminium foil, the temperatures are higher as it moves away from the floor. That is because the convection has more importance than the radiation and due to the air getting hotter as it rises. The temperatures do not have a big temperature gradient. The difference of temperatures at most differs five degrees in the case number seven seen in the table one. Also there is not much difference in the different cases depending on the distance between the wall and the radiator or the temperature of this one; all the temperatures are gathered between 22 and 16 C. In the case with a radiator temperature of 60 C, the tendency differs from the other ones. That is because with higher radiator temperature, the radiation is more important. The same kinds of results for wall temperature were obtained in [8]. 37

38 y Fig.20: Temperatures of the wall behind the radiator with aluminium If the temperatures are compared for the same case with and without aluminium foil, it can be seen in the next figure the reduction of these ones. In the figure 21, the radiator has a temperature of 40 C. Trad = 40 C y Fig.21: Temperatures of the wall behind the radiator with and without aluminium 38

39 The following table shows the percentage of reduction of the wall temperatures. As said the reduction is more important when the temperature of the radiator is higher. d 5 cm 9 cm T rad % Reduction 35 41,9 35,5 43,1 48,9 Table 4: Reduction of the wall temperatures The thermocouples on the floor showed that the radiator temperature does not have much influence in the floor temperature. It has the same temperature as the room and the highest value reached is 22 C when the radiator has a temperature of 60 C. Regarding the external wall temperature, it has always a temperature around 17 C in all cases. Therefore it seems that it does not matter what temperature the radiator has. However in the laboratory the insulation was very good so that might be the reason of no influence from the radiator temperature. The cases were performed setting a voltage but because of the regulating system, it cannot be assured that the power of the radiator is the same in every case. The temperatures in the cases with the aluminium foil are slightly higher than the same without it. That can be explained with the reflection of the heat that makes the temperature of the radiator increase. The temperatures can be seen in the next table. d 5 cm 9 cm T rad 39,7 50,0 39,9 48,5 59,6 T radal 42,2 53,2 41,4 51,6 60,8 Table 5: Radiator temperatures Concerning the heat fluxes, table six the reduction through the back wall can be seen. However, since the power is not the same, it cannot be assured that this is the real reduction. When the distance between the radiator and the wall increases, the losses in the back wall decreases [9]. 39

40 d 5 cm 9 cm T rad % Reduction 32,51 33,46 25,62 32,83 34,76 Table 6: Reduction of the heat flux 4.2 CFD D Validation In this part, a comparison between the two methods will be made in order to validate the CFD model. The first graph, fig.22, compares the temperatures in the wall behind the radiator in the case of a 40 C in the radiator and five centimetres distance to the wall. T [ C] 35 T rad = 40 C 30 Lab with Al 25 CFD with Al Lab without Al 20 CFD without Al y [cm] Fig.22: Comparison of the two models with T rad = 40 C As it can be seen in the figure 22, the temperatures are more similar in the cases without aluminium foil. The reason that it may differ more in the aluminium cases may be because of the emissivity. The CFD emissivity was 0,1 but this is an estimation of a new foil since it was not possible to measure the emissivity in the laboratory. Also there is also another explanation: aluminium is a superior 40

41 conductor of heat, having the thermal conductivity of 200 W/m K. This will have the effect that it will reduce all temperature gradients and strive to make the aluminium layer isothermal. This tendency is noticed since the curve is almost a straight line. If the deviation is quantified, without aluminium it is about 4 C and with aluminium 3 C. It can be seen in the table 7. Lab CFD Deviation Al No Yes No Yes No Yes Radwall1 27,35 20, ,35 3,03 Radwall2 31,37 19, ,37 1,73 Radwall3 30,76 18, ,24 2,66 Radwall4 29,87 17, ,13 2,58 Radwall5 22,40 16, ,60 1,79 Table 7: Deviation in the temperatures with T rad = 40 C Regarding the heat fluxes, the error is higher than the temperatures. They are not similar, that can be explained with the fact that the problem is not a two dimensional case. The radiator in the laboratory was 59 centimetres long. This is a short radiator and could cause different air flows at the edges. As well as with the temperatures, in the CFD the heat flux is higher than the experimental data. Therefore, a 3D case will be done in order to see the effects all around the radiator. In the next table can be seen the calculated deviation with the heat flux in W/m 2. Without Al With Al q Lab 14,88 10,04 q CFD 18,70 15,00 Deviation 25,70 49,39 Table 8: Deviation (%) in the heat flux with T rad = 40 C The following graph shows also the temperatures behind the radiator in the case of 50 C. Like the 40 C case, the CFD temperatures are higher but not very different from each other. Also the temperatures are similar without the aluminium foil than with it. 41

42 T [ C] 40 T rad = 50 C Lab with Al CFD with Al Lab without Al CFD without Al y [cm] Fig.23: Comparison of the temperatures with T rad = 50 C This time the heat fluxes have a deviation of the same order as in the case of 40 C. Without Al With Al q Lab 15,60 10,38 q CFD 21,00 16,05 Deviation 34,62 54,63 Table 9: Deviation (%) in the heat flux with T rad = 50 C 42

43 D Validation In this part, it will be checked the 3D model. Due to not having enough time, it was only made one simulation with the 3D model. This one has a radiator temperature of 50 C, an external temperature of 20 C and a U value of 0,36 W/m 2 K. The case was without aluminium foil, so it will be compared to the case two in the table one. T [ C] Lab CFD Fig.24: Comparison of the temperatures y [cm] The temperatures, as it happened with the 2D model, are very similar the maximum error is 12%. In the next table the heat flux will be compared. q Lab q CFD Deviation 16,085 15,65 2,70 15,115 15,38 1,75 Table 9: Deviation (%) in the heat flux As the results show, the error has an acceptable value for both types of measurements. Therefore the 3D model can be validated. All the studied cases are in 2D since there was not enough time for do them all with 3D. The mesh for both cases was the same, therefore it is assumed that the 2D model is good for assemblies with wider radiators and windows as it will behave as a 2D model. 43

44 4.2.3 Savings Calculation As explained in the methodology part in the chapter three, the Q req and the Q rad can be plotted. These are seen in the figure 24 and 25. The cases shown are with and outdoor temperature of 20 C and a U value of 0,36 W/m 2 K. Q rad [W] y = 6,4764x 1,0648 R² = 0,9993 With Al Without Al y = 5,8948x 1,0664 R² = 0,9993 Power (With Al) Power (Without Al) T rad T i [ C] Fig.25: Power of the radiator Q req [W] y = 6,056x 1,0771 R² = 0,9994 y = 5,7719x 1,069 R² = 0,9993 With Al Without Al Power (With Al) Power (Without Al) T rad T i [ C] Fig.26: Heat requirement 44

45 The next table shows the savings in the case of outdoor temperature 20 C and a U value of 0,36 W/m 2 K. T rad Q rad Q radal Savings 30 75,67 73,89 2,36 % ,50 151,96 1,64 % ,88 241,66 1,32 % Table 10: Savings As it is shown in the table 10 the savings are approximately around 2%. This savings are not really high but it has to be considered that the thermal insulation was really good and a conclusion cannot be reached with only this results Comparison of the different cases In this part of the thesis, the comparison of the 54 different cases will be done. The data will be analysed considering the different values that the variables took. It will compare the savings for cases with a constant U value, a constant radiator temperature and a constant outdoor temperature. First, the savings will be analysed with a constant U value. The figure 27 shows the savings for the different U values. 45

46 % 4,5 U=0,36 4,0 3,5 3,0 2,5 2,0 1,5 Te= 20 Te= 10 Te=0 1,0 0,5 0, T rad [ C] % 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 U=0, T rad [ C] Te= 20 Te= 10 Te=0 % 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 U=0, T rad [ C] Te= 20 Te= 10 Te=0 46 Fig.27: Savings for different T e with constant U

47 As can be seen in the previous figure, with a constant U value, with a higher radiator temperature, the savings are smaller. This pattern is followed with all the different U values. This is because even though the radiator power with the aluminium foil it is reduced, it doesn t reduce as much as with the low temperatures. The tendency of the decrease is logarithmic. Regarding the outdoor temperature, it follows a different tendency with the every U value. With the lower U value, the higher savings are made with an external temperature of 10 C and the less savings are made with 20 C. With a U value of 0,48 W/m 2 K, the higher savings are made with an external temperature of 10 C meanwhile the lowest savings are made with 0 C. Finally with the lowest U value, it seems to follow what it would be expected. The highest savings are made with the lowest external temperature and the savings decrease gradually as the external temperature arises. The next figure shows the savings with a constant external temperature comparing them with the different radiator temperatures and U values. % 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 T e = 20 C U=0,36 U=0,48 U=0,62 T rad [ C] 47

48 % 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 T e = 10 C U=0,36 U=0,48 U=0,62 T rad [ C] % 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 T e = 0 C U=0,36 U=0,48 U=0,62 T rad [ C] Fig.28: Savings for different U with constant T e These graphs show, as it was seen with the ones with a U constant value, that with a higher radiator temperature the savings are lower. Again if it is compared with the different U values in every external temperature, they do not follow a pattern. With an outdoor temperature of 20 C, follows what would be thought as logical. With the poorest insulation, the savings are the highest and gradually decreasing as the insulation gets higher. Regarding the 10 C outdoors, the highest saving depends on the radiator temperature. With 30 C temperature, the highest savings are with the 48

49 richest insulation on meanwhile with 50 C the highest are with a U of 0,48 W/m 2 K. Lastly with 0 C, the highest savings are with the poorest insulation and the lowest with the intermediate insulation. These phenomena can be seen clearer in the figure 28. The following figure shows the savings with a constant radiator temperature. % T rad = 30 C 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0, U=0,36 U=0,48 U=0,62 T e [ C] % T rad = 40 C 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0, U=0,36 U=0,48 U=0,62 T e [ C] 49

50 % T rad = 50 C 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0, U=0,36 U=0,48 U=0,62 T e [ C] Fig.29: Savings for different T e with constant T rad The last figure shows an unusual tendency that was not predicted. In one hand, the U values of 0,48 and 0,62 W/m 2 K follow a curve with a highest saving in the outdoor temperature of 10 C. On the other hand, the poorest insulation follows a decreasing tendency when the outdoor temperature gets higher. Comparing the results with the different radiator temperatures, as it gets higher the savings decrease but not in the same rate. With 30 C temperature, it predominates the highest insulation meanwhile with 50 C, it predominates the intermediate. This pattern suggests the there is an optimum with every condition. With only these results, it can be assured the reason of these happenings. This phenomenon can be associated with the fact of the combination of the radiation and convection. A study of this phenomenon can be seen in [13]. Also, it has to be mentioned that in reality not all the cases will be performed on a normal basis. For example with an outdoor temperature of 0 C, it is unlikely that the radiator temperature is 50 C. The savings in all the cases performed do not go higher than 4%. That result is not high but anyway it is a saving. It has to be considered that the area of the aluminium foil was really small compared to the whole room. In a regular home this area will increase so it will probably also increase the savings. 50

51 A recommendation for future works is to study the problem in CFD with a 3D model and investigate the reason for the tendencies seen in the cases studied in this thesis. Also make a study with a wider radiator and window in order to resemble the real heating systems used nowadays. 51