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Thermal transmittance of multiple glazing: computational fluid dynamics prediction
Applied Thermal Engineering 21 (2001) 1583±1592
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Thermal transmittance of multiple glazing: computational ¯uid dynamics prediction Guohui Gan * Institute of Building Technology, School of the Built Environment, University of Nottingham, Nottingham NG7 2RD, UK Received 16 November 2000; accepted 28 January 2001
Abstract Computational ¯uid dynamics (CFD) is applied for predicting the convective heat transfer coecient, thermal resistance and thermal transmittance for a double glazing unit. The predicted thermal resistance of glazing is compared with reference data and good agreement is achieved. The convective heat transfer coecient and thermal transmittance vary with the air space width and the temperature dierence across glazing. The CFD technique can be used to gain insight into multiple glazing performance and also optimise the design and operation of novel multiple glazing systems such as air ¯ow windows or double skin facades in terms of energy eciency and thermal comfort. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Thermal transmittance; Heat transfer coecient; Double glazing; Computational ¯uid dynamics
1. Introduction The thermal transmittance, or U value, of glazing is the rate of heat transfer under steady state conditions from the air on one side of the glazing to the air on the other side for unit area and for unit temperature dierence. The reciprocal of the thermal transmittance is the overall thermal resistance. Heat transfer through windows is a major component of conduction heat loss from a perimeter room in winter. The thermal resistance of a single-glazed window is very low. To increase the resistance, a double- or multiple-glazed window can be employed. In a double glazing
*
Tel.: +44-115-951-4876; fax: +44-115-951-3159. E-mail address: [email protected] (G. Gan).
1359-4311/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 1 ) 0 0 0 1 6 - 3
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G. Gan / Applied Thermal Engineering 21 (2001) 1583±1592
unit, a second pane of glass is separated from the ®rst pane by an air space, thereby increasing the thermal resistance due to the low thermal conductivity of air and the extra barrier to long wave radiation exchange provided by the second pane. The thermal resistance of a tall air cavity associated with conductive heat transfer increases with the width of air space, therefore increasing the width between two panes of glass decreases the thermal transmittance and improves the insulation eect. However, it is known that there is a limit in the eect of increasing the air space on the improvement of insulation. This limit is the ÔoptimumÕ separation of the panes and is usually considered to be between 20 and 25 mm. For air spaces wider than the limit, there is little improvement in the thermal transmittance. Below the limit, a number of measures can be taken to increase the thermal insulation of double glazing, e.g., using glass with low emissivity coatings, inhibiting convection in the air space, replacing the cavity air with gases of lower conductivity and evacuating the air space [1]. The thermal performance of glazing systems is often investigated by means of laboratory or ®eld tests. Recent work in this area includes the determination of local heat transfer coecients for window assemblies by Schrey et al. [2] based on the direct measurement of glazing surface temperatures. Bernier and Bourret [3] experimentally studied the eects of glass plate curvature due to barometric pressure and gas space temperature variations on the thermal transmittance of sealed glazing units. Hutchins and Platzer [4] measured the thermal performance of advanced glazing materials for windows whereas Clarke et al. [5] described an approach to apply combined thermal/daylight simulations to building designs incorporating advanced glazing systems. In recent years, numerical methods have also been used to determine the thermal performance of glazing systems. It has been shown that air ¯ow and heat transfer in tall cavities such as double glazing units can be predicted using computational ¯uid dynamics (CFD) [6]. The accuracy of the numerical prediction was found to be in¯uenced by the turbulence models employed [6]. Griths et al. [7,8] determined the thermal transmittance of evacuated glazing based on experimental solar simulation and computer based simulation modelling. A ®nite volume model was used to predict the temperature distribution in the air space and overall heat loss coecient of the glazing unit. Wright and Sullivan [9] developed a simple two-dimensional numerical model for glazing system thermal analysis. The model accounted for natural convection of the ®ll gas, conduction within the solid materials and radiant exchange between various surfaces facing the ®ll-gas cavity. Results were used to gain insights into heat transfer patterns in glazing systems with various combinations of low-emissivity coatings, ®ll gases and edge-seal designs. Zhao et al. [10] predicted the multi-cellular laminar ¯ow regime of natural convection in fenestration glazing cavities using a general-purpose ¯uid ¯ow and heat transfer computer program. Numerical calculations were performed over a range of aspect ratios to determine the critical Rayleigh number at which multicellular ¯ow began to form. The ¯ow in glazing cavities can be laminar or turbulent depending on the Rayleigh number. The thermal performance of multiple glazing under turbulent ¯ow has not been fully investigated. This paper presents a numerical method for predicting the thermal transmittance of multiple glazing systems under both laminar and turbulent regimes. The method was demonstrated for a double glazing unit with varying widths of air space at dierent temperature dierences across glazing. The same method can also be used to determine the thermal performance of other types of multiple glazing such as triple glazing.
G. Gan / Applied Thermal Engineering 21 (2001) 1583±1592
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2. Derivation of thermal transmittance Analytical solution of heat transfer through a multiple glazing system can be derived from a double glazing unit. Fig. 1 illustrates the heat transfer through a double glazing unit in winter conditions. The thermal transmittance of a multiple glazing unit is given by the following equation [11]: U
1 1 he
h1t h1i
1
where U is the thermal transmittance (W/m2 K), he and hi are the external and internal heat transfer coecients (W/m2 K), respectively, and ht is the conductance of the multiple glazing unit (W/m2 K). The conductance of a multiple glazing unit is obtained from 1 X1 d 2 ht h k n where h is the overall heat transfer coecient between an air space (W/m2 K), n is the number of air spaces, d is the total thickness of glass (m) and k is the thermal conductivity of glass (W/m K). The overall heat transfer coecient between an air space is given by h hc hr
3
Fig. 1. Schematic of heat transfer through a double glazing unit in winter.
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where hc and hr are the convective and radiative heat transfer coecients between an air space (W/ m2 K), respectively. The thermal resistance of an air space, R (m2 K/W), is the reciprocal of the overall heat transfer coecient for the gas space, i.e.: R
1 h
4
The radiative heat transfer coecient for a tall continuous vertical air space is given by hr 1
4rTm3 e1 1 e2e2 F112 e1
5
where r is Stefan±Boltzmann constant (5:67 10 8 W/m2 K4 ), e1 and e2 are the corrected emissivities of two panes of glass at mean temperature Tm (K), F12 is the view factor between two panes of glass and can be calculated from [12] 8 " #1=2 p 2 < 1 X 2 1 Y 2 X F12 ln X 1 Y 2 tan 1 p pXY : 1 X2 Y2 1 Y2 9 = p Y Y 1 X 2 tan 1 p X tan 1 X Y tan 1 Y 6 ; 1 X2 where X and Y are the width and height of glass normalised by the width of the air space between glass panes. The convective heat transfer coecient for a vertical air space is given by hc Nu
ka s
7
where Nu is the average Nusselt number, ka is the thermal conductivity of air (W/m K) and s is the mean width of air space (m). For experimental determination of the thermal transmittance of vertical glazing, the following empirical equation has been used to calculate the Nusselt number [11] Nu 0:35Ra0:38
8
where Ra is the Rayleigh number which is de®ned as gbDT s3 9 ma where g is the gravitational acceleration (m/s2 ), b is the thermal expansion coecient of air (1 K 1 ), m is the kinematic viscosity of air (m2 /s) and a is the thermal diusion coecient of air (m2 / s), DT is the temperature dierence between the hot surface Th (°C) and cold surface Tc (°C), for double glazing Th and Tc representing the surface temperatures of outdoor side of indoor pane and indoor side of outdoor pane of glass, respectively. Ra
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The Nusselt number for the air space can also be determined numerically from oT s ox w Nu 10 DT where oT =oxw is the gradient of the air temperature near a glass surface. Substituting Eq. (10) into Eq. (7) gives oT k ox w a 11 hc DT Hence, for given Th and Tc , hc can be obtained from oT =oxw for either the hot or cold surface. In this work CFD was used to compute the gradient oT =oxw from the temperature distribution in a glazing air space. The value of hc for the hot surface is generally dierent from that for the cold surface due to the dependence of thermal properties of air on temperature. However, when the temperature dierence between the two surfaces is small, say 10 K, the dierence in the convective heat transfer coecient is negligible (<1% for all the cases computed). The convective heat transfer coecient was therefore taken as the average for the hot and cold surfaces. Besides convective heat transfer, radiative heat transfer can be incorporated in the CFD model [13]. However, for known isothermal boundary conditions, the radiative heat exchange between two panes of glass can be considered constant and hence decoupled from the convective heat transfer in the CFD model. This improves the stability of computation and increases the speed of numerical solution. 3. Computational ¯uid dynamics model CFD was used to determine the convective heat transfer coecient of a double glazing unit based on the predicted air movement and temperature distribution in the unit under a temperature dierential across the air space. The unit was an unventilated enclosure and so ¯ow within would be buoyancy-induced natural convection. The ¯ow model consists of the governing equations for mass, momentum and heat transfer as well as turbulence. For steady-state natural convection ¯ow in the enclosure, the CFD model can be represented by the following equation: o o o/ qUi / C/ 12 S/ oxi oxi oxi where q is the air density (kg/m3 ), / represents the ¯ow variable such as the mean velocity component Ui (m/s) in xi (m) direction, pressure, temperature and turbulent parameters, C/ is the diusion coecient (N s/m2 ) and S/ is the source term. Turbulence in ¯uid ¯ow can be simulated by means of a turbulence model. The standard k±e model [14] is the most commonly used turbulence model for engineering ¯uid ¯ow simulations. However, it has been shown [6] that for buoyancy-induced natural convection involving both laminar and turbulent ¯ows, the renormalisation group k±e model [15] is superior to the standard k±e model. Because buoyant ¯ow in a double glazing unit could range from laminar to turbulent regimes, the renormalisation group turbulence model was used to represent turbulence characteristics of air ¯ow. Details of the model equations and solution method are described by Gan [6].
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3.1. Assumptions The numerical method was demonstrated for a 1:5 1:5 m2 double glazing unit. The glazing was assumed to be made of uncoated glass with an emissivity of 0.84 and ®lled with air. The basic thermal boundary conditions were the internal surface temperatures for the unit Th 15°C and Tc 5°C, so the mean surface temperature Tm 10°C and the temperature dierence between the surfaces DT 10 K. The internal surface temperature dierence would approximately correspond to a temperature dierence of 20 K between indoor and outdoor air, e.g. at 20°C and 0°C, respectively, for the thermal performance of glazing in winter. For calculating the thermal transmittance under winter conditions, the external surface resistance 1=he for normal conditions of exposure was taken to be 0.06 m2 K/W and the internal surface resistance 1=hi was 0.12 m2 K/ W [16]. The edges of the unit were insulated. Consequently, the resulting thermal transmittance would be comparable with data for the central area of the glazing excluding the eects of edges and frame. In addition, it was assumed that the eect of temperature on the air space dimensions of the glazing unit would be negligible.
4. Results and discussion The convective heat transfer coecient was ®rst predicted for the glazing unit with a range of widths of air space. The thermal resistance of the air space and thermal transmittance of the glazing unit were then calculated using Eqs. (4) and (1), respectively. To investigate the possible eect on the convective heat transfer coecient and the thermal transmittance, predictions were also performed for temperature dierences between the internal surfaces DT 5, 15 and 20 K in addition to DT 10 K. The mean temperature of two internal surfaces was ®xed at 10°C. To con®rm the validity of the numerical method, the predicted thermal resistance of air space was compared with reference data. Fig. 2 shows the predicted air space resistance for a temperature dierence between the internal surfaces of 10 K as compared with standard data from CIBSE [16]. It is seen that the predicted thermal resistance agrees very well with the standard values. The predicted thermal resistance increases with increasing width of air space.
Fig. 2. Comparison of predicted air space resistance with standard data (DT 10 K).
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Fig. 3. Predicted heat transfer coecient and thermal transmittance (DT 10 K).
Fig. 3 shows the predicted convective and radiative heat transfer coecients and thermal transmittance for the same temperature dierence between the internal surfaces of 10 K. The radiative heat transfer coecient decreases with increasing air space because of the decreasing view factor with the distance between two panes. The convective heat transfer coecient also decreases with the width of air space up to 20±25 mm. When the width of air space is larger than 25 mm, the convective heat transfer coecient increases slightly with air space. This results from the fact that the increase in the convective heat transfer is larger than the decrease in the conductive heat transfer when the width of air space is larger than 25 mm. Fig. 3 also shows that the variation in the thermal transmittance with air space occurs for widths up to about 25 mm. For air space widths larger than 25 mm, the thermal transmittance almost remains constant because a slight increase in convective heat transfer is oset by a similar magnitude of the decrease in radiative heat transfer. For the internal surface temperature dierence of 10 K, for example, the predicted thermal transmittance was 3.33 W/m2 K for an air space width of 5 mm. The thermal transmittance was reduced to 2.93 W/m2 K when the width was increased to 10 mm. It was reduced further to 2.71 W/m2 K when the width was increased to 25 mm. Fig. 4 shows the variation in the thermal transmittance with the width of air space for four internal surface temperature dierences. The calculated thermal transmittance decreases with the
Fig. 4. Variation of thermal transmittance with the width of air space.
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Fig. 5. Eect of the temperature dierence on glazing thermal performance (s 25 mm).
width of air space up to 25 mm regardless of the magnitude of the temperature dierence across an air space. However, a higher temperature dierence results in a larger thermal transmittance, particularly when the air space is wider than 20 mm. According to the CIBSE Guide [16], the temperature dierence across an air space has little eect on either the radiative or convective heat transfer coecient. Fig. 5 shows that both the heat transfer coecient and thermal transmittance increase with the internal surface temperature dierence. The increase in the thermal transmittance with the temperature dierence is due to the increased convective heat transfer coecient. However, the eect of the temperature dierence on the variation in the thermal transmittance is not as signi®cant as that on the convective heat transfer coecient. This results from two sources. First, the radiative heat transfer which is largely independent of the temperature dierence (see Eq. (5)) accounts for about two-thirds of the total heat transfer. Secondly, in the calculation of thermal transmittance, the thermal resistance for the external surface was assumed constant. This assumption is reasonable because the convective heat transfer due to wind generally plays a more important role in the external thermal resistance than does the temperature-dependent radiative heat transfer. For an air space of 25 mm and internal surface temperature dierence across an air space (DT) between 5 and 20 K, the convective heat transfer coecient and the thermal transmittance can be correlated as follows: R2 0:99
13
U 0:0148 DT 2:55 R2 0:98
14
hc 0:0625 DT 1:22
Obviously, the eect of the temperature dierence across an air space is appreciable on the convective heat transfer coecient but the eect is much less on the thermal transmittance. According to correlation (14), for example, when the internal surface temperature dierence across an air space changes from 5 to 10 K, corresponding to a change in the indoor and outdoor temperature dierence from 10 to 20 K approximately, the thermal transmittance varies by about 3% only. Therefore, for the UK environmental conditions, the thermal transmittance can approximately be taken as a constant when calculating the overall heat transfer through a multipleglazed window. However, for designing a device or structure with an air space, consideration
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should be given to the in¯uence of the air space width on the heat transfer, particularly if the air space is less than 20 mm wide. The above results demonstrate CFD as an alternative to the analytical/empirical method (Eq. (8)) for assessing the eects of variables such as the air space and surface temperature dierence on glazing thermal performance. The CFD method can also be used to gain insight into ¯ow mechanisms and assess other thermal aspects of air spaces where an analytical method may not be readily available. For example, an air space may be ventilated as in the case of air ¯ow windows or double skin facades. An air ¯ow window is a special type of triple-glazed window where in winter outdoor air is preheated by drawing it through an air space between two of the three panes or where in summer room air is exhausted to outdoors or returned to the air-handling system through the air space. Unlike conventional unventilated multiple glazing where the surface temperature is uniform during tests at standard conditions, the surface temperature of an air ¯ow window varies along the ¯ow path. The thermal transmittance of such a window is in¯uenced by the ¯ow rate and distribution of air through the ¯ow path. It would be dicult to calculate the thermal transmittance accurately using the conventional analytical method. By contrast, a validated CFD technique can be used not only to predict the thermal transmittance but also optimise the design and operation of the window in terms of energy eciency and thermal comfort.
5. Conclusions A numerical method is presented for the prediction of the thermal transmittance of multiple glazing. The predicted thermal resistance of glazing agrees with reference data for a double glazing unit. The results con®rm that the heat transfer coecient, thermal resistance and thermal transmittance vary with the width of air space between glazing panes up to about 25 mm. As the width of air space increases, the thermal resistance increases while the thermal transmittance decreases. It is shown that both the convective heat transfer coecient and thermal transmittance increase linearly with the temperature dierence between the hot and cold panes of glass. The eect of the temperature dierence across an air space on the convective heat transfer coecient is signi®cant. For moderate climate conditions such as in the UK, the eect of the temperature dierence on the thermal transmittance may be considered negligible. One of the advantages of the CFD technique over the analytical method is that it can easily be applied to performance evaluation of novel ¯ow devices such as air ¯ow windows.
References [1] D. Button, B. Pye, Glass in Building, Butterworth Architecture, Oxford, 1993. [2] A. Schrey, R.A. Fraser, P.F. de Abreu, Local heat transfer coecients for a ¯ush-mounted glazing unit, ASHRAE Transactions 104 (1) (1998) 1207±1221. [3] M.A. Bernier, B. Bourret, Eects of glass plate curvature on the U-factor of sealed insulated glazing units, ASHRAE Transactions 103 (1) (1997) 270±277. [4] M.G. Hutchins, W.J. Platzer, Thermal performance of advanced glazing materials, Renewable Energy 8 (1) (1996) 540±545.
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[5] J.A. Clarke, M. Janak, P. Ruyssevelt, Assessing the overall performance of advanced glazing systems, Solar Energy 63 (4) (1998) 231±241. [6] G. Gan, Prediction of turbulent buoyant ¯ow using an RNG k±e model, Numerical Heat Transfer Part A: Applications 33 (1998) 169±189. [7] P.W. Griths, P.C. Eames, B. Norton, Thermal properties of evacuated glazing based on experimental solar simulation and computer based simulation modelling, Proceedings of ICBEST Õ97, Bath, UK, 1997, pp. 343±348. [8] P.W. Griths, B. Norton, P.C. Eames, S.N.G. Lo, Detailed simulation of heat transfer across evacuated glazing, Building Research and Information 24 (3) (1996) 141±147. [9] J.L. Wright, H.F. Sullivan, Two-dimensional numerical model for glazing system thermal analysis, ASHRAE Transactions 101 (1) (1995) 819±831. [10] Y. Zhao, D. Curcija, W.P. Goss, Prediction of the multicellular ¯ow regime of natural convection in fenestration glazing cavities, ASHRAE Transactions 103 (1) (1997) 1009±1020. [11] BS EN 573, Glass in building ± determination of thermal transmittance (U value) ± Calculation method, British Standards Institution, London, 1998. [12] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, second ed., Hemisphere Publishing Corporation, Washington, 1981. [13] G. Gan, Numerical method for a full assessment of indoor thermal comfort, Indoor Air 4 (3) (1994) 154±168. [14] B.E. Launder, D.B. Spalding, The numerical computation of turbulent ¯ows, Computer Methods in Applied Mechanics and Engineering 3 (1974) 269±289. [15] V. Yakhot, S.A. Orszag, S. Thangam, T.B. Gatski, C.G. Speziale, Development of turbulence models for shear ¯ows by a double expansion technique, Physics of Fluids Part A 4 (7) (1992) 1510±1520. [16] CIBSE Guide Section A3 ± Thermal properties of building structures, Chartered Institution of Building Services Engineers, London, 1999.
www.elsevier.com/locate/apthermeng
Thermal transmittance of multiple glazing: computational ¯uid dynamics prediction Guohui Gan * Institute of Building Technology, School of the Built Environment, University of Nottingham, Nottingham NG7 2RD, UK Received 16 November 2000; accepted 28 January 2001
Abstract Computational ¯uid dynamics (CFD) is applied for predicting the convective heat transfer coecient, thermal resistance and thermal transmittance for a double glazing unit. The predicted thermal resistance of glazing is compared with reference data and good agreement is achieved. The convective heat transfer coecient and thermal transmittance vary with the air space width and the temperature dierence across glazing. The CFD technique can be used to gain insight into multiple glazing performance and also optimise the design and operation of novel multiple glazing systems such as air ¯ow windows or double skin facades in terms of energy eciency and thermal comfort. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Thermal transmittance; Heat transfer coecient; Double glazing; Computational ¯uid dynamics
1. Introduction The thermal transmittance, or U value, of glazing is the rate of heat transfer under steady state conditions from the air on one side of the glazing to the air on the other side for unit area and for unit temperature dierence. The reciprocal of the thermal transmittance is the overall thermal resistance. Heat transfer through windows is a major component of conduction heat loss from a perimeter room in winter. The thermal resistance of a single-glazed window is very low. To increase the resistance, a double- or multiple-glazed window can be employed. In a double glazing
*
Tel.: +44-115-951-4876; fax: +44-115-951-3159. E-mail address: [email protected] (G. Gan).
1359-4311/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 1 ) 0 0 0 1 6 - 3
1584
G. Gan / Applied Thermal Engineering 21 (2001) 1583±1592
unit, a second pane of glass is separated from the ®rst pane by an air space, thereby increasing the thermal resistance due to the low thermal conductivity of air and the extra barrier to long wave radiation exchange provided by the second pane. The thermal resistance of a tall air cavity associated with conductive heat transfer increases with the width of air space, therefore increasing the width between two panes of glass decreases the thermal transmittance and improves the insulation eect. However, it is known that there is a limit in the eect of increasing the air space on the improvement of insulation. This limit is the ÔoptimumÕ separation of the panes and is usually considered to be between 20 and 25 mm. For air spaces wider than the limit, there is little improvement in the thermal transmittance. Below the limit, a number of measures can be taken to increase the thermal insulation of double glazing, e.g., using glass with low emissivity coatings, inhibiting convection in the air space, replacing the cavity air with gases of lower conductivity and evacuating the air space [1]. The thermal performance of glazing systems is often investigated by means of laboratory or ®eld tests. Recent work in this area includes the determination of local heat transfer coecients for window assemblies by Schrey et al. [2] based on the direct measurement of glazing surface temperatures. Bernier and Bourret [3] experimentally studied the eects of glass plate curvature due to barometric pressure and gas space temperature variations on the thermal transmittance of sealed glazing units. Hutchins and Platzer [4] measured the thermal performance of advanced glazing materials for windows whereas Clarke et al. [5] described an approach to apply combined thermal/daylight simulations to building designs incorporating advanced glazing systems. In recent years, numerical methods have also been used to determine the thermal performance of glazing systems. It has been shown that air ¯ow and heat transfer in tall cavities such as double glazing units can be predicted using computational ¯uid dynamics (CFD) [6]. The accuracy of the numerical prediction was found to be in¯uenced by the turbulence models employed [6]. Griths et al. [7,8] determined the thermal transmittance of evacuated glazing based on experimental solar simulation and computer based simulation modelling. A ®nite volume model was used to predict the temperature distribution in the air space and overall heat loss coecient of the glazing unit. Wright and Sullivan [9] developed a simple two-dimensional numerical model for glazing system thermal analysis. The model accounted for natural convection of the ®ll gas, conduction within the solid materials and radiant exchange between various surfaces facing the ®ll-gas cavity. Results were used to gain insights into heat transfer patterns in glazing systems with various combinations of low-emissivity coatings, ®ll gases and edge-seal designs. Zhao et al. [10] predicted the multi-cellular laminar ¯ow regime of natural convection in fenestration glazing cavities using a general-purpose ¯uid ¯ow and heat transfer computer program. Numerical calculations were performed over a range of aspect ratios to determine the critical Rayleigh number at which multicellular ¯ow began to form. The ¯ow in glazing cavities can be laminar or turbulent depending on the Rayleigh number. The thermal performance of multiple glazing under turbulent ¯ow has not been fully investigated. This paper presents a numerical method for predicting the thermal transmittance of multiple glazing systems under both laminar and turbulent regimes. The method was demonstrated for a double glazing unit with varying widths of air space at dierent temperature dierences across glazing. The same method can also be used to determine the thermal performance of other types of multiple glazing such as triple glazing.
G. Gan / Applied Thermal Engineering 21 (2001) 1583±1592
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2. Derivation of thermal transmittance Analytical solution of heat transfer through a multiple glazing system can be derived from a double glazing unit. Fig. 1 illustrates the heat transfer through a double glazing unit in winter conditions. The thermal transmittance of a multiple glazing unit is given by the following equation [11]: U
1 1 he
h1t h1i
1
where U is the thermal transmittance (W/m2 K), he and hi are the external and internal heat transfer coecients (W/m2 K), respectively, and ht is the conductance of the multiple glazing unit (W/m2 K). The conductance of a multiple glazing unit is obtained from 1 X1 d 2 ht h k n where h is the overall heat transfer coecient between an air space (W/m2 K), n is the number of air spaces, d is the total thickness of glass (m) and k is the thermal conductivity of glass (W/m K). The overall heat transfer coecient between an air space is given by h hc hr
3
Fig. 1. Schematic of heat transfer through a double glazing unit in winter.
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where hc and hr are the convective and radiative heat transfer coecients between an air space (W/ m2 K), respectively. The thermal resistance of an air space, R (m2 K/W), is the reciprocal of the overall heat transfer coecient for the gas space, i.e.: R
1 h
4
The radiative heat transfer coecient for a tall continuous vertical air space is given by hr 1
4rTm3 e1 1 e2e2 F112 e1
5
where r is Stefan±Boltzmann constant (5:67 10 8 W/m2 K4 ), e1 and e2 are the corrected emissivities of two panes of glass at mean temperature Tm (K), F12 is the view factor between two panes of glass and can be calculated from [12] 8 " #1=2 p 2 < 1 X 2 1 Y 2 X F12 ln X 1 Y 2 tan 1 p pXY : 1 X2 Y2 1 Y2 9 = p Y Y 1 X 2 tan 1 p X tan 1 X Y tan 1 Y 6 ; 1 X2 where X and Y are the width and height of glass normalised by the width of the air space between glass panes. The convective heat transfer coecient for a vertical air space is given by hc Nu
ka s
7
where Nu is the average Nusselt number, ka is the thermal conductivity of air (W/m K) and s is the mean width of air space (m). For experimental determination of the thermal transmittance of vertical glazing, the following empirical equation has been used to calculate the Nusselt number [11] Nu 0:35Ra0:38
8
where Ra is the Rayleigh number which is de®ned as gbDT s3 9 ma where g is the gravitational acceleration (m/s2 ), b is the thermal expansion coecient of air (1 K 1 ), m is the kinematic viscosity of air (m2 /s) and a is the thermal diusion coecient of air (m2 / s), DT is the temperature dierence between the hot surface Th (°C) and cold surface Tc (°C), for double glazing Th and Tc representing the surface temperatures of outdoor side of indoor pane and indoor side of outdoor pane of glass, respectively. Ra
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The Nusselt number for the air space can also be determined numerically from oT s ox w Nu 10 DT where oT =oxw is the gradient of the air temperature near a glass surface. Substituting Eq. (10) into Eq. (7) gives oT k ox w a 11 hc DT Hence, for given Th and Tc , hc can be obtained from oT =oxw for either the hot or cold surface. In this work CFD was used to compute the gradient oT =oxw from the temperature distribution in a glazing air space. The value of hc for the hot surface is generally dierent from that for the cold surface due to the dependence of thermal properties of air on temperature. However, when the temperature dierence between the two surfaces is small, say 10 K, the dierence in the convective heat transfer coecient is negligible (<1% for all the cases computed). The convective heat transfer coecient was therefore taken as the average for the hot and cold surfaces. Besides convective heat transfer, radiative heat transfer can be incorporated in the CFD model [13]. However, for known isothermal boundary conditions, the radiative heat exchange between two panes of glass can be considered constant and hence decoupled from the convective heat transfer in the CFD model. This improves the stability of computation and increases the speed of numerical solution. 3. Computational ¯uid dynamics model CFD was used to determine the convective heat transfer coecient of a double glazing unit based on the predicted air movement and temperature distribution in the unit under a temperature dierential across the air space. The unit was an unventilated enclosure and so ¯ow within would be buoyancy-induced natural convection. The ¯ow model consists of the governing equations for mass, momentum and heat transfer as well as turbulence. For steady-state natural convection ¯ow in the enclosure, the CFD model can be represented by the following equation: o o o/ qUi / C/ 12 S/ oxi oxi oxi where q is the air density (kg/m3 ), / represents the ¯ow variable such as the mean velocity component Ui (m/s) in xi (m) direction, pressure, temperature and turbulent parameters, C/ is the diusion coecient (N s/m2 ) and S/ is the source term. Turbulence in ¯uid ¯ow can be simulated by means of a turbulence model. The standard k±e model [14] is the most commonly used turbulence model for engineering ¯uid ¯ow simulations. However, it has been shown [6] that for buoyancy-induced natural convection involving both laminar and turbulent ¯ows, the renormalisation group k±e model [15] is superior to the standard k±e model. Because buoyant ¯ow in a double glazing unit could range from laminar to turbulent regimes, the renormalisation group turbulence model was used to represent turbulence characteristics of air ¯ow. Details of the model equations and solution method are described by Gan [6].
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3.1. Assumptions The numerical method was demonstrated for a 1:5 1:5 m2 double glazing unit. The glazing was assumed to be made of uncoated glass with an emissivity of 0.84 and ®lled with air. The basic thermal boundary conditions were the internal surface temperatures for the unit Th 15°C and Tc 5°C, so the mean surface temperature Tm 10°C and the temperature dierence between the surfaces DT 10 K. The internal surface temperature dierence would approximately correspond to a temperature dierence of 20 K between indoor and outdoor air, e.g. at 20°C and 0°C, respectively, for the thermal performance of glazing in winter. For calculating the thermal transmittance under winter conditions, the external surface resistance 1=he for normal conditions of exposure was taken to be 0.06 m2 K/W and the internal surface resistance 1=hi was 0.12 m2 K/ W [16]. The edges of the unit were insulated. Consequently, the resulting thermal transmittance would be comparable with data for the central area of the glazing excluding the eects of edges and frame. In addition, it was assumed that the eect of temperature on the air space dimensions of the glazing unit would be negligible.
4. Results and discussion The convective heat transfer coecient was ®rst predicted for the glazing unit with a range of widths of air space. The thermal resistance of the air space and thermal transmittance of the glazing unit were then calculated using Eqs. (4) and (1), respectively. To investigate the possible eect on the convective heat transfer coecient and the thermal transmittance, predictions were also performed for temperature dierences between the internal surfaces DT 5, 15 and 20 K in addition to DT 10 K. The mean temperature of two internal surfaces was ®xed at 10°C. To con®rm the validity of the numerical method, the predicted thermal resistance of air space was compared with reference data. Fig. 2 shows the predicted air space resistance for a temperature dierence between the internal surfaces of 10 K as compared with standard data from CIBSE [16]. It is seen that the predicted thermal resistance agrees very well with the standard values. The predicted thermal resistance increases with increasing width of air space.
Fig. 2. Comparison of predicted air space resistance with standard data (DT 10 K).
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Fig. 3. Predicted heat transfer coecient and thermal transmittance (DT 10 K).
Fig. 3 shows the predicted convective and radiative heat transfer coecients and thermal transmittance for the same temperature dierence between the internal surfaces of 10 K. The radiative heat transfer coecient decreases with increasing air space because of the decreasing view factor with the distance between two panes. The convective heat transfer coecient also decreases with the width of air space up to 20±25 mm. When the width of air space is larger than 25 mm, the convective heat transfer coecient increases slightly with air space. This results from the fact that the increase in the convective heat transfer is larger than the decrease in the conductive heat transfer when the width of air space is larger than 25 mm. Fig. 3 also shows that the variation in the thermal transmittance with air space occurs for widths up to about 25 mm. For air space widths larger than 25 mm, the thermal transmittance almost remains constant because a slight increase in convective heat transfer is oset by a similar magnitude of the decrease in radiative heat transfer. For the internal surface temperature dierence of 10 K, for example, the predicted thermal transmittance was 3.33 W/m2 K for an air space width of 5 mm. The thermal transmittance was reduced to 2.93 W/m2 K when the width was increased to 10 mm. It was reduced further to 2.71 W/m2 K when the width was increased to 25 mm. Fig. 4 shows the variation in the thermal transmittance with the width of air space for four internal surface temperature dierences. The calculated thermal transmittance decreases with the
Fig. 4. Variation of thermal transmittance with the width of air space.
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Fig. 5. Eect of the temperature dierence on glazing thermal performance (s 25 mm).
width of air space up to 25 mm regardless of the magnitude of the temperature dierence across an air space. However, a higher temperature dierence results in a larger thermal transmittance, particularly when the air space is wider than 20 mm. According to the CIBSE Guide [16], the temperature dierence across an air space has little eect on either the radiative or convective heat transfer coecient. Fig. 5 shows that both the heat transfer coecient and thermal transmittance increase with the internal surface temperature dierence. The increase in the thermal transmittance with the temperature dierence is due to the increased convective heat transfer coecient. However, the eect of the temperature dierence on the variation in the thermal transmittance is not as signi®cant as that on the convective heat transfer coecient. This results from two sources. First, the radiative heat transfer which is largely independent of the temperature dierence (see Eq. (5)) accounts for about two-thirds of the total heat transfer. Secondly, in the calculation of thermal transmittance, the thermal resistance for the external surface was assumed constant. This assumption is reasonable because the convective heat transfer due to wind generally plays a more important role in the external thermal resistance than does the temperature-dependent radiative heat transfer. For an air space of 25 mm and internal surface temperature dierence across an air space (DT) between 5 and 20 K, the convective heat transfer coecient and the thermal transmittance can be correlated as follows: R2 0:99
13
U 0:0148 DT 2:55 R2 0:98
14
hc 0:0625 DT 1:22
Obviously, the eect of the temperature dierence across an air space is appreciable on the convective heat transfer coecient but the eect is much less on the thermal transmittance. According to correlation (14), for example, when the internal surface temperature dierence across an air space changes from 5 to 10 K, corresponding to a change in the indoor and outdoor temperature dierence from 10 to 20 K approximately, the thermal transmittance varies by about 3% only. Therefore, for the UK environmental conditions, the thermal transmittance can approximately be taken as a constant when calculating the overall heat transfer through a multipleglazed window. However, for designing a device or structure with an air space, consideration
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should be given to the in¯uence of the air space width on the heat transfer, particularly if the air space is less than 20 mm wide. The above results demonstrate CFD as an alternative to the analytical/empirical method (Eq. (8)) for assessing the eects of variables such as the air space and surface temperature dierence on glazing thermal performance. The CFD method can also be used to gain insight into ¯ow mechanisms and assess other thermal aspects of air spaces where an analytical method may not be readily available. For example, an air space may be ventilated as in the case of air ¯ow windows or double skin facades. An air ¯ow window is a special type of triple-glazed window where in winter outdoor air is preheated by drawing it through an air space between two of the three panes or where in summer room air is exhausted to outdoors or returned to the air-handling system through the air space. Unlike conventional unventilated multiple glazing where the surface temperature is uniform during tests at standard conditions, the surface temperature of an air ¯ow window varies along the ¯ow path. The thermal transmittance of such a window is in¯uenced by the ¯ow rate and distribution of air through the ¯ow path. It would be dicult to calculate the thermal transmittance accurately using the conventional analytical method. By contrast, a validated CFD technique can be used not only to predict the thermal transmittance but also optimise the design and operation of the window in terms of energy eciency and thermal comfort.
5. Conclusions A numerical method is presented for the prediction of the thermal transmittance of multiple glazing. The predicted thermal resistance of glazing agrees with reference data for a double glazing unit. The results con®rm that the heat transfer coecient, thermal resistance and thermal transmittance vary with the width of air space between glazing panes up to about 25 mm. As the width of air space increases, the thermal resistance increases while the thermal transmittance decreases. It is shown that both the convective heat transfer coecient and thermal transmittance increase linearly with the temperature dierence between the hot and cold panes of glass. The eect of the temperature dierence across an air space on the convective heat transfer coecient is signi®cant. For moderate climate conditions such as in the UK, the eect of the temperature dierence on the thermal transmittance may be considered negligible. One of the advantages of the CFD technique over the analytical method is that it can easily be applied to performance evaluation of novel ¯ow devices such as air ¯ow windows.
References [1] D. Button, B. Pye, Glass in Building, Butterworth Architecture, Oxford, 1993. [2] A. Schrey, R.A. Fraser, P.F. de Abreu, Local heat transfer coecients for a ¯ush-mounted glazing unit, ASHRAE Transactions 104 (1) (1998) 1207±1221. [3] M.A. Bernier, B. Bourret, Eects of glass plate curvature on the U-factor of sealed insulated glazing units, ASHRAE Transactions 103 (1) (1997) 270±277. [4] M.G. Hutchins, W.J. Platzer, Thermal performance of advanced glazing materials, Renewable Energy 8 (1) (1996) 540±545.
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[5] J.A. Clarke, M. Janak, P. Ruyssevelt, Assessing the overall performance of advanced glazing systems, Solar Energy 63 (4) (1998) 231±241. [6] G. Gan, Prediction of turbulent buoyant ¯ow using an RNG k±e model, Numerical Heat Transfer Part A: Applications 33 (1998) 169±189. [7] P.W. Griths, P.C. Eames, B. Norton, Thermal properties of evacuated glazing based on experimental solar simulation and computer based simulation modelling, Proceedings of ICBEST Õ97, Bath, UK, 1997, pp. 343±348. [8] P.W. Griths, B. Norton, P.C. Eames, S.N.G. Lo, Detailed simulation of heat transfer across evacuated glazing, Building Research and Information 24 (3) (1996) 141±147. [9] J.L. Wright, H.F. Sullivan, Two-dimensional numerical model for glazing system thermal analysis, ASHRAE Transactions 101 (1) (1995) 819±831. [10] Y. Zhao, D. Curcija, W.P. Goss, Prediction of the multicellular ¯ow regime of natural convection in fenestration glazing cavities, ASHRAE Transactions 103 (1) (1997) 1009±1020. [11] BS EN 573, Glass in building ± determination of thermal transmittance (U value) ± Calculation method, British Standards Institution, London, 1998. [12] R. Siegel, J.R. Howell, Thermal Radiation Heat Transfer, second ed., Hemisphere Publishing Corporation, Washington, 1981. [13] G. Gan, Numerical method for a full assessment of indoor thermal comfort, Indoor Air 4 (3) (1994) 154±168. [14] B.E. Launder, D.B. Spalding, The numerical computation of turbulent ¯ows, Computer Methods in Applied Mechanics and Engineering 3 (1974) 269±289. [15] V. Yakhot, S.A. Orszag, S. Thangam, T.B. Gatski, C.G. Speziale, Development of turbulence models for shear ¯ows by a double expansion technique, Physics of Fluids Part A 4 (7) (1992) 1510±1520. [16] CIBSE Guide Section A3 ± Thermal properties of building structures, Chartered Institution of Building Services Engineers, London, 1999.