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EFFECT OF GLASS THICKNESS ON THE THERMAL

PERFORMANCE OF EVACUATED GLAZING

Yueping Fang*, Philip C. Eames*, Brian Nortonº and Trevor J. Hyde*

* Centre for Sustainable Technologies, School of the Built Environment,

University of Ulster, Newtownabbey, BT37 0QB, N. Ireland

º Dublin Institute of Technology, Aungier Street, Dublin 2, Ireland

Abstract

Flat evacuated glazing consists of two plane glass panes separated by a narrow internal evacuated

space. Separation of the space is maintained by an array of support pillars typically 0.32mm in

diameter and 0.12mm high arranged on a regular square grid with an inter-pillar separation of up to

40mm. A detailed 3-dimensional finite volume model has been employed to determine the variation

of thermal performance of an evacuated glazing as a function of glass pane thickness. It was

predicted that for an evacuated glazing with dimension of less than 1m by 1m, reducing glass pane

thickness gave improved thermal performance. For evacuated glazings with dimensions larger than

1m by 1m, the opposite was predicted.

Keywords: Evacuated glazing; thermal performance; glass thickness; finite volume model.

1. Introduction

Evacuated glazing as shown in Fig. 1 comprises two contiguously sealed glass panes between

which the presence of a vacuum of less than 0.1Pa effectively eliminates gaseous conduction and

convection. Transparent low-emittance coating on one or both interior surfaces of the glass panes

reduces the radiative heat transfer to a low level. Conductive heat transfer occurs through both the

support pillars and the vacuum glazing edge seal. The successful fabrication of

an evacuated glazing with low

gas conduction was first

reported by Robinson and

Collins (1989) using a solder

glass edge seal formed at a

temperature of about 400

0C

.

The drawback of a solder

glass edge seal is that its

melting temperature is too

high to be used in conjunction

with many soft low-emittance

coatings and with tempered

glass. Subsequently Griffiths

et al (1998) have fabricated

successfully an evacuated

glazing with a metal edge seal

with a melting point well below 200

0C

. Many of low-emittance coatings can tolerate this

temperature and the use of tempered glass is made possible.

2. Finite Volume Model Solution to Heat Transfer in an Evacuated Glazing

Low

emittance

coatings

Glass

panes

Metal

edge seal

Separating

pillars

Not to scale

Fig. 1 Cut-away schematic diagram of an evacuated glazing with a metal

edge seal.

A three dimensional finite volume heat transfer model of an evacuated glazing has been established.

The geometry of the

system modelled is

illustrated

schematically in Fig.

2. Due to symmetry

considerations, only

a quarter section of a

full evacuated

glazing was

simulated.

The evacuated

glazing modelled

consisted of two

6mm thick glass

panes with a narrow

0.12mm internal

evacuated space. The

separation of the

panes under

atmospheric pressure

was maintained by

an array of small support pillars of diameter 0.32mm spaced at up to 40mm separation on a regular

square grid. A finite volume model was used to simulate the thermal performance of this evacuated

glazing with different glass thicknesses. The temperatures of the warm indoor and cold outdoor air

were set at 21.1

0C

and -17.8

0C

respectively. The convective heat transfer coefficients from the

cold outdoor ambient and warm indoor side external glazing surfaces were set to be

0

h

=

30

Wm K

2 1

and

i

h

= 8.3

Wm K

2 1

respectively to correspond to the measurement standards for

winter conditions (ASTM, 1991). The emittances of the low-emittance coatings on both interior

glass surfaces within the vacuum gap were set to be 0.2, the edge seal width was 3mm and the

height of frame insulation was 20mm.

3. Thermal Performance of an Evacuated Glazing with Different Glass Pane Thicknesses

3.1 Finite volume model

analysis

The thickness of the glass

panes is a determinant of

pillar separation for an

evacuated glazing system

(Simko, 1996). In

simulations, the glass sheet

thickness was varied but the

pillar separation was

maintained at a constant

distance. Tensile stress

within the glazing was not

considered. The predicted

thermal performance

variations with changing

Glass

panes

Illustrative

support

pillars

Vacuum

space

0.12

Outdoor

condition

Indoor

condition

Toutdoor

ho

Tindoor

hi

Not to scale

Metal edge

seal

Frame

Length unit: mm

250

250

Low emittance

coatings

Edge

seal

Fig. 2 A quarter section of a 500mm by 500mm evacuated glazing was modelled using the

finite volume model: (a) full view, and (b) cross sectional view (on a different scale). Two

glass panes joined at their edges by a metal edge seal are separated by an array of support

pillars, 0.12mm high with a diameter of 0.32mm spaced at 40mm. The emittances of the

interior vacuum surfaces were 0.2.

15

15.5

16

16.5

17

17.5

18

3 4 5 6

Thickness of glass panes (mm)

Temperature (°C)

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

C,U-value (WK

-1m-2 )

Centre glass C-value

Total system C-value

Total system U-value

Internal average

surface temperature

Fig. 3 Thermal performance variation due to changing thickness of glass

sheets. The emittances of coatings on the both interior vacuum gap surfaces

were 0.2. The dimensions of the evacuated glazing were 500mm by 500mm

with pillars of 0.32mm diameter separated at 40mm. The vacuum space was

0.12mm wide and the frame insulation height was 20mm.

thickness of glass sheet are shown in Fig. 3.

It can be seen from Fig. 3 that the U-value of the evacuated glazing increases with increasing

thickness of glass panes when using a constant pillar separation. The average internal glass surface

temperature decreases and the heat transfer rate through the full glazing system increases.

3.2 Analytic model analysis

The heat flow per unit length of edge due to edge conduction is given by (Simko, 1996):

021

0//

)(

hkthktww

TTkt

Q

i

i

edge

(1)

The heat transfer resistance and U-value through one pillar is given by (Wilson et al., 1998):

Ah

ak

AhAk t

Ah

Rg

radgi

airtoair 0

1

11

2)

12

(

1

(2)

)/(1

,ARU airtoairpillarone

(3)

The rate of heat transfer per unit

length of edge calculated by

equation (1) corresponding to

different glass sheet thickness t is

presented in Fig. 4. The heat

transfer rate through a single pillar

calculated using equations (2) and

(3) is also shown in Fig. 4. The heat

transfer rate through the glazing

system and the U-value of the

glazing system calculated by the

finite volume model is included.

It can be seen from Fig. 4 that with

increasing glass sheet thickness, the

air to air U-value through a single

pillar decreases, this is because the

increased glass thickness increases

the thermal resistance above the

two pillar ends. The heat transfer

per unit length of the edge due to

edge conduction increases with

increasing glass sheet thickness.

This rate of increase is larger than

the rate of decrease of heat transfer through the pillar array, which leads to the heat transfer rate

through the whole glazing increasing, thus the U-value of the whole glazing system increases. A

schematic diagram for heat transfer in an evacuated glazing is shown in Fig. 5.

1

1.2

1.4

1.6

1.8

2

2.2

2.4

3 4 5 6

Thickness of glass sheets (mm)

Heat transfer (W)

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

U-valu e (W K

-1m-2 )

Heat trans fer through total

glazing s ystem

Heat trans fer per

unit length of edge

U-value of total

glazing s ystem

U-value through

one pillar

Fig. 4. The effect of glass sheet thickness on the thermal performance

of an evacuated glazing calculated by both an analytic and a finite

volume model. In the 500mm by 500mm evacuated glazing modelled,

two glass panes with low-e coatings with emittance of 0.2 were sealed

by a 3mm wide metal edge seal, and supported by a pillar array with

diameter of 0.32mm separated at 40mm. The height of the frame

insulation was 20mm.

It can be concluded that if the pillar separation is kept constant for the evacuated glazing system

modelled, the thicker the glass sheet, the larger the resultant U-value of the glazing system.

Consideration of the tensile stress for thinner glass sheets would indicate the pillar separation

should decrease. 4. Predicted Surface

Temperature of Evacuated

Glazing

The predicted isotherms on the

outdoor ambient surfaces of

0.5m by 0.5m evacuated glazing

with 6mm and 4mm thick glass

panes were calculated by the

finite volume model and shown

in Fig.6 (a) and (b). The

isotherms on the zoomed

corners are shown in Fig.7 (a)

and (b) respectively. The

evacuated space was sealed by

3mm wide metal edge seal and

supported by a pillar array with

diameter of 0.32mm separated

at 40mm. The emittances of

low-e coating on both interior

glass surfaces were 0.2. No

frame insulation was used.

Comparing Fig.6 (a) and Fig.6 (b), it can be seen that the centre-of-glass area with average

temperature –16.5C in Fg.6 (a) is less than that in Fig.6 (b). For the outdoor side, the average

ambient surface temperature of evacuated glazing with 6mm glass panes is higher than that of

evacuated glazing with 4mm glass panes. Similarly indoor side average surface temperature of the

evacuated glazing with 6mm glass panes is lower than that with 4mm glass panes. The heat transfer

due to edge conduction through the evacuated glazing with 4mm glass panes is less that that

through the evacuated glazing with 6mm glass panes.

This result is identical with the analytic analysis by Simko, 1996. The analytic model presented that

the temperature of each glass pane approaches the centre-of-glass value exponentially with a

characteristic distance of:

hktl/

(4)

Where h is the heat transfer coefficient being considered (i.e.

i

hh ,

0

). In the evacuated glazing

modelled under ASTM winter condition, k =1

Wm K

1 1

, for glazing with

1

t

of 6mm, for the external

side,

o

l1

= 14.1mm; for the internal side,

i

l1

= 26.9mm. For glazing with a thickness

2

t

of 4mm, for

the cold side,

o

l2

= 11.5mm; for the warm side,

i

l2

= 22.0mm. The areas in Fig.6 (a) from the glass

edge to the centre-of-glass with a characteristic distance

o

l1

are larger than those in Fig.6 (b) with

distance

o

l2

. The average surface temperature of the full glazing in Fig.6 (a) is therefore greater

than that in Fig.6 (b). Similarly the average temperature of the indoor side surface of evacuated

glazing with 4mm thick glass panes is higher than that with 6mm thick glass panes. The heat

0.12mm

Frame insulation

w

Conductive heat transfer

through pillars

Cold air Warm air

o

h

i

h

500mm Radiative heat transfer

between surfaces

Conductive heat transfer

per unit length of edge

Metal edge

Fig. 5. Schematic diagram of heat transfer in an evacuated glazing

transfer due to edge conduction effect through an evacuated glazing with 4mm thick glass panes is

less than that for an evacuated glazing with 6mm glass panes.

It can be seen from Fig.6 and Fig.7 that the surface temperatures above the first row of pillars are

higher than that of the central pillars. This is because heat transfer through the edge seal increases

the temperature of edge area on the external glass surface. In Fig.7 (a) the temperatures above the

second row of pillars are affected clearly by the heat conduction through the edge seal, as

conduction in this evacuated glazing fabricated from 6mm thick glass panes is larger than that in the

evacuated glazing fabricated with 4mm glass panes. Comparing Fig. 7 (a) and (b), it can be seen

that the heat transfer through the pillars in an evacuated glazing with 4mm thick glass panes is

larger than that with 6mm thick glass panes. This is identical with the analytic results discussed in

the above sections.

5. Effect of Frame Insulation Height on the Variation of the Thermal Performance of an

Evacuated Glazing with Different Thickness of Glass Panes

Frame insulation reduces

heat transfer through the

edge seal and so affects the

heat transfer coefficient of

an evacuated glazing system

fabricated with different

thickness glass panes. The

heat transfer within an

evacuated glazing system

with different edge

insulation heights was

simulated with the finite

volume model, and the

predicted heat transfer

coefficients are presented in

Fig. 8.

From Fig. 8 it can be seen

that the gradients of the

curves decrease with

increasing insulation height,

the gradient variation is now very small. For the glazing system of 500mm by 500mm, when no

insulation present, the heat transfer coefficient increases about 0.30

12 KWm

when the glass pane

thickness increases from 3mm to 6mm. When the insulation is 48mm, the heat transfer coefficient

increases by 0.13

12 KWm

when the glass pane thickness increases from 3mm to 6mm. The

difference in heat transfer coefficient variations between evacuated glazing systems with 48mm and

without any frame insulation is 0.17

12 KWm

. Increasing frame insulation height influences the

rate of increase of heat transfer coefficient with increasing glass sheet thickness in an evacuated

glazing unit is small. This is because the heat flow per unit length of edge due to edge conduction

mainly depends on the heat conduction within the glass sheets, although the U-value of the overall

system decreases significantly with increasing frame insulation height. This can be seen from

equation (1).

6. Variations in the Thermal Performance of an Evacuated Glazing with Different Thickness

of Glass Pane due to Different Edge Seal Widths

0.5

1

1.5

2

3 4 5 6

Thick ness of glass pane (m m)

He at tran sfer coefficien t of gla zing (WK

-1m-2 )

No insulation

Insulation

height=6mm

Insulation

height=14mm

Insulation

height=20mm

Insulation

height=48mm

Fig. 8. The variations of heat transfer coefficient of an evacuated glazing with

different thickness glass panes and frame insulation heights. The glazing size

simulated was 500mm by 500mm. The two glass panes coated with low-e

coatings on the both interior glass surfaces were sealed by a 3mm wide metal

edge seal and were supported by an array of pillars with a diameter of 0.32mm

and a separation of 40mm.

The effect of the edge seal width on the thermal performance of an evacuated glazing with different

thickness glass panes was simulated using the finite volume model. The predicted results are

presented in Fig. 9.

It can be seen that decreasing the

edge seal width has less effect on

the rate of increase of the heat

transfer coefficient with increasing

thickness of glass pane. For the

evacuated glazing with edge seal

width of 2mm, with increasing glass

pane thickness from 3mm to 6mm,

the heat transfer coefficient

increases 0.28

12 KWm

. For

evacuated glazing with edge seal

width of 12mm, the heat transfer

coefficient increases 0.36

12 KWm

.

The edge seal width affects the rate

of increasing of heat transfer

coefficient with increasing glass

pane thickness, this effect is very

small. This is because the heat flow

per unit edge mainly depends on the heat conduction within the glass sheets, which is determined

mainly by the thickness of glass sheets and edge insulation height of evacuated glazing.

7. Effect of Glazing Size on the Thermal Performance of an Evacuated Glazing with Different

Thickness of Glass Pane

The ratio of the heat transfer through

the edge seal to the heat transfer

through the whole evacuated glazing

is different for evacuated glazings of

different dimensions. When the edge

seal width and the frame insulation

height are constant, the larger the

glazing dimensions, the smaller the

ratio of the heat transfer through the

edge seal to the heat transfer through

the centre region and thus the whole

evacuated glazing. Evacuated

glazings with dimensions of 0.3m by

0.3m, 0.5m by 0.5m, 1m by 1m, 1.5m

by 1.5m and 2m by 2m were

simulated using the finite volume

model. The results are presented in

Fig. 10.

It can be seen from Fig. 10 that the rate of increase of heat transfer coefficient with increasing glass

pane thickness decreases when the dimension of the evacuated glazing increases. When the glazing

size is 2m by 2m, the variation of heat transfer coefficient is minimal. It can be concluded that if the

dimension is less than 2m by 2m, the thinner the glass panes, the smaller the heat transfer

1

1.2

1.4

1.6

1.8

2

3 4 5 6

Thick ness of glass pane (m m)

He at tra nsfer c oeffi cien t of g lazin g (WK

-1m-2 )

Edge se al: 2mm

Edge se al: 4mm

Edge se al: 3mm

Edge se al: 6mm

Edge se al: 12mm

Fig. 9. Predicted heat transfer coefficient of an evacuated glazing as a

function of the thickness of glass panes and edge seal width. The

simulated glazing size was 500mm by 500mm and comprised two

glass panes with low-e coatings of emittance 0.2 on both interior

surfaces of the glass with an array of 0.32mm diameter pillars

separated at 40mm. The frame insulation height was 6mm.

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

3 4 5 6

Thick ness of glas s pane (mm )

Heat tran sfer co ef fici ent of gl azi ng (Wm

-2K-1)

Glazin g size : 0.3m

by 0.3m

Glazin g size : 0.5m

by 0.5m

Glazin g size : 1m by

1m

Glazin g size : 1.5m

by 1.5m

Glazin g size : 2m by

2m

Fig. 10. The effect of different glass thickness on the thermal

performance of evacuated glazings with various dimensions. The

array of pillars with 0.32mm diameter and 40mm separation

supported the glass sheets with low-e coatings with 0.2 emittance.

The edge seal width was 3mm. The frame insulation height was

6mm.

coefficient will be; if the glazing size is greater than 2m by 2m, the thicker the glass pane, the

smaller the heat transfer coefficient will be. In this section when the glass thickness changes, the

pillar separation and pillar radius are kept constant, i.e. the stress is not considered.

8. Optimal Glass Thickness for an Evacuated Glazing

In practical evacuated glazing design, the stress within the glazing must be considered. The pillar

separation, pillar radius and glass thickness should be determined from the following four

restrictions (Collins and Simko, 1998):

that conical indentation fractures do not occur;

compressive stresses in pillars are less than a set given value, which is determined by the pillar

material; for pillars of stainless steel material this value is 1.3GPa;

maximum external tensile stress above pillars is less than 4MPa;

thermal conductance of the pillar array is less than a given value. The minimal value of

conductance can be determined by equation (5) (Collins and Robinson, 1991) with the greatest

pillar separation and smallest pillar radius that satisfies the three stress related design criteria

above.

C k a p

pillar array glass,/22

(5)

The design process for pillar

separation, pillar radius and minimal

conductance of pillar array is

illustrated in Fig. 11.

Evacuated glazings with different

dimensions of 0.3m by 0.3m, 0.5m by

0.5m and 1m by 1m were simulated.

Using the four restrictions (Collins

and Simko, 1998) (i.e. the stress in

the evacuated glazing being

considered), for 3mm, 4mm, 5mm

and 6mm thick glass panes, the values

of pillar separation, pillar radius and

minimal conductance of pillar array

were determined and are listed in

Table 1. By the finite volume model,

the thermal performances of these

glazing systems were analysed and

the results are illustrated in Fig. 12.

It can be seen that for the three

systems selected, the 3mm thick glass pane is the optimal thickness for the 0.3m by 0.3m and 0.5m

by 0.5m systems. For systems of these dimensions, increasing the glass thickness leads to the heat

transfer coefficient of the evacuated glazing system increasing. When the evacuated glazing size is

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

2.1

2.3

2.5

3 4 5 6

Glass thickness (m m)

Heat tra nsfer coeffi cient (Wm

-2K-1)

0.3m by 0.3m pane

0.5m by 0.5m pane

1m by 1m pane

Fig. 12 The predicted thermal performance of an evacuated glazing

with the values of pillar separation and pillar radius specified in

Table 1. For all of the systems in this diagram, the emittances of

low-e glass coatings on both interior surfaces were 0.16, the frame

insulation width is 6mm and the edge seal width was 12mm.

Glass pane thickness

(mm)

Pillar radius

(mm)

Pillar separation

(mm)

Minimal conductance of pillar

array (

Wm K

2 1

)

3

0.10

20

0.50

4

0.13

25

0.40

5

0.15

30

0.34

6

0.16

35

0.30

Table 1. Pillar radius, pillar separation and minimal conductance of pillar array commensurate to different glass pane

thickness. The above values were determined using the four restrictions specified by Collins and Simko, 1998.

1m by 1m or greater, increasing glass thickness leads to a decrease in the heat transfer coefficient.

The ratio of the heat transfer through the edge seal to the heat transfer through the whole glazing

system determines the optimal glass thickness for each glazing size. The optimal glass thickness of

those systems simulated with dimension equal to or larger than 1m by 1m is 6mm.

Comparing Fig. 10 and Fig. 12, it can be seen that after considering the stress, i.e. when glass pane

thickness changes, the pillar separation and radius change according to the four design restrictions,

the critical dimension of evacuated glazing reduces from 2m by 2m to 1m by 1m. When dimension

of evacuated glazing is less than this critical dimension, with increasing the glass pane thickness,

the U-value of an evacuated glazing increases; when the dimensions of an evacuated glazing is

larger than this critical value, with increasing glass pane thickness, the U-value of an evacuated

glazing decreases.

9. Conclusions

In general, for a standard glazing system, the thicker the glass sheets are, the smaller the U-value of

the system will be, i.e. the thermal performance of the glazing will be better. For evacuated glazing

with dimensions of less than about 1m by 1m, the opposite effect was observed if the pillar size and

pillar separation were designed according to the four restrictions detailed by Collins and Simko,

1998. Increasing the glass sheet thickness leads to a decrease in the heat transfer through a single

pillar, this is due to the thermal resistance of the glass sheet above the two pillar ends increasing.

However increasing the glass sheet thickness leads to an increase in the heat transfer per unit length

of the edge due to edge conduction. The rate of this increase is larger than the rate of decrease of

heat transfer through the pillar array. This leads to an increase in the total heat transfer and thus U-

value through the whole glazing system.

When the glazing dimension equals to or is greater than 1m by 1m, the ratio of the heat transfer

through the edge seal to the heat transfer through the overall glazing reduces. The rate of increase in

the heat transfer per unit length of edge is less than the rate of decrease in heat transfer through the

glass central area with increasing glass pane thickness. If the evacuated glazing size equals to or is

greater than 1m by 1m, the thicker the glass pane, the better the thermal performance of the

evacuated glazing will be.

An optimal glass thickness exists for evacuated glazing systems of a given size. For the simulation

undertaken it was found that if the glazing dimension is less than 1m by 1m, the thinner the glass

thickness, the better the thermal performance will be. If the glazing size equals to or is greater than

1m by 1m, the thicker the glass sheets, the better the thermal performance will be. Increasing the

frame insulation height or decreasing the edge seal width decreases the magnitude of the variation

of heat transfer coefficient resulting from changing thickness of glass panes. This is due to the heat

flow resulting from edge seal conduction decreasing.

Nomenclature

Symbol Definition Unit

a

Pillar radius, m

A Area of model, or of unit cell, over which heat transfer

process occurs,

m2

h Heat transfer coefficient at the external surface of

the glass sheets,

Wm K

2 1

U Thermal transfer coefficient,

Wm K

2 1

k Thermal conductivity,

Wm K

1 1

Q Heat flow, W

R Thermal resistance, KW

1

t Thickness of glass sheet, m

T Temperature, K

w Height of frame insulation, m

C Thermal conductance,

Wm K

2 1

p Pillar separation, m

l Characteristic distance from the glass edge to the central m

glass area whose temperature is approximately uniform.

Subscripts

i,o Refer to internal and external glass surfaces

References

ASTM (1991) Standard procedures for determining the steady state thermal

transmittance of fenestration systems, ASTM Standard E 1423-91. In 1994

Annual Book of ASTM Standard 04.07. American Society of Testing and

Materials, pp.1160-1165.

Collins R.E. and Simko T.M. (1998) Current status of the science and technology of

vacuum glazing. Solar Energy 62, 189-213.

Collins R.E. and Robinson S.J. (1991) Evacuated glazing. Solar Energy 47, 27-38.

Griffiths P.W., Norton B., Eames P.C., and Lo S.N.G. (1996) Detailed Simulation of

Heat Transfer Across Evacuated Glazing, Building Research Information 24,

141-147.

Griffiths P.W., Leo M.Di, Cartwright P., Eames P.C. , Yianoulis P., Leftheriotis G

and Norton B. (1998) Fabrication of Evacuated Glazing at Low Temperature,

Solar Energy 63, 243-249.

Robinson S.J. and Collins R.E. (1989) Evacuated window theory and practice. In

ISES Solar World Congress, Internal Solar Energy Society, Kobe, Japan.

Simko T.M., (1996) Heat transfer process and stresses in vacuum glazing. Ph.D.

thesis, University of Sydney.

Wilson C.F., Simko T.M., and Collins R.E., (1998) Heat Conduction Through The

Support Pillars in Vacuum Glazing, Solar Energy 63, 393-406.

y (m)

z (m)

0.05 0.1 0.15 0.2 0.25

0.05

0.1

0.15

0.2 temperature

-8.0

-8.5

-9.0

-9.5

-10.0

-10.5

-11.0

-11.5

-12.0

-12.5

-13.0

-13.5

-14.0

-14.5

-15.0

-15.5

-16.0

-16.5

oC

( a )

y (m)

z (m)

0.05 0.1 0.15 0.2 0.25

0.05

0.1

0.15

0.2 temperature

-8.0

-8.5

-9.0

-9.5

-10.0

-10.5

-11.0

-11.5

-12.0

-12.5

-13.0

-13.5

-14.0

-14.5

-15.0

-15.5

-16.0

-16.5

oC

( b )

Fig. 6 The predicted isotherms on the glass surface of a 0.5m by 0.5m evacuated glazing fabricated

from 6mm (a) and 4mm (b) thick glass panes with low-e coatings of 0.2 emittance on the two

interior surfaces. The evacuated space was sealed by 3mm wide metal edge seal and supported by a

pillar array with a diameter of 0.32mm separated at 40mm.

y (m)

z (m)

0.05 0.1 0.15 0.2

0.05

0.1

0.15 temperature

-16.0

-16.1

-16.1

-16.2

-16.3

-16.4

-16.4

-16.5

-16.6

-16.6

-16.7

-16.8

-16.9

-16.9

-17.0

oC

(a)

y (m)

z (m)

0.05 0.1 0.15 0.2

0.05

0.1

0.15

temperature

-16.0

-16.1

-16.1

-16.2

-16.3

-16.4

-16.4

-16.5

-16.6

-16.6

-16.7

-16.8

-16.9

-16.9

-17.0

oC

(b)

Fig. 7 The predicted isotherms on the enlarged corner region of the 0.5m by 0.5m evacuated glazing

with 6mm (a) and 4mm (b) thick glass panes. Other parameters are the same as those in Fig.6.

( a ) ( b )

( c ) ( b )

Fig. 11 The design process for the pillar array in evacuated glazing according to the four restrictions

discussed in the section 11. The diagram (a) for evacuated glazing with 3mm glass panes, (b) with

4mm glass panes, (c) with 5mm glass panes and (d) with 6mm glass panes.

0

10

20

30

40

50

60

70

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Pillar radius (mm)

Pillar separation (mm)

3mm glass

Compressive stress

in pillars < 1.3GPa

Max external

tensile stress

above

pillars<4MPa

Conductance of pillar

array<0.5Wm-2K-1

Conical

indentation

fractures

do not

occur

Design

point

0

10

20

30

40

50

60

70

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Pillar radius (mm)

Pillar separation (mm)

Conical

indentation

fractures do

not occur

Compressive

stress in

pillars<1.3GPa

Max.external

tensile stress

above

pillars<4MPa

Conductance of pillar

array<0.4Wm-2K-1

Design

point

4mm glass

0

10

20

30

40

50

60

70

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Pillar radius (m m)

Pillar separation (mm)

Max.external tensile

stress above

pillars<4MPa

Compressive stress

in pillar<1.3GPa

Conical

indentation

fractures do

not occur

Conductance of pillar

array<0.34Wm-2K-1

Design

point

5mm glass

0

10

20

30

40

50

60

70

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Pillar radius (mm)

Pillar separation (mm)

Max.external

tensile stress

above pillars<4MPa

Compressive

stress in

pillar<1.3GPa

Conductance of pillar

array<0.3Wm-2K-1

Conical

indentation

fractures do

not occur

6mm glass

Design

point