Proceedings of HT9 9 ASME Summer Heat Transfer Conference July 9-3 9 San Francisco California USA HT9-88344 SIMULATED THEMAL PEFOMANCE OF TIPLE VACUUM GLAZING Yueping Fang Trevor J. Hyde Neil Hewitt School of the Built Environment University of Ulster BT37 QB Newtownabbey N. Ireland UK ABSTACT The simulated triple vacuum glazing consists of three 4 mm thick glass panes with two vacuum gaps with each internal glass surface coated with a low emittance coating. The two vacuum gaps are sealed by an indium based sealant and separated by a stainless steel pillar array with a height of. mm and a pillar diameter of.3 mm spaced at 5 mm. Both solder glass and indium based sealants have been successfully applied in vacuum glazing previously. The thermal performance of the triple vacuum glazing was simulated using a finite volume model. The simulation results show that although the thermal conductivity of solder glass ( W.m -.K - ) and indium (83.7 W.m -.K - ) are very different the increase in heat transmission of triple vacuum glazing with a mm frame rebate resulting from the use of an indium edge seal compared to a solder glass edge seal was.48%. Increasing both edge seal widths from 3 mm to mm led to a 4.7% increase in heat transmission of the triple vacuum glazing without a frame and an 8.3% increase for a glazing with a mm frame rebate depth. Increasing the rebate depth in a solid wood frame from to 5 mm decreased the heat transmission of the triple vacuum glazing by 3.9%. The heat transmission of a simulated.5 m by.5 m triple vacuum glazing was 3.% greater than that of m by m triple vacuum glazing. INTODUCTION Double vacuum glazing has been successfully produced using two fabrication methods [ 3]. In the first method developed by a team at the University of Sydney the edge area of the glazing was sealed using solder glass with a melting of 5 C. A heat transmission of.8 W.m -.K - in the centre-of-glazing area has been achieved in a glazing size up to m by m fabricated in the laboratory [4]. The design method is based on the optimisation of the minimal number and smallest diameter of support pillars (which determines the heat conduction through the pillar array) under the level of bearable stress induced by the atmospheric pressure acting on the glazing system. The second method developed at the University of Ulster UK used an indium based alloy with a melting of less than C as the sealant enabling the use of all soft coatings and tempered glass (which degrades at high ). A heat transmission of.9 W.m -.K - in the centre-of-glazing area has been achieved experimentally [5]. To further reduce the heat transmission of vacuum glazing the concept of triple vacuum glazing has been presented by a team of Swiss Federal Laboratories for Material Testing and esearch [6]. The mechanical design constrains were investigated and a heat transmission of. W.m -.K - in the centre-of-glazing area using a stainless steel pillar array was predicted. To date no thermo physical behaviour of the entire triple vacuum glazing has been reported. In this work a three-dimensional (3-D) finite volume model was developed to simulate the thermal performance of the entire triple vacuum glazing with the support pillar arrays within the two vacuum gaps incorporated and modeled directly. The circular cross section of the pillar in a fabricated system is replaced by a square cross section pillar of equal area in the model. A graded mesh is used with a high density of nodes in and around the pillar to provide adequate representation of the heat transfer. Using this finite volume model this paper investigated the effects of (i) solder glass and indium edge seals; (ii) edge seal width; (iii) size of triple vacuum glazing; and (iv) frame rebate depth on the thermal performance of triple vacuum glazing. The numerical Copyright 9 by ASME
simulation results were compared with those calculated using the analytical model. NOMENCLATUE Edge seal Wood insulation not shown A area of test sample (m ) a radius of support pillar (m) h surface heat transfer coefficient (W.m -.K - ) k thermal conductivity (W.m -.K - ) l thickness of glass pane (m) p pillar separation (m) Q heat transfer (W) thermal resistance (m.k.w - ) S pillar separation (m) t time T (ºC) U thermal transmission (W.m -.K - ) X in the m th finite volume Y vector of m th finite volume nodal points Greek letters ε hemispheric emittance of a surface σ Stefan-Boltzmann constant (5.67-8 W.m.K 4 ) Subscripts refer to vacuum gaps and shown in Fig. I I refer to the first second and third glass panes io refer to warm and cold ambient s j k refer to the glass surfaces g glass m glass pane number of the triple vacuum glazing n vacuum gap number p pillar r radiation tot total resistance of triple vacuum glazing Heat conduction through edge seal Edge seal Wood frame Wood frame (a) Warm side T i Cold side T o (b) Heat conduction Surface A through pillars adiative heat flow Not to scale Surface B Glass panes Surface C Fig. (a) Plan view of the triple vacuum glazing in which the frame is not shown; (b) Schematic of heat flow through triple vacuum glazing. The dots within the glass panes represent the grids of the mesh of the finite volume model. Figs. (a) and (b) are not to scale. a / T i h i HEAT TANSFE THOUGH TIPLE VACUUM GLAZING The schematic diagrams of triple vacuum glazing plan view and heat transfer mechanisms through the triple vacuum glazing are shown in Figs. (a) and (b). Both diagrams have different scales. The heat transfer through the glazing includes ). heat flow from the warm side ambient to the glass pane at the warm side involving radiation and convection; ). radiation between the two glass surfaces within the two vacuum gaps; 3). conduction through the two pillar arrays and two edge seals within the two vacuum gaps; 4). Heat flow from the cold side glass pane to the cold side ambient by convection and radiation. Vacuum gap Pillar Pillar Vacuum gap p Glass pane I Glass pane Glass pane I T h o o p t I t t I T i p p T o i I r r o ANALYTICAL MODEL APPOACH (a) (b) The heat transmission across a 5 mm by 5 mm cell with a pillar in the centre at the centre-of-glazing area was investigated. Due to symmetry a quarter of the cell is shown Fig. Cross section and plan view of a quarter of a unit cell (a) and thermal network of the unit cell at the central glazing area (b). Copyright 9 by ASME
to represent the thermal network of a full cell whose schematic diagram is shown in Fig. (a) in which a quarter of the pillar is shown at the corner of the square cell. The thermal network is shown in Fig. (b). The thermal resistance of each glass pane due to heat conduction is given by equation : lm g l = () k A g where l m is thickness of glass pane m where m () A is the area of the unit cell of the glazing; k g is the thermal conductivity of glass. The thermal resistance due to radiative heat flow between the two glass surfaces within the two vacuum gaps is given by: 3 r n = ( + )(4σ Tjk A) () ε ε j k where ε j and ε k are the hemispheric emittance of the glass surfaces j and k opposite each other within the vacuum gaps and ; σ is the Stefan-Boltzmann constant and T jk is the mean glass surface in the cavity in Kelvin. The thermal resistance due to heat conduction through the support pillars in vacuum gap n ( or ) is determined by equation 3 [4]: p n = (3) k a g where a is the radius of the cylindrical pillar. The thermal resistance of the middle glass pane is divided into two equal thermal resistances the total thermal resistance between the outdoor and indoor glass pane surfaces is determined by equation 4: tot = p p ( g + r ) + + r p p ( g I + g I + r ) + r The thermal resistances i and o at the indoor and outdoor glazing surfaces are the inverse of surface the heat transfer coefficients i.e. i =/h i and o =/h o. The total heat transmission at the centre of glazing area is then given by [6]: U = (5) + + i tot o (4) The heat flow through the entire triple vacuum glazing is the sum of heat flow across the centre-of-glazing area and the heat flow through the edge area including the heat conduction through the edge seal. NUMEICAL MODELLING APPOACH The finite volume model employed leads to a sparse well structured system of equations that can be efficiently solved. The basic equations used to develop the finite volume model can be found in standard reference on the subject [7]. The governing equation used in the finite volume model is the heat diffusion equation as shown in equation 6 which is derived from consideration of Fourier s Law and the control volume (differential) surface areas: T T T T + + = x y z α t where T is the of each finite volume of glass or support pillars t is the time parameter α = k /( ρc) is the thermal diffusivity k is the thermal conductivity ρ is the density and c is the specific heat capacity. Assuming the view factor between the two internal surfaces within the vacuum gap to be the radiative heat transfer between the two surfaces is determined by equation 7: 3 Qr = ( + ) (4σT j k A)( Tj Tk ) (7) ε ε j k The boundary conditions (EN ISO 77- [8]) are listed in table (6) Table Boundary conditions of the triple vacuum glazing Ambient Outdoor ºC Indoor ºC Glazing surface heat transfer coefficient External surface Internal surface 5 W.m -.K - 7.7 W.m -.K - The developed finite volume model implementation enables a large number of volumes to be employed to represent the vacuum glazing geometry and allows the direct representation of the small pillars. The equation bandwidth using the finite volume method is smaller than that obtained for the finite element method using 3 node brick elements and consequently requires fewer numerical operations and less CPU time to obtain a satisfactory solution. The parameters of the simulated triple vacuum glazings are listed in Table. Due to symmetry conditions only one quarter of the triple vacuum glazing was simulated to represent the whole glazing system under the boundary conditions of the EN ISO 77- [8] experimental test. In the 3-D finite volume model the support pillars were Copyright 9 by ASME
.3 6 mm.3 mm. mm 5 mm mm 83.7 W.m-.K- W.m-.K- W.m-.K-.7 W.m-.K- X Y Outdoor side 67 6.8.4 8 3..4 7 4.. 87.4 3.6.4 7.4 8.6 In order to test the accuracy of simulations with specified mesh number the thermal performance of a unit cell with width p = 5 mm and with a single pillar in the centre was simulated using a mesh of 85 85 3 nodes. The 3 nodes (x diretion) were distributed in a graded mesh through the glazing thickness of.4 mm. The thermal conductance of this simulated unit with a pillar in the centre was in good agreement with the analytical result calculated by equations to 5 with a.8% variation which is comparable with the result (%) of Manz et al. [6]. With the same number of nodes (85 85) and distribution in the y and z directions on the glazing surface and nodes on the x direction the thermal transmission of double vacuum glazing at the centre-of-glazing was calculated to be.36 W.m-.K-. This is exactly same as the results of Griffiths et al. [] and comparable to the result of Wilson et al []. This level of agreement indicates that the density of nodes is sufficient to simulate the realistic level of heat flow with a high accuracy. The 3-D isotherms of the triple vacuum glazing are illustrated in Fig. 3 which shows the gradient across the three glass panes due to the high thermal resistance of the two vacuum gaps. The isotherms of the Z 5.5. Indoor side..5.5. 6. 9.9 8 9. 9 y.5 7.4 z VALUE.4.5 m by.5 m 4 mm PAAMETE Vacuum glazing Thickness dimensions width length Glass pane thickness Emittance Four surfaces Edge seal width Pillar diameter Pillar height Pillar separation Frame rebate depth Thermal Indium conductivity Glass & solder glass Pillar Wood frame 3. 3. 3.6 Table Parameters of modeled triple vacuum glazing. three glass surfaces A B and C as defined in Fig. are shown in Figs. 4 (a) (b) and (c). Figs. 3 and 4(a) show that the mean surface at the central glazing area is 7.4 C the lowest at the edge area is 7.4 C the difference between the centre and edge areas is C. The mean of the entire warm glass surface A is 5. C. Fig. 4(b) shows that the surface at the surface B of the middle glass pane is more uniform than surface A. The highest of 6.6 C is located at the edge area the mean of the entire glass surface B is C. Fig. 4(c) shows that the highest of C is located at the edge area of surface C the lowest of.3 C is located at the central area. The difference between the centre and the edge areas of surface C is 5.9 C the mean of the entire surface C is.9 C. The difference between the indoor glass pane and the middle glass panes is 9. C; that between the middle glass pane and the outdoor glass panes is 5.3 C; that between the indoor glass pane and the outdoor glass pane is 4.3 C. The thermal transmission of the entire glazing and the central glazing area are.65 W.m-.K- and.6 W.m.K- respectively. Due to the significant influence of heat conduction through the edge seal the thermal transmission of the entire glazing is approximately two times larger than that at the central glazing area. The thermal transmission at the central glazing area of the triple vacuum glazing with a pillar separation of 5 mm is similar to the result of Manz et al. [6]. integrated and modeled into the complete system for ease of computation in the simulation. The cylindrical pillars employed in fabricated systems were replaced by the same number of cubical pillars with the same areas of cross section since both pillar shapes conduct similar amounts of heat under the same boundary conditions [9]. The length of the square base of each cubical pillar is π a where a is the radius of the equivalent cylindrical pillar. A graded mesh is used with a high density of nodes in and around each pillar to provide adequate representation of the heat transfer. 8...5.4.8 x. 8. 7.4 6.8 4.9 4. 3.6 3..4.8..5 9.9 9. 8.6 8. 7.4 6.8 4.9 4. 3.6 3. Fig. 3 Isotherms of triple vacuum glazing with boundary conditions and configuration parameters shown in Tables and. Copyright 9 by ASME
y (m) y (m) y (m)..5...5...5. 9..3..5.4 3.5 3. 8.6 9.7.6 5. 3.9 4. 5..5 4.4 3.3 3.6.8 4.7.7.9.9 5. 4.3 3.9 9.4 Isotherms of indoor glass surface 4.7.8 3. 3.5.4. 6.9 9. 6.6 7.3 5.4 5...5.3..5..5 z (m) (a) Middle glass surface 5.9 6. 6.6..5..5 z (m).8.6.4. (b) Isotherms of outdoor surface.3.6.8.7. 3..5 3.9 5.4. 5...5..5 z (m) 7.7 7.3 6.9 6.6 5.4 5. 4.7 4.3 3.9 3.5 3..8.4..6.3.9.5. 9.7 9.4 9. 8.6 6.7 6.7 6.6 6.6 6. 6. 6. 5.9 5.9 6.6 5. 5. 4.7 4.4 4. 3.9 3.6 3.3 3..8.5..9.7.4..8.6.3. (c) Fig. 4 Isotherms of three glass surfaces A (a) B (b) and C (c) of the triple vacuum glazing. INFLUENCE OF VACUUM EDGE SEAL MATEIALS AND SEAL WIDTH The thermal performance of a.5 m by.5 m triple vacuum glazing with various widths (3 mm 6 mm mm) of indium and solder glass edge seal were simulated using the boundary conditions of EN ISO 77- () listed in Table and the results are listed in Table 3. All other configuration parameters are shown in Table except frame rebate depth. The thermal transmissions of the triple vacuum glazing without and with a mm frame rebate depth are compared in Table 3. Table 3 Heat transmission of the complete.5 m by.5 m triple vacuum glazing with the indium and solder glass edge seals. Edge seal widt h (mm) Indium sealant total glazing U-value (W.m -.K - ) Solder glass sealant total glazing U- value (W.m -.K - ) U-value deviation due to Indium and solder glass edge seal (%) Frame rebate depth (mm) 3.77.6.76.59.5.37 6.86.65.85.64.63.48.96.7.95.7.75.6 It can be seen from Table 3 that with no frame rebate the thermal transmission of the triple vacuum glazing with an indium edge seal width of 3 mm is.5% larger than that with a solder glass edge seal width of 3 mm and.37% larger for a glazing with a mm frame rebate and edge seal width of 3 mm i.e. the frame reduced the influence of indium and solder glass edge seal by.5%. With no frame rebate the thermal performance of the triple vacuum glazing with a mm wide indium edge seal is.75% larger than that with a mm wide solder glass edge seal i.e. the difference in thermal transmission due to indium and solder glass edge seal is larger than that with a smaller edge seal width. However the deviation of the thermal transmission due to using indium and solder glass edge seals is less than %. Table 3 also shows that for indium edge sealant increasing the edge seal width from 3 mm to mm increases the thermal transmission of the triple vacuum glazing by 4.7% when the frame rebate is mm and by 8.3% with a frame rebate depth of mm. For a solder glass edge seal increasing the edge seal width from 3 mm to mm increases the thermal transmission of the triple vacuum glazing by 5% when the frame rebate is mm and by.3% with a frame rebate depth of mm. The rate of increase in thermal transmission with increasing the edge Copyright 9 by ASME
seal width is approximately the same when using indium or solder glass edge seals. INFLUENCE OF FAME EBATE DEPTH Thermal performance of the triple vacuum glazing with various frame rebate depths was simulated and the results are shown in Fig. 5. Increasing the frame rebate depth from to 5 mm increased the mean of the indoor glass pane by.8 C the outdoor glass pane decreased by.4 C the middle glass pane increased by less than. C and the thermal transmission of the entire glazing reduced from.86 W.m -.K - to.58 W.m -.K - by 3.9%. Increasing the frame rebate depth significantly reduces the thermal transmission by reducing the heat conduction through the edge seal. U-value (W.m -.K - )..8.6.4. Temperature of indoor glass pane U-value of total glazing Temperature of middle glass pane Temperature of outdoor glass pane 4 6 8 4 6 Frame rebate depth (mm) Fig. 5 Mean s of three glass sheets and U-values of the entire triple vacuum glazing. The configuration parameters are listed in Table except frame rebate depth. INFLUENCE OF GLAZING SIZE ON THE THEMAL PEFOMANCE OF TIPLE VACUUM GLAZING Thermal performance of m by m and.5 m by.5 m triple vacuum glazings were simulated and the results are presented in Fig. 6. All parameters of both glazing systems are listed in Table except dimensions. The thermal transmission of the.5 m by.5 m and m by m triple vacuum glazing are.65 W.m -.K - and.49 W.m -.K - respectively. It can be seen that the mean s of the indoor and middle glass panes of the m by m glazing are larger than those of the.5 m by.5 m glazing. The mean of the outdoor glass pane of the m by m glazing is lower than that of the.5 m by.5 m glazing since less heat transfers from the indoor glass pane of the m by m glazing to the outdoor glass pane than that of.5 8 4 6 - Glass pane ( o C ) m by.5 m glazing. The thermal transmission of m by m triple vacuum glazing is less than that of the.5 m by.5 m triple vacuum glazing by 4.6% this is due to the larger ratio of heat conduction through the edge seal to that of the entire glazing area for the.5 m by.5 m glazing compared to the m by m triple vacuum glazing. Temperature ( o C) & U-value (W.m -.K - ) 8 6 4 8 6 4.5m by.5m m by m Outdoor Middle Indoor U-value of glazing Glass pane Fig. 6 Glass pane mean s and the heat transmission of the.5 m by.5 m and m by m triple vacuum glazings. The configuration parameters are listed in Table except dimensions. CONCLUSIONS The thermal performance of the triple vacuum glazing was simulated using a finite volume model. The results show that although the thermal conductivity of solder glass ( W.m -.K - ) and indium (83.7 W.m -.K - ) are very different the increase in heat transmission of triple vacuum glazing with configuration parameters shown in Table resulting from the use of an indium edge seal compared to a solder glass edge seal was.37%.48% and.6% for 3 mm 6 mm and mm edge seal widths respectively with a mm frame rebate. With no frame rebate this difference is.5%.63% and.75% therefore the difference in thermal transmission resulting from the use of indium or solder glass as sealant is very small. The wider the edge seal the greater the difference will be however the frame can reduce these differences. For an indium edge seal increasing the edge seal width from 3 mm to mm increases the thermal transmission of the triple vacuum glazing by 4.4% with no frame rebate and by 9.6% with a frame rebate depth of mm. For a solder glass edge seal increasing the edge seal width from 3 mm to mm increases the thermal transmission of the triple vacuum glazing by 4.% with no frame rebate and by 9.4% with a Copyright 9 by ASME
frame rebate depth of mm. The thermal transmission of.5 m by.5 m triple vacuum glazing is 3.% greater than that of m by m triple vacuum glazing this is due to the larger ratio of the edge seal area compared to glazing area for smaller glazing sizes thereby increasing the influence of heat flow through the edge seal area compared to the entire glazing area for the.5 m by.5 m glazing compared to the m by m glazing. Increasing the rebate depth in a solid wood frame from to mm decreased the heat transmission of the glazing by 4.4%. ACKNOWLEDGMENTS The authors acknowledge the support from the Charles Parson Energy esearch Awards through the National Development 7-3 of the Department of Communications Marine and Natural esources Dublin Ireland. The international travel grant from oyal Academy of Engineering is appreciated. EFEENCES [] S. J. obinson and.e. Collins Evacuated windowstheory and practice ISES Solar World Congress International Solar Energy Society Kobe Japan (989). [] P. W. Griffiths Di M. Leo P. Cartwright P.C. Eames P. Yianoulis G. Leftheriotis and B. Norton Fabrication of evacuated glazing at low. Solar Energy 63 43-49 (998). [3] T. J. Hyde P. W. Griffiths P.C. Eames and B. Norton Development of a novel low edge seal for evacuated glazing. In Proc. World enewable Energy Congress VI Brighton U.K. pp. 7-74 (). [4]. E. Collins T. M. Simko Current status of the sciences and technology of vacuum glazing Solar Energy 6 89-3 (998). [5] Y. Fang P.C. Eames B. Norton T.J. Hyde Experimental validation of a numerical model for heat transfer in evacuated glazing Solar Energy 8 564-577 (6). [6] H. Manz S. Brunner L. Wullschleger Triple vacuum glazing: Heat transfer and basic mechanical constraints Solar Energy 8 63-64 (6). [7] S. S. ao The finite element method in Engineering Fourth ed. Elsevier Butterworth Heinemann (5). [8] EN ISO 77-. Thermal performance of windows doors and shutters Calculation of thermal transmittance Part : Simplified method. European Committee for Standardization CEN Brussels (). [9] J. P. Holman Heat Transfer (SI Metric Edition) McGraw-Hill (989). [] C. F. Wilson T.M. Simko and.e.collins Heat conduction through the support pillars in vacuum glazing. Solar Energy 63 (6) 393 46 (998). Copyright 9 by ASME