DEVELOPMENT AND VALIDATION OF A VERSATILE METHOD FOR THE CALCULATION OF HEAT TRANSFER IN WATER-BASED RADIANT SYSTEMS METHODS

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1 Eleventh International IBPSA Conference Glasgo, Scotland July 27-30, 2009 DEVELOPMENT AND VALIDATION OF A VERSATILE METHOD FOR THE CALCULATION OF HEAT TRANSFER IN WATER-BASED RADIANT SYSTEMS Massimiliano Scara, 3, Karl Grau 2, Bjarne W. Olesen 3 Deartment of Alied Physics, University of Padua, Padua, Italy 2 Danish Building Research Institute, Aalborg University, Hørsholm, Denmark 3 International Centre for Indoor Environment and Energy, Technical University of Denmark, Lyngby, Denmark ABSTRACT The descrition of the thermal behaviour of radiant systems is comlex due to the 3D heat transfer and the relevant thermal inertia characterising the active surface. As a consequence, it is necessary to define modelling simlifications in order to achieve a reliable forecast of the thermal field inside the structure and, hence, of the heat exchange beteen the active structure and the room. This aer resents the hole rocess erformed ithin the develoment of a calculation module integrated ithin softare BSim (.bsim.dk, by the Danish Building Research Institute) for the descrition of radiant systems. The resent ork started ith the examination of existing calculation models for radiant systems. Then a model ith further extensions as imlemented and tested. Such a module is able to cover a ide range of cases ith just one calculation tool. In the end, it as tested against field measurements in a climatic chamber at the Danish Technical University, Lyngby (Coenhagen). INTRODUCTION The calculation module starts from the simlification of the thermal field taking lace in the active surface. As a matter of fact, that is strictly 3D due to the resence of ies embedded in the slab and the ater temerature variation along the circuit. Hence, the folloing simlifications ere decided: The interaction beteen the ie and the building structure is calculated through the definition of a thermal resistance that connects the external ie surface ith the ie level, i.e. the fictitious lane here ies are assumed to lie. In a fe ords, ies are assumed to act as a thin active layer laced at the level here the axes of the ies lie. There, ies erform their on action, filtered by a thermal resistance, that resumes the uneven heat distribution caused by the resence of ies embedded in the slab. This ay, it is ossible to take into account the ie layout ithout maintaining a 2D thermal descrition. The variation of ater temerature along the circuit is modelled considering the ater circuit as a heat exchanger. The efficiency of such a heat exchanger is comuted via the ε-ntu (effectiveness-number of Transfer Units) method. The consequent model transoses a 3D roblem into a D R-C netork, ith a great advantage in comutation time. As a consequence, the average temeratures at the ie, floor and ceiling surfaces are obtained. They are necessary in order to determine the heat flos exchanged beteen the ater circuit and the room. Obviously, such an aroach is aimed at energy analyses of radiant systems, hereas it might be limiting hen a detailed descrition of the thermal rofile on the floor and ceiling surfaces is needed. Such a detailed aroach is anyay requested in fe and articular research toics, and is over the requests of engineers and energy consultants. METHODS The connection beteen the hydronic circuit and the embedding structure The achieved model results as an extension of the resistance method imlemented in the ne Standard EN 5377 and aimed at sizing thermo-active building systems. The original model rises from studies by Glück (982, 989). In fact, Glück has found the analytical solution of the thermal field determined by the resence of ies embedded in an infinitely long slab. The folloing figure shos the thermal domain solved by Glück. In articular, the main boundary conditions at the basis of this mathematical model are exlained as follos: Steady state conditions Imosed heat transfer coefficients at the floor and ceiling surfaces Homogeneous slab Pies are modelled via unctiform heat sources/sinks able to kee a fixed temerature at a distance equal to the ie external radius

2 s t s u 2 t o θ o θ 2 u h o h2 u Figure Domain and boundary conditions for Glück s analytical solution The consequent analytical solution is very comlex, so it cannot be idely alied. This analytical solution as hoever the basic starting oint for the ork of Dorer, Koschenz and Lehmann (2000, 2007). In fact, they continued the ork by Glück and imlemented the revious analytical solution into a simle method that describes the interaction beteen the hydronic circuit and the building structure via a thermal resistance netork. One of the main concets arising from this research consists in the definition of the ie level thermal node. Basically this means that the action of the ies is suosed to take lace just at the lane here they lie. In this ay, the 2D thermal field collases into a D structure consisting of a sequence of thermal nodes, among hich the thermal node reresenting the ie level is included. This method as rimarily aimed at sizing thermo-active systems in inter conditions. In more detail, the thermal resistances connect the suly ater temerature and the ie level temerature and are defined as follos: Rc 2 m& s c is the thermal resistance describing the connection beteen the suly ater temerature and the mean ater temerature along the circuit. R PS S d 2 8 t π m&, s l is the thermal resistance due to the convective heat transfer from the ater to the inner surface of the ie. R d S ln d t 2 2 π λ is the thermal resistance related to the conduction heat transfer from the inner side of the ie to the outer one. S S ln π d R x 2 π λe is the thermal resistance connecting the temerature at the external side of the ie ith the temerature at the fictitious ie level. It comes from the simlification of the Glück s equation, under the folloing geometrical conditions: to > 0.3 S tu > 0.3 S d < 0.2 S In fact, under such hyotheses, the analytical solution by Glück can be efficaciously simlified. As a consequence, such a model is still limited by the basic assumtions of the Glück model and moreover by the assumtions needed for its simlification. This ay, the alication of the method ould be limited to radiant systems characterised by high thicknesses over and under the ie level and by long ie sacings. Afterards, the ork of Dorer, Koschenz and Lehmann became the starting oint for De Carli, Koschenz, Olesen and Scara (2006), ho imlemented the method ithin the ne Standard EN 5377 for sizing thermo-active building systems. In the frame of that ork, the accuracy of the method as evaluated in conditions different from the ones assumed for the develoment of the model. In articular, the model as tested under unsteady state boundary conditions and imosing heat flos at the floor and ceiling surfaces instead of heat transfer coefficients. At the end of that testing hase, the accuracy shon by the method as still good, but the above mentioned geometrical limits still held. As a consequence, in EN 5377 the method is alied to thermo-active building elements, even in summer conditions, even if the method as originally develoed for steady state conditions. As regards this asect, the ork resented in this aer can be considered as an extension of the EN 5377 roject. In fact, ithin the frame of this ork further tests ere erformed in order to verify the accuracy of the resistance method in unsteady state conditions, even for comlex shae slabs. The tested slabs are resented in the folloing figures:

3 Figure 5 Slab, tye G Figure 2 Slab, tye A 2D calculations have been contrasted against the D model by comaring the corresonding thermal behaviours along a eriod ith imosed temeratures at the surfaces of the floor, ceiling and ie. Figure 6 shos an examle of temerature rofiles used in the comarisons Temerature imosed at the floor surface Temerature imosed at the ceiling surface Temerature imosed at the ie surface 27.5 Temerature [ C] Figure 3 Slab, tye E Time [s] Figure 6 Examle of boundary conditions imosed for the validation of the D simlification of the thermal domain Figure 4 Slab, tye X The first art of the simulation eriod shos the difference of the thermal dynamic behaviour. Such a comarison is erformed in terms of heat flos (through the floor, ceiling and ie surfaces), temeratures (mean temerature at the ie level, i.e. along the ie sacing, but the diameter of the ie), and erceived thermal resistance (beteen the temerature at the external side of the ie and the mean temerature at the ie level). At the end of each simulation, constant boundary conditions ere imosed in order to reach the steady state behaviour. The thermal resistance R x used in the D model is not calculated using the equation achieved by Dorer, Koschenz and Lehmann. In fact, in order to extend the method over the geometrical constraints imosed

4 by the resistance method, R x is derived after a 2D simulation erformed under steady state conditions. From the 2D simulation under steady state conditions, the heat flo assing through the ie and the average temerature of the ie level are used to calculate R x using the equation: θpl θ Rx S Q& R x is laced at the ie level and acts during the entire simulation eriod. Afterards, heat flos and temeratures of the D model are comared ith the 2D ones under the same boundary conditions. If they aroach each other at the end, it means that the 2D model can be substituted by a D model here the thermal resistance acting beteen the ie level and the external surface of the ie is derived from a 2D model running under steady state conditions. The analysis of the results focused on: the mean temerature at the ie level the erceived thermal resistance beteen the external surface of the ie and the ie level the heat flos assing through the floor, the ceiling and the ie. Figure 7 shos an examle of the comarisons, in terms of heat flos. The analysis of the simulations erformed led to the assumtion that a D simlification can be adoted in the descrition of each kind of slab simulated, since differences in heat flos erceived by the rooms and the circuit are really small, even during unsteady state conditions. In articular, the accuracy obtained in the forecast of heat flos through the ie level is above the exectations, since the differences in the heat exchange by the circuit are alays lo, desite the imortant simlification that has been assumed, just in modelling the region here ies are laced. QFloor - D QCeiling - D QPies - D Time [s] Heat flo [W/m] QFloor - 2D QCeiling - 2D QPies - 2D Figure 7 Examle of differences in heat flos imlied by the 2D simlification The comarisons in Figure 8 sho the difference in the average temerature at the ie level and in the erceived thermal resistance beteen the external surface of the ies and the ie level (R x ). In articular, the forecast of the average temerature of the ie level is accurate, hereas the erceived thermal resistance R x suffered large variations during the simulation. Anyay, the largest variations in R x haen hen sudden increases/decreases in ie temerature take lace. Under such conditions, an inversion of heat flos is encountered. As a consequence, under these conditions, the large variation in the erceived thermal resistance R x does not imly large variations in heat flos, since heat flos have lo absolute values. Temerature [ C] TPieLevel - 2D R - 2D TPieLevel - D R - D Time [s] Figure 8 Examle of differences in ie level temerature and erceived thermal resistance imlied by the 2D simlification The hydronic circuit as a heat exchanger The hydronic circuit can be reduced to a heat exchanger in hich the ater exchanges heat ith the thermal node at the ie level. At this oint, it is assumed that the ie level is at uniform temerature. It is an assumtion consistent ith the formulation of energy simulation rograms (assumtion of D heat transfer through the surfaces) and is suorted by the diffusivity of materials embedding the circuit, usually increased in order to get better erformances by the radiant system. In these conditions, the ε-ntu method is ritten in the folloing ay: Out In Q& θ θ ( NTU) ε In e Q& Max θpl θ U c U c As Uc As m& NTU ε e ( m& c) Min m& c here: U c R + R + Rx As a consequence, ε can be calculated through knon arameters and hence the actual heat transfer can be calculated via the next equation: In Q& ε Q& ε m& c θ θ Max ( ) PL Thermal resistance [mk/w] A c s

5 Presentation of the calculation module The inut data to be entered by the user consist of data related to the building construction here ies are going to be laced and of data related to the ie and the circuit. Moreover, additional inut data may be required, deending on the tye of slab to be simulated. Figure 9 shos the indo dialog collecting the main inut data for the descrition of the slab: Basic control (Figure 0): Such a control consists in a modulation based on outdoor temerature Control of the ater suly temerature based on the outdoor and indoor oerative temeratures, via the folloing equation (Olesen, 2004): θ ( 20. θ ) ( θ 22. ) W Ext O 0.52 Control of the ater average temerature based on the outdoor and indoor oerative temeratures, via the folloing equation (Olesen, 2004): θ ( 20. θ ) ( θ 22. ) W Ext O 0.52 Such a value is defined by considering the value of heat flo rate from/to the ie to/from the ie level during the revious time ste: W ( 20. θ ) ( 22. ) θ 0.52 θ Ext O Q& PL + 2 m& c W W Figure 9 Main indo of the calculation module Section Destination collects the data regarding the building construction here ies are embedded, hereas section Pie gets together the main data regarding the ie and the circuit. With the arameter Maximum Area er Circuit, it is ossible to create arallel circuits for the ater. Moreover, additional data may be necessary for some tyes of slab. EXPERIMENTAL APPARATUS The facility used for the tests is located at the Civil Engineering Deartment of the Technical University of Denmark, Lyngby, and consists of a room rovided ith to levels of thermo-active comonents laced as floor and ceiling. The dimensions of the room are: Length: 6 m Width: 3.6 m Height: 3.6 m The vertical alls are insulated and a guard box is laced around the room (Figure ). This box encloses the room, so that it searates the room and the thermo-active comonents from the rest of the building, in order to revent that the external environment influences the system. Moreover, the air temerature inside the guard is controlled by a PID device that forces the air temerature to follo the test room air temerature. Inside the guard, to fans are laced to mix the air and to avoid temerature stratification. Figure 0 Control indo of the calculation module At the resent status, three kinds of controls are imlemented in the module. In the folloing, such controls are described:

6 26 Mean Radiant Temerature [ C] Mean Air Temerature [ C] Ceiling Temerature [ C] Temerature [ C] Time [h] Figure Sketch of the test facility Floor and ceiling both consist in three refabricated hollo-core concrete decks ith ies embedded in the concrete. Each deck is 6.6 m long,.2 m ide and 0.27 m high (Figure 2). The sizes of cavities are 50x08 mm at the highest and at the idest sots. The distance beteen the vertical axes of symmetry is 50 mm. Figure 3 Main temeratures obtained from measurements under unsteady state conditions Temerature [ C] Mean Radiant Temerature [ C] Mean Air Temerature [ C] Ceiling Temerature [ C] Time [h] Figure 2 Sketch of the active slab resent in the test facility Figure 4 Results obtained by the calculation module under unsteady state conditions The thermo-active comonents have integrated PEX ies laced belo each cavity. The ie level is 50 mm above the ceiling surface of the deck. The diameters of the ies are: inner diameter 6 mm, outer diameter 20 mm. RESULTS Tests have been erformed in order to check the calculation module develoed. Steady state as ell as unsteady state tests ere carried out. Steady state tests ere useful for checking the 2D simlification on the thermal domain, together ith the alication of the ε NTU aroach. In a fe ords, the ossibility of avoiding henomena related to the thermal caacity of the room makes it ossible to focus solely on the circuit. When unsteady state measurements are considered instead, even dynamic henomena can be considered. Figure 3 and Figure 4 sho the main temeratures obtained by measurements and simulations, hereas Figure 5 and Figure 6 sho differences in heat extracted by the cooling unit. The results resented refer to the folloing oerating conditions: Heat loads: 5 W/m 2 from 08:00 to 8:00 System o On from 20:00 to 08:00 o Suly ater temerature: 9 C o Setoint in air temerature: 2 C To summarise, the regulation is similar to the one used in thermo-active building systems: the slab is cooled don during the night, so it is reared to absorb heat from the room hen heat loads take lace. From the comarison of temerature rofiles, the trends of temeratures in the test room looks ell described. As a matter of fact, maximum and minimum temeratures corresond and the temerature trends are similar. Some differences, anyay may be encountered. In articular, the simulation tool looks to underestimate the thermal inertia of air. Esecially, that could deend on the additional thermal inertia resent in the room, due to desks and aliances used to simulate office heat loads in the test facility. Thus the air temerature in the simulation quickly looses internal energy and assumes the same temerature value as the surfaces,

7 hen no heat loads are resent. So the air temerature cools don quickly and reaches the setoint temerature earlier than in the reality. That is considered to be one of the main causes of the different shaes of the cooling rate rofile, hich are shon in Figure 5 and in Figure 6. In fact, the simulation tool imoses the circuit to sitch off earlier than in the test room. But further notes may be derived via the analysis of cooling rate trends. For instance, the simulation tool looks to overestimate the action of the system. In fact, the system alays extracts more heat than the real circuit. Anyay, such a difference can be ascribed even to the values of the thermal roerties estimated in the calculation tool, and to an imrovable distribution of radiant and convective heat loads. Moreover, even the values of the real convective heat transfer coefficients may be different from the ones assumed in the simulation tool, so more accuracy in the forecast of the heat exchange beteen the test room and the slab might be acquired via a better estimation of the convective heat transfer coefficients characteristic of the simulated room. To summarise, desite of these discreancies due to the incomlete knoledge of the room characteristics and heat load distributions, the simulation tool shos consistent results and allos the user to forecast temeratures and heat loads in an accurate ay Cooling Rate [W] Figure 5 Cooling rate from measurements under unsteady state conditions Cooling Rate [W] Cooling Rate [W] Time [h] Figure 6 Cooling rate from simulation under unsteady state conditions CONCLUSION In the resent roject, the accuracy achievable by imortant simlifications in the descrition of radiant systems has been studied. After this numerical art, a simulation tool has been develoed and integrated ithin softare BSim. The hole softare has been contrasted against measurements erformed in an aroriate test facility. The simulation tool shos consistent results, imrovable via a better knoledge of the thermal characteristics of the simulated room, and accurate enough for use in energy simulations. REFERENCES Glück, B., 982. Strahlungsheizung Theorie und Praxis, Verlag C.F. Müller, Karlsruhe. Glück, B., 989. Wärmeübertragung, Wärmeabgabe von Raumheizflächen und Rohren, VEB Verlag für Bauesen. Berlin. Koschenz, M., Lehmann. B., Thermoaktive Bauteilsysteme, EMPA, Dübendorf (CH). Lehmann, B., Dorer, V., and Koschenz, M., Alication range of thermally activated buildingsystems tabs, Energy and Buildings, Volume 39, Issue 5, May 2007, Pages De Carli, M., Koschenz, M., Olesen, B.W., Scara, M., Dynamic Evaluation of the Cooling Caacity of Thermo Active Building Systems, ASHRAE 2006 WINTER MEETING - Chicago, IL, January CEN, Standard EN Heating systems in buildings - Design of embedded ater based surface heating and cooling systems. Olesen, B.W., Currò Dossi F., Oeration and Control of Activated Slab Heating and Cooling Systems, Proceedings of CIB World Buildings Congress 2004, 2004, Toronto, Canada. NOMENCLATURE Magnitudes 2 A : Area [ m ] c : Secific heat caacity d : Diameter [ m ] kg m& : Flo s l : Circuit length [ m ] J kg K NTU: Number of Transfer Units [-] W q& : Secific heat flo 2 m Q & : Heat flo [ W ]

8 S : Pie sacing [ m ] t : Thickness [ m ] U : Global heat transfer coefficient ε : Heat exchange efficiency [ ] θ : Temerature [ C] W λ Thermal conductivity m K W 2 m Subscrits c : refers to the circuit e : refers to the material embedding the ies Ext : refers to the exterior environment Max: maximum Min: minimum o : refers to the art of the slab laced on the ie level O : oerative : refers to the ie PL : refers to the ie level s : refers to m 2 of floor area u : refers to the art of the slab laced under the ie level : refers to the ater Suerscrits In : refers to the inlet side of the circuit Out : refers to the outlet side of the circuit