Surface Temperatures on Flat Roofs and Hygrothermal Consequences

Surface Temperatures on Flat Roofs and Hygrothermal Consequences Christian Bludau, Dipl.-Ing., Department of Hygrothermics, Fraunhofer Institute for Building Physics; christian.bludau@ibp.fraunhofer.de Daniel Zirkelbach, Dipl.-Ing., Department of Hygrothermics, Fraunhofer Institute for Building Physics; daniel.zirkelbach@ibp.fraunhofer.de Hartwig M. Künzel, Dr.-Ing., Head of Department of Hygrothermics, Fraunhofer Institute for Building Physics; hartwig.kuenzel@ibp.fraunhofer.de KEYWORDS: temperature, long wave radiation, cold pond, flat roof. SUMMARY: In this paper the temperature conditions on flat roofs are discussed considering the influence of long-wave radiation to the sky and the effect of a parapet as an important factor for the nighttime roof temperature. The parapet leads to retention of cold air on the roof. Results of measurements on flat roofs and special meteorological data collected at the field test site in Holzkirchen are presented. For realistic assumptions of the boundary conditions a heat transfer coefficient depending on the ambient conditions including the temporary insulation effects of a cold surface air pond forming between the parapet walls is determined for flat roofs. The surface measurements on flat roofs with a parapet show a significant decrease of the temperature below the ambient air conditions during night time. These surface temperature recordings and meteorological data are used to validate hygrothermal simulations. Furthermore the possibility of interstitial condensation is investigated using an adapted hygrothermal simulation tool. The results show that the use of reflecting surfaces on flat roofs can lead to severe moisture accumulation in colder regions of Europe. Thus the color of the roofing membrane appears to be an important factor for the hygrothermal performance and moisture tolerance of certain constructions. 1. Introduction For the results of hygrothermal simulations the boundary conditions play a significant role. A drop in surface temperatures of flat roofs may result in moisture accumulation in the construction. For this reason it is important to research the prevailing conditions. In this paper the thermal behavior of flat roofs is discussed with special consideration of the effect of an existing parapet wall as an important factor for the nighttime roof temperature. The parapet leads to retention of cold air on the roof. Some approaches are given to include the formation of a cold pond of stagnant air in an existing hygrothermal simulation tool. Further calculations are performed to show the influence of different colors of the roofing membrane on the behavior of a typical flat roof construction. 2. Fundamentals 2.1 Nighttime Cooling below ambient air temperatures Long wave radiation is permanently emitted by all terrestrial objects and by some gases in the atmosphere. This thermal radiation can reach several hundred W/m 2 depending on the temperature of the emitting surface. The

intensity of the atmospheric counter radiation strongly depends on the current amount of cloud cover. Typical values at temperate latitudes for the counter radiation emitted by a cloudless sky range between about 180 W/m² (cold, dry air) and about 400 W/m² (warm, humid air). With a closed opaque cloud cover, the sky behaves like a Planckian emitter whose temperature is equal to the dew point temperature of the air. Building components absorb long-wave radiation emitted from other objects, but they also emit this radiation themselves and are thus in continuous radiation exchange with their surroundings. By day, this heat loss is not noticeable because of the heat gained by incident solar radiation. By night, however, the loss is not compensated and usually causes cooling of the surface below ambient air temperature ("overcooling"). This overcooling can lead to temperature differences from the ambient air temperature of about 5 to 10 C and more. Dew deposition and the risk of algae and mold growth may result from overcooling. 2.2 Development of a cold pond on a flat roof A typical construction for flat roofs is to surround the roof top by parapet walls. Such a wall forms a closed dam around the roof where the cold and thus heavier air can not flow out. The accumulated cold air is cooling below the ambient air temperature due to the long wave radiation of the roof surface and the interaction of the trapped air with higher air layers. Further the effects of wind in the area protected by the parapet walls can be lower reducing natural convection. Measurements show that the cold within the parapet walls lead to temperatures clearly beneath the temperatures that can develop on an unobstructed flat roof surface. The data presented here are recorded on a flat roof with a size of about 19 m by 6 m. The influence of the pond of cold air development should appear on a bigger roof as well depending on the air flow conditions caused by wind. Ignoring this effect during the design of a roof can lead to hygrothermal problems in the construction. 3. Measurements On the field test site in Holzkirchen many different roofing types have been build up and the hygrothermal behaviors have been investigated over many years. An important source for data is the weather station where in addition to the usual recordings like temperature, relative humidity and wind speed special radiation values like the diffuse solar radiation, the radiation in west direction, atmospheric counter radiation, the vertical counter radiation and surface temperatures of black and white surfaces in horizontal and vertical direction are measured. Further a new measuring device was installed at one of the flat roofs in the area. This allows measuring the thermal behavior of the surface. In Fig. 1 in the left picture the test setup is shown; in the right picture a detail of the sensor ladder to measure the temperature in different heights in the surrounded roof is shown. Each of the both test areas contains of four measuring fields with different colors. A black one, a white one, a gray one (this is the typically one used for flat roof constructions in Germany) and a reflecting one. The test areas are insulated below the surface and separated from the roof by a ventilated air gap to assure that there is no influence to the construction below. The one in the front is free-standing to eliminate influences from the parapet walls. The short wave absorptivity for the different surfaces is given in Table 1. The long wave emissivity is assumed to be around 0.9. It will be determined after the final tests. The silver surface is covered with a thin plastic layer so the emissivity should be close to the one of the other layers. It will be replaced by a uncoated metal foil in the next test period. TABLE. 1: Short wave absorptivity of the different surfaces.. Surface color Absorptivity [-] black 0.949 grey 0.849 silver 0.130 white 0.234 The test setup in the back is surrounded by parapet walls with a height of about 40 cm. The sensor ladder in the right picture allows measuring the temperatures at 11.5 cm below the surface top of the test setup in the back (on the roof surface) and further in heights of 0, 10, 20, 30 and 40 cm beginning on the surface top of the test setup.

FIG. 1: Test setup for temperature recordings. The left picture shows test patches to measure the surface temperatures; the right picture shows the sensor ladder for measuring the stratification between the parapet walls. The nighttime overcooling of surfaces is shown in Fig. 2. The thicker black line is the ambient air temperature measured two meters over the ground at our weather station close to the test setup. The other lines show the temperatures of the different colored surfaces. In the left diagram the temperature of the free-standing surfaces are shown (Fig. 1 right picture test setup in the front). FIG. 2: Surface temperatures for the black, gray, silver and white surface, free-standing an d surrounded by parapet walls. Examining the temperatures for the displayed five days in Fig. 2 during the night one can see the cooling below the ambient air temperatures. There is no recognizable overcooling in the morning of the 13 th of Oct. due a cloudy night. Analysis of the climatic data for the displayed days have shown that the sky most time was cloudy during the nights from 12 th to 14 th Oct. and then clear for the 15 th and 16 th of October. In the morning of the 15 th of Oct. a overcooling of the surfaces of about 7.3 C down to -6.7 C was measured. The lowest temperatures were measured at 4 a.m.. The color of the surface is not important for the overcooling only the long wave emissivity has an influence. During the day time a high temperature develops on the surface depending on the color (more precisely the short-wave radiation absorptivity). In the right diagram the temperatures of the test surfaces which are surrounded by parapet walls are shown (Fig. 1 right picture test setup in the back). Comparing the two diagrams the test setup surrounded by the parapet walls nearly shows the same behavior like the free standing one except for the maximum and minimum temperatures forming. For example at the 15 th of Oct. the temperature at 4 a.m. shows a difference to the ambient air temperature of 9.0 C down to a surface temperature of -8.4 C. This confirms earlier measurements where temperatures down to 10 C beneath the ambient air temperatures where measured on the same roof but without the test setup

In Fig. 3 the measured temperatures of the sensor ladder (Fig. 1 right picture) in the same time period are shown. Again concerning the morning of the 15 th of Oct. one can recognize a temperature gradient between the free moving air and the surface in the surrounded area. The sensor at 0 cm in the diagram is not the surface level of the roof but the surface level of the lower test setup. The sensor is situated 11.5 cm over the top of the roof surface. FIG. 3: Measured temperature in different heights above the roof surface in the area protected by parapet walls. 4. Calculations All calculations were performed with the at the Fraunhofer Institute for Building Physics developed and validated method for simultaneous calculation of heat and moisture transport in building components WUFI [Künzel 1994]. The simulation program allows calculating nearly any construction using measured climatic values as boundary conditions for example. Further it includes an explicit consideration of the different appearing radiations. Aim of the investigations is to develop more detailed models to simulate the short term surface conditions on flat roofs and include them into simulation tools. The models are validated using the performed measurements. 4.1 Heat Transfer Coefficient 4.1.1 Flat roofs For the use of the hygrothermal simulation tool WUFI a heat transfer coefficient was determined by comparing calculated profiles with measured profiles of certain flat roofs at Holzkirchen. Only the convective part was determined because WUFI can calculate an explicit part for radiation [Kehrer and Schmidt 2006]. The convective part for flat roofs was determined to α = 12.8 W/m 2 K. This value is close to the coefficient used in WUFI to calculate roofs α = 12.5 W/m 2 K which was determined for measured values below the roof tiles for an inclined roof [Kaufmann 1995]. Fig. 4 shows the comparison of the measurement and the calculation using the determined heat transfer coefficient for flat roofs. The determination of the coefficient for flat roofs is not completely exact at the moment. The influence of the wind is not included yet.

FIG. 4: Comparison of measurement and calculation using the determined heat transfer coefficient for flat roofs. 4.1.2 Simulation of the cold pond influence The behavior of cold air which can not flow out though the surrounded walls is not totally investigated yet. There are a few possibilities on how to include the factor of the insulating air layers into the used calculation model. One possibility is to simulate it by adapting the heat transfer coefficient as well as the radiation absorptivity and emissivity of the surface. Another possibility is to simulate the pond of cold air as one or more air layers which insulate the surface of the roof from the ambient air. The investigations are running and are not finished at the moment. 4.1.3 Snow and wind Free-standing surfaces like the here discussed flat roofs offer a large contact surface for the wind. The model for the wind dependent heat transfer coefficient used in the current version of the software was developed for vertical construction parts. This model only uses fixed parameters and seems not to be accurate enough for the explicit calculation of the short term variation of surface temperatures. FIG. 5: Insulation effect of a snow layer on a flat roof.. Snow is hard to include in simulation tools, because the appearance like the layer thickness strongly depends on the exhibition of the researched surface like angle, wind, construction (e.g. parapet walls). A snow layer leads to an insulation layer which keeps the temperature of the surface constant at about 0 C. Fig. 5 shows the insulating effect of a snow layer. The thickness of the layer is not very important. This effect can be observed at very thin

layer thicknesses. Considering thin layers of snow there is a translucency so there may be a small energy increase by absorption of solar radiation of the roof surface leading to a faster melting of the layer. Including the snow in a hygrothermal simulation tool would not be very complicated. It is enough just to set the temperature and the heat transfer coefficient to zero during the snow is laying on the surface. The problem is getting the data of the snow periods. Most stations do not measure this value and it is not included in the available climatic data files. Not including snow layers leads to an underestimation of the prevailing temperature. This leads to a calculation on the unfavorable side most of the time. If the mean temperatures are higher than the snow temperature during the covered time the temperatures is more moderate than the ambient air temperature. This can lead to a lower accumulation of condensation water than calculated. 4.2 Investigation of interstitional condensation For determining the interstitional condensation in a typical flat roof the construction displayed in Fig. 6 was chosen and simulated with a dark (short wave radiation absorption factor 0,9) and a bright (absorption factor 0,2) surface at for different climatic locations. FIG. 6: Flat roof construction. From inside to outside the construction consists of a gypsum board, a vapor retarder with a s d -value of 20 m, a mineral wool insulation layer with a thickness of 20 cm. On the top there is an oriented strand board and the construction is sealed with a bituminous felt. Helsinki (Finland) is used as cold location, Holzkirchen (Germany) and Copenhagen (Denmark) are used as moderate location and Dubai (United Arab Emirates) is used as warm location. From this locations hourly given climatic data were used as boundary conditions for the simulation. Table 1 shows the minimum, mean and maximum temperatures for the used climatic data. For the investigations the indoor conditions according to the [WTA-Guideline 2004] are used. The temperature moves in the yearly course between 20 and 22 degree Celsius while the relative humidity show values between 40 and 60 % RH. The calculations were performed for three years, starting in October. TABLE. 2: Minimum, mean and maximum temperatures at the climatic locations. Location Min. Temperature [ C] Mean Temperature [ C] Max. Temperature [ C] Helsinki -30.0 4.3 28.5 Holzkirchen -20.1 6.6 31.1 Copenhagen -9.6 8.3 26.8 Dubai 10.9 27.0 43.1 Fig. 7 shows in the left diagram the water content in mass percent in the OSB layer and in the right diagram the total water content of the construction. Many standards do not accept moisture contents in wooden materials above 20 M.-% to avoid damage by rot or mould growth. The value of the total water content is not significant but the tendency shows if there is water accumulating in the construction or if the construction has enough potential to dry out.

In Helsinki the winters are quite cold and the summers only show moderate high temperatures. In this climate using the discussed construction the water content in the OSB layer as well as the total water content is increasing over the years (black lines). At this location the color only show a low influence on the hygrothermal behavior of the construction. This construction will fail after some years and is not useable at this location. For Holzkirchen the graph for the roof with the dark roofing membrane (red solid line) shows a moisture content in the OSB layer between 12 and 19 M.-% which is not increasing over the calculated years. The course of the total water content is decreasing. This shows that the roof has enough potential to dry out. Concerning the courses of the roof with the bright surface the results change. The water accumulates in the OSB layer (red broken line). The temperatures in the construction during summer and day time are too low. The total water content is increasing during the calculated three years. The construction has no potential to dry out. Already in the first winter the OSB board reaches critical moisture values. The construction in Copenhagen shows the same behavior (blue lines). Analogical to the courses of the calculations with the climate in Holzkirchen the dark surface color leads to high enough temperatures to dry out the construction during the summer periods. The water content in the OSB layer oscillates between about 13 M.- % in summer and about 19 M.-% in winter. The course of the total water content again decreases. This construction can be build at locations with similar climatic behavior without restrictions. On the other hand the bright construction again shows moisture problems. The water content in the OSB layer exceed the limit of 20 M.-% during the first winter. The total water content is steady increasing. This construction can fail after a view years only by using a bright surface color instead of a dark one. In Dubai the construction is unproblematic. The water contents (green graphs) stay very low at this location. During the year there is nearly no change of water content in the OSB layer (swinging between about 10 and 13 M.-%). The total water content is decreasing very fast which points to a drying of the build up water content. In Dubai this construction can be engineered with any color of the surface. There are no restrictions due to the hygrothermal behavior. For saving cooling energy a bright roof can be useful. FIG. 7: Water content in the OSB layer and in the complete construction calculated with two surface colors for four different climatic locations. 5. Summary and conclusions In this paper measurements and a test setup are presented dealing with temperature conditions of flat roofs. The measurements clarify the overcooling effect due to long wave radiation and due to this the building of a cold pond on surfaces that are surrounded by parapet walls. The temperatures of the surfaces within the parapet walls are even lower than of the unobstructed. Surface temperatures about 10 C lower than the ambient air temperature were measured. For unobstructed flat roofs a heat transfer coefficient is determined, not yet including the factor wind. Possibilities are suggested to include the formation of a pond of cold air into simulation models as well as the influence of wind or snow. Further investigations are needed on flat roofs surrounded with parapet walls. Here especially the air flow pattern due to wind have to be determined.

The effect of the surface color by simulating a dark and a bright roof are discussed on the interstitional condensation of a typical flat roof construction at four different locations. The calculations show that accumulation of water occurs in the construction using a bright surface in moderate climate zones. In these locations the bright surface reaches not very high temperatures during the day and low temperatures below the ambient temperature during the night. The construction can not dry out. In warm regions the color does not show a high influence on the hygrothermal behavior of the used construction. In very cold regions the roof considered here will fail. 6. References Kaufmann, A. (1995). Untersuchungen zur Auswahl geeigneter Materialien für den Einsatz als feuchteabhängige Dampfbremse bei vollgedämmten Dachkonstruktionen und rechnerische Abschätzung ihrer praktischen Feuchtewirkung. Diplomarbeit Technische Physik, Fachhochschule München, Germany Kehrer M., Schmidt Th. (2006).Temperaturverhältnisse an Aussenoberflächen unter Strahlungseinflüssen, Proceedings BauSIM2006, 9.-11. Okt., TU München, Germany Künzel, H.M. (1994). Simultaneous Heat and Moisture Transport in Building Components. One- and twodimensional calculation using simple parameters. Dissertation Universität Stuttgart WTA-Guideline (2004). WTA Merkblatt 6-2-01/ E: Simulation of heat and moisture transfer. Fraunhofer IRB Verlag, ISBN 978-3-8167-6827-2