- Email: [email protected]
Theoretical and experimental analysis of the vacuum pressure in a vacuum glazing after extreme thermal cycling
Available online at www.sciencedirect.com
Solar Energy 83 (2009) 1723–1730 www.elsevier.com/locate/solener
Theoretical and experimental analysis of the vacuum pressure in a vacuum glazing after extreme thermal cycling Yueping Fang a,*, Trevor Hyde a, Philip C. Eames b, Neil Hewitt a a
Centre for Sustainable Technologies, School of the Built Environment, University of Ulster, Newtownabbey, BT37 0QB N. Ireland, UK b Centre for Renewable Energy Research, University of Loughborough, UK Received 4 December 2007; received in revised form 24 February 2009; accepted 26 March 2009 Available online 18 July 2009 Communicated by: Associate Editor Yogi Goswami
Abstract Details of theoretical and experimental studies of the change in vacuum pressure within a vacuum glazing after extreme thermal cycling are presented. The vacuum glazing was fabricated at low temperature using an indium–copper–indium edge seal. It comprised two 4 mm thick 0.4 m by 0.4 m glass panes with low-emittance coatings separated by an array of stainless steel support pillars spaced at 25 mm with a diameter of 0.4 mm and a height of 0.15 mm. Thermal cycling tests were undertaken in which the air temperature on one side of the sample was taken from 30 °C to +50 °C and back to 30 °C 15 times while maintaining an air temperature of 22 °C on the other side. After this test procedure, it was found that the glass to glass heat conductance at the centre glazing area had increased by 10.1% from which the vacuum pressure within the evacuated space was determined to have increased from the negligible level of less than 0.1 Pa to 0.16 Pa using the model of Corrucini. Previous research has shown that if the vacuum pressure is less than 0.1 Pa, the effect of conduction through the residual gas on the total glazing heat transfer is negligible. The degradation of vacuum level determined was corroborated by the change in glass surface temperatures. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Vacuum glazing; Vacuum pressure; Thermal cycling
1. Introduction Flat vacuum glazing as shown in Fig. 1 consists of two plane glass sheets, separated by a narrow internal evacuated space, contiguously sealed together around their periphery. The space, maintained by an array of tiny support pillars, is evacuated to a pressure of less than 0.1 Pa, effectively eliminating both gaseous conduction and convection. The low-emittance (low-e) coatings on the internal glass surfaces within the evacuated gap reduce the radiative heat transfer through the vacuum glazing to a very low level. The vacuum glazing concept was first patented by Zoller (1924). However, after many years the first success*
Corresponding author. Tel.: +44 2890368241; fax: +44 2890238227. E-mail address: [email protected] (Y. Fang).
0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.03.017
ful vacuum glazing was fabricated by Robinson and Collins (1989). A solder glass powder laid along the periphery of the glass sheets melted to form the edge seal of the vacuum space when the entire glazing unit was heated to 450 °C. This high temperature method of fabricating vacuum glazing prevents the use of tempered glass and some types of soft low-e coatings thus preventing the high levels of performance predicted from being achieved. The University of Ulster has developed a methodology and system for the manufacture of low temperature sealed vacuum glazing that can incorporate soft low-e coatings and tempered glass (Griffiths et al., 1998; Hyde et al., 2000). A total heat transmission U-value of less than 1.0 W m2 K1 for a vacuum glazing of small size (0.4 m by 0.4 m) has been experimentally determined (Fang et al., 2006) using a guarded hot box calorimeter (GHBC).
1724
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
Nomenclature a C h k M s P R T y
radius of support pillars (m) heat conductance (W m2 K1) surface heat transfer coefficient (W m2 K1) thermal conductivity of glass (W m1 K1) molar mass of gas pillar separation (m) pressure (Pa) molar gas constant temperature (°C) uncertainty of heat flow
Greek letters e hemispherical emittance of a surface r Stefan–Boltzmann constant (5.67108 W m2 K4) a accommodation coefficient c specific heat ratio of the gas Subscripts 1, 2 internal and external sample surfaces 3 refers to the uncertainty of heat transfer through the test sample
Outgassing and long-term vacuum stability of vacuum glazing is an important issue (Collins and Simko, 1998; Lenzen et al., 1999). The levels of outgassing in vacuum glazing subject to static aging conditions at different temperatures were measured using a spinning rotor gauge and found to be in good agreement with the predictions made (Lenzen et al., 1999; Ng et al., 2005). In the research reported in this paper vacuum glazing manufactured at low temperature was subjected to extreme dynamic thermal cycling, and the effect on the vacuum pressure in the evac-
Glass disc seal In/Cu/In edge seal Support pillars
Vacuum gap
Evacuation hole
Low-emittance coatings Fig. 1. Schematic diagram of a vacuum glazing.
4 5 6 7 a amb b c e f a 1, a 2 g1 , g 2 i.o m n r t vg
refers to the uncertainty of flanking loss refers to the uncertainty of electric power input refers to the uncertainty of heat transfer through the metering box refers to the uncertainty of heat transfer through the mask wall air ambient metering box convection flanking loss frame air in the hot and cold boxes glass surfaces in the hot and cold boxes air in hot and cold chambers mask wall refers to environment temperature radiation refers to input power vacuum glazing
uated gap analysed using a model for heat conduction at low pressure (Corrucini, 1957). The thermal conductances measured were compared with those of thermal testing using a GHBC (Fang et al., 2006). 2. Modelling approaching The investigated vacuum glazing comprised two 4 mm thick 0.4 m by 0.4 m glass panes each with a low-emittance coating of 0.18 emittance separated by an array of stainless steel support pillars spaced at 25 mm with a diameter of 0.4 mm and a height of 0.15 mm. A three dimensional finite volume model (Eames and Norton, 1993) and a two dimensional finite element model (Fang et al., 2006) extensively validated experimentally in previously reported research (Griffiths et al., 1998; Fang, 2002) were used to analyse heat transfer through a vacuum glazing with the applied boundary conditions representative of those within the experimental GHBC. In the finite volume model, the analytic model for heat flow through individual support pillars (Collins and Simko, 1998) was not employed since the pillar array was incorporated and modelled directly. The circular cross section of the pillar in the fabricated system was replaced by a square cross section pillar of equal area in the model. A graded mesh was used with a high density of nodes in and around the pillar to provide adequate representation of the heat transfer in this region. The residual gas pressure was assumed to be below that at which conduction was an issue. It has been experimentally and theoretically
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
proved that the temperature of each glass sheet approaches the value at the centre of glass pffiffiffi pane exponentially with a characteristic distance of l ¼ k glass t=h, where h is the exterior heat transfer coefficient from the surface being considered (i.e. h1 and h2). The total heat flow per unit length of the edge seal (Collins and Simko, 1998) is determined by rffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffi k glass t k glass t þ w1 þ w2 þ Qedge ¼ ðT 1 T 2 Þk glass t h1 h2 ð1Þ The total heat flow through the edge area along the four edges is Qlateral ¼ 4‘edge Qedge
ð2Þ
Where ‘edge is the length of indium edge seal. When the width of edge seal is 6 mm of 0.4 m by 0.4 m vacuum glazing, the ‘edge is 0.388 m. The area of the evacuated gap is 0.15 m2. The finite element model used the Galerkin (Brenner and Scott, 2005) approach with eight-node isoparametric elements. Further details of the finite element model employed can be found in Eames and Norton (1993). In the finite element model, the conductance of the central evacuated gap was determined using the analytic model for heat transfer in the support pillars and radiative heat transfer between the two glass panes. For similar boundary conditions, the difference in heat conductance through the vacuum glazing predicted by the finite volume model and the finite element model is less than 3% (Fang and Eames, 2006; Fang et al., 2009). In the finite element model used, the influence of the residual gas on the heat conductance of the glazing can be modelled. When the experimentally measured surface temperature profiles do not match the predictions made using the finite element model, the effects of the residual gas must be considered (Fang et al., 2006). The total glass to glass heat conductance of the central glazing area is determined by: C centre ¼ C gas þ C radiation þ C pillars þ C lateral
ð3Þ
¼ C gas þ 4eeffective rT 3average þ 2k glass a=s2 þ C lateral
ð4Þ
where Cgas is the residual gas heat conductance, Cradiation is the radiative heat conductance between the two glass panes, Clateral is the lateral heat conductance, r is the Stefan Boltzmann constant (5.67 108 W m2 K4), Taverage is the average of the two glass temperatures T1 and T2, kglass is the glass thermal conductivity, a is the pillar radius, s is the pillar separation and the effective hemispheric emittance eeffective is calculated from the two glass surface hemispheric emittances e1 and e2 by: 1 1 1 ¼ þ 1 eeffective e1 e2
ð5Þ
Using the value of Clateral predicted by the finite volume model and the experimentally determined heat conductance of the centre glass area Ccentre, the value of Cgas can be
1725
determined using Eq. (2). The effective heat conductance of the evacuated gap can then be determined and temperature profiles calculated using the finite element model. 3. The laboratory production of vacuum glazing Two fabrication methods for producing vacuum glazing have been developed by the team at the University of Ulster. In the first single stage method, the vacuum glazing is fabricated in a stainless steel vacuum chamber (Hyde et al., 2000), in which the seal is formed with no subsequent pump-out process required. In the second method, there are two stages (Zhao et al., 2007). Firstly, the edge seal is formed in a vacuum or an oxygen-free nitrogen atmosphere with subsequent evacuation through a pre-drilled pumpout hole, typically 3 mm in diameter. The pump-out hole is then sealed by heating a glass disc pre-coated with indium/indium alloy located over the hole. Prior to the hole being sealed, the sample is baked at 120 °C for 8 h while the space between the glass panes is evacuated to a pressure less than 105 Pa. This novel indium– copper–indium (In/Cu/In) edge seal reduced the quantity of indium in the seal, replacing it with the cheaper alternative of copper. The fabrication process included the following steps. The glass panes, one of which is predrilled for subsequent pump-out, were cleaned using a solvent such as acetone, and then baked at 240 °C in an oven for 8 h. The glass panes were allowed to cool and a 0.05 mm thick by 6 mm wide indium peripheral band was applied to both glass panes using an ultrasonic soldering procedure. A 0.15 mm diameter copper wire was soldered into the indium band on one glass pane. The pillars were placed on the glass pane in a 25 mm by 25 mm grid array using a wand and the upper glass pane located on the lower pane. The unit was positioned in a vacuum chamber. The chamber was evacuated to a pressure of 105 Pa and the temperature raised to 160 °C to create the In/Cu/In sandwich edge seal. After cooling to the room temperature, the unit was removed and placed in a conventional area and evacuated using the modified pump-out system described in Zhao et al. (2006). 4. Experimental determination of the heat conductance of a vacuum glazing before and after thermal cycling Samples of vacuum glazing measuring 0.4 m by 0.4 m fabricated at the University of Ulster were subjected to thermal cycling tests in a purpose built large scale GHBC. Fig. 2 is a schematic diagram of the new GHBC with a photograph of the constructed GHBC presented in Fig. 3. Heat transfer through the test sample located in the guarded hot box shown in Fig. 2 can be determined from: Qs ¼ Qinput Qb Qm Qe
ð6Þ
1726
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730 Expanded polystyrene mask wall
Electric fan
Isothermal baffles
Electric fan
Expanded polystyrene mask wall
× ×
Chiller ×
Qb × ×
Vacuum glazing
Qinput
×
×
×
Qs ×
×
×
×
×
× × ×
×
Cooling coils
Qe Qm ×
× × × × ×
×
×
× × × ×
× × Frame Electric fans
Heaters
Metering box
Vacuum glazing
Thermocouple locations
Air plenum
Fig. 2. Schematic diagram of the large scale GHBC for thermal cycling tests of vacuum glazing (not to scale).
where
4m Control chamber
Environmental chamber
3m Control gear 2m
Mask wall holding glazing sample
Compressor/ condenser
1m
ð7Þ
Radiant and air temperatures can be combined into a single environmental temperature Tn (ISO, 1994), which represents the appropriate weighting of air and radiant temperatures for the purpose of determining the heat flow to the surface: Tn ¼
T a QAs þ ehr ðT a T r ÞT s Qs A
þ ehr ðT a T r Þ
þ Ts 2
ð10Þ
Qs AðT s2 T n2 Þ
ð12Þ
0m
Heat flow through the metering box, Qb was controlled to be negligible. Heat transfer through the mask wall, Qm was determined by measurement of mean mask wall surface temperatures in both the hot and cold chambers. The flanking loss, Qe, i.e. the heat transfer through the edge area of the expanded polystyrene mask wall adjacent to the test sample, was determined experimentally using standard samples of known thermal properties. The heat transfer coefficient of a test sample was determined from: Qs AðT s1 T s2 Þ
ð9Þ
where T 0r is the temperature of copper baffle in both hot and cold chambers. Using Eq. (8), the environmental temperatures in the hot and cold chambers, Tn1 and Tn2 can be calculated. The surface heat transfer coefficients in the hot and cold chambers are given by: Qs ð11Þ hi ¼ AðT n1 T s1 Þ ho ¼
Fig. 3. The large scale GHBC constructed at the University of Ulster.
C¼
Tm ¼
T 0r
hr ¼ 4rT 3m
ð8Þ
To determine the uncertainty in the calculated heat transfer coefficient, the uncertainty in each measurement made was estimated and then combined to give a single total uncertainty value (Zarr et al., 1987), i.e. y t ¼ ðy 23 þ y 24 þ y 25 þ y 26 þ y 27 Þ
1=2
ð13Þ
The values of y3 to y7 are the uncertainty in heat flow through the test sample, flanking loss, electrical power input, and the calculated heat transfer through the metering box and mask wall resulting from errors in surface temperature measurements. The values for each of these parameters were +1%, +1%, ±0.25%, ±1% and ±1%, respectively. The overall uncertainty yt was thus calculated to be 2.01%. Inclusion of the effect of uncertainty in glass surface temperature measurement of ±2% gave an upper limit of uncertainty in the overall heat transfer coefficient of 2.83%, which is less than ±3%. During GHBC calibration using two 18 mm and 25 mm thick polystyrene sheets as the sample, the greatest deviation of the heat conductance from the mean value of five time tests was 0.01 W m2 K1. Considering the worst case scenario, the resolution of this GHBC was determined to be the value of three times this deviation value, i.e. 0.03 W m2 K1.
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
a
30
Temperature ( o C)
25
20
Residual gas pressure: 0.01 Pa 15
10
5
Cold side Predicted
Warm side predicted
Cold side Measured
Warm side measured
0
0
b
20
40
60 80 100 120 140 Distance from sightline (mm)
160
180
30
25
20
o
Temperature ( C)
The air temperature in the metering box was maintained at 22 °C while the air temperature in the environmental box was cycled down to 35 °C over a period of 4 h, maintained at 35 °C for 30 min, raised to 50 °C over a period of 3 h and then maintained at 50 °C for 30 min. This is one complete 8 h cycle test (Papaefthimiou et al., 2006), 15 cycles were completed. To eliminate the influence of large temperature variations that occurred during thermal cycling on the accuracy of the GHBC, the heat conductance of the sample before and after thermal cycling was evaluated. The air temperatures in the hot and cold boxes, surface heat transfer coefficients determined using equations 12 and 13 and the heat flow through mask wall and vacuum glazing before and after thermal cycling are listed in Table 1. When testing the sample after the thermal cycling, the input DC power within the GHBC was the same (12.6 W) as before the thermal cycling. Since the heat conductance of the sample had changed, the measured glass mean surface temperature difference at the exposed glass area was very different (12.4 °C) from that before the thermal cycling (14.1 °C) as shown in Fig. 4. Due to the heat conduction through the edge seal, the temperature difference between the complete vacuum glazing including the edge seal area was determined to be 13.2 and 11.1 °C before and after thermal cycling respectively using the finite element model. When testing the sample after thermal cycling, the mean temperature of the internal surface of the metering box was lower by 0.2 °C than that of the guard box, since more heat flowed across the sample than before the thermal cycling. Heat of 1.25 W was conducted into the metering box from the external surface of the box according to the calibration results using the polystyrene calibration sheet. Therefore the effective input power within the GHBC was 13.85 W. The approximate estimation of heat conductance through pillar conduction and radiation and the heat flow calculated by using the analytic model before and after thermal cycling within the vacuum glazing are listed in Table 2. The heat flow due to the residual gas levels were calculated by the heat flow Qvg through the glazing in Table 1 minus Qpillar+radiation+lateral in Table 2. The heat conductance Cgas due to the residual gas is thus determined to be 0.13 W m2 K1. In Table 2 the edge conductance reduced the heat flow Qradiation+pillar by 10% for the vacuum glazing (Simko et al., 1999) before thermal cycling and by 5% by the finite element model simulation. In Table 2, Ctotal is the combined conductance of pillar and radiation. The heat conductance at the centre glass area was 1.18 W m2 K1 before thermal cycling
1727
15
Residual gas pressure: 0.16 Pa
10
5
Cold side Predicted Cold side Measured
Warm side predicted Cold side Measured
0
0
20
40 60 80 100 120 140 Distance from sightline (mm)
160
180
Fig. 4. Temperature profiles along the central line of glass surfaces, (a) before and (b) after thermal cycling. In (a) the temperature profiles were calculated when the influence of residual gas was ignored; In (b) the temperature profiles were calculated when the influence of residual gas was considered.
and 1.30 W m2 K1 after thermal cycling due to the contribution of Cgas. It can be seen from Table 2 that lateral heat conduction contributes over one third of total heat flow for the vacuum glazing before thermal cycling while less than one third of total heat flow for the vacuum glazing after thermal cycling, since part of heat flows through the residual gas. In the finite element model, the heat conductance of the evacuated gap is determined by the residual gas and pillar array conductance and the effective radiative conductance.
Table 1 Date for measurement of 0.4 m by 0.4 m vacuum glazing sample before and after thermal cycling in the GHBC. Thermal cycling (TC)
Before TC After TC
Air temperature (°C)
Heat transfer coefficient (Wm2 K1)
Input power (W)
Flanking loss (W)
Heat flow through mask wall (W)
Heat flow through frame (W)
Heat flow through vacuum glazing (W)
Ta1
Ta2
h1
h2
Qt
Qe
Qm
Qf
Qvg
27.4 26.4
7.9 4.7
5.25 4.08
11.82 8.33
12.60 13.85
1.6 1.8
5.11 5.70
2.74 2.98
3.15 ± 0.09 3.36 ± 0.10
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
1.06 0.95 2.09 2.19
Net Qradiation+pillars (W)
0.23 0.12
Reduction of Qradiation+pillars near edge (W)
1.18 1.17 289.5 286.5
0.54 0.53
2.32 2.31
Gross Qradiation+pillars through 0.15 m2 (W) Ctotal (Wm2 K1) Cradiation (Wm2 K1) T (K)
Before TC After TC
T2 T1
23.1 19.0
9.9 7.9
13.2 11.1
DTglass–glass (oC) Glass temperature (oC) Thermal cycling (TC)
Table 2 Approximation of contribution to heat flow through vacuum glazing before and after thermal cycling within the GHBC using analytic models.
Qlateral flow (W)
3.15 3.14
Qpillar+radiation+lateral (W)
0 0.22
Qresidual (W)
gas
1728
The calculated temperature profiles on the surface of the glass pane before and after thermal cycling are shown in Figs. 4(a) and (b). The predicted results are within the range of ±3% variation of the experimental results, which are represented by the error bars in Figs. 4(a) and (b). In Fig. 4(a) the temperature profiles were calculated when the influence of residual gas was ignored; in Fig. 4(b) the temperature profiles were calculated when the influence of residual gas was considered. It can be seen that the measured temperatures are in good agreement with the predictions calculated using the finite element model. The temperature decrease in the edge area in Fig. 4(a) occurs at a faster rate than that in Fig. 4(b) at the edge area. A possible cause of the increase in heat conductance after thermal cycling could be the inelastic increase in support pillar diameter and edge seal width due to the atmospheric pressure exerted on the glass surfaces. The Yield strength of stainless steel is 520 MPa (Anon, 2008). With a 0.4 mm diameter pillar at a spacing of 25 mm, the calculated mechanical stress within the pillar is 502 MPa, which is less than the yield strength of Stainless Steel. Therefore it is unlikely that the pillars suffered inelastic deformation. It has been proven both theoretically and experimentally that the Clateral component of heat conductance in Eq. (2) depends on the thickness and thermal conductivity of the glass pane, and the frame rebate depth (Collins and Simko, 1998), which are not affected by the thermal cycling tests. The increase in heat conductance must therefore be the result of outgassing to the evacuated space. After subjecting a vacuum glazing with a solder glass edge seal to a large temperature differential, significant bending of the glass panes occurred (Simko et al., 1998) as the edge seal is rigid and not flexible. This led to shear cracks in the glass panes adjacent to the pillars. The application of a large temperature differential to a vacuum glazing with an indium edge seal in the thermal cycling test undertaken led to minimal bending and no shear fractures adjacent to the pillars because of the flexibility of the edge seal.
5. Heat conductance of residual gas within the vacuum glazing When gas pressure is reduced to a level at which the mean free path for molecule-molecule collisions is of the same order as the distance over which the heat is transported, a significant reduction of residual gas heat conductance takes place. The width of the evacuated gap in a vacuum glazing is approximately 0.2 mm, this equates to a mean free path at a pressure of 30 Pa (Collins and Simko, 1998). The gaseous conductance of the low pressure gas is proportional to gas pressure p (Corrucini, 1957): C molecular
cþ1 ¼a c1
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi R p 8pMT
ð14Þ
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
1729
where c is the specific heat ratio of the gas, M is the molar mass of the gas, T is the mean temperature of the two surfaces and R is the molar gas constant. The combined accommodation coefficient a is determined by the accommodation coefficients on the two surfaces, a1 and a2 by
the glass surface temperature difference predicted using a finite element model. Vacuum glazing fabricated with an indium edge seal can accommodate large temperature differentials.
1 1 1 ¼ þ 1 a a1 a2
Acknowledgements
ð15Þ
Water vapour has been determined to be the main gas species in the thermally degraded samples of vacuum glazing (Collins and Simko, 1998). Water molecules interact strongly with the internal surfaces of the glazing. A combined accommodation coefficient of 0.9 was assumed. The gaseous conductance in the low pressure gap of vacuum glazing is Cgas = 0.8P W m2 K1, where P is the gas pressure measured in Pascals. The pressures within the evacuated gap of the vacuum glazing after thermal cycling was increased from an ignorable level (less than 0.1 Pa) to 0.16 Pa. Two different physical mechanisms of vacuum degradation within vacuum glazing have been investigated by the team at the University of Sydney. When stored in a high temperature environment, the evolution of water vapour can occur (Lenzen et al., 1999; Ng et al., 2005); if exposed to sunlight (Ng et al., 2003) or under external energy excitation (Minaai et al., 2005) such as from a laser, the evolution of CO and CO2 can take place. The vacuum glazing tested was not subject to either sunlight or laser, therefore water evolution could be the cause of the measured vacuum degradation resulting after thermal cycling. 6. Conclusions Fabricated vacuum glazing measuring 0.4 m by 0.4 m with a U-value of 1.0 W m2 K1 was subjected to extreme thermal cycling resulting in significant thermal gradients over the glazing. In a GHBC, an air temperature of 22 °C was maintained in the metering box while in the environmental box air temperature was cycled over 8 h between 30 °C and 50 °C for 15 cycles. After thermal cycling it was found that the heat conductance at the centre region of the vacuum glazing had increased by 10.1% from 1.18 W m2 K1 to 1.30 W m2 K1. It has been found that before thermal cycling the lateral heat conduction contributes more than one third of the total heat flow for the vacuum glazing while after thermal cycling lateral heat flow contributes to less than one third of the total heat flow for the vacuum glazing since part of heat flows through the residual gas. Using the model for heat conduction in a vacuum, it was determined that the vacuum pressure within the evacuated gap increased from the negligible level (less than 0.1 Pa) to 0.16 Pa. This is approaching the upper limit of the range developed by Collins and Simko (1998), for which the residual gas contribution to the thermal performance of a vacuum glazing can be neglected. The degradation of vacuum pressure determined by this model agreed well with
The support from the Charles Parson Energy Research Awards through the National Development Plane 2007– 2013 of the Department of Communications, Marine and Natural Resources, Dublin, Republic of Ireland is appreciated. References Anon, 2008. Tensile stress. Available from:. Brenner, S., Scott, R.L., 2005. The Mathematical Theory of Finite Element Methods, second ed. Springer, ISBN 0-3879-5451-1. Collins, R., Simko, T.M., 1998. Current state of the science and technology of vacuum glazing. Solar Energy 62, 189–213. Corrucini, R.J., 1957. Gaseous heat conduction at low pressure and temperatures. Vacuum 7–8, 19–29. Eames, P.C., Norton, B., 1993. A validated unified model for optics and heat transfer in line-axis concentrating solar energy collectors. Solar Energy 50, 339–355. Fang, Y., 2002. An experimental and theoretical investigation into the design, development and performance of evacuated glazing. Ph.D. thesis, University of Ulster, UK. Fang, Y., Eames, P.C., 2006. The effect of glass coating emittance and frame rebate on the heat transfer through vacuum and electrochromic vacuum glazed windows. Solar Energy Material and Solar Cells 90, 2683–2695. Fang, Y., Eames, P.C., Norton, B., Hyde, T.J., 2006. Experimental validation of a numerical model for heat transfer in evacuated glazing. Solar Energy 80, 564–577. Fang, Y., Hyde, T., Hewitt, N., Eames, P.C., Norton, B., 2009. Comparison of vacuum glazing thermal performance predicted using two- and three-dimensional models and their experimental validation. Solar Energy Materials and Solar Cells 93, 1492–1498. Griffiths, P.W., Di Leo, M., Cartwright, P., Eames, P.C., Yianoulis, P., Leftheriotis, G., Norton, B., 1998. Fabrication of evacuated glazing at low temperature. Solar Energy 63, 243–249. Hyde, T.J., Griffiths, P.W., Eames, P.C., Norton, B., 2000. Development of a novel low temperature edge seal for evacuated glazing. In: Pro. World Renewable Energy Congress VI, Brighton, UK, pp. 271–274. ISO, 1994. Thermal insulation. Determination of steady-state thermal transmission properties. Calibrated and guarded hot box. (ISO 8990) Geneva, Switzerland. Lenzen, M., Turner, G.M., Collins, R.E., 1999. Thermal outgassing of vacuum glazing. J. Vac. Sci. Technol. A 17, 1002–1017. Minaai, T., Kumagai, M., Nara, A., Tanemura, S., 2005. Study of the outgassing behaviour of SnO2:F films on glass in vacuum glazing under external energy excitation. Materials Science & Engineering B 119, 252–257. Ng, N., Collins, R.E., So, L., 2003. Photodesorption of Gases in Vacuum Glazing. J. Vac. Sci. Technol. A 21 (5), 1776–1783. Ng, N., Collins, R.E., So, L., 2005. Thermal and Optical Evolution of Gas in Vacuum Glazing. Materials Science and Engineering B 119, 258– 264. Papaefthimiou, S., Leftheriotis, G., Yianoulis, P., Hyde, T.J., Eames, P.C., Fang, Y., Pennarun, P.-Y., Jannasch, P., 2006. Development of electrochromic evacuated advanced glazing. Energy and Buildings 38, 1455–1467.
1730
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
Robinson, S.J., Collins, R.E., 1989. Evacuated windows-theory and practice, ISES Solar World Congress, International Solar Energy Society, Kobe, Japan. Simko, T.M., Fischer-Cripps, A.C., Collins, R.E., 1998. Temperatureinduced Stress in Vacuum Glazing: Modelling and Experimental Validation. Solar Energy 63, 1–21. Simko, T.M., Elmahdy, H., Collins, R.E., 1999. Determination of overall heat transmission coefficient (U-value) of vacuum glazing. ASHRAE Transactions 105, 891–899. Zarr, R.R., Burch, D.M., Faison, T.K., Arnold, C.E., O’Connell, M.E., 1987. Calibration of the NBS Calibrated hot box. Journal of Testing and Evaluation 15, 167–177.
Zhao, J.F., Eames, C. Philip, Hyde C. Trevor, Fang, Y., Wang, J., 2006. A new type of In/Cu/In seal for vacuum glazing. In: Proceeding of Renewable Energy in Maritime Island Climates Conference 26–28 April, Dublin, Ireland, pp. 189–194. Zhao, J.F., Eames, P.C., Hyde, T.J., Fang, Y., Wang, J., 2007. A modified pump-out technique used for fabrication of low temperature metal sealed vacuum glazing. Solar Energy 81, 1072–1077. Zoller, F., 1924, ‘‘Hollow pane of glass”, German Patent No. 387655.
Solar Energy 83 (2009) 1723–1730 www.elsevier.com/locate/solener
Theoretical and experimental analysis of the vacuum pressure in a vacuum glazing after extreme thermal cycling Yueping Fang a,*, Trevor Hyde a, Philip C. Eames b, Neil Hewitt a a
Centre for Sustainable Technologies, School of the Built Environment, University of Ulster, Newtownabbey, BT37 0QB N. Ireland, UK b Centre for Renewable Energy Research, University of Loughborough, UK Received 4 December 2007; received in revised form 24 February 2009; accepted 26 March 2009 Available online 18 July 2009 Communicated by: Associate Editor Yogi Goswami
Abstract Details of theoretical and experimental studies of the change in vacuum pressure within a vacuum glazing after extreme thermal cycling are presented. The vacuum glazing was fabricated at low temperature using an indium–copper–indium edge seal. It comprised two 4 mm thick 0.4 m by 0.4 m glass panes with low-emittance coatings separated by an array of stainless steel support pillars spaced at 25 mm with a diameter of 0.4 mm and a height of 0.15 mm. Thermal cycling tests were undertaken in which the air temperature on one side of the sample was taken from 30 °C to +50 °C and back to 30 °C 15 times while maintaining an air temperature of 22 °C on the other side. After this test procedure, it was found that the glass to glass heat conductance at the centre glazing area had increased by 10.1% from which the vacuum pressure within the evacuated space was determined to have increased from the negligible level of less than 0.1 Pa to 0.16 Pa using the model of Corrucini. Previous research has shown that if the vacuum pressure is less than 0.1 Pa, the effect of conduction through the residual gas on the total glazing heat transfer is negligible. The degradation of vacuum level determined was corroborated by the change in glass surface temperatures. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Vacuum glazing; Vacuum pressure; Thermal cycling
1. Introduction Flat vacuum glazing as shown in Fig. 1 consists of two plane glass sheets, separated by a narrow internal evacuated space, contiguously sealed together around their periphery. The space, maintained by an array of tiny support pillars, is evacuated to a pressure of less than 0.1 Pa, effectively eliminating both gaseous conduction and convection. The low-emittance (low-e) coatings on the internal glass surfaces within the evacuated gap reduce the radiative heat transfer through the vacuum glazing to a very low level. The vacuum glazing concept was first patented by Zoller (1924). However, after many years the first success*
Corresponding author. Tel.: +44 2890368241; fax: +44 2890238227. E-mail address: [email protected] (Y. Fang).
0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.03.017
ful vacuum glazing was fabricated by Robinson and Collins (1989). A solder glass powder laid along the periphery of the glass sheets melted to form the edge seal of the vacuum space when the entire glazing unit was heated to 450 °C. This high temperature method of fabricating vacuum glazing prevents the use of tempered glass and some types of soft low-e coatings thus preventing the high levels of performance predicted from being achieved. The University of Ulster has developed a methodology and system for the manufacture of low temperature sealed vacuum glazing that can incorporate soft low-e coatings and tempered glass (Griffiths et al., 1998; Hyde et al., 2000). A total heat transmission U-value of less than 1.0 W m2 K1 for a vacuum glazing of small size (0.4 m by 0.4 m) has been experimentally determined (Fang et al., 2006) using a guarded hot box calorimeter (GHBC).
1724
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
Nomenclature a C h k M s P R T y
radius of support pillars (m) heat conductance (W m2 K1) surface heat transfer coefficient (W m2 K1) thermal conductivity of glass (W m1 K1) molar mass of gas pillar separation (m) pressure (Pa) molar gas constant temperature (°C) uncertainty of heat flow
Greek letters e hemispherical emittance of a surface r Stefan–Boltzmann constant (5.67108 W m2 K4) a accommodation coefficient c specific heat ratio of the gas Subscripts 1, 2 internal and external sample surfaces 3 refers to the uncertainty of heat transfer through the test sample
Outgassing and long-term vacuum stability of vacuum glazing is an important issue (Collins and Simko, 1998; Lenzen et al., 1999). The levels of outgassing in vacuum glazing subject to static aging conditions at different temperatures were measured using a spinning rotor gauge and found to be in good agreement with the predictions made (Lenzen et al., 1999; Ng et al., 2005). In the research reported in this paper vacuum glazing manufactured at low temperature was subjected to extreme dynamic thermal cycling, and the effect on the vacuum pressure in the evac-
Glass disc seal In/Cu/In edge seal Support pillars
Vacuum gap
Evacuation hole
Low-emittance coatings Fig. 1. Schematic diagram of a vacuum glazing.
4 5 6 7 a amb b c e f a 1, a 2 g1 , g 2 i.o m n r t vg
refers to the uncertainty of flanking loss refers to the uncertainty of electric power input refers to the uncertainty of heat transfer through the metering box refers to the uncertainty of heat transfer through the mask wall air ambient metering box convection flanking loss frame air in the hot and cold boxes glass surfaces in the hot and cold boxes air in hot and cold chambers mask wall refers to environment temperature radiation refers to input power vacuum glazing
uated gap analysed using a model for heat conduction at low pressure (Corrucini, 1957). The thermal conductances measured were compared with those of thermal testing using a GHBC (Fang et al., 2006). 2. Modelling approaching The investigated vacuum glazing comprised two 4 mm thick 0.4 m by 0.4 m glass panes each with a low-emittance coating of 0.18 emittance separated by an array of stainless steel support pillars spaced at 25 mm with a diameter of 0.4 mm and a height of 0.15 mm. A three dimensional finite volume model (Eames and Norton, 1993) and a two dimensional finite element model (Fang et al., 2006) extensively validated experimentally in previously reported research (Griffiths et al., 1998; Fang, 2002) were used to analyse heat transfer through a vacuum glazing with the applied boundary conditions representative of those within the experimental GHBC. In the finite volume model, the analytic model for heat flow through individual support pillars (Collins and Simko, 1998) was not employed since the pillar array was incorporated and modelled directly. The circular cross section of the pillar in the fabricated system was replaced by a square cross section pillar of equal area in the model. A graded mesh was used with a high density of nodes in and around the pillar to provide adequate representation of the heat transfer in this region. The residual gas pressure was assumed to be below that at which conduction was an issue. It has been experimentally and theoretically
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
proved that the temperature of each glass sheet approaches the value at the centre of glass pffiffiffi pane exponentially with a characteristic distance of l ¼ k glass t=h, where h is the exterior heat transfer coefficient from the surface being considered (i.e. h1 and h2). The total heat flow per unit length of the edge seal (Collins and Simko, 1998) is determined by rffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffi k glass t k glass t þ w1 þ w2 þ Qedge ¼ ðT 1 T 2 Þk glass t h1 h2 ð1Þ The total heat flow through the edge area along the four edges is Qlateral ¼ 4‘edge Qedge
ð2Þ
Where ‘edge is the length of indium edge seal. When the width of edge seal is 6 mm of 0.4 m by 0.4 m vacuum glazing, the ‘edge is 0.388 m. The area of the evacuated gap is 0.15 m2. The finite element model used the Galerkin (Brenner and Scott, 2005) approach with eight-node isoparametric elements. Further details of the finite element model employed can be found in Eames and Norton (1993). In the finite element model, the conductance of the central evacuated gap was determined using the analytic model for heat transfer in the support pillars and radiative heat transfer between the two glass panes. For similar boundary conditions, the difference in heat conductance through the vacuum glazing predicted by the finite volume model and the finite element model is less than 3% (Fang and Eames, 2006; Fang et al., 2009). In the finite element model used, the influence of the residual gas on the heat conductance of the glazing can be modelled. When the experimentally measured surface temperature profiles do not match the predictions made using the finite element model, the effects of the residual gas must be considered (Fang et al., 2006). The total glass to glass heat conductance of the central glazing area is determined by: C centre ¼ C gas þ C radiation þ C pillars þ C lateral
ð3Þ
¼ C gas þ 4eeffective rT 3average þ 2k glass a=s2 þ C lateral
ð4Þ
where Cgas is the residual gas heat conductance, Cradiation is the radiative heat conductance between the two glass panes, Clateral is the lateral heat conductance, r is the Stefan Boltzmann constant (5.67 108 W m2 K4), Taverage is the average of the two glass temperatures T1 and T2, kglass is the glass thermal conductivity, a is the pillar radius, s is the pillar separation and the effective hemispheric emittance eeffective is calculated from the two glass surface hemispheric emittances e1 and e2 by: 1 1 1 ¼ þ 1 eeffective e1 e2
ð5Þ
Using the value of Clateral predicted by the finite volume model and the experimentally determined heat conductance of the centre glass area Ccentre, the value of Cgas can be
1725
determined using Eq. (2). The effective heat conductance of the evacuated gap can then be determined and temperature profiles calculated using the finite element model. 3. The laboratory production of vacuum glazing Two fabrication methods for producing vacuum glazing have been developed by the team at the University of Ulster. In the first single stage method, the vacuum glazing is fabricated in a stainless steel vacuum chamber (Hyde et al., 2000), in which the seal is formed with no subsequent pump-out process required. In the second method, there are two stages (Zhao et al., 2007). Firstly, the edge seal is formed in a vacuum or an oxygen-free nitrogen atmosphere with subsequent evacuation through a pre-drilled pumpout hole, typically 3 mm in diameter. The pump-out hole is then sealed by heating a glass disc pre-coated with indium/indium alloy located over the hole. Prior to the hole being sealed, the sample is baked at 120 °C for 8 h while the space between the glass panes is evacuated to a pressure less than 105 Pa. This novel indium– copper–indium (In/Cu/In) edge seal reduced the quantity of indium in the seal, replacing it with the cheaper alternative of copper. The fabrication process included the following steps. The glass panes, one of which is predrilled for subsequent pump-out, were cleaned using a solvent such as acetone, and then baked at 240 °C in an oven for 8 h. The glass panes were allowed to cool and a 0.05 mm thick by 6 mm wide indium peripheral band was applied to both glass panes using an ultrasonic soldering procedure. A 0.15 mm diameter copper wire was soldered into the indium band on one glass pane. The pillars were placed on the glass pane in a 25 mm by 25 mm grid array using a wand and the upper glass pane located on the lower pane. The unit was positioned in a vacuum chamber. The chamber was evacuated to a pressure of 105 Pa and the temperature raised to 160 °C to create the In/Cu/In sandwich edge seal. After cooling to the room temperature, the unit was removed and placed in a conventional area and evacuated using the modified pump-out system described in Zhao et al. (2006). 4. Experimental determination of the heat conductance of a vacuum glazing before and after thermal cycling Samples of vacuum glazing measuring 0.4 m by 0.4 m fabricated at the University of Ulster were subjected to thermal cycling tests in a purpose built large scale GHBC. Fig. 2 is a schematic diagram of the new GHBC with a photograph of the constructed GHBC presented in Fig. 3. Heat transfer through the test sample located in the guarded hot box shown in Fig. 2 can be determined from: Qs ¼ Qinput Qb Qm Qe
ð6Þ
1726
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730 Expanded polystyrene mask wall
Electric fan
Isothermal baffles
Electric fan
Expanded polystyrene mask wall
× ×
Chiller ×
Qb × ×
Vacuum glazing
Qinput
×
×
×
Qs ×
×
×
×
×
× × ×
×
Cooling coils
Qe Qm ×
× × × × ×
×
×
× × × ×
× × Frame Electric fans
Heaters
Metering box
Vacuum glazing
Thermocouple locations
Air plenum
Fig. 2. Schematic diagram of the large scale GHBC for thermal cycling tests of vacuum glazing (not to scale).
where
4m Control chamber
Environmental chamber
3m Control gear 2m
Mask wall holding glazing sample
Compressor/ condenser
1m
ð7Þ
Radiant and air temperatures can be combined into a single environmental temperature Tn (ISO, 1994), which represents the appropriate weighting of air and radiant temperatures for the purpose of determining the heat flow to the surface: Tn ¼
T a QAs þ ehr ðT a T r ÞT s Qs A
þ ehr ðT a T r Þ
þ Ts 2
ð10Þ
Qs AðT s2 T n2 Þ
ð12Þ
0m
Heat flow through the metering box, Qb was controlled to be negligible. Heat transfer through the mask wall, Qm was determined by measurement of mean mask wall surface temperatures in both the hot and cold chambers. The flanking loss, Qe, i.e. the heat transfer through the edge area of the expanded polystyrene mask wall adjacent to the test sample, was determined experimentally using standard samples of known thermal properties. The heat transfer coefficient of a test sample was determined from: Qs AðT s1 T s2 Þ
ð9Þ
where T 0r is the temperature of copper baffle in both hot and cold chambers. Using Eq. (8), the environmental temperatures in the hot and cold chambers, Tn1 and Tn2 can be calculated. The surface heat transfer coefficients in the hot and cold chambers are given by: Qs ð11Þ hi ¼ AðT n1 T s1 Þ ho ¼
Fig. 3. The large scale GHBC constructed at the University of Ulster.
C¼
Tm ¼
T 0r
hr ¼ 4rT 3m
ð8Þ
To determine the uncertainty in the calculated heat transfer coefficient, the uncertainty in each measurement made was estimated and then combined to give a single total uncertainty value (Zarr et al., 1987), i.e. y t ¼ ðy 23 þ y 24 þ y 25 þ y 26 þ y 27 Þ
1=2
ð13Þ
The values of y3 to y7 are the uncertainty in heat flow through the test sample, flanking loss, electrical power input, and the calculated heat transfer through the metering box and mask wall resulting from errors in surface temperature measurements. The values for each of these parameters were +1%, +1%, ±0.25%, ±1% and ±1%, respectively. The overall uncertainty yt was thus calculated to be 2.01%. Inclusion of the effect of uncertainty in glass surface temperature measurement of ±2% gave an upper limit of uncertainty in the overall heat transfer coefficient of 2.83%, which is less than ±3%. During GHBC calibration using two 18 mm and 25 mm thick polystyrene sheets as the sample, the greatest deviation of the heat conductance from the mean value of five time tests was 0.01 W m2 K1. Considering the worst case scenario, the resolution of this GHBC was determined to be the value of three times this deviation value, i.e. 0.03 W m2 K1.
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
a
30
Temperature ( o C)
25
20
Residual gas pressure: 0.01 Pa 15
10
5
Cold side Predicted
Warm side predicted
Cold side Measured
Warm side measured
0
0
b
20
40
60 80 100 120 140 Distance from sightline (mm)
160
180
30
25
20
o
Temperature ( C)
The air temperature in the metering box was maintained at 22 °C while the air temperature in the environmental box was cycled down to 35 °C over a period of 4 h, maintained at 35 °C for 30 min, raised to 50 °C over a period of 3 h and then maintained at 50 °C for 30 min. This is one complete 8 h cycle test (Papaefthimiou et al., 2006), 15 cycles were completed. To eliminate the influence of large temperature variations that occurred during thermal cycling on the accuracy of the GHBC, the heat conductance of the sample before and after thermal cycling was evaluated. The air temperatures in the hot and cold boxes, surface heat transfer coefficients determined using equations 12 and 13 and the heat flow through mask wall and vacuum glazing before and after thermal cycling are listed in Table 1. When testing the sample after the thermal cycling, the input DC power within the GHBC was the same (12.6 W) as before the thermal cycling. Since the heat conductance of the sample had changed, the measured glass mean surface temperature difference at the exposed glass area was very different (12.4 °C) from that before the thermal cycling (14.1 °C) as shown in Fig. 4. Due to the heat conduction through the edge seal, the temperature difference between the complete vacuum glazing including the edge seal area was determined to be 13.2 and 11.1 °C before and after thermal cycling respectively using the finite element model. When testing the sample after thermal cycling, the mean temperature of the internal surface of the metering box was lower by 0.2 °C than that of the guard box, since more heat flowed across the sample than before the thermal cycling. Heat of 1.25 W was conducted into the metering box from the external surface of the box according to the calibration results using the polystyrene calibration sheet. Therefore the effective input power within the GHBC was 13.85 W. The approximate estimation of heat conductance through pillar conduction and radiation and the heat flow calculated by using the analytic model before and after thermal cycling within the vacuum glazing are listed in Table 2. The heat flow due to the residual gas levels were calculated by the heat flow Qvg through the glazing in Table 1 minus Qpillar+radiation+lateral in Table 2. The heat conductance Cgas due to the residual gas is thus determined to be 0.13 W m2 K1. In Table 2 the edge conductance reduced the heat flow Qradiation+pillar by 10% for the vacuum glazing (Simko et al., 1999) before thermal cycling and by 5% by the finite element model simulation. In Table 2, Ctotal is the combined conductance of pillar and radiation. The heat conductance at the centre glass area was 1.18 W m2 K1 before thermal cycling
1727
15
Residual gas pressure: 0.16 Pa
10
5
Cold side Predicted Cold side Measured
Warm side predicted Cold side Measured
0
0
20
40 60 80 100 120 140 Distance from sightline (mm)
160
180
Fig. 4. Temperature profiles along the central line of glass surfaces, (a) before and (b) after thermal cycling. In (a) the temperature profiles were calculated when the influence of residual gas was ignored; In (b) the temperature profiles were calculated when the influence of residual gas was considered.
and 1.30 W m2 K1 after thermal cycling due to the contribution of Cgas. It can be seen from Table 2 that lateral heat conduction contributes over one third of total heat flow for the vacuum glazing before thermal cycling while less than one third of total heat flow for the vacuum glazing after thermal cycling, since part of heat flows through the residual gas. In the finite element model, the heat conductance of the evacuated gap is determined by the residual gas and pillar array conductance and the effective radiative conductance.
Table 1 Date for measurement of 0.4 m by 0.4 m vacuum glazing sample before and after thermal cycling in the GHBC. Thermal cycling (TC)
Before TC After TC
Air temperature (°C)
Heat transfer coefficient (Wm2 K1)
Input power (W)
Flanking loss (W)
Heat flow through mask wall (W)
Heat flow through frame (W)
Heat flow through vacuum glazing (W)
Ta1
Ta2
h1
h2
Qt
Qe
Qm
Qf
Qvg
27.4 26.4
7.9 4.7
5.25 4.08
11.82 8.33
12.60 13.85
1.6 1.8
5.11 5.70
2.74 2.98
3.15 ± 0.09 3.36 ± 0.10
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
1.06 0.95 2.09 2.19
Net Qradiation+pillars (W)
0.23 0.12
Reduction of Qradiation+pillars near edge (W)
1.18 1.17 289.5 286.5
0.54 0.53
2.32 2.31
Gross Qradiation+pillars through 0.15 m2 (W) Ctotal (Wm2 K1) Cradiation (Wm2 K1) T (K)
Before TC After TC
T2 T1
23.1 19.0
9.9 7.9
13.2 11.1
DTglass–glass (oC) Glass temperature (oC) Thermal cycling (TC)
Table 2 Approximation of contribution to heat flow through vacuum glazing before and after thermal cycling within the GHBC using analytic models.
Qlateral flow (W)
3.15 3.14
Qpillar+radiation+lateral (W)
0 0.22
Qresidual (W)
gas
1728
The calculated temperature profiles on the surface of the glass pane before and after thermal cycling are shown in Figs. 4(a) and (b). The predicted results are within the range of ±3% variation of the experimental results, which are represented by the error bars in Figs. 4(a) and (b). In Fig. 4(a) the temperature profiles were calculated when the influence of residual gas was ignored; in Fig. 4(b) the temperature profiles were calculated when the influence of residual gas was considered. It can be seen that the measured temperatures are in good agreement with the predictions calculated using the finite element model. The temperature decrease in the edge area in Fig. 4(a) occurs at a faster rate than that in Fig. 4(b) at the edge area. A possible cause of the increase in heat conductance after thermal cycling could be the inelastic increase in support pillar diameter and edge seal width due to the atmospheric pressure exerted on the glass surfaces. The Yield strength of stainless steel is 520 MPa (Anon, 2008). With a 0.4 mm diameter pillar at a spacing of 25 mm, the calculated mechanical stress within the pillar is 502 MPa, which is less than the yield strength of Stainless Steel. Therefore it is unlikely that the pillars suffered inelastic deformation. It has been proven both theoretically and experimentally that the Clateral component of heat conductance in Eq. (2) depends on the thickness and thermal conductivity of the glass pane, and the frame rebate depth (Collins and Simko, 1998), which are not affected by the thermal cycling tests. The increase in heat conductance must therefore be the result of outgassing to the evacuated space. After subjecting a vacuum glazing with a solder glass edge seal to a large temperature differential, significant bending of the glass panes occurred (Simko et al., 1998) as the edge seal is rigid and not flexible. This led to shear cracks in the glass panes adjacent to the pillars. The application of a large temperature differential to a vacuum glazing with an indium edge seal in the thermal cycling test undertaken led to minimal bending and no shear fractures adjacent to the pillars because of the flexibility of the edge seal.
5. Heat conductance of residual gas within the vacuum glazing When gas pressure is reduced to a level at which the mean free path for molecule-molecule collisions is of the same order as the distance over which the heat is transported, a significant reduction of residual gas heat conductance takes place. The width of the evacuated gap in a vacuum glazing is approximately 0.2 mm, this equates to a mean free path at a pressure of 30 Pa (Collins and Simko, 1998). The gaseous conductance of the low pressure gas is proportional to gas pressure p (Corrucini, 1957): C molecular
cþ1 ¼a c1
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi R p 8pMT
ð14Þ
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
1729
where c is the specific heat ratio of the gas, M is the molar mass of the gas, T is the mean temperature of the two surfaces and R is the molar gas constant. The combined accommodation coefficient a is determined by the accommodation coefficients on the two surfaces, a1 and a2 by
the glass surface temperature difference predicted using a finite element model. Vacuum glazing fabricated with an indium edge seal can accommodate large temperature differentials.
1 1 1 ¼ þ 1 a a1 a2
Acknowledgements
ð15Þ
Water vapour has been determined to be the main gas species in the thermally degraded samples of vacuum glazing (Collins and Simko, 1998). Water molecules interact strongly with the internal surfaces of the glazing. A combined accommodation coefficient of 0.9 was assumed. The gaseous conductance in the low pressure gap of vacuum glazing is Cgas = 0.8P W m2 K1, where P is the gas pressure measured in Pascals. The pressures within the evacuated gap of the vacuum glazing after thermal cycling was increased from an ignorable level (less than 0.1 Pa) to 0.16 Pa. Two different physical mechanisms of vacuum degradation within vacuum glazing have been investigated by the team at the University of Sydney. When stored in a high temperature environment, the evolution of water vapour can occur (Lenzen et al., 1999; Ng et al., 2005); if exposed to sunlight (Ng et al., 2003) or under external energy excitation (Minaai et al., 2005) such as from a laser, the evolution of CO and CO2 can take place. The vacuum glazing tested was not subject to either sunlight or laser, therefore water evolution could be the cause of the measured vacuum degradation resulting after thermal cycling. 6. Conclusions Fabricated vacuum glazing measuring 0.4 m by 0.4 m with a U-value of 1.0 W m2 K1 was subjected to extreme thermal cycling resulting in significant thermal gradients over the glazing. In a GHBC, an air temperature of 22 °C was maintained in the metering box while in the environmental box air temperature was cycled over 8 h between 30 °C and 50 °C for 15 cycles. After thermal cycling it was found that the heat conductance at the centre region of the vacuum glazing had increased by 10.1% from 1.18 W m2 K1 to 1.30 W m2 K1. It has been found that before thermal cycling the lateral heat conduction contributes more than one third of the total heat flow for the vacuum glazing while after thermal cycling lateral heat flow contributes to less than one third of the total heat flow for the vacuum glazing since part of heat flows through the residual gas. Using the model for heat conduction in a vacuum, it was determined that the vacuum pressure within the evacuated gap increased from the negligible level (less than 0.1 Pa) to 0.16 Pa. This is approaching the upper limit of the range developed by Collins and Simko (1998), for which the residual gas contribution to the thermal performance of a vacuum glazing can be neglected. The degradation of vacuum pressure determined by this model agreed well with
The support from the Charles Parson Energy Research Awards through the National Development Plane 2007– 2013 of the Department of Communications, Marine and Natural Resources, Dublin, Republic of Ireland is appreciated. References Anon, 2008. Tensile stress. Available from:
1730
Y. Fang et al. / Solar Energy 83 (2009) 1723–1730
Robinson, S.J., Collins, R.E., 1989. Evacuated windows-theory and practice, ISES Solar World Congress, International Solar Energy Society, Kobe, Japan. Simko, T.M., Fischer-Cripps, A.C., Collins, R.E., 1998. Temperatureinduced Stress in Vacuum Glazing: Modelling and Experimental Validation. Solar Energy 63, 1–21. Simko, T.M., Elmahdy, H., Collins, R.E., 1999. Determination of overall heat transmission coefficient (U-value) of vacuum glazing. ASHRAE Transactions 105, 891–899. Zarr, R.R., Burch, D.M., Faison, T.K., Arnold, C.E., O’Connell, M.E., 1987. Calibration of the NBS Calibrated hot box. Journal of Testing and Evaluation 15, 167–177.
Zhao, J.F., Eames, C. Philip, Hyde C. Trevor, Fang, Y., Wang, J., 2006. A new type of In/Cu/In seal for vacuum glazing. In: Proceeding of Renewable Energy in Maritime Island Climates Conference 26–28 April, Dublin, Ireland, pp. 189–194. Zhao, J.F., Eames, P.C., Hyde, T.J., Fang, Y., Wang, J., 2007. A modified pump-out technique used for fabrication of low temperature metal sealed vacuum glazing. Solar Energy 81, 1072–1077. Zoller, F., 1924, ‘‘Hollow pane of glass”, German Patent No. 387655.