Available online at ScienceDirect. 11th Nordic Symposium on Building Physics, NSB2017, June 2017, Trondheim, Norway

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1 Available online at.sciencedirect.com ScienceDirect Energy rocedia 32 (207) elsevier.com/locate/procedia th Nordic Symposium on Building hysics, NSB207, -4 June 207, Trondheim, Noray A method to determine heating poer and heat up time for intermittent heating of churches Magnus Wessberg a *, Tor Broström b, Tomas Vyhlidal a a Dept. of Instrumentation and Control Eng., Faculty of Mechanical Eng., Czech Technical University in rague, Technicka 4, rague 6, 66 07, Czech Republic b Uppsala University Cramergatan Visby Seden Abstract Intermittent heating, common in churches, requires higher heating poer than steady state heating. With respect to energy use and preservation aspects, the heat up time should be short. Systems for intermittent heating are often designed using rule of thumb estimates or inadequate steady state calculations. This paper presents a method to relate heating poer and heat up time for a specific building here thermal characteristics of a building are determined using a step response test. 207 The Authors. ublished by Elsevier Ltd. eer-revie under responsibility of the organizing committee of the th Nordic Symposium on Building hysics. Keyords: intermittent heating;. Introduction Many churches in Seden are unheated during the periods hen they are not used. Diminishing populations in the countryside is gradually forcing congregations to join together resulting in feer services at each church []. Further, small congregations have often limited resources ith the result that climate control for conservation must be minimized to save booth energy and costs [2]. Traditionally most churches are heated intermittently [3] hich requires much higher heating poer than steady state heating. In todays practice, intermittent heating systems are designed using rule of thumb estimates or, in the orst case, steady state calculations. This paper presents a method to determine heating poer and heat up time for a specific building. When a church is heated intermittently, a major part of the energy is used to heat up the alls. This means that conventional methods for calculating the heating load at steady state conditions are not applicable. The underlying theory as developed already in the 9 th century and results in a simple and manageable model that describes the relation beteen heating poer and heat up time for a given building. Hoever, difficulties in determining the thermal properties of a historic masonry construction have been a barrier for the application. Furthermore, the simplified model as not validated against actual data. In buildings ith heavy stone alls it is generally most energy efficient to use heating systems ith as high poer as possible and thereby let the heating period be as short as possible. Long heating periods do not only lead to higher energy cost but also an increased risk for damage on the artefacts due to drying. In Scandinavia recommendations of 6-2 hours are common. A draback is that this course of action requires high heating poer resulting in high costs due to investments or electrical tariffs. From the * Corresponding author. Tel.: ; fax: address: magnus.essberg@konstvet.uu.se The Authors. ublished by Elsevier Ltd. eer-revie under responsibility of the organizing committee of the th Nordic Symposium on Building hysics 0.06/j.egypro

2 96 Magnus Wessberg et al. / Energy rocedia 32 (207) energy efficiency point of vie it is important to minimize energy consumption by turning on the heat at the right time before service. When the heating system is controlled manually, this is often based on either practical aspects such as orking hours etc. or in some cases the experience of the staff [4]. There are intelligent control systems that aim to predict heat up time but they are based on insufficient physical models. The present paper presents a method here the thermal characteristics of a building are determined using a step response test. The building is heated ith constant poer input hile air and all temperatures are measured. This allos for a parameter study in the design phase, relating heating poer and heat up time for that particular building. 2. Theoretical model for intermittent heating Intermittent heating in historic buildings has been studied since the 9 th century hen heating systems started to be installed in churches. In 922 the Sedish state-oned energy company Vattenfall financed theoretical and practical studies to facilitate the introduction of electric heating in churches [5]. In 930 Krischer presented a study that as in line ith the results from Vattenfall [6]. They both concluded that a simplified mathematical model could be derived from the heat transfer equation solved for the case of a semi-infinite slab heated ith constant heat flux. This solution is no common knoledge and can be found in texts on heat conduction or building physics e.g. [7]. According to the simplified model, the increase in temperature during a heating occasion ith constant heat flux is proportional to the square root of time. The solution is based on the folloing conditions: In the beginning of the heating occasion the temperature distribution in the all is constant and equal to the indoor air temperature The heating occasion is so short that only a part of the all is affected by the heat ave The heat flux into the all is constant The area of indos, doors etc. is small compared ith the all area. The infiltration rate is small. The to last points imply that the loss due to infiltration and conduction, l, is small compared to the heat flux into the all. It is assumed that the loss factor F= / s is constant here and s is the heat flo into the all respectively the heat supplied, see figure a. The temperature increase at the all surface, Δϑ, during a heating occasion is determined by A 0, t 0, t 0, u t () 0 here 2 u (2) c and is the thermal effusivity of the all (W/(m 2 K s ½ ) c The air temperature can be expressed as i u t (3) A A here α is the heat-transfer coefficient beteen air and all (W/(m 2 C)). Under the assumption that α is constant e have a linear relation for both the all temperature and the air temperature, see figure b.

3 Magnus Wessberg et al. / Energy rocedia 32 (207) Δϑ i Δϑ =sf l= s(-f) s Heater Fig.. (a) Heat flux at intermittently heating; (b) Theoretical temperature increase according to eq. () and eq.(3). 3. Method to determine thermal characteristics in of the building Equations () and (3) can be used to calculate the heating poer as a function of heat up time, or vice versa, for a given building. Based only on the physical characteristics of a given historic masonry all, it is difficult to determine the buildings material parameter, u. Broström developed a method to determine the parameters u/a and /αa from measurements of temperature during a step response test, i.e. a heating occasion ith constant heating poer [8]. As the increase of temperature in the air and on the surface of the all, according to eq. () and (3), are linear functions of square root of time the folloing reasoning must apply. If eq. (3) is compared ith a standard linear equation y = kx + m (4) Where yy is the increase of temperature, Δϑ, during a heating occasion and x t, it is easy to identify the slope of the line as k u (5) A and the intercept as m i (6) A hich is the difference beteen air and all surface temperature. Knoing the supplied poer ss, the building characteristics u/a and /(αa) can thus be determined from measured data during the step response test at a heating occasion. A large number of step response tests ere carried out in medieval stone churches to validate eq.() and eq.(3). To of the tests are shon in figure 2. Every test follos the same pattern. In the beginning it takes some time to heat up the interior air but after some time, depending of the church s characteristics, the temperature increases according to the model as described by eq. () and eq. (3).

4 98 Magnus Wessberg et al. / Energy rocedia 32 (207) Fig. 2. (a) A heating occasion in Väskinde church Gotland Seden; (b) A heating occasion in Tingstäde church Gotland Seden Some observations from the step response tests need to be commented. In the beginning of the heating occasion it takes some time before the all heat flux reaches its maximum value due to the thermal inertia of indoor air and interiors. The heat accumulation in air and interiors can be modelled using time constant β [9] t s F e (7) As shon in fig 2, after an initial time period of approximately, 5β, the data follo the theoretical model The intercept of the straight lines in Fig 2 are -3 degrees higher than ϑ 0 i.e. the initial all temperature. According to equation (3) the intercept should theoretically be the same as ϑ 0. In reality it ill be a little bit loer than ϑ 0 due to the thermal inertia of air. The difference can to some extent be explained by a measurement error of the all surface temperature ϑ e [8]. The temperature sensors ere applied on the all surface and the measured value is therefore a eighted average of the all surface temperature and the air temperature. The absolute size of the error is thus dependent of the difference beteen all and air temperature. The measured value, ϑ m, at the all surface can be estimated by ϑ m = ν ϑ +ν i ϑ i (8) here ν and ν i are eighting factors. It is suggested that ν = 2/3 and ν i = /3 are reasonable estimations of the eighting factors [8]. The measurement error, ϑ e, ill thus be ϑ e = ϑ m - ϑ = (ϑ i - ϑ m)/2 (9) The parameters u/a, /αa and F also need to be commented. u/a is a material specific constant but can change during the year depending on the degree of moisture in the all. The heat transfer coefficient α is temperature dependent and the energy loss factor F is dependent on booth indoor and outdoor temperature difference and ind conditions. Hoever all step response tests, hich as carried out under different seasons, shoed that the variations in all these above mentioned factors are small and is not much influenced by seasonal climate changes. 3.. Method to determine thermal characteristics To determine the thermal characteristics u/a and /αa of a building during a heating occasion, a step response test can be carried out as follos:. Set the heating system to constant (maximal) poer s0 2. Log all temperature, ϑ m, and air temperature, ϑ im 3. Determine t i, defined as the time hen the temperature difference beteen air and all surface has become constant indicating that the initial time period has passed. See figure From data measured after t i, calculate the measurement error, ϑ e, at an arbitrary time and perform numerical linear regression on ith ϑ i = a 0+a x for indoor air temperature and

5 Magnus Wessberg et al. / Energy rocedia 32 (207) ϑ + ϑ e = b 0+b x for all temperature x = t for both ϑ i and ϑ, 5. The thermal parameters can then be determined by u/a = a / s0 and /αa = (a 0 - b 0+ϑ e)/ s0. The increase of air temperature as a function of time can be described as: a a0 b0 e i i i0 t (8) s0 s Calculate heat up time ith a given heating poer The model can be used to calculate the heat up time by using eq. (8), and set = s i.e. the same poer as used at the step response test ts iset i0 a a b 0 e 2 (9) here t s is time to reach desired set point temperature ϑ iset ϑ iset is the desired set point temperature ϑ i0 is initial air temperature a 0, b 0 and a are parameters from the regression analysis made at the step response test Calculate heating poer needed for a given heat up time The model, eq. (8), can also be used to determine the required poer to heat up the building ithin a certain time s0 i0 a b a 0 0 e iset t (0) here t is time to reach set point temperature ϑ iset ϑ iset is the set point temperature. ϑ i0 is initial air temperature. a 0, b 0 and a are parameters from the regression analysis made at the step response test. s0 is the poer used at the step response test Economic optimisation of heating poer For design purposes, it is possible to determine the optimal heat up time hich results in the loest overall cost. Higher heating poer results in shorter heat up time and loer energy cost but tariffs and the installation costs increase. Loer heating poer, on the other hand, ill lead to longer heat up time ith the opposite effects on costs. The total annual heating cost depends thus on the installed heating poer and the energy use. C tot C tc C () i e f Where C i Cost for installation and tariff per heating occasion and kw(cost/kw) C e Energy cost per heating occasion (cost/kwh) C f Fixed cost, independent of energy consumption and installed poer Required installed poer according to eq. (0) Fig 3 shos, in principal, ho the different poer cost, energy cost and total cost depend on heat up time. Short heat up time reduces energy cost but requires higher poer cost. The cost optimal heat up time is hen the total cost curve is at its loest.

6 920 Magnus Wessberg et al. / Energy rocedia 32 (207) Fig. 3. Cost for intermittent heating as a function of heat up time. 4. Conclusions This paper shos that ith a relatively simple method it is possible to determine the thermal properties of a historic stone building here both construction and materials in the masonry alls are unknon. By performing a step response test the thermal properties can be derived hich in turn can be used to calculate heat up time before service. This allos for a model based control of the intermittent heating here selecting the right heat up time ill minimise both energy use and the negative effects on sensitive interiors of the building. In an iterative process, the model parameters can be adjusted each time the building is heated. Furthermore the proposed method can be used to for designing ne heating systems. In that case a step response can be carried out ith the old heating system or ith portable heaters to derive the parameters hich then can be used to determine the appropriate heating poer ith respect to the required heating time and the properties of the building. Finally method can be used before the installation of a ne heating system hen it comes to optimize the economic trade-off beteen the fixed cost for the installed heaters and variable cost for energy used at every heat up time. Even though the theoretical model is based on a number of simplifications, it still improves accuracy, in comparison to common practice, in both design and control of systems for intermittent heating. In the next stage this method ill be applied in a control unit that automatically updates the thermal parameters every time the church is heated and calculates the heat up time for next service. Acknoledgements This ork as supported by the Grant Agency of the Czech Technical University in rague, grant No. SGS7/76/OHK2/3T/2 and the Sedish Energy Agency s research program for energy efficiency in cultural heritage buildings, Spara och Bevara. References [] Larsen Klenz, Wessberg M, Brostrom T. Adaptive ventilation for occasionally used churches. 3th Eur. Work. Cult. Herit. reserv. EWCH 203, 203, p [2] Wessberg M, Larsen K, Broström T. Solar energy augmented adaptive ventilation in historic buildings. NSB Nord. Symp. Build. hysic 204, 204, p [3] Legnér M. Conservation versus Thermal Comfort - Conflicting Interests? The Issue of church heating, Seden c Konsthistorisk Tidskr 204. [4] Broström T, Klenz Larsen. Climate Control in Historic Buildings. Linköping University Electronic ress; 205. [5] Jacobsson F. Effektbehovet vid elektrisk uppvärmning av kyrkor samt uppvärmningsförsök i Gripsholms slott. Fritzes bokh.; 926. [6] Krischer O. Der Wärmebedarf von Gebäuden mit einzelnem und seltenem Betrieb [7] Hagentoft, C-E. Introduction to building physics. st ed. Lund: Studentlitteratur; 200. [8] Broström T. Uppvärmning i kyrkor Fukt och värmetekniska beräkningar för dimensionering och klimatstyrning. Kungliga Tekniska Högskolan, 996. [9] Henning T. Om intermittent uppvärmning av byggnader. Tek Tidskr Häfte 9 Sept 936:4.