2nd Canadian Solar Buildings Conference Calgary, June 10 – 14, 2007
SIMULATION OF THERMAL COMFORT CONDITIONS IN HIGHLY-GLAZED PERIMETER ZONES WITH SHADING DEVICES Mark Bessoudo, Athanassios Tzempelikos, Andreas Athienitis and Radu Zmeureanu Department of Building, Civil and Environmental Engineering, Concordia University, 1455 de Maisonneuve W., H3H 2N3 Montreal, Quebec, Canada Tel.: 514-848-2424 ext. 7080, E-mail:
[email protected] Type of paper : Refereed ABSTRACT This paper presents a numerical simulation and experimental study of the thermal environment in a perimeter zone near a highly-glazed façade. A finite difference thermal network approach was used to determine the daily variation in temperature of façade components (glazing and shading device) and indoor environmental parameters (air and operative temperature, radiant asymmetry) under variable climatic conditions (outdoor temperature and incident solar radiation). A transient, two-node thermal comfort model was used to determine the level of occupant comfort. The comfort model takes into account the solar radiation falling directly on the occupant. The simulation results are compared to experimental measurements taken from an experimental façade at Concordia University. The aim of this study is to develop a mathematical model than can provide recommendations for components of high-performance façades (glazing U-value and shading device type and properties) for different climatic conditions and orientations that will allow for the elimination or reduction of perimeter heating as a secondary system while maintaining comfort conditions in perimeter zones.
INTRODUCTION Occupants situated near windows often experience thermal discomfort. In the winter, window surface temperatures usually fall below indoor air temperature, possibly causing discomfort due to high radiant temperature asymmetry and low operative temperature (ASHRAE, 2004). In the summer, glazing interior temperatures are usually higher than indoor air temperature, often causing discomfort due to high radiant temperature asymmetry and increased operative temperature. In addition, solar radiation falling directly on the occupant can exacerbate discomfort. Shading devices, which are typically used for visual comfort purposes (glare control), can also be used to improve thermal comfort conditions in perimeter zones. To date, there has been limited work done on thermal comfort of occupants in glazed perimeter zones; also,
few take into account the effect of solar radiation (La Gennusa et al., 2005, Huizenga et al., 2006). Most of the work that has investigated the effect of solar radiation on comfort, however, assumed steady-state thermal conditions, thereby allowing the use of a simplified one-node steady-state thermal comfort model. In reality, the thermal environment of glazed perimeter zones is highly transient. This study explores thermal comfort conditions using a two-node transient thermal comfort model as well as the effects of solar shading devices on comfort and how they can be used to improve thermal comfort.
METHODOLOGY In order to quantify thermal comfort in a perimeter zone, the thermal environment must be evaluated, including climatic conditions, indoor air temperature, mean radiant temperature and radiant temperature asymmetry, in addition to defining other environmental and personal parameters. Mean Radiant Temperature The mean radiant temperature (MRT) is defined as “the uniform surface temperature of an imaginary black enclosure in which an occupant would exchange the same amount of radiant heat as in the actual nonuniform space” (ASHRAE, 2005). It is the weighted average of the internal surface temperatures, Ti, and the respective view factor to a subject, Fs-i, for N surfaces. The view factors between a seated or standing subject and the internal surfaces have been documented by Fanger (1972) and developed into charts. For simulation purposes, however, this method proves inadequate since the view factors can only be determined visually from the charts. Therefore, an algorithm to calculate the view factors between a subject and internal surfaces, Fp-i, was used (Cannistraro et al., 1992):
⎛ − b / c ⎞⎤ (1) ⎡ ⎛ − (a / c ) ⎞⎤ ⎡ Fp −i = Fmax ⋅ ⎢1 − exp⎜ ⎟⎥ ⋅ ⎢1 − exp⎜⎜ ⎟⎟⎥ ⎝ τ ⎠⎦ ⎣ ⎣ ⎝ γ ⎠⎦ where τ and γ are:
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2nd Canadian Solar Buildings Conference Calgary, June 10 – 14, 2007
τ = A+ B
a c
(2)
b c
γ =C+D +E
a c
(3)
The coefficients A, B, C, D, E, and Fmax are parameters which depend on each surface’s position relative to the subject’s orientation and the subject’s posture (seated or standing). The coefficients a, b, and c, are parameters that define the geometry of the interior surfaces (width, height, and distance) relative to the center of the subject.
Radiant Temperature Asymmetry The plane radiant temperature is described as the “uniform temperature of an enclosure in which the incident radiant flux on one side of a small plane element is the same as that in the actual environment” (ASHRAE 2005). The plane radiant temperature describes thermal radiation in one direction, and directionally dependent. Thus, radiant temperature asymmetry (RTA) is defined as “the difference between the plane radiant temperature of the two opposite sides of a small plane element” (ASHRAE, 2005). The angle factors between a small plane element and surrounding surfaces can be determined from Figure 1.
Therefore, the MRT of an enclosed space, taking into account interior surfaces, can be calculated by: N
Tmrt = ∑ Fs →i ⋅ Ti
(4)
i =1
When a person is seated near glazing exposed to solar radiation (beam and diffuse), the calculation of MRT becomes more complex since one must take into account not only the low-temperature interior surfaces, but also the components of solar radiation falling on the person. A generalized algorithm to calculate the MRT of an indoor space under these circumstances has been developed by La Gennusa et al. (2005): M ⎞ 1 ⎛ Tmrt,solar=∑Fs→i ⋅Ti + ⎜⎜αirr,d ∑Fs→j Id, j +αirr,b f p Ib ⎟⎟ (5) εsσ ⎝ i=1 j=1 ⎠ N
The first term in the expression denotes the MRT due to the low-temperature surfaces within the indoor space. The second part of the expression includes the effect of solar radiation hitting the occupant where εs is the emissivity of the subject, σ is the Stefan-Boltzmann constant, αirr,d and αirr,b are the diffuse and beam absorptance of the subject, respectively, and Id and Ib are the values of diffuse and beam solar radiation hitting the occupant, respectively. The parameter fp represents the projected area factor of the sun on the subject. It is a function of the solar altitude (β), the subject’s orientation and posture, and the azimuth angle between the subject and the sun (α). A method to calculate fp has been developed by Rizzo et al. (1991): 4
f p (α , β ) = ∑ Ai (β ) ⋅ α i
(6)
i =0
Figure 1 - Analytical formulas for calculating angle factors for small plane element (ASHRAE, 2005). The plane radiant temperature in the direction of the façade is given by: N
τ facade
i=1
εsσ
Tpr1 = ∑Fd1→i ⋅Ti +
(α
F
I +αirr,b f p Ib ) (8)
irr,d d1→glazing d, j
where Fd1Æ i is the angle factor between the small plane element and the interior surfaces in the direction of the façade, τfacade is the transmittance of the façade (with or without roller shade), and Fd1Æglazing is the angle factor between the small plane element and the glazing. The plane radiant temperature in the opposite direction is: N
Tpr 2 = ∑ Fd 1→i ⋅ Ti
(9)
i =1
where Fd1Æ i is the angle factor between the small plane element and the interior surfaces in the opposite direction of the façade. Thus, RTA is equal to:
Δ T pr = T pr 1 − T pr 2
(10)
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where
Ai (β ) = ∑ Aij ⋅ β j
(7)
j =0
The coefficients for a seated person in this model are contained in the parameter Aij.
Thermal comfort model Due to the transient nature of the external climatic conditions and of the indoor air temperature, the transient two-node thermal comfort model was selected (ASHRAE, 2005, Zmeureanu & Doramajian, 1992).
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2nd Canadian Solar Buildings Conference Calgary, June 10 – 14, 2007 The two-node model evaluates the skin (TSK) and core (TCR) temperatures and predicts the physiological thermal response of the occupant. Heat loss from the core occurs through conduction to the skin, convection via respiration and blood flow; heat loss from the skin occurs via radiation, convection, and evaporation of sweat to in the indoor environment as follows:
dTSK S ⋅A = SK D dt α ⋅ m ⋅ C p,B
(11)
dTCR S CR ⋅ AD = (1 − α ) ⋅ m ⋅ C p ,B dt
(12)
where SSK and SCR is the thermal storage of the skin and core compartments, respectively, AD is the surface area of the body, α is the mass of the skin compartment, m is the mass of the body, and Cp,B is the specific heat of the body (3490 kJ/kg ºC). Thermal storage of the skin and core is given by: S CR = M − W − (C RES − E RES ) − QCRSK (13)
S SK = QCRSK − (CS + RS + E SK )
(14)
where M is the metabolic heat generation in the core, W is the work exerted in the body, CRES and ERES are the convective and evaporative heat loss from respiration, respectively, and QCRSK is the heat transfer from the core to the skin via blood flow. CS, RS, and ESK are the convective, radiative, and evaporative heat losses from the skin, respectively. The index of thermal sensation (TSENS) is determined by the deviation of the mean body temperature from the cold and hot set-point of the evaporation regulation zone. Thermal sensation can be evaluated on an 11-point scale, with +5 being intolerably hot and -5 being intolerably cold. The index of thermal discomfort (DISC) is affected by the body temperature when it is in the sweating regulation zone; when the body temperature is below its cold set-point, DISC is equal to TSENS. The index of thermal discomfort is evaluated using a 6-point scale, with 0 being comfortable and 5 being intolerable. Parameters and Assumptions The finite difference thermal network approach was used to model the transient thermal response of the perimeter zone (Figure 19). In this approach, the zone was divided into a network of nodes (shading device, glazing layers, interior surfaces, interior and exterior air) with interconnecting paths through which energy flows. One-dimensional energy flow included all heat transfer processes (convection, conduction, and radiation) and was represented as resistances between the interconnecting nodes. Heat transfer by conduction through the building envelope was solved using the explicit finite difference method (Athienitis and Santamouris, 2002). Its general form is represented as:
Ti
p +1
T jp − Ti p ⎤ ⎛ Δt ⎞ ⎡ p = ⎜⎜ ⎟⎟ ⋅ ⎢qi + ∑ ⎥ + Ti C R j ⎥⎦ i, j ⎝ i ⎠ ⎢⎣
(15)
where Ti p+1 is the temperature of node i at timestep p+1, Δt is the timestep, Ci is the capacitance of node i, qi a heat source at node i, and Ri,j is the resistance between nodes i and j. The dimensions and properties of the perimeter zone in the simulations were modeled after the experimental façade in the Solar & Lighting Laboratory at Concordia University where earlier experiments had taken place. The experimental façade was divided into smaller zones by curtains in order to isolate six different façade sections, each with different shading devices. Each zone is 1.5m wide, 3.4m high and 2.5m deep. The façade is orientated 20º west of south. Thermal environmental parameters were measured using an indoor climate analyzer and a thermal comfort meter. In the studied section, the window is double-glazed, low-e (e=0.1), argon-filled with a U-value of 2.0 W/m2.K; it is 2.6m high (reaching 0.2m from the ceiling) and 1.5m wide. The cream-colored roller shade has a solar absorptance of 40% and transmittance of 5%. Properties of the other assemblies can be found in Table 2. An internal gain of 50 W was assumed, similar to the experimental equipment that was in the space while the measurements were taken. Infiltration through the façade was negligible. There were small gaps between the top of the curtain and the ceiling; therefore, air changes between the perimeter zone and core zone were taken into consideration. Set-points of 18 ºC for the night-time and 24 ºC for the daytime were used for the adjacent zone temperature. Since perimeter heating was turned off during the measurements, the model treats the perimeter zone as free-running. Due to a small opening between the ceiling and curtain that was used to isolate the zone, convection occurred between the perimeter zone and adjacent core zone. During the experiments, air was measured to be leaving the space with a velocity of about 0.25 m/s. For the calculated values of MRT, it was assumed that the person was seated in the center of the room (1.25m from façade) facing parallel to the façade. The emissivity of the person was taken to be 0.9 and the beam and diffuse absorptance of a clothed person were estimated to be 0.8 (Blazejczyk et al., 1993). For calculation of the RTA from plane radiant temperatures, the plane element was assumed to be at a height of 1.1m. Hourly values of beam and diffuse solar radiation incident on the façade were simulated using the Perez irradiance model (Perez et al, 1990) and TMY data for Montreal. Environmental and personal variables used in the comfort model are shown in Table 1.
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2nd Canadian Solar Buildings Conference Calgary, June 10 – 14, 2007 Table 1 - Variables used in the comfort model M (W/m2)
W (W/m2)
AD (m2)
mb (kg)
RH (%)
vair (m/s)
clo
58.2
0
1.8
70
30
0.1
1.0
RESULTS & DISCUSSION Case 1: cold, sunny day without shading For this case, the model used an minimum outdoor temperature of -16 ºC and a peak solar radiation incident on the façade of 950 W/m2. The simulated indoor air temperature, MRT, and inner glass surface temperature values are in good agreement with the measured data (Figures 2-3). The small fluctuations in experimental MRT and glass temperature values around solar noon are due to passing clouds. Figure 4 presents the simulation results of the MRT comparing the difference between values when taking into account the interior surface temperatures and the solar radiation falling directly on the person. These results clearly demonstrate the impact of solar radiation on MRT, showing a difference of about 10 ºC at their peak. This result is important since it shows the need to model the comfort conditions in perimeter zones differently than for typical enclosures. Furthermore, Figure 5 shows the difference in MRT isotherm distribution in the zone when taking into account the solar radiation in the calculation. For RTA results (Figure 6), the plane radiant temperature transducer exceeded its maximum limit of 50 ºC in any one direction. However, even with the transducer exceeding its maximum limit, it is clear that the RTA exceeded its allowable maximum value of 10ºC and will cause discomfort (ASHRAE, 2005). The sharp increase and decrease in RTA at about 11:00am and 3:00pm is due to internal shading of beam solar radiation caused by the window frame and divider curtains. The simulation predicted RTA exceeding 45ºC. The simulated transient thermal comfort conditions in the zone are shown in Figure 7. As expected, the predicted thermal sensation reaches “very hot” since there is no shading device and high solar radiation. This corresponds to slightly uncomfortable but acceptable conditions. Although these conditions are predicted to be physiologically “acceptable”, for the purpose of an occupant in an office building it may be uncomfortable since it is within the sweating regulation zone.
Figure 2 - MRT and indoor air temperature on a cold, sunny day without shading.
Figure 3 –Interior glass surface temperature on a cold, sunny day with no shading device.
Figure 4 - MRT values due to a) interior surface temperatures, and b) interior surfaces and solar radiation.
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2nd Canadian Solar Buildings Conference Calgary, June 10 – 14, 2007 good agreement with the experimental measurements (Figure 9 and Figure 10). The difference in MRT due to solar radiation is minimal since the roller shade has a transmittance of only 5% (Figure 11). The difference in the horizontal distribution of MRT in the zone with and without a roller shade is shown in Figure 12. The comfort conditions in the zone are improved as expected; a 10ºC decrease in MRT and 40ºC decrease in RTA can be seen. The predicted thermal sensation is “slightly warm” corresponding to a comfortable environment (Figure 14).
Figure 5 - Comparison between MRT on horizontal plane due to interior surfaces (top) and due to interior surfaces and solar radiation (bottom). Figure 8 - MRT and indoor air temperature on a cold, sunny day with roller shade.
Figure 6 - Radiant temperature asymmetry on cold, sunny day with no shading device. Figure 9 - Interior glass surface temperature on a cold, sunny day with roller shade.
Figure 7 – Predicted thermal sensation and level of discomfort on a cold, sunny day without shading. Case 2: cold, sunny day with roller shade For this case, the outdoor temperature was modeled to be about -10ºC with peak incident solar radiation incident on the façade reaching 1000 W/m2. Roller shade and interior glass surface temperatures are in
Figure 10 - Roller shade temperature on a cold, sunny day.
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2nd Canadian Solar Buildings Conference Calgary, June 10 – 14, 2007
Figure 11 - MRT values due to a) interior surface temperatures, and b) interior surfaces and solar radiation transmitted through roller shade.
Figure 12 - Comparison between MRT on a horizontal plane with roller shade (top) and with no shade (bottom) at solar noon on a cold, sunny day.
Figure 13 - RTA on cold, sunny day with roller shade.
Figure 14 - Predicted thermal sensation and level of discomfort on a cold, sunny day with roller shade. Case 3: cold, cloudy day without shading For this case, the outdoor temperature was modeled to be about -5ºC and peak incident solar radiation was 170 W/m2. Simulated glass temperature (Figure 16) shows some difference from the measured data – this could be due to a difference in ratio of beam-to-diffuse solar radiation. It is also interesting to note the slight increase in MRT close to the façade when taking solar radiation into consideration (Figure 17). This result, however, shows the strong influence of absorbed diffuse solar radiation in the model. Therefore, further exploration into an appropriate value to use for diffuse absorptance will be needed.
Figure 15 - MRT and indoor air temperature on a cold, cloudy day.
Figure 16 - Interior glass surface temperature on a cold, cloudy day.
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2nd Canadian Solar Buildings Conference Calgary, June 10 – 14, 2007
CONCLUSIONS This paper presents the results of computer simulations of the thermal environment in a perimeter zone near a highly-glazed façade using a finite difference thermal network and two-node comfort model. Simulation results were compared with experimental measurements taken in the simulated space.
Figure 17 - Comparison between MRT on horizontal plane due to interior surfaces (top) and due to interior surfaces and solar radiation (bottom) at solar noon on a cold, cloudy day.
The simulations show the importance of including the effect of solar radiation when evaluating thermal comfort in perimeter zones. and demonstrate the ability of shading devices to improve thermal comfort conditions near facades. The simulation model is being fine-tuned and generalized in order to be able to evaluate comfort conditions for typical office spaces equipped with any kind of shading device. Eventually, this model will help provide recommendations for components of high-performance facades in order to reduce or eliminate perimeter heating as a secondary source of heating in perimeter zones.
ACKNOWLEDGEMENTS Financial support of this work was provided by NSERC through the Solar Buildings Research Network.
REFERENCES
Figure 18 - Predicted level of thermal discomfort on a cold, cloudy day. It should be noted that possible errors in both the simulation and experimental results could have arisen. Since the climatic conditions (solar radiation and outdoor air temperature) in the thermal model were close but not identical to the measured data, it is expected that some small differences would occur with the simulation results compared to measured results. Air exchange between the adjacent zone and perimeter zone was unavoidable, although minimized. Table 2 - Properties of wall assemblies
R-value (ºC/W) Absorp -tance
Ceiling
Floor
Internal walls
Exterior wall
0.831
0.165
0.11
2.56
-
0.9
0.2
0.9
ASHRAE, “ASHRAE Handbook – Fundamentals”, Chapter 8. Atlanta: American Society of Heating, Refirigerating and Air-Conditioning Engineers, Inc., 2005. Athienitis A., Santamouris M., (2002) Thermal Analysis and Design of Passive Solar Buildings, James & James Ltd., London, UK. Blazejczyk, Krzysztof, Ingvar Holmér, and Hakån Nilsson. "Solar Heat Load on Man." International Journal of Biometeorology 37 (1993): 125-132. Cannistraro G., Franzitta G., Giaconia C., Rizzo G. “Algorithms for the calculation of the view factors between human body and rectangular surfaces in parallelepiped environments.” Energy and Buildings 19 (1992): 51-60. Fanger PO. Thermal comfort. New York: McGrawHill, 1972. Gagge AP, Stolwijk JAJ, Nishi Y. “An effective temperature scale based on a simple model of human physiological response.” ASHRAE Transactions 1971;77(Part 1):247–62. Huizenga, Charlie, Hui Zhang, Pieter Mattelaer, Tiefeng Yu, Edward Arens, and Peter Lyons. Window Performance for Human Thermal Comfort. National Fenestration Rating Council.
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2nd Canadian Solar Buildings Conference Calgary, June 10 – 14, 2007 Berkeley, CA: Center for the Built Environment, 2006. La Gennusa, Maria, Antonio Nucara, Gianfranco Rizzo, and Gianluca Scaccianoce. "The Calculation of the Mean Radiant Temperature of a Subject Exposed to the Solar Radiation - a Generalised Algorithm." Building and Environment 40 (2005): 367-375. Perez, R., Ineichen P., Seals R., Michalsky J., Stewart R., “Modeling daylight availability and irradiance components from direct and global irradiance.” Solar Energy 44 (1990): 271-289.
Rizzo G., Franzitta G., Cannistraro G. “Algorithms for the calculation of the mean projected area factors of seated and standing persons.” Energy and Buildings 17 (1991): 221-230. Zmeureanu R. & Doramajian A. "Thermally Acceptable Temperature Drifts Can Reduce the Energy Consumption for Cooling in Office Buildings." Building and Environment 27 (1992): 469-481.
Figure 19 – The thermal network that was used in the simulation.
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