Modelling and simulation of building components : thermal interaction between multilayer wall and hydronic radiator

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Modelling and simulation of

building components

Thermal interaction between multilayer wall

and hydronic radiator

Christian Brembilla

Licentiate Thesis in Energy Technology, 2016 Department of Applied Physics and Electronics Umeå University, SE-901 87, Umeå, Sweden

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e-mail: christian.brembilla@umu.se

ISBN: 978-91-7601-515-5

Electronic version at http://umu.diva-portal.org/

Printed by: Print & Media Umeå Sweden, 2016

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Abstract

Background and Scope The scope of this thesis is to investigate the

ther-mal behaviour of building components as hydronic radiator and multilayer walls subjected to dynamic conditions. The modelling and simulation of these building components provide information on how these components thermally interact among each other. The thermal interaction is fundamental to know how the energy is used in buildings. In particular, the thermal energy used in rooms can be expressed as the efficiencies for emission in a space heating system. This thesis analyzes the efficiencies for emission of a space heating system equipped with hydronic radiator for Swedish buildings by providing a comprehensive and detailed approach on this topic.

Methodology The methods used in this thesis are: experiment, modelling

of multilayer wall and hydronic radiator, the dynamic simulation of the build-ing and the efficiencies for emission of a space heatbuild-ing system. Here, the

ex-periment, known as step response test, shows the heating up process of a

hy-dronic radiator. The observation of the qualitative measurements suggests the most suitable technique of modelling the radiator known as transient

mod-elling with multiple storage elements. The multilayer wall has been discretized

both in space and time variable with a Finite Difference Method. Dynamic

sim-ulation of the building provides the efficiencies for emission of a space heating

system.

Findings The experimental results show how the radiator performs the

charging phase. The performance of the transient model is compared with lumped steady state models in terms of temperature of exhaust flow and total

heat emitted. Results of the dynamic simulation show how buildings located in a Northern climate use the energy in a better way than Southern climates in Sweden. Heavy active thermal mass provides higher efficiencies for

emis-sion than light thermal mass. Radiators with connection pipes located on the

same side react faster at the thermodynamic changing of the mass flow rate by providing higher efficiencies for emission than radiators with connection pipes located on the opposite side.

Conclusion and Outlook This thesis increases the knowledge about the

modelling and simulation of hydronic radiators and multilayer walls. More research is needed on this topic to encompass modelling details of building components often ignored. The modelling and simulation of building com-ponents are the key to understand how building comcom-ponents thermally inter-act with each other. The thermal interinter-action among building components is a fundamental parameter for the assessment of efficiencies of emission of the space heating system. In the near future, the concept of efficiencies of emission can be implemented in National Building Code, therefore, this study provides guidelines on how to assess these efficiencies.

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List of original publications

The dissertation is based on the following papers:

I. Brembilla, C., Lacoursiere, C., Soleimani-Mohseni, M., Olofsson, T.,

Investigation of thermal parameters addressed to abuilding simulation model,

in Proceeding of the 14th International Conference of the International Build-ing Performance Simulation Association IBPSA, December 2015, Hyderabad,

India

II. Brembilla, C., Soleimani-Mohseni, M., Olofsson, T., Transient model

of a panel radiator,in Proceeding of the 14th International Conference of the

International Building Performance Simulation Association IBPSA,

Decem-ber 2015, Hyderabad, India Papers submitted to Journals:

III. Brembilla, C., Vuolle,M., Östin, R., Olofsson T., Practical support

for the evaluation of efficiencies for emission of Swedish buildings: Modelling and simulation of hydronic radiators with different location of connection pipes, submitted to Energy Efficiency, April 2016

Manuscript:

IV. Brembilla, C., One dimensional model of transient heat

conduc-tion through multilayer walls/slabs: The funcconduc-tionality of insulaconduc-tion and brick materials in terms of decrement factor and time lag, submitted to Building

Simulation, May 2016

Other publications related to this dissertation:

V. Brembilla C., Soleimani-Mohseni, M., Olofsson, T., Hybrid

heat-ing system for open-space office/laboratory, in Proceedheat-ing of Energy Science

and Technology 2015: Book of Abstracts, Karlsruher Institut für Technologie

(KIT), Karlsruher, Germany, May 2015, Vol. 1, pp. 315-315

Poster: http : //opentechnicum.com/?mbtbook = transient − model − of − panel − radiator

VI. Brembilla C., Soleimani-Mohseni, M., Olofsson, T., Transient model

of a panel radiator, in Proceeding of Energy Science and Technology 2015:

Book of Abstracts, Karlsruher Institut für Technologie (KIT), Karlsruher,

Ger-many, May 2015, Vol. 1, pp. 321-321

Poster: http : //opentechnicum.com/?mbtbook = hybrid − heating − system − f or − open − space

VII. Brembilla, C., Lacoursiere, C., Soleimani-Mohseni, M., Olofsson,

T., Investigations of thermal parameters addressed to a building simulation model, in Proceeding of Energy Science and Technology 2015: Book of

Ab-stracts, Karlsruher Institut für Technologie (KIT), Karlsruher, Germany, May

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The abstracts of the papers submitted to journals and the full paper pub-lished in conference proceedings are pubpub-lished at the following website: http://www.umu.se/sok/english/staff-directory?uid=chbr0038&guiseId= 246761&orgId=06092b7ea8ef3cfe8b9ef541d553da11d9543b45&name= Christian%20Brembilla

Other publications not related to this dissertation:

VIII. Brembilla C., A control strategy for reducing electricity cost in

detached houses using tank and PCM in Proceeding of Eurotherm Seminar #

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Acknowledgements

I would like to thank my supervisor Prof. Thomas Olofsson for his constant support and interest in my work. I am also grateful to Prof.s Mohsen Soleimani-Mohseni and Ronny Östin and Dr. Claude Lacoursiere for their suggestions during these years. I want to express my gratitude to all EQUA simulation team, in particular Mika Vuolle, Erkki Karjalainen and Patrick Skogqvist for their help during the project development.

I also would like to thank foundations as K.V. Lindholm, Kempe and Wal-lenberg for supporting and trusting in my ideas.

It is difficult to mention all the people that influence my approach to the re-search and I am sorry in the case I forgot someone. Firstly, Elena Pushkareva always helped and motivated me for continuing in the research. Francesco De-voto and Andrea Ferrantelli superb researchers were always open to new inter-esting discussions. Maksim Surov outstanding researcher has always shared his profound knowledge during the time passed at TFE Department. A special thank to Manu Raster for giving me advice regard Latex.

I want to express my gratitude to my colleagues, I Yung, Sikander, Szabolcs for keeping me company and offering me suggestions and improvements while I was struggling with modelling.

Special thanks to Prof. Kai Erik Siren to be an example for hundreds of researchers and Prof. Jouko Pakanen for his silence.

I am also grateful to Annika Bindler for her corrections of this dissertation and all TFE staff, Leif Johansson, Mona-Lisa Gunnarsson, Marie Fransson and Åke Fransson for helping me during these years.

My gratitude goes also to my parents Aldo, Giacomina, my sisters Federica, Celeste my grandchildren Pietro and Emma and my brother in law Maurizio for their understanding.

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Preface

The preface provides to the reader a general overview of how this dissertation is organized by presenting general information about the contents of each sec-tion.

Before that the dissertation starts with a Road Map in Section 2 that pro-vides to the reader the idea of how the papers are connected with each other. In particular, the author emphasizes the Research Questions which are the driv-ing force for the development of each paper.

The dissertation explains in Section 3 the Scope of this thesis. In particu-lar, the Scope introduces the concept of thermal interaction of building com-ponents and how the energy is used in a space heating system.

Section 4 describes the Background and the motivations to study build-ing envelopes and hydronic radiators with the problematic connected to the causes of variation and oscillation of indoor temperature. Lastly, the author emphasizes on the terminology and definitions about steady state and tran-sient models.

Section 5 explains the Methodology used throughout this dissertation. In particular, the Methodology presents all the methods used in the dissertation listed as: the experiment, the modelling of multilayer wall and the hydronic radiator, the dynamic simulation of the building and the efficiencies of emis-sion.

Section 6 shows the Findings of this dissertation by providing the main and significant results of each papers.

Section 7 discusses the Results and Achievements of each papers.

Lastly Sections 8 and 9 present the Conclusion and possible Future

re-search.

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Nomenclature

Symbols Q Heat loss/Power W γ Parameter Φ Heat gain C Capacitance J K−1 C Capacitance J K−1

c Specific heat capacity J kg−1_K−1

H1, ..., H4 Coefficients W K−1

M Mass kg

m Mass flow rate kg · s−1

q Ventilation load W K−1

α Thermal diffusivity m2_s−1

∆x Wall layers portion m

η Efficiency θ Time s A Surface area m2 T Temperature K U Thermal transmittance W m−2K−1 Subscripts air Air al Active layer emitted Heat emitted

ex Exhaust

injected Heat injected log Logarithmic met Metal n Nominal out Outside rad Radiator sol Solar

stored Heat stored

su Supply

tot Total

w Water

ctrl Control

em Emission

embed. Embedded system ideal Ideal inc Increased/Decreased str Stratification 1/2 out Outdoor Superscripts n Radiator exponent v v-esima Iteration Acronyms

F DM Finite Difference Method P DE Partial Differential Equation BBR Boverket’s Building Regulations F DM Finite Difference Method

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1 Road Map and Research questions

The road map guides the reader into the dissertation by providing a more com-prehensive picture of this thesis. The road map gives the idea of how the papers are connected to each other. Fig. 1 shows the road map indicating the disser-tation development process. The results from each paper serve as the basis for the next paper. The dissertation can be read as a process of: questions → answers → observations → questions → answers... and so on. The questions are enclosed by rectangular question mark, the titles of each paper are written in circles, the answers are enclosed by a rectangular and the observations in rectangular exclamation mark.

The starting point of this dissertation is the study of the heat conduc-tion through a multilayer slab. In particular, the main research quesconduc-tion is:

how does the outside temperature affect the temperature of internal mass/ac-tive layer in the case when 20 cm thick of insulation material separates the internal mass from the external mass?. The paper produced has the following

title: One-dimensional model of transient heat conduction through multi-layer walls/slabs. This study is suitable for knowing how the temperature of

each thermal capacitance varies when the wall is subjected to dynamic condi-tions. The results reveal that the temperature in the internal mass is mostly influenced by the temperature of indoor air; thus, it is reasonable to neglect the effect of outside temperature on the internal mass.

This result is significant because it allows to consider the internal mass as the building part which thermally interacts with the indoor air. In fact, it is supposed that all the internal mass, known as active layer, has ap-proximately the same thermal behaviour. The research question of the second paper is: which is the thermal parameter that most influences the behaviour

of room temperature?. The answer to the research question produces the

sec-ond paper which has the following title: Investigation of thermal parameters

addressed to a building simulation model. One of the results suggests that the

load mostly affects the behaviour of indoor temperature is the convective heat. The convective heat is in large part generated by the radiator. For this reason, the author decided to investigate hydronic radiators.

The third research question is: why does transient modelling have

to be used to model hydronic radiators? The answer can be found in the third

paper, Transient model of a panel radiator, which focuses on the transient modelling of the heat emitter. The goal of this paper is to show the potential of transient modelling in comparison with the steady state approach. The an-swer shown in the paper results reveals that steady state models overestimate both the heat emitted and the temperature of exhaust flow during the radiator charging phase.

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Up to now the building components as the multilayer wall (or active layer) and hydronic radiator have been studied ignoring the thermal inter-action between them. The active layer is able to store/loose thermal energy, whereas, the hydronic radiator is the main heat source of the room. The con-cept that is able to bridge the heat stored/lost by the active layer and the heat emitted from the hydronic radiator is the use of energy in the space heating system. The use of energy in a space heating system can be expressed by the performance indicator known as the efficiencies of emission.

The fourth research question is how radiators with different

loca-tion of connecloca-tion pipes can influence the efficiencies of emission?. The study

is analysed in the fourth paper Practical support for the evaluation of

efficien-cies for emission of Swedish buildings. This study is suitable for designers and

researchers who want to compare the efficiencies of the space heating system among different technical solutions. The paper´s results reveal that radiators with connection pipes located on the same side have higher efficiencies of

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2 Scope of Thesis

The objective of this thesis is to investigate the thermal behaviour of build-ing components defined as multilayer wall and hydronic radiator when they are subjected to dynamic conditions. The investigation of these building com-ponents is actuated by modelling and simulation of their thermal behaviour. In particular, multilayer wall and hydronic radiator thermally interact among each other. The hydronic radiator provides the energy to maintain the room temperature requirements, whereas, the energy is lost through the multilayer wall.

This thermal relation can be analysed with the concept of efficiencies of emission of a space heating system. The efficiencies of emission of a space heating consist of a coupled problem between the heat input from the heat emitter and the heat losses from the building envelope. This thesis provides to the reader comprehensive analysis of the thermal behaviour of these building components and how the energy is used in a space heating system for Swedish buildings.

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3 Background on building envelopes and

hy-dronic radiators

This section covers the general background about the building envelope and hydronic radiator. In particular, the following sub-sections explain the rea-sons and motivations for studying heavy building envelope and aluminium radiators. The advantages and drawbacks of different types of building en-velopes and hydronic radiator materials are discussed in relation to the causes of variation and oscillation of indoor temperature. The behaviour of indoor temperature is an important parameter influencing the efficiencies of emis-sion of a space heating system. Section3.1explains the causes of variations of indoor temperature in relation to the building thermal mass and Section3.2

explains the oscillations of indoor temperature in relation to the type of ra-diator material. In addition to the methods analysed, Sections3.3presents a short overview regarding terminology and definition of steady state and tran-sient models. Strictly speaking the models should not be part of the method-ology because the methodmethod-ology describes the techniques used to solve models. Section3.3.1illustrates the most common boundary condition for models of building components. Section.3.3.2shows how different types of wall model response to different excitation of temperature. Section3.3.3discusses about the terminology and definition of dynamic models.

3.1 Causes of variation of indoor temperature in

rela-tion to the heaviness of building envelope

During the last century, the building envelope had a light thermal mass, thin thickness of insulation material and poor thermal property of each material employed (high Uvalue). Thus, the room internal surfaces were cold and the heat lost through the envelope was relatively high.

A building envelope with poor thermal performance causes variations of the indoor temperature. The building envelope changes its temperature quickly at the variation of the outside temperature. Consequently, the perature variation of building envelope affects the behaviour of indoor tem-perature.

The building envelopes have changed during the last sixty years to meet the regulatory requirements. Buildings employ materials with better ther-mal performance and new technical solutions.

One technical solution used for building envelopes is to employ large thickness of insulation material and to increase the heaviness of internal mass. The internal mass is typically made by concrete or bricks. This solution has several benefits. Firstly, the increase in thickness of insulation material has

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minimized the influence from the outside temperature on the indoor temper-ature. Secondly, the heavy internal mass enables to maintain a stable indoor temperature for more time than light mass. This is because the internal mass stores a relatively high amount of heat, which is released into the environment when needed. Lastly, this solution avoids the problem of cold surfaces and it reduces the heat lost towards the outside environment. These type of building envelopes are known as heavy building envelopes [6].

3.2 Oscillations of indoor temperature in relation to the

type of radiator material

Radiators have changed material from cast iron to aluminium. The change from cast iron to aluminium is due to the need, but not only, of materials able to transfer quickly the heat from the liquid medium to the radiator’s external surface. The velocity of transferring heat can be evaluated by comparing the thermal diffusivity α of aluminium which is 2-2.5 times higher than cast iron. Materials of large α will respond quickly to changes in their thermal environ-ment, whereas materials of small α will respond more sluggishly, taking longer to reach a new equilibrium condition [26].

In addition to the intrinsic thermal properties of the material α, cast iron radiators have a mass almost triple of aluminium radiators due to the thickness of the metal part. As the technical norm states, cast iron radiators must have a thickness of the metal part of 2.5 mm, whereas, it is required 1.1 mm for aluminium radiators [16] [17]. The thin thickness makes aluminium radiators able to store less amount of heat and to be further faster in transfer-ring heat towards the indoor environment. Aluminium radiators are able to change quickly the thermal state (temperature of metal part) at the thermo-dynamic changing of the liquid medium and consequently to vary quickly the amount of heat released into the environment.

The velocity of changing the heat emitted towards the environment affects the amplitude and frequency of oscillations of the indoor temperature. The indoor temperature oscillates due to the adjustment of the mass flow rate injected into the radiator. These oscillations have lower amplitude and higher frequency for aluminium radiators in comparison with cast iron radiators by maintaining the other conditions constant, e.g., radiator size, control and the heat generated by free thermal sources.

3.3 Steady state vs. transient models

The steady state models assess the heat flux across the medium by setting its thermal properties and the boundary conditions of the domain studied. The transient models are distinguished from steady state models because they also

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evaluate the heat stored in the volume of the domain analysed. The heat stored in the volume is responsible of the change in the energy content of the medium with time until the steady state condition is achieved. When the steady state condition is achieved the energy content in the volume does not vary anymore throughout time [11], [26] [36] [34].

3.3.1 Boundary conditions

The boundary condition can be grouped in three types: Dirichlet, Neumann and Robin boundary conditions.

Dirichlet boundary condition, known as isothermal boundary

condi-tion, specifies the values of the solution along the boundary.

Neumann boundary condition, known as heat flux or adiabatic

bound-ary condition, specifies the values that the derivative of a solution take along the boundary.

Robin boundary condition is a linear combination of Dirichlet and

Neumann boundary condition, known as convective boundary condition. Robin boundary condition applies the values of the function and the values of its derivative along the boundary. Other types of boundary conditions exist but they are not handle in this dissertation.

Here, it is necessary to specify that the boundary condition can be either static or dynamic.

The words static boundary condition means that the boundary con-dition has one and only one value. This means to take a “picture” of what hpens in a precise instant of time. For instance, this condition is typically ap-plied in the HVAC field for designing the maximum power required from the heat emitter to meet the design conditions.

The word dynamic boundary condition, means that the value of bound-ary condition changes over time. A classical example of dynamic boundbound-ary condition is the temperature profile of outdoor temperature employed in com-mercial building simulation software.

A brief note is required to explain that the value of boundary condi-tion can have constant values over time. This condicondi-tion is explained in the next section by showing the model response at such application of boundary condi-tion. The last observation is about the application of boundary condition at the domain studied. Static or dynamic boundary conditions can be either applied to steady state or transient models as shown in the following section [34].

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3.3.2 Model response to excitation of temperature

To better understand the differences between steady state models and tran-sient models at the application of static boundary conditions and dynamic bound-ary conditions, simple qualitative examples are used to illustrate the tempera-ture response of a wall subjected to external temperatempera-ture excitation.

Fig.s2aand Fig.2bshow the response in terms of temperature profile of steady state and transient wall models subjected to temperature difference on both wall sides. Such conditions are perhaps not possible to achieve in prac-tice but it provides to the reader an immediate understanding of the response in terms of temperature profile in the wall.

Fig.2ashows the temperature profile of a steady state model of a wall subjected to temperature on side A of -20◦_{C and temperature on side B of +20} ◦_{C. The temperature profile of the steady state model is a line which connects} the two temperatures on the wall sides. This means that the response of the steady state model to such boundary condition is static.

In the case of transient model, Fig.2b, the wall has an initial temper-ature profile of +20◦_{C. When the outside temperature is applied at the} exter-nal boundary, the temperature profile changes only nearby the wall boundary. This happens because it takes time before all the energy stored in the wall is lost through the boundary by achieving the steady state condition as in the case in Fig.2a.

(a) Steady state model (b) Transient model Figure 2: Response to a static boundary condition

In the case of dynamic boundary condition with constant values the steady state model give the same temperature profile over the time as in Fig.2a. This means that the response of the steady state model to such boundary condi-tion is static. Instead, the output of the transient model provides different tem-perature values at each time step until the steady state condition is achieved. The output of the constant boundary condition for transient models is a dy-namic response and it is also known as step response test.

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In the case of non-constant value of boundary condition both steady state and transient models gives different profile at each time step. Fig.3aand Fig.3bshow the temperature profile at each time step [36] [34].

(a) Steady state model (b) Transient model

Figure 3: Response to a dynamic boundary condition with non-constant values The coupling of dynamic boundary condition applied to a model (steady state or transient) is known as dynamic simulation, or dynamic method as stated at Section 5.4 of the technical standard EN 15316-1. A simple schema about the types of expected responses of steady state and transient models is presented in Fig.4and Fig.5. In this context a dynamic

simulation/dy-namic method is only addressed when the type of model response is dysimulation/dy-namic.

Thus, the application of either static or dynamic boundary condition to tran-sient models produces dynamic output and these type of modelling is address as dynamic simulation or dynamic method. On the other hand, we address as dynamic simulation/dynamic method only when dynamic boundary con-dition is applied to steady state model.

3.3.3 Confusion on dynamic models

The difficulty in understanding of the meaning of the words dynamic models is due to the lack of correct and precise terminology in the scientific litera-ture which is unable to describe effectively those words. At first glance, the two words dynamic model seem to refer to the time dependency of variables in transient models. Instead, the scientific literature mixes up the concepts of time dependency of variables for transient models and the time dependency of variables for dynamic boundary conditions. Transient models enable the change in the energy content of the medium with time, until the steady state condition is achieved. The dynamic boundary conditions enable the change of boundary value during the time. Since there are time dependent variables involved in both cases, the authors of such scientific literature often conclude that the model is dynamic.

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In reality, the two words dynamic models are an erroneous label for somehow describing the dependency from the time of such variables. Tran-sient models and dynamic boundary condition communicate with each other but they are different concepts. The correct terminology refers the word

dy-namic to either the values of the boundary conditions or to the response of

the main model variables. Fig.s4and5show for either steady state and tran-sient models when is possible to speak about dynamic simulation or dynamic method. The dash lines track the regions in which it is possible to identify the dynamic simulations.

Lastly, transient models should not be addressed as dynamic models because, for instance, when the steady state condition is achieved the energy content of the medium does not vary anymore with time. Ergo, the words

dy-namic models generate confusion, they do not have to be used in this context

also because dynamic models simply do not exist.

Figure 4: Dynamic simulatuion/Dynamic method with steady state models

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4 Methodology

The methodology section explains all the methods employed in the disserta-tion to analyze the thermal behaviour of building components and the efficien-cies of emission of a space heating system. Section4.1introduces the exper-iment known as step response test which regards how the radiator performs the charging phase. Section4.2shows the numerical modelling of the hydronic radiator. Section.4.3discusses the modelling of multy-layer wall. Section4.4

shows the modelling and simulation of a room and Section4.5illustrates the settings of the dynamic simulation of a building with commercial software. Lastly, the energy efficiencies of emission of a space heating system are pre-sented in Section4.6

4.1 Experiment

The experiment known as step response test investigates how the hydronic panel radiator performs the charging phase [23]. The experiment was con-ducted during a weekend in November 2014 at the laboratory of Umeå Uni-versity. The panel radiator is a Lenhovda MP 25 500 [28] connected to the do-mestic hot water of the building. The hydronic panel radiator studied is part of a heating system composed by four hydronic panel radiators. The return valve of the hydronic panel radiators not involved in the experiment has been closed; thus, the fluid cannot circulate in those heat emitters.

Non-insulted copper pipes compose the distribution system of the heating system. Balancing valves (red spots in Fig.6aare positioned on return pipes of the system. The balancing valve on the lower part in Fig.6ais closed, whereas the valve in the middle is fully open and the last one adjusts the mass flow rate according to kvcoefficient. The manometer, positioned at the begin-ning of the supply line, detects the flow pressure, thus the supply mass flow rate is calculated. The latter data are needed to set-up the kvcoefficient of the balancing valve for controlling the mass flow rate. The domestic hot water of the building injects the supply flow into the hydronic panel radiator. The water runs for 10 min in the sink to reach a constant temperature of 55◦_{C. Then, the} supply line is connected to the hydronic radiator at the pressure of 5000 Pa. The panel radiator has the supply and return connection on the same side of the unit. The supply is on the top right corner and the return connection is on the right bottom corner. The blue spot in Fig.6ais the meeting point of supply and exhaust flows. The panel radiator has positioned thermocouples on the supply, exhaust and in the middle of the panel surface to detect its behaviour during the test. Fig.6bshows the data tracker at which wires were connected to detect the change of temperature of the hydronic radiator. Lastly, a ther-mocamera has been positioned to check the temperature changing of radiator surface during its charging process.

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Qualitative measurements are the only expected outcome of the ex-periment, since the panel radiator is located in a room not following the re-quirements listed in the EN 442 (EN 442-2 et al.1996). Moreover, the heating system is not able to provide a controlled pressure of the injected fluid flow.

(a) Hydronic panel radiator (b) Data tracker Figure 6: Experiment facilities

4.2 Modelling hydronic radiator

The heat emitter is modelled according to the heat balance between the heat injected into the panel, the heat emitted towards the indoor environment and the heat stored into the thermal unit. The model assumptions are the follow-ing:

- no hydraulic process of the fluid flow and relative hydraulic resistance of the panel are considered in the process,

- the panel radiator is divided into five equal elements connected in series, this means that, the temperature of the supply flow of the following element is the temperature of the exhaust flow of the previous one,

- the radiator thermal mass, sum of the water and metal mass, is concentrated at the exhaust point of each radiator element/capacitance,

- the surface temperature of panel radiator is equal to the flow temperature for each element,

- air temperature of an ideal room is assumed constant at 20◦_C_{during the} test,

- no additional time delay is considered in the simulation,

- the radiator can only heats the room, the cooling process is not considered. Eq.1shows the heat balance of the panel radiator.

Q_injected= Q_stored+ Q_emitted (1) Eq.2describes mathematically each term of Eq.1, formulating a sys-tem of first order partial non-linear differential equations with autonomous parameters [49], [50], [22] and [37] . The PDEs are evaluated in time and in

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the panel length L named as x direction. m_w· c_w·∂T (x, θ) ∂x = Crad· ∂T (x, θ) ∂x + Qn· ∆Tlog ∆T_N n (2) where: Cradis the total radiator capacitance calculated as sum of metal plus water capacitance. Eq.3shows how to calculate the total radiator capac-itance.

C_rad= M_w· c_w+ M_met· c_met (3) The third term of Eq.2is the logarithmic temperature difference be-tween the temperature of supply flow, exhaust flow and indoor air as shown in Eq4.

∆T_log = (Tsu− Tex) log(Tsu−Tair)

Tex−Tair

(4) ∆T_Nis the logarithmic temperature difference at nominal conditions. The latter coefficient is usually found on technical catalogue as the exponent n. Fig.7shows the modeling of the panel radiator divided into five equal el-ements or thermal capacitances. These elel-ements are connected in series, this technique is also known as system with multiple storage elements [43]. More-over, Fig.7shows the terms of Eq.2, the power injected and emitted towards the indoor environment. The capacity to store thermal heat does not appear in the picture since it is hidden in each element.

Figure 7: Model of hydronic radiator

The mathematical model in Eq.2is discretized and resolved by means of Newthon Rahpson method, a second order method (quadratic) which finds successively approximations of a real-value function [25] [46]. The method starts with the guessing of the first value of Texh. The new value of Texh, is found by applying the N-R algorithm described in Eq.5

Tex,new= Tex,old−F · (Tex,old)

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where:

F (Texh,old) = mw· cw· (Tsu− Texh) + Crad·(Tex,new−Tex,old) ∆T + QN· _∆T log ∆TN n (6) F0(T_exh,old) = −m_w· c_w− C_rad/dθ − Q_N/_N· (∆T_log,n)−n·

n · (∆T_log)n−1(((T_su− T_ex/(T_exh− T_air)) − logA))/(logA)2 (7) A = (T_su− T_air)/(T_exh− T_air) (8)

4.3 Modelling multilayer wall

Let us assume that the wall is infinitive in y direction and the heat transferred between the wall sides occurs only by conduction. The wall thermal properties (k, ρ, cs) are assumed time-invariant and isotropic. The heat flux through the wall is proportional at the temperature gradient between different wall points. The temperature profile between wall points is assumed linear.

These hypotheses aid the application of the mathematical model of Heat Equation to solve the conductive heat through walls [38], [29]. The heat equation shown in Eq.9is a parabolic partial differential equation PDE also known as second-order partial differential equation.

∂T ∂θ = α

∂2T

∂x2 (9)

A FDM discretizes the continuous problem for both space and time variables and the numerical model is produced in Eq.10. The γ method ap-plied to the numerical model of heat equation illustrates the possible first or-der solver of the problem. The parameter γ in Eq.10can have values between 0 and 1.

T_mv+1− T_mv = α ∆θ ∆x2 (1 − γ)(T_m−1v − 2T_mv+ T_m+1v ) + γ (T_m−1v+1 − 2T_mv+1+ T_m+1v+1)

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For γ = 0 the solver adopted is known with the name of Euler explicit. If γ = 1/2 the solver adopted is known as Cranck-Nicholson method. If γ = 1 the solver adopted is known with the name of Euler implicit. According to Myers (1971) the explicit method (or Euler forward) is the least accurate among the solvers presented. Euler forward presents oscillations in the solution and in-stability when too large time increments are set. Crank-Nicolson solver is the most accurate method among the solvers presented because it uses the arith-metic mean value of the derivatives at the beginning and the end of the time in-terval. Cranck-Nicholson has the highest computational cost among the three methods, it presents oscillations but stable solutions for this type of problem. Lastly, Euler implicit (or Euler backwards) is less accurate than Cranck Nichol-son but more accurate than Euler forward. The solution of Euler backwards is unconditionally stable without having oscillations.

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The evaluation of the accuracy of the solution and the solver computa-tional cost lies outside the scope of this study. The author aims to find a solver able to provide robust and stable solution ignoring setting stability constrains or to obtain a solution after a long waiting period. For these reasons, Euler implicit is the solver chosen for solving this problem.

4.4 Modelling and simulation of the building

The numerical model of the room consists of two lumped capacitances that represent the air volume and the room active layer [48]. The left side of Fig.8

shows a typical cross section of a room where the active thermal mass is in yellow. The right side of Fig.8shows the network made by resistances and capacitances. The model does not consider the thermal effect of the furniture.

Figure 8: Room model

The mathematical model is a system of two non linear ordinary differ-ential equations with non-homogeneous parameters resolved simultaneously as shown in Eq.s11aand11b. The equations are coupled by means of the tem-perature of indoor air and the average temtem-perature of active layer.

       CadTair

dθ = H1( ¯Tal− Tair) + H2(Tout− Tair) + qout(Tout− Tair) + ΣΦi,c Cald sTal

dθ = H3(Tair− sTal) + H4(Tsol− sTal) + ΣΦi,r

(11a) (11b) Eq.11ais the heat balance of the air volume, which exchanges heat through windows, ventilation, cracks, active thermal mass, and the heat gen-erated by convection from the radiator and other free heat thermal sources. Eq.11bshows the heat balance of the active layer. In this equation the heat is exchanged between indoor and outside air, and the radiative heat generated by radiation. In the heat transfer through the envelope appears the variable Tsol

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that is the temperature on the external surface of the wall facing the outside environment [54] [35]. Walls have set the adiabatic condition, this means that no heat passes to the neighbouring rooms unless the wall facing to the outside environment.

The input parameters addressed to the simulation model are the out-door temperature Toutand the sun radiation on horizontal surface read from TRNSYS simulation software for Umeå location [51]. The sun radiation strikes on the external surface and its hourly behaviour has been modelled according to the solar model proposed by Jones [24]. The internal loads are modelled according to weakly schedule. The convective and radiative heat gains from all the free sources are evenly divided for the air volume and the active layer. The model parameters as Uwi, Uenvetc. are assessed according to Adamson [1].

4.5 Dynamic simulation of the building with

commer-cial software

The simulation model consists in a room adjacent to other heated rooms. Ide-ally no heat is transferred towards the others conditioned rooms, thus all the internal walls, ceiling and floor have set the adiabatic boundary condition. The performance of structure, fenestration, HVAC system are set according to the Swedish Building Code BBR [40]. These parameters are summarized in Ta-ble1.

Table 1: Building thermal characteristics

U_value Exterior wall 0.15W K−1m−2

Window 1.1 W K−1m−2

Ventilation Mechanical ventilation 20 ls−2 Air leakage rate q50Pa 0.6 ls−1m−2

Internal gains Occupancy 1 person

Lighting 8 W m−2

Electrical appliances 5 W m−2 Energy required S < 50m2 North I No required

Central II No required

Central III No required

South IV No required

The room is equipped with the mechanical ventilation system which mixes the indoor temperature. Calculations were made to design the size of pipes for the distribution system, the power required of circulating pumps, the power required from the radiator and the power need of the air handling unit. The radiator is connected to the storage system which consists of a stratified hot tank. An electrical resistor inside the tank guarantees the required tem-perature at the supply fluid according to weather compensation heating curve.

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Circulating pumps work according to a constant curve of duty. The distribu-tion pipes are supposed isolated and integrated in the building envelope. A schema of the HVAC system can be seen in Fig.9. The room is simulated with the commercial building energy simulation software IDA ICE [27].

Figure 9: Schema HVAC system of the room

4.6 Energy efficiencies of emission of a space heating

system

The efficiency serves as a ”practical and straightforward comparison of effec-tiveness of systems or sub-systems of different types and/or different sizes”. The efficiencies method explained in EN 15316-1,2-1 [18] [19] standardizes the heat input and extra thermal losses towards the building envelope. The ef-ficiencies for emission are determined by estimating the heat input (or heat emitted) from the radiator and the extra thermal losses towards building en-velope [32].

The extra thermal losses towards building envelope are as follows: heat loss due to non-uniform internal temperature distribution Qem,str, and heat loss due to the control strategy Qctrl. Qem,stris split between the heat loss resulting in an increased/decreased internal temperature nearby the build-ing boundaries Qem,str1, and the heat loss due to the emitter position Qem,str2. Q_em,str1is referred to the boundaries close to the ceiling and to the windows, where the indoor temperature is affected by the convection flow from radia-tor and cold surfaces. Qem,str2is referred to the heat loss towards back wall of the radiator accounted as convection and the radiation. For both terms, Qem,str 1 and 2, the technical norm specifies how to calculate them by applying the general equation for the transmission heat lost as shown in Eq.12.

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Eq.12considers the locally increased/decreased of internal temper-ature Tint,inc, and the locally increased/decreased of heat transfer coefficient calculated from the insulation material towards the internal surface Uinc. Most likely, Eq.12can be applied at the results of room models developed with com-putational fluid dynamic software. It is not obvious to calculate the locally in-creased/decreased of indoor temperature by using building energy simulation software. For this reason, Tsurf, the temperature of wall internal surfaces, re-places Tint,incin Eq.12by maintaining the same heat transfer coefficient Uiof the structure considered. Special consideration is due to the increasing of in-door temperature nearby the ceiling. According to the Annex A.2 of EN 15316-2-1 (2007), the efficiencies for stratification for over-temperature nearby the ceiling is of 0.95% with heating curve 55/45◦_C_{and ∆T = 30K for radiators.} This increase of indoor temperature near the ceiling is considered as constant throughout the simulation time.

The heat loss due to the control of indoor temperature Qctrlrefers to the non-recoverable heat over the room temperature set point. A non-ideal control causes variations and drifts around the prefixed set-point temperature due to the physical characteristics of control system, the heating system itself and the sensor location. In this paper to simplify the problem the sensor was ideally located in the center of the room, so that it only detects the behaviour of air temperature. Fig.s10ashows the heat losses towards window, back wall radiator and the increasing of temperature nearby the ceiling. Fig.10bshows the heat losses due to the control.

According to the standard EN 15316 2-1 (2007), the efficiency for stratification ηem,str,1and2and control ηem,ctr may be quantified with the ratio between the thermal loss calculated with an ideal heating system over the heat loss of the real case as shown in Eq.s13aand13b. The ideal case calculates the energy demand for heating the living space according to the EN 13790 (2008). The indoor temperature is kept constant (or approximately constant) over the heating period. The room is equipped with both ideal control and heating sys-tem. This means that the heating system does not consider eventual delays from the control, the heat stored in heat emitter and the heat emitted from distribution pipes. The heat gains from sun, occupancy, electrical appliances, lighting and mechanical ventilation are the same for both real and ideal cases.

η_em,str1/2= Qem,ideal,str1/2

Q_em,str1/2 (13a) ηem,ctrl=

Q_{em,ideal,ctrl}

Q_em,ctrl (13b)

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(a) Stratification heat losses (b) Control heat loss Figure 10: Heat losses

in Eq.14as stated in Section 7.2 of EN 15316 2-1 (2007).

η_em= 1

4 − (ηem,str+ ηem,ctr+ ηem,embedded) (14) ηem,embeddedhas the value of 1 since the radiator does not have pipes embedded into the building structure. The term ηem,str is the average value between ηem,str1and ηem,str2.

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5 Findings

The following sections present the main findings of each Paper. In particular, Section5.1presents the thermal imaging for the charging phase of hydronic radiators. Section5.2illustrates the performance of transient modelling of hy-dronic radiator in comparison with the steady state approach. Section5.3 de-scribes the thermal response of each thermal capacitance in a wall. Section5.4

shows the modelling and simulation of a room model. Section5.5illustrates the heat emitted from hydronic radiator when pipes are located on different position. Section5.6shows the energy efficiencies of emission of a space heat-ing system.

5.1 Charging phase of hydronic radiator

Fig.s from11ato11dshow the process of heating up of the radiator with the temperature field pattern on the radiator surface. At 18:44:00, the tempera-ture of the panel radiator is 20◦_{C. The experiment starts at 18:45:00 and the} radiator begins the charging phase. The thermal imaging clearly shows that the process of heating up is from right side to left side with these type of loca-tion of connecloca-tions pipes. However, already at 18:48:15, a hot area is visible in the lower part of the heat emitter. This means that a fraction of flow recir-culates inside the panel. In the lower part of the second image at 18:51:15, the hot area is larger than before. The radiator is loaded backwards and the pro-cess of heating up now is upwards. This is because some residual air inside of the panel radiator does not allow a normal charging of the unit. By opening the vent valve, the process of charging becomes from top to down as shown in 19:03:20. At 19:10:06, the charging process is over. To conclude, this quali-tative experiment clearly shows that the normal charging process of the panel radiator is from right to left.

(a) 18:48:15 (b) 18:51:15

(c) 19:03:20 (d) 19:10:06

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5.2 Performance transient model of hydronic radiator

vs. steady state

The performance of the transient model are compared in terms of heat emitted and temperature of exhaust flow with the steady state model developed in IDA ICE energy simulation software.

Fig.12shows the temperature of the exhaust flow, when the panel radiator is modelled with steady state and transient models. The red line rep-resents the Texhof the steady state model developed by eliminating from Eq.1

the heat stored in the radiator mass. The magenta line is the Texhof the steady state model developed in IDA ICE software. It is possible to notice a discrep-ancy between the two exhaust temperatures due to the different mechanism of heat transfer into the environment. The dash blue lines represent the exhaust temperature when the hydronic radiator is modelled with transient approach according to N=1,2,4,8 thermal capacitances. Dead and balancing time are computed numerically with Tdof 6 minutes and 30 seconds and Tbof 9 min-utes and 30 seconds.

Fig.13shows the total heat emitted by the models. The dash blue lines represent the total heat emitted from the radiator modelled according to N=1,2,4,8 thermal capacitances and the red line in steady state condition as previously. When the radiator is modelled with 8 capacitance the heat emitted is lower at the beginning of the charging phase in comparison with the other transient models. The grey area is the amount of energy overestimated from the steady state model in comparison with the transient model. This area is about 50 Wh.

Fig.14shows the temperature distribution in the panel during the charging phase. x is discretized by subdividing the panel in 8 chunks of the same length. It is possible to notice that, when the charging process starts, only the capacitances close to the supply line begin the heat process [9].

Time [min] 0 20 40 60 80 Temperature [deg] 10 20 30 40 50 60 Td Tb IDA ICE

Solution of transient model with:

N=4 N=8 N=2 N=1 Steady state solution of the transient model

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Time [min] 0 20 40 60 80 Heat emission [W] 50 100 150 200 250 300 350

Steady state solution of transient model N=1

N=2 N=4 N=8

Figure 13: Heat emitted

1 2 3 4 5 6 7 8 10 20 30 40 50 60 Capacitance Temperature [deg] After 500s After 10s

After 50s After 16.7 min

T supply

After 50 min

Figure 14: Temperature distribution in the panel during charging phase

5.3 Termodynamic decoupling from external to

inter-nal mass

Fig.15shows the multilayer wall composed by the three layers: brick, insula-tion material and brick. The nodal points are equally spaced along the x axis. The dash lines identify each wall portion or wall layer.

Fig.s16a,16band16cshow the temperature behaviour of each ther-mal capacitances in the multilayer wall. In particular, Fig.16ashows the be-haviour of thermal capacitance in the external brick layer, Fig.16bfor the in-sulation layer and Fig.16cfor the external brick layer. It is possible to notice that the temperature behaviour of the outside brick layer adjacent to the ex-ternal environment follows the behaviour of the exex-ternal temperature. The decrement factor d1in the outside brick layer is of 1.9682◦Cand the time lag ∆ais of about 5 hours. The temperature in the insulation layer in Fig.16bhas a decrement factor d2of 3.44◦_C_{and a time lag of about 1 hour between the} first and last capacitance. Similar values are also determined in Asan work in [3] [4] [5].

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Figure 15: Multylayer wall

(a) Outer brick layer (b) Insulation layer

0 5 10 15 20 Time (hours) 23 23.5 24 24.5 25 Temperature ( °C) (c) Inner layer Figure 16: Temperature behaviour of wall nodal points

5.4 Convective heat

The different thermodynamic behaviour of the internal brick from the exter-nal brick allows to set the hypothesis that the room interexter-nal mass has approxi-mately the same thermal behaviour. This hypothesis means that, the tempera-ture differences among the internal surfaces of the room are roughly negligible. The internal mass of the room is known as active layer. The active layer is the first layer in contact with indoor air [2], [20] and [33]. It is supposed that the active layer thermally interact with the indoor air. Thus, all the room internal mass is concentrated in the capacitance Calas shown in Fig.8.

The results of the uncertainty analysis of the room parameters are re-ported for the convective heat. The convective heat affects the the behaviour of indoor temperature. The convective heat is the thermal parameter which provides, with the outside temperature, the highest variation of the room tem-perature. The convective heat generated by free heat gains as lighting, occu-pancy, electrical appliances and sun is deterministic in the period of low heat demand. A low heat demand occurs when the outside temperature is mild (be-tween 10-5◦_{C); thus, the heat lost from building envelope is moderate. During} winter time, the convective heat is mainly generated by the heat emitter.

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In particular, Fig.17shows the variability of indoor temperature at the small variation of the convective heat. The green spots are the values of room temperature when the convective heat is subjected to a small positive perturbation and the blue spots when the convective heat is subjected to small negative perturbation [31] [12]. The small variation of the convective heat is due to the application of local sensitivity analysis on the parameters of the room model. The local sensitivity analysis identifies which parameter gives the larger variation in the model outcome [45] [44] . The input values varies locally one at a time by keeping all the other factors constant. Such sensitivity approach accounts on finite-difference approximations based on the central differences. The input parameter selected is subjected to a small perturbation of ±1% around its nominal value. Small perturbation are preferred than large variations since the latter violets the assumption of local linearity. This prop-erty is known as the first order effect of sensitivity analysis [8].

19.50 20 20.5 21 21.5 22 22.5 23 500 1000 1500 2000 2500 3000 3500 4000

Temperature of indoor air [°C]

Convective heat gains (W)

Convective heat gains sensitivity analysis

Figure 17: Variability of convective heat

5.5 Dynamic simulation of hydronic radiators with

dif-ferent location of connection pipes.

The integration of the transient model in IDA ICE environment is actuated by making some modifications at the programming structure of the radiator model presented in Section4.2. These modifications are essential to make the transient model work without any fix time step and to correctly communicate with the room zone [10]. The radiator is modelled with several capacitances for the liquid medium inside the radiator as shown in Fig.18and one capacitance for the metal part. The metal mass can be modelled as one capacitance since the heat conduction through the metal is assumed constant over time.

The hydronic radiator with connection pipes located on opposite side, the supply line is positioned at the top corner Tsup, whereas the exhaust line

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(a) Connection pipes on same sides (b) Connection pipes on opposite sides Figure 18: Hydronic radiator schema

is positioned at the opposite bottom corner Texh as shown in Fig.18b. The temperature of supply flow of the i-esimo element is the exhaust temperature of the i-1-esimo element. Instead, the hydronic radiator with connection pipes located on the same side has the temperature of exhaust flow as the average exhaust temperature among the capacitance as shown in Fig. 18a. It is also assumed that the capacitance adjacent to the connection pipes gets a mass flow rate 10% higher than the further capacitance.

Radiators with connection pipes located on the same side react quicker at variation of mass flow rate injected in comparison with radiators with con-nection pipes on the opposite side. The total heat emitted by the radiators with different location of connection pipes is shown in Fig19. It is possible to no-tice that radiators with connection pipes on the same side have slightly higher heat emitted than the other type of connection at the beginning of the charg-ing phase. In the long run the heat emitted from the two solutions reaches the same value.

5.6 Efficiencies of emission

Table2presents the results of efficiencies for emission of hydronic radiators. To be notice the term ηstr1 refers at the average efficiency between the heat loss through the window and the overheat temperature near the ceiling. The results from IDA ICE simulation software are post processed by integrating the heat losses towards window and back wall over the heating period. The heating period is assumed from the September 1 to May 30 for all the simulations. The integration of the heat transmission losses as explained in Eq.12is performed according to the trapezoidal rule.

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Figure 19: Total heat emitted of hydronic radiator with different location of connection pipes

The table encompasses all the possible variations on the extra ther-mal losses towards the building envelope. The simulation plan consists of sen-sitivity analysis on the building location, on the building envelope and on the characteristic of the heating system.

The first sensitivity analysis was carried out by locating the building in four different climates in Sweden: North, North-Central, South-Central and South. The climate affects the amount of free heat available in the room space, thus, the heating can be decreased to meet the comfort requirements for occu-pants [7].

The second sensitivity analysis was performed by changing the ac-tive thermal mass.The acac-tive thermal mass is the first material layer in contact with the indoor air taking also into account all the material layers till the insu-lation [8]. The thermal mass stores thermal energy which it is released into the indoor space. Many authors have considered the advantages and drawbacks of changing the building thermal mass. Heavy thermal mass can smooth sharp oscillations of indoor temperature by guaranteeing a stable room temperature. During heating seasons, the stored heat will be released into the conditioned space; whereas, during the cooling seasons, implemented night ventilation dis-sipates the heat stored [33]. The active thermal mass also has a positive effect by load shifting and by peak shaving the electricity use of house auxiliaries [20]. The third sensitivity analysis focused on the local control of the ra-diator. The local control was switched between P and PI control. P control enables a proportional flow adjustment for the variation of indoor tempera-ture. PI control also guarantees an integration time that reduces the response

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of the system and it stabilizes the oscillations of indoor temperature [42], [39] The last sensitivity analysis was carried out by switching the connec-tion pipes locaconnec-tion. The connecconnec-tion pipes are first located on the same side of the radiator and then on the opposite side. All sensitivity analysis account of 48 real cases and 8 ideal cases. The ideal cases are set for each climate zone analysed and for both heavy and light active thermal mass. The latter consid-eration make a slightly modification to the EN 13790 which it only considers the structure U value by neglecting the heat stored in the mass.

Table 2: Efficiencies of emission for heating curve 55/45◦_C

Control Climate Heaviness Same side connection (η) Opposite side connection (η)

ctrl str1 str2 em ctrl str1 str2 em

North I Heavy 0.9842 0.9816 0.9965 0.9739 0.9752 0.9924 0.9963 0.9704

Light 0.9787 0.9806 0.9951 0.9676 0.9746 0.9805 0.9646 0.9635

Central II Heavy 0.9565 0.9681 0.9939 0.9411 0.9468 0.9669 0.9907 0.9307

P (K=1) Light 0.9506 0.9669 0.9911 0.9342 0.9465 0.9650 0.9895 0.9291

Central III Heavy 0.9709 0.9735 0.9902 0.9548 0.9571 0.9735 0.9919 0.9432

Light 0.9610 0.9714 0.9933 0.9463 0.9570 0.9716 0.9546 0.9260 South IV Heavy 0.9641 0.9683 0.9988 0.9457 0.9488 0.9662 0.9909 0.9322 Light 0.9524 0.9675 0.9947 0.9376 0.9483 0.9641 0.9908 0.9309 North I Heavy 0.9649 0.9901 0.9951 0.9592 0.9505 0.9852 0.9905 0.9419 Light 0.9621 0.9788 0.9879 0.9482 0.9500 0.9768 0.9624 0.9255 Central II Heavy 0.9350 0.9647 0.9847 0.9171 0.9197 0.9627 0.9780 0.9009 P (K=2) Light 0.9323 0.9640 0.9730 0.9097 0.9189 0.9612 0.9769 0.8992

Light 0.9435 0.9680 0.9729 0.9207 0.9276 0.9671 0.9744 0.9077 South IV Heavy 0.9434 0.9646 0.9879 0.9256 0.9222 0.9617 0.9781 0.9026 Light 0.9369 0.9623 0.9759 0.9140 0.9207 0.9604 0.9777 0.9006 North I Heavy 0.9950 0.9986 0.9979 0.9932 0.9990 0.9806 0.9972 0.9880 Light 0.9915 0.9950 0.9972 0.9877 0.9950 0.9780 0.9964 0.9825 Central II Heavy 0.9750 0.9710 0.9942 0.9593 0.9742 0.9712 0.9945 0.9588 PI Light 0.9658 0.9696 0.9941 0.9502 0.9734 0.9710 0.9939 0.9577

Light 0.9704 0.9734 0.9931 0.9557 0.9811 0.9757 0.9932 0.9669

South IV Heavy 0.9741 0.9750 0.9938 0.9601 0.9707 0.9703 0.9933 0.9546

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6 Discussion

The thesis explains the thermal interaction between the building envelope and hydronic radiator in the room domain. The room is the fundamental “brick” of the building where the heat is transferred from the heat emitter towards the indoor environment. The use of energy plays a key role to understand the energy efficiency among different technical solutions employed in the building.

In this context, the modelling of building components with transient approach is necessary to assess their thermal behaviour throughout the simu-lation time and to assess the efficiencies of emission.

In particular, the dynamic simulation of the multilayer wall shows how the thermal behaviour of the inner thermal mass does not follow the be-haviour of the external mass due to the large thickness of insulation material. This means that the heat generated in the room by hydronic radiator and the free thermal sources are stored into the internal mass/active layer. This fact is significant for cold climates where the heat has to be stored in the active layer during winter time.

The second building component is the hydronic radiator which is the primary heat sources of the room. The modelling of the hydronic radiator and the heat transferred towards the environment have to be addressed as a priority not only for the research point of view but also for commercial purposes. Little and often not satisfactory researches regarding the hydronic radiator do not describe with sufficient details the mechanism of radiator charging and the heat transfer towards the environment. The hydronic radiator has to be study more especially in cold climates where the yearly energy demand for heating is relatively high in comparison with temperate climates. For instance, Gritzki presents a model of a thermostatic room and hydronic radiator developed with the coupling of three software TRNSYS, PArallelNS and Fluent [21]. Gritzki model enables to assess the time of charging phase among different sizes and types of radiators.

The efficiencies of emission provides overview on how the energy is used in a space heating system. The results obtained in Table2have to be read in relative terms by comparing the results among each others. This means that more details room/radiator models could give different results, but the general trend have to be the same.

The internal masses enable to use the energy in more efficient manner than light thermal masses. Heavy thermal masses have to be considered as standard for Swedish building envelope because they provide relatively high energy efficiencies of emission.

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The climate affects the efficiencies values, in particular the efficiency for control. In Northern climate the efficiency for control is higher than the Southern climate because less amount of sun influences the indoor temper-ature. This means that, in Northern climates P controller with proportional band of 2K enables similar results of efficiencies for emission of PI controller in Southern climates. The cases located in the climate Central III (Stockholm is the location of reference) enable better efficiencies for emission than Climate II (located in Malung). This perhaps is due to the free available heat from the sun which is higher in Malung in comparison with Stockholm.

Sensitivity analysis of weather compensated heating curve are not en-compassed in Table2because of software restirctions. The room model em-ployed is unable to compute a vertical temperature gradient of the indoor air volume. However, many authors have studied the high potential in energy savings of the space heating system by applying modification at the heating curves [30] [52], [53]. In fact the modification of the heating curve during rush hours has the benefits in terms of lowering the amount of mass flow rate supplied to the heat emitter. There is also high potential in energy savings up to 35%, by using optimal heating and cooling curve [14]. The heating curve has an impact of the efficiency of emission for stratification of the indoor air. Higher heating curve means to have lower energy efficiency for air stratifica-tion as shown in Annex A.2 of the EN 15316-2-1 [19].

Lastly, the efficiency for emission of the hydronic radiator is higher when the radiator is connected with pipes located on the same side of the heat emitter.

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7 Conclusion

The thesis has moved from modelling and simulation of building components to the investigation of efficiencies of emission of a space heating system. The efficiencies of emission are a coupled problem between the heat losses towards the building envelope and the heat input from the heat emitter. The building envelope and the hydronic radiator have been analyzed with transient mod-elling to encompass essential and deterministic details influencing the effi-ciencies of emission of the space heating system. The thesis provides practical support to designers and researchers of a space heating system about the as-sessment of efficiencies for emission of Swedish buildings.

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8 Outlook

Paper I can be further developed by analyzing global sensitivity analysis of each thermal parameters. The global sensitivity analysis changes the value of all pa-rameters simultaneously. Perhaps, a tool which identifies the model parame-ters uncertainties can be developed to support modellers in set up simulation models.

The transient model of radiator in Paper II can be further developed by encompassing all the panel spatial dimensions. A tri-dimensional model of a radiator allows to compare the length of charging phase among hydronic radiators of different sizes.

Paper III can be further developed by analyzing the effect of the heat-ing curve on the efficiencies of emission in particular on the heat losses for air stratification. A more detail room model needs to be used to detect the increas-ing of temperature nearby the ceilincreas-ing.

Paper IV can be improved by analizing more in detail the transient heat conduction in the multilayer wall. The hypothesis of temperature conti-nuity between each material layer can be replaced with a disconticonti-nuity of tem-perature between adjacent layers. Swedish multilayer wall can be analyzed by evaluating the energy storage of different technical solutions.

Modelling and simulation of building components : thermal interaction between multilayer wall and hydronic radiator