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Glass Struct. Eng. (2023) 8:19–39
https://doi.org/10.1007/s40940-022-00172-2
RESEARCH PAPER
Measurement of heat flow through vacuum insulating glass
part 2: measurement area separated from glass sheets
with buffer plates
Cenk Kocer ·Antti Aronen ·Richard Collins ·
Osamu Asano ·Yumi Ogi s o
Received: 1 February 2021 / Accepted: 29 March 2022 / Published online: 18 July 2022
© The Author(s) 2022
Abstract This is the second of two papers concern-
ing errors in the measurement of the thermal insulat-
ing properties of Vacuum Insulating Glass (VIG) due
to non-uniformities in the heat flow due to the sup-
port pillars. Part 1 deals with the situation where the
measurement area is in direct thermal contact with
the glass sheets. This paper discusses how the non-
uniformities and associated measurement errors can
be reduced using thermally insulating buffer plates on
each side of the specimen. A single parameter is devel-
oped that characterises the maximum error for mea-
surement areas of all sizes. Values of this parameter
are given for all practically relevant designs of the VIG
and properties of the buffer plates. Methods are devel-
oped for selecting measurement conditions that lead to
acceptable tradeoffs between reducing the errors asso-
ciated with non-uniformities in the heat flow and errors
due to heat flow through the edges of the specimen.
Keywords Vacuum insulating glass ·Vacuum
glazing ·Measurement ·Thermal insulation ·Support
pillars ·Buffer plates
C. Kocer (B)·A. Aronen ·R. Collins
School of Physics, A28, University of Sydney, Sydney,
NSW 2006, Australia
e-mail: cenk.kocer@sydney.edu.au
O. Asano ·Y. O g i s o
Nippon Sheet Glass Co., Ltd., 6 Anesaki-Kaigan, Ichihara, Chiba
299-0107, Japan
List of symbols
AArea (m2)
DDistance (m)
dDiameter (m)
HHeight of pillar (m)
hHeat transfer coefficient (W m−2K−1)
kThermal conductivity (W m−1K−1)
nInteger (–)
QHeat flow (W)
RThermal resistance (m2KW
−1)
rPillar radius (m)
sSeparation (m)
TTemperature (K or °C)
tGlass thickness (m)
U Unit cell
UU-Value (W m−2K−1)
wDimension of measuring area (m)
xPosition coordinate (m)
Greek letters
δFraction (–)
Change (–)
εEmittance (–)
λSeparation of pillars (m)
ζSpecific resistance of one pillar (K W−1)
σStefan Boltzmann constant (K W−2K−4)
123
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20 C. Kocer et al.
Subscripts
CCold
eExternal
gGlass
iInternal
HHot
mMean
pPillars
rRadiation
vVacuum
1, 2, 3, 4 Identifying surfaces of glass sheets
1 Introduction
Vacuum Insulating Glass (VIG) consists of two sheets
of glass that are hermetically sealed together around
the edges, with a thin evacuated internal space (Collins
et al. 1995). A square array of small support pillars
separated by λpmaintains the separation of the glass
sheets under the forces due to atmospheric pressure.
The localised heat flow through the pillars results in
non-uniformities in the heat flux, defined as the heat
flow per unit area, over the surfaces of the VIG.
This is the second of two papers discussing the mea-
surement of the thermal insulation properties of VIG
specimens. The first paper (Part 1) considers configura-
tions in which the measuring area of the apparatus is in
direct thermal contact with the glass sheets of the VIG.
In this situation, the non-uniformities in the heat flux
can be quite large, leading to large errors in the esti-
mates of the thermal insulating properties of the spec-
imen. This paper (Part 2) discusses configurations in
which the spatial non-uniformities in the heat flux over
the measurement area are reduced by inserting slabs of
material, referred to as buffer plates, between the glass
sheets and the measurement area. This is the approach
taken in a recent Standard (International Organisation
for Standardization 2018).
Methods are developed for estimating the maximum
possible errors for measurement areas of any size and
all practically relevant VIG design parameters. In addi-
tion to reducing the non-uniformities in the heat flow
through the pillars, the buffer plates increase the size
of the peripheral region of the VIG over which heat
flow through the edge seal can contribute significantly
to the measured heat flow. Achieving acceptably small
measurement errors associated with these two compet-
ing effects imposes limitations on the parameters of the
buffer plates and the size of the specimen.
2 Heat transfer processes in VIGs
The following relationships, discussed in Part 1, are
relevant to the analysis in this paper. A unit cell of the
pillar array is defined as a square area of dimensions
λp×λp, with sides oriented parallel to the rows of
pillars. For glass sheets with average temperatures TC
and TH, the magnitude of the heat flow through a single
highly conducting support pillar is:
Qonepi llar 2kgrp(TH−TC),(1)
where rpis the radius of the pillar and kgis the thermal
conductivity of the glass.
The thermal conductance of the pillar array hp,is
(Wilson et al. 1998):
hp2kgrp/λ2
p.(2)
For a VIG with glass sheets having mean tempera-
ture Tmand individual hemispherical emittances εhot
and εcold (at temperatures Thot and Tcold ), the thermal
conductance hrassociated with radiative heat transport
through the evacuated space is (Zhang et al. 1997):
hr4εσ T3
m,(3)
where σis the Stefan–Boltzmann constant (5.67 ×10–8
Wm
−2K−4), and εis the effective emittance of the two
surfaces, given by:
1/ε [1/εhot]+[1/εcold ]−1.(4)
The total thermal conductance between the glass
sheets of the VIG, hv, can be written:
hvhp+hr.(5)
In a practical VIG installation, the thermal conduc-
tances associated with heat flow between the surround-
ing external hot and internal cold environments to the
respective surfaces of the glass sheets are heand hi.The
overall heat transfer coefficient, hH−C, (also referred
to as the U-value of the glazing) associated with heat
123
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Measurement of heat flow through vacuum insulating glass 21
flow through the specimen between the environments
on the hot and cold sides is:
1/hH−C1/U1/he+1/hv+1/hi.(6)
In these papers, U-values are calculated using val-
ues of heand hiof 23 W m−2K−1and 8.3 W m−2
K−1, respectively (International Organisation for Stan-
dardization 1994). Here the glass contribution is not
included since the conductance of the panes is quite
high compared to the other contributions and therefore
has a negligible effect on the final U-value.
The thermal resistance R(having units m2KW
−1)
associated with individual or combined physical heat
transfer processes is the inverse of the relevant thermal
conductance:
R1/h.(7)
In this paper, the buffer plates on both sides of the
VIG are assumed to be identical with thickness tband
thermal conductivity kb. For such buffer plates, the heat
transfer coefficients heand hiin Eq. (6) are replaced
by the heat transfer coefficient of the buffer plate hb:
hehihbkb/tb.(8)
The respective thermal resistances Rband Rvasso-
ciated with the heat flow through unit area of the buffer
plates and between the glass sheets are, respectively:
Rb1/hbtb/kb,(9)
Rv1/hv.(10)
3 Measurement configuration
3.1 Principle of the measurement method
The guarded measurement configuration described in
Part 1 is also used in the procedures discussed in this
paper for the measurement of the thermal insulation
properties of VIG remote from the edge seal. As shown
in Fig. 1, two measurements are made in which the
external surfaces of the measured assembly are placed
in good thermal contact with isothermal plates at tem-
peratures THand TC.
Measurement A gives the combined thermal resis-
tance of the VIG specimen and the two buffer plates in
series:
RARv+2Rb.(11)
Measurement B gives the thermal resistance of the
two buffer plates:
RB2Rb.(12)
The thermal resistance of the VIG is obtained by dif-
ference (International Organisation for Standardization
2018):
RvRA−RB.(13)
Although not immediately obvious, there is an
intrinsic error in Eq. (13) because the heat flow through
the buffer plates in Measurement A is non-uniform,
whereas in Measurement B the heat flow is uniform.
Numerical modelling procedures discussed in Sect. 4
show that the associated error in Rvis small provided
that:
RvRb.(14)
As discussed in Sect. 6, the restriction in Eq. (14)
does not impose a significant practical limitation on the
method.
3.2 Errors associated with different types
of measuring instrument
These two papers discuss measurements made with
instruments having a square detection area with sides
parallel to the rows of pillars. Figure 7of Part 1 shows
that the maximum and minimum measured heat flows
through such areas are always in two specific positions:
when the centre of the measurement area is directly
above a support pillar, and when the centre of the area
mid-way between 4 pillars. The size of the area deter-
mines which of these two positions has the maximum
heat flow and which has the minimum heat flow.
As discussed in Part 1, large area measurements of
the thermal insulating properties of VIGs can be made
123
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22 C. Kocer et al.
Fig. 1 Schematic diagrams
of the two measurement
configurations for
determining the thermal
insulating properties of VIG
with buffer plates
with two different types of instruments—the guarded
hot plate apparatus and the heat flow meter. In the
guarded hot plate apparatus, the heat flux is continuous
between the measuring area and the VIG specimen, as
assumed in the analysis in this paper. In contrast, in
the heat flow meter the heat flow is determined using
a heat flux transducer that is in direct contact with the
specimen. When this type of instrument is used to mea-
sure a specimen with non-uniform heat flux such as a
VIG, there are significant discontinuities in the spa-
tial distribution of the heat flux across this transducer.
This results in a reduction in the magnitude of the non-
uniformities in the heat flux, and the associated errors
compared with a guarded hot plate instrument. Exam-
ples of this reduction are given in Part 1 for a measure-
ment without buffer plates.
The practical significance of this result is that the
analysis presented in this paper may significantly over-
estimate the measurement errors that could occur when
a heat flow meter is used. The extent to which the spatial
non-uniformities in the heat flux are reduced depends
on the detailed design of the heat flux transducer. In
the absence of publically available information about
the transducer design in commercial instruments, this
currently cannot be modelled with confidence.
Quite independently of the analysis in this paper,
and as discussed in Part 1, it is possible experimen-
tally to obtain an upper limit for the magnitude of the
measurement errors that could occur in any specific
measurement situation with both types of measuring
instrument. This can be done by using the instrument
to measure the heat flow at the two extreme positions
—with the centre of the measuring area above a pillar,
and mid-way between 4 pillars.
Tabl e 1 Modelling parameters
Pillar separation λp5, 10, 20, 30, 40, 50, 60, 80,
100 mm
Glass thickness tg3, 5, 7, 10 mm
Buffer plate resistance Rb0.01, 0.03, 0.1, 0.2 m2KW
−1
Buffer plate thickness tb0, 1, 5, 10, 20 mm
4 Modelling methods
4.1 Finite element modelling
Part 1 describes the finite element model used to deter-
mine the spatial distribution of the heat flux over a unit
cell of the pillar array in a VIG for which the external
surfaces of the glass sheets are isothermal. As shown in
Fig. 2a, the unit cell is modelled in the same way here,
with the addition of the two buffer plates between the
external surfaces of the glass sheets and the isothermal
surfaces.
This system was modelled for all combinations of
the parameters given in Table 1. The cases with tb0
correspond to no buffer plates.
The parameters of the system modelled are the same
as those given at the beginning of Sect. 6 of Part 1. The
pillar is 0.5 mm in diameter and 0.2 mm high and made
of material with thermal conductivity of 20 W m−1
K−1. The temperatures of the hot and cold isothermal
surfaces are 17.5 °C and 2.5 °C.
As in Part 1, the finite element modelling data pre-
sented here are for heat flow due to the pillars only,
although radiative heat flow can be included in the
model if desired. Section 6.6 shows how the effects
of radiation are included analytically when estimating
the measurement errors.
123
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Measurement of heat flow through vacuum insulating glass 23
Fig. 2 Finite element model
for aa single unit cell of the
pillar array with buffer
plates, and bone quarter of
the VIG including the edge
seal, with buffer plates
Edge effects are analysed using the finite element
model by building up an array of individual unit cells
with a surrounding edge seal. One quarter of the rect-
angular VIG is modelled with adiabatic boundary con-
ditions over the planes of symmetry (Fig. 2b). The edge
seal is 6 mm wide with the same height of the support
pillars and has thermal conductivity kg. The pillar array
is positioned so that the rows of pillars are equidistant
from the adjacent planes of symmetry in the full struc-
ture. The buffer plates extend well beyond the edge seal
to simulate practical measurement configurations.
4.2 Analytic model of heat flow in the vicinity
of an edge seal
The analytic model described here provides a useful
way of quantitatively evaluating how various system
parameters influence the way in which edge effects
contribute to the measured heat flow. This modelling
approach, illustrated in Fig. 3, is based on previously
described methods (Simko et al. 1995).
The heat flow through the evacuated space due to
radiation and the pillar array is simulated by the thermal
conductance hv(or its inverse, the thermal resistance
Rv) of the space between the glass sheets. As with the
123
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24 C. Kocer et al.
Fig. 3 Analytic model for
estimating the effect of the
edge seal
finite element model, the glass sheets of the VIG are
plane slabs of thickness tgand thermal conductivity kg.
However, in the analytic model the temperature of each
glass sheet is assumed to be uniform through the thick-
ness and depend only on the distance xfrom the inner
extremity of the edge seal. We write the temperature of
the hot glass sheet as Tg(x). The heat flow through the
buffer plates is simulated by a thermal conductance hb
(or its inverse, a thermal resistance Rb). This is equiv-
alent to assuming that the heat flow through the buffer
plates is perpendicular to the plane of the VIG.
Remote from the edge seal, the total heat flow
through unit area of the assembly Qmeas,sample can be
determined using the thermal resistances:
Qmeas,sample (TH−TC)/(Rv+2Rb).(15)
In this region, the temperature differences across the
buffer plates Tb,largex and between the glass sheets
Tv,largex are, respectively:
Tb,largex (TH−TC)×[Rb/(Rv+2Rb)],(16)
Tv,largex (TH−TC)×[Rv/(Rv+2Rb)].(17)
It is convenient to write the temperature of the edge
seal as (Simko et al. 1995):
Tedge (TH+TC)/2.(18)
The analysis involves calculating heat flow through
an elemental piece of each glass sheet of length dx
perpendicular to the edge, and unit width parallel to
the edge, as shown in Fig. 3. Such energy flow can
occur from the contacting buffer plate, between the
glass sheets, and along the glass sheet. Under steady
state conditions, the sum of these heat flows is zero.
As has been previously shown (Simko et al. 1995),
this analysis generates two coupled second order dif-
ferential equations involving the temperatures of each
glass sheet. In general, these equations cannot be sepa-
rated and must be solved numerically. However, in the
symmetric case considered here, the equations decou-
ple, and can be solved analytically. For the hot glass
123
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Measurement of heat flow through vacuum insulating glass 25
sheet, the equation is:
d2Tg(x)
dx2hb+2hv
kgtgTg(x)−Tedge.(19)
This equation can be solved exactly:
Tg(x)Tedge +Tv,largex /2exp(−x/L),(20)
where the characteristic length Lof the exponential is
given by:
Lkgtg/(hb+2hv).(21)
The temperature difference across the buffer plate
can then be written:
Tb(x)Tb,largex +Tv,largex/2exp(−x/L).
(22)
We consider a square measuring area of side length w
in the plane of the hot isothermal surface, oriented with
its nearest edge parallel to the VIG edge seal and located
a distance Dfrom the inner extremity of this seal, as
shown in Fig. 3. The amount of heat that flows from
this area through the buffer plate due to the specimen
and edge seal is:
Qmeas,specimen+edge whb∫D+w
DTb(x)dx.(23)
Integration of this equation gives:
Qmeas,specim en+edge
whbwTb,largex +LTv,largex/2exp(−D/L).(24)
In Eq. (24), the exponential term from the upper limit
of integration is omitted because it is negligible com-
pared with the term from the lower limit in all practical
situations.
When the measurement area is a large distance from
the edge, the measured heat flow has negligible contri-
bution from the edge, and can be written:
Qmeas,specim en w2hbTb,largex w2hvTv,largex.(25)
The additional heat flow through the measuring area
due to the presence of the edge seal is therefore:
Qmeas,edge whbLTv,largex/2exp(−D/L).
(26)
Combining Eqs. (25) and (26), the additional heat
flow through the measuring area due to the edge seal
can be written as a proportion of the heat flow through
the measuring area remote from the edges:
Qmeas,edge/Qmeas,speci men hbL/2whvexp(−D/L).(27)
The heat flow through the measuring area due to
the edge seal results in an error hvin the measured
value of the thermal conductance hvof the VIG. To
determine this error, Eq. (15) is rewritten in terms of the
heat transfer coefficients in the measurement system:
1/hv(TH−TC)/Qmeas,specim en−2/hb.(28)
Taking differentials and using Eqs. (21) and (27), to
first order we obtain the proportional error hv/hvin
the measured thermal conductance of the specimen:
hv/hv(L/w)[1+(hb/2hv)]exp(−D/L).(29)
To the same level of approximation, the consequen-
tial proportional error U/Uin the U-value of the
specimen is:
U/U(U/hv)(L/w)[1+(hb/2hv)]exp(−D/L).
(30)
Figure 4shows the proportional error hv/hvin the
measured value of the thermal conductance for several
VIG designs and buffer plate resistances. These data
were obtained from Eq. (29) for a single edge and a
square measuring area of dimension 100 mm.
The dependence of hv/hvon system parameters
is dominated by the exponential term in Eq. (29). For
parameters of practical relevance, Eq. (21) shows that
the characteristic length Lin the exponent of this term
is approximately proportional to √Rband √tg.The
hv/hvvalues in Fig. 4at distances DLare there-
fore larger for higher thermal resistance buffer plates
(Lines A, B and C in Fig. 4) and for VIGs with thicker
glass sheets (Line E in Fig. 4). For all cases of interest,
Eqs. (21) and (29) show that the thermal conductance
123
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26 C. Kocer et al.
Fig. 4 Proportional error
hv/hvdue to a single
edge in the measured value
of the thermal conductance
of VIGs having different
thermal conductances hv
and glass thicknesses tgand
buffer plates of different
resistances Rb, as a function
of the distance Dof a
100 mm square measuring
area from the edge seal
0
1
2
3
4
5
6
7
8
9
10
0306090120150
h
v
/h
v
(%)
Distance from edge seal (mm)
A [ 5, 0 .6, 0.2]
B [5, 0.6, 0.1]
C [5, 0.6, 0.03]
D [3, 0.6, 0.1]
E [8, 0.6, 0.1]
F [5, 1.0, 0.1]
Parameter:
[tg(mm), hv(W m -2 K-1), Rb(m2KW
-1)]
Δ
hvof the VIG specimen has only a small effect on hv.
For specified values of other parameters, hv/hvis
therefore approximately inversely proportional to hv
(Lines B and F in Fig. 4). The quantitative extent to
which the specimen and buffer plate properties affect
the choice of measurement parameters is discussed in
Sect. 6.
4.3 Validation of the analytic model
The validation of the unit cell finite element model is
discussed in Part 1. In this Section we discuss the val-
idation of the analytic model.
Figure 5compares analytic (lines) and experimental
(points) U-value data for a specific VIG specimen as a
function of the closest distance of the measuring area
from an edge seal. The specimen is 395 mm square
with 5 mm thick glass sheets, has a 6 mm wide edge
seal, and contains 0.45 mm diameter pillars separated
by 30 mm. One internal glass surface has a coating with
hemispherical emittance 0.04.
The experimental U-value data in Fig. 5are obtained
from measurements of heat flow at different distances
from an edge of a VIG specimen and applying Eq. (6)
with values of external heat transfer coefficients given
in Sect. 2. The measurements were made with buffer
plates of different resistances using an EKO HC-
074/630 heat flow meter with a square measuring area
of side 100 mm. The centre of the measuring area was
positioned along an axis of symmetry of the specimen.
The horizontal axis in this figure is the distance of the
edge of the measuring area from the inner extremity of
the nearest edge seal. As shown in Sect. 6below, the
position of a measuring area of this size relative to the
pillars has a negligible effect on the measured U-value
for a VIG specimen with these parameters and buffer
plates of resistance and thickness given in Fig. 5.
The analytic data in Fig. 5are calculated using
Eq. (30) and include the effect of all four edges of
the VIG specimen, estimated by adding the separate
contributions from each edge, as shown to be valid by
the finite element model. The U-value of the specimen
used to obtain the analytic data is 0.61 W m−2K−1,
as measured using lower resistance buffer plates at dis-
tances from the edge seal where the contribution from
the edge seal is calculated to be negligible. To within
the accuracy of the nominal design parameters of the
experimental specimen, this U-value is consistent with
that calculated using Eqs. (2), (3) and (6). These results
provide strong validation of the analytic model.
4.4 Comparison of finite element and analytic
modelling of edge effects
The analytic and finite element modelling approaches
provide independent estimates of the temperature of the
external surface of each glass sheet in the vicinity of
the edge seal. These estimates can be compared using
123
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Measurement of heat flow through vacuum insulating glass 27
Fig. 5 Calculated (lines)
and experimental (points)
COG U-values
(Centre-Of-Glazing) for a
VIG specimen measured
with buffer plates of
resistance 0.26 m2KW
−1
and 0.103 m2KW
−1,and
thickness 10 mm and 6 mm,
respectively, as a function of
distance of the measuring
area from an edge seal
0.6
0.65
0.7
0.75
0.8
050100150
Measured U-value (W m
-2
K
-1
)
Distance from edge seal (mm)
COGU-valueofVIGunit=0.61Wm
-2
K
-1
g
=5mm
Parameter: R
b
(m
2
KW
-1
)
0.26 (ex periment)
0.26 (mo del)
0. 103 (ex per ime nt)
0.103 (mo del)
λ
finite element modelling data along a plane of symme-
try of the one quarter model shown in Fig. 2b. Except
in regions very close to the edge seal, the temperature
of the external glass surface along this line is very close
to the local average temperature through the thickness
of the glass sheets.
For all practically relevant conditions, the tempera-
ture of the glass sheets determined by the finite element
model decreases approximately exponentially with dis-
tance from the edge seal, consistent with the analytic
model. Figure 6compares the characteristic length
of this exponential dependence as obtained with both
modelling approaches for buffer plates of two different
resistances and a VIG with 3 mm and 5 mm thick glass
sheets and thermal conductance of 0.46 W m−2K−1.
Similar results are obtained for all relevant buffer plate
resistances and VIG properties.
For thin buffer plates, the characteristic lengths
obtained with the two modelling approaches agree rea-
sonably well. For thicker buffer plates, the character-
istic lengths obtained with the finite element model
increase, reflecting the greater significance of off-
normal heat flow through these plates. The increases in
the characteristic length are relatively small for buffer
plates of thickness up to about the analytic estimate
of the characteristic length, which is between about
10 mm and 20 mm for typical VIG designs and mea-
surement parameters. For the remainder of this paper,
the buffer plates are specified to be sufficiently thin that
the edge effects are well-characterised by the analytic
model:
tbkgtg/(hb+2hv).(31)
Clearly, the analytic model only accounts for the heat
flow contribution that is due to a single edge. However,
the contribution from all four edges of the VIG unit
should be taken into account.
The edge contribution from all 4 edges of the VIG
unit to the measured heat flow was analysed using the
finite element models. In all practically relevant cases,
the combined heat flow from the 4 edges of the VIG
unit, as measured by a heat flux sensor, is approximately
equal to the sum of the individual heat flows due to
each edge. For example, if the measurement area is
equidistant from the 4 edges of a square specimen, the
total contribution from all 4 edges is approximately 4
times the contribution from a single edge.
5 Conditions for tolerably small edge effects
The errors associated with edge effects can, in princi-
ple, be reduced to any level by positioning the measur-
ing area at a sufficiently large distance from the edge. In
practice, however, the size of the VIG specimen limits
this distance. In addition, as shown in Eq. (29), errors
associated with edge effects are greater for smaller
measuring areas. The effect of the edges on the mea-
surement of heat flow can therefore only be quantified
123
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28 C. Kocer et al.
Fig. 6 Characteristic length
of the exponential
dependence of the
temperature of the glass
sheets in the vicinity of the
edge seal of a VIG, as
determined by analytic and
finite element modelling
0
5
10
15
20
25
30
0 10203040
Characteristic distance L(mm)
Buffer plate thickness tb(mm)
5, 0.1 (Analytic)
5, 0.1 (FEM)
3, 0.1 (Analytic)
3, 0.1 (FEM)
5. 0.03 (An alytic)
5, 0.03 (FEM)
3, 0.03 (Analytic)
3, 0.03 (FEM)
h
v
=0.46Wm
-2
K
-1
Parameter:
t
g
(mm), R
b
(m
2
KW
-1
)
in the context of a specific specimen size and mea-
surement area. The analysis in this Section illustrates
how these effects are determined. The VIG specimens
are assumed to have external dimensions of 350 mm ×
500 mm—a size often specified in Standards for testing
highly insulating glazing units (International Organisa-
tion for Standardization 2008). The width of the solder
glass seal is assumed to be 6 mm, so that the dimen-
sions of the evacuated space 338 mm ×488 mm. The
measurement area is assumed to be square, with side
dimension 100 mm—a size commonly used in heat
flow measuring equipment.
In this analysis, the centre of the measurement area
is positioned along the short axis of symmetry of the
specimen. In this configuration, only the two long edges
of the specimen make significant contributions to the
measured heat flow.
For the purposes of characterising the performance
of highly insulating window glazing, a total error in
the measured VIG thermal conductance of up to ~ 5%
is probably acceptable. To allow for errors from other
sources, particularly due to the non-uniformities in the
heat flow through the pillars, the contribution to the
total error from the edge seal should be somewhat less
than this value (~ 2–3%). Obviously, if very high accu-
racy is required, correspondingly smaller errors would
be appropriate.
Figure 7shows analytic modelling data for the pro-
portional contributions hv/hvto the measured VIG
thermal conductance from the two closer edges for sev-
eral specimens and buffer plate resistances. The buffer
plate resistances in these data are chosen to illustrate
limiting values that will be appropriate in practice. For
comparison, Line C (1) in Fig. 7shows data for a single
edge with the same measurement and specimen param-
eters as Line C.
For distances up to ~ 90 mm from the edge seal, the
error in the measured thermal conductance decreases
rapidly, and there is negligible contribution from the
opposite edge seal (Lines C and C(1) in Fig. 7). For
larger distances, the error decreases much less rapidly
with distance as contributions from the second edge
seal become progressively more significant. The total
edge error is least when the measuring area is equidis-
tant from the two edges (119 mm from the edge seal
in these data). For most measurements in which the
edge errors are large enough to be of concern (~ 4%
at 90 mm), relatively limited additional reductions (
factor of 2) are obtained if the measurement area is
more than ~ 90 mm from the edge seal.
The data in Fig. 7illustrate how the maximum resis-
tance of the buffer plates must be less for VIGs with
larger glass thicknesses. For 3 mm thick glass, (Line A
in Fig. 7), a buffer plate resistance of 0.2 m2KW
−1
results in adequately small edge contributions. How-
ever, this resistance leads to unacceptably large errors
for all VIGs with thicker glass (see, for example, Line A
in Fig. 4). Buffer plates of resistance ~ 0.1 m2KW
−1
can be used when measuring VIGs with 4 mm thick
glass sheets (Line B in Fig. 7). For VIGs with glass
thickness 5 mm, buffer plates of resistance 0.03 m2
123
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Measurement of heat flow through vacuum insulating glass 29
Fig. 7 Analytic modelling
data for the proportional
error hv/hvin the thermal
conductance due to heat
flow through both edges of a
VIG specimen for several
VIG and buffer plate
parameters
0
1
2
3
4
5
6
7
8
9
10
30 60 90 120 150
h
v
/h
v
(%)
Distance from edge seal (mm)
A [ 3, 0.86, 0. 2]
B [4, 0.56, 0.1]
C[5,0.43,0.1]
C(1) [one ed ge]
D [5, 0 .4 3, 0 .03]
E [6, 0.33, 0.03]
F [8, 0.33, 0.03]
Parameter:
t
g
(mm), h
v
(W m
2
K
-1
), R
b
(m
2
KW
-1
)
Δ
Fig. 8 Heat flux along the
diagonal of a unit cell for a
pillar separation of 20 mm,
glass sheets of different
thickness, and no buffer
plates
0
50
100
150
200
250
-15 -10 -5 0 5 10 15
Heat flux (W m-2)
Distance from pillar along diagonal of unit cell (mm)
3
5
7
10
Parameter:
Glass thickness (mm)
KW
−1are required (Lines C, D and E in Fig. 8, and
Line B in Fig. 4).
As shown in Sect. 6, non-uniformities in the heat
flow due to the pillars result in a lower limit to the
resistance of the buffer plates for VIGs with large pillar
separations. However, a buffer plate resistance of 0.03
m2KW
−1still results in adequately small errors due
to the edges for quite large glass thickness (Line F in
Fig. 7).
In summary, when measuring the thermal conduc-
tance of most VIGs of dimension 350 mm ×500 mm
using a 100 mm square measuring area, the edge of the
area should be at least 90 mm from the closest edge
seal, and buffer plates with resistance between 0.1 m2
KW
−1and 0.03 m2KW
−1should be used. For 5 mm
thick glass sheets, Eq. (31) specifies that the thickness
of these buffer plates should be 20 mm.
These buffer plate parameters have been adopted
in a recent VIG measurement Standard (International
Organisation for Standardization 2018).
6 Errors in the measurement of centre-of-glazing
heat flow utilising a large area instrument
This Section discusses the magnitude of the largest pos-
sible errors in the measurement of heat flow through a
VIG remote from the edges using a large area instru-
ment. The discussion in Sects. 6.1–6.5 is for heat flow
due to the pillars alone. The effect of radiation is sub-
sequently included in Sect. 6.6.
123
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30 C. Kocer et al.
6.1 Nomenclature for quantities relating to heat flow
due to the pillar array
The non-uniformities in the local heat flux in regions of
the VIG remote from the edge seal are periodic along
the orthogonal rows of pillars, with period equal to the
pillar separation λp. It follows that the heat flow QU
through a unit cell U is independent of the position of
the cell relative to the individual pillars.
This Section defines the nomenclature used for
describing the dependence on position of the heat flow
QMthrough a square measurement area M with sides
of length woriented parallel to the rows of pillars. The
maximum and minimum values of QMare respectively
written QM,max and QM,min.
The area of M is equal to w/λp2unit cells of the
pillar array. We define the accurately characterised heat
flow QMthrough M as:
QMQUw/λp2.(32)
The largest positive and negative departures of the
measured heat flow from the accurately characterised
heat flow are respectively:
QM,max QM,max −QM,(33)
QM,min QM,min −QM.(34)
We write QMas the larger of the magnitudes of
these maximum departures:
QMlarger
QM,max
,
QM,min
.(35)
The following analysis develops a parameter that can
be used to obtain a reasonable estimate of the maximum
proportional error QM/QMin the measured heat flow
due to the pillars through a square area of any size
greater than a unit cell. This ratio is also equal to the
maximum proportional error hp/hpin the measured
thermal conductance of the pillar array:
QM/QMhp/hp.(36)
6.2 Examples of heat flux data for specific VIG
designs and measurement configurations
This Section presents examples of finite element mod-
elling data for the heat flux distribution and the total
heat flow at the isothermal plates due to a single pillar
at the centre of a unit cell of the pillar array (Fig. 3a).
These data are given for several values of the four
parameters that affect the heat flux: glass thickness tg,
buffer plate resistance Rb, buffer plate thickness tband
pillar separation λp.
6.2.1 Heat flux distribution
In order to illustrate the greatest variation, the heat flux
data presented in this Section are plotted along a diag-
onal of a unit cell.
For comparison with subsequent data, the heat flux
data for the case with no buffer plates given in Part
1 are repeated here, and shown in Fig. 8for a pillar
separation of 20 mm.
Figure 9illustrates how the heat flux is affected by
buffer plate resistance and glass thickness. These data
are for 10 mm thick buffer plates and a pillar separation
of 20 mm. Larger values of buffer plate resistance and
glass thickness reduce the absolute and relative spatial
non-uniformities in the heat flux (note suppressed zero
in Fig. 9). More resistive buffer plates also reduce the
overall magnitude of the heat flux due to the larger total
thermal resistance between the hot and cold isothermal
surfaces.
Figure 10 provides examples of how thicker buffer
plates reduce the non-uniformities in the heat flow.
These data are for 3 mm thick glass, a pillar separa-
tion of 40 mm, and buffer plates of resistance 0.1 m2
KW
−1. Figure 11 illustrates how larger pillar sepa-
rations increase the proportional and absolute spatial
variations in the heat flux. Obviously, larger pillar sep-
arations also lead to lower average heat fluxes because
of the greater unit cell area. These data are for 3 mm
thick glass and 10 mm thick buffer plates of resistance
0.03 m2KW
−1.
123
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Measurement of heat flow through vacuum insulating glass 31
Fig. 9 Heat flux along the
diagonal of a unit cell for a
pillar separation of 20 mm,
glass sheets of 3 mm and
7 mm thickness, and a
10 mm thick buffer plate
with different values of
resistance
12
13
14
15
16
17
18
19
-15 -10 -5 0 5 10 15
Heat flux (W m
-2
)
Distance from pillar along diagonal of unit cell (mm)
3mmglass
7mmglass
3mmglass
7mmglass
3mmglass
7mmglass
0.03
0.2
0.1
p=20mm,tb=10mm
Parameter: Rb(m2KW
-1)
λ
Fig. 10 Heat flux along the
diagonal of a unit cell for a
pillar separation of 20 mm,
3 mm thick glass sheets, and
different values of thickness
for a buffer plate of
resistance 0.1 m2KW
−1
2
4
6
8
10
12
-30 -20 -10 0 10 20 30
Heat flux (W m
-2
)
Distance from pillar along diagonal of unit cell (mm)
1
5
10
20
p
=40mm
t
g
=3mm
R
b
=0.1m
2
KW
-1
Parameter: t
b
(mm)
λ
The data in Figs. 8,9,10 and 11 are typical of those
obtained for all practically relevant VIG and measure-
ment parameters.
6.2.2 Total heat flow
The total heat flow for each set of parameters is obtained
by integrating the heat flux data at the isothermal sur-
face over the unit cell. This total heat flow value is used
to calculate the thermal resistance between the hot and
cold isothermal surfaces of the VIG/buffer plate sys-
tem. The glass-to-glass thermal resistance associated
with heat flow through the pillar array is then obtained
by subtracting the combined resistance of the two buffer
plates, as shown in Eq. (13).
These modelling values of pillar array thermal
resistance with buffer plates agree to within ~ 2%
with the value obtained assuming highly conducting,
non-interacting pillars between two semi-infinite glass
plates (Eq. 1). This agreement is observed for all prac-
tically relevant VIG designs and measurement param-
eters, provided that the resistance of the buffer plates
is less than the resistance of the unit cell. This condi-
tion, noted in Eq. (12), does not impose a significant
123
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32 C. Kocer et al.
Fig. 11 Heat flux along the
diagonal of a unit cell for
pillar separations of 20, 30
and40mm,3mmthick
glass sheets, and buffer
plates of thickness 10 mm
and resistance 0.03 m2
KW
−1
0
5
10
15
20
-30 -20 -10 0 10 20 30
Heat flux (W m
-2
)
Distance from pillar along diagonal of unit cell (mm)
20
20 (ave)
30
30 (ave)
40
40 (ave)
t
g
=3mm,R
b
=0.03m
2
KW
-1
,t
b
=10mm
Parameter:
p
(mm)
λ
limitation on the measurement method for two rea-
sons. Firstly, consistent with good experimental prac-
tice, Eq. (14) ensures that the use of Eq. (13) does
not involve calculating the small difference between
two large quantities. Secondly, as shown in the previ-
ous Section, Eq. (14) is satisfied for buffer plates that
achieve tolerably small edge effects for all practical
measurement conditions and VIG design parameters.
In summary, the finite element modelling data show
that the measured thermal resistance of the pillar can
be accurately determined using Eq. (2) and is effec-
tively independent of glass thickness and buffer plate
parameters.
6.3 Parameter for characterising non-uniformities
in the heat flux due to the pillars
The heat flow through a square measurement area of
side wnλpis obviously equal to n2QU, and is inde-
pendent of the position of the area.
It is also clear that the heat flow through an area of
side
w(n+1/
2)λp(37)
is equal to n2+n+1/
4QU. Figure 12a illustrates this
situation for n1, when one corner of the area is
located at a pillar. Of relevance to the discussion in
Sect. 6, it is noted that in this position the centre of
the measuring area is mid-way between a pillar and the
centre of 4 pillars for all values of nin Eq. (37).
Figure 12b and c show a measuring area M with side
1.5λpwith the centre respectively at the mid-point of
4 pillars and directly above a pillar. The measured heat
flow in each case is respectively the largest (QM,max)
and smallest (QM,mi n) that could occur for an area of
this size. This situation applies for all values of nin
Eq. (37), except that the positions of maximum and
minimum heat flow are reversed for even values of n.As
will be shown in Sect. 7, the magnitudes of the relative
departures of the measured heat flow from the average
heat flow through areas of dimension (n+1/
2)λpare
very close to the greatest that could occur for any square
area of dimension (n+δ)λp, where 0 <δ<1. Areas
of dimension (n+1/
2)λptherefore give very close to
the largest positive and negative errors in the measured
heat flow when respectively positioned with their cen-
tres mid-way between a pillar and at the centre of 4
pillars for nodd. The positions are exchanged for n
even.
123
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Measurement of heat flow through vacuum insulating glass 33
Fig. 12 Area of side 1.5λpat positions of aaverage heat flow,
bmaximum heat flow, and cminimum heat flow
The accurately characterised heat flow through an
area having the "worst case" dimension in Eq. (37)is:
QM(n+1/
2)2QU.(38)
The measuring area in Fig. 12b and c can be divided
into 6 separate square areas: a single larger area of
side λpthat is a unit cell (U) of the pillar array, and
5 smaller areas of side λp/2. In both cases, two of the
smaller areas (called Type L areas in this discussion) are
located midway along a line between adjacent pillars.
In Fig. 12a, the three remaining smaller areas (Type C
areas) are centred over individual pillars. In Fig. 12b,
the three remaining smaller areas (Type E areas) are
equidistant from four pillars.
If the heat flow over the unit cell were uniform, the
heat that would pass through each of the smaller areas
would be QU/4. We define the parameter PCfor a Type
C area as the proportional difference between the actual
heat flow through this area and that which would occur
for uniform heat flow:
PC[QC−(QU/4)]/(QU/4).(39)
Equivalent definitions apply for Type L and Type E
areas.
Figure 12c also shows how a unit cell can be parti-
tioned into one Type C area, one Type E area, and two
Type L areas. Thus:
QUQC+2QL+QE.(40)
It follows that:
PC+PE+2PL0.(41)
The heat flux in the vicinity of the pillar is always at
least slightly greater than the average over the unit cell
and decreases with distance from the pillar. In addition,
the Type E area is further from the pillar than the Type L
areas. Thus QC>(QU/4),QL<QC, and QE<QL.
It follows that PCis positive, PEis negative and smaller
in magnitude than PC, and PLis negative and smaller in
magnitude than PE. If the heat flux is nearly uniform,
QC∼
QL∼
QE∼
QU/4, and PC,PLand PEare
all very small. In the limiting case where the heat flux
is highly localised around the pillar, QC∼
QUand
QL∼
QE∼
0, so PC∼
3, and PL∼
PE∼
−1.
The parameters for the 5 small areas in Fig. 12b
and c respectively can be combined to calculate the
largest positive and negative proportional departures
from the accurately characterised heat flow through the
measurement area QM:
QM,max/QM(2PL+3PC)/9,(42)
QM,min/QM(2PL+3PE)/9.(43)
It is straightforward to generalise Eqs. (42) and (43)
for measurement areas M of side wdefined by any
123
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34 C. Kocer et al.
Tabl e 2 Values of the
parameters PC,PLand PE
for the values of tg,λp,Rb
and tbthat apply in Figs. 8,
9,10 and 11
λp(mm) tg(mm) Rb(m2KW
−1)tb(mm) PCPEPL
Figure 820 3 0 0 2.34 −0.926 −0.705
20 5 0 0 1.33 −0.705 −0.332
20 7 0 0 0.694 −0.411 −0.141
20 10 0 0 0.255 −0.141 −0.038
Figure 920 3 0.03 10 0.052 −0.041 −0.005
20 7 0.03 10 0.013 −0.011 −0.001
20 3 0.1 10 0.0198 −0.0159 −0.0019
20 7 0.1 10 0.0048 −0.0042 −0.0003
20 3 0.2 10 0.0105 −0.0084 −0.0010
20 7 0.2 10 0.0022 −0.0022 −0.0002
Figure 10 40 3 0.1 1 0.365 −0.194 −0.086
40 3 0.1 5 0.323 −0.179 −0.072
40 3 0.1 10 0.222 −0.139 −0.042
40 3 0.1 20 0.070 −0.054 −0.008
Figure 11 20 3 0.03 10 0.052 −0.041 −0.005
30 3 0.03 10 0.233 −0.158 −0.038
40 3 0.03 10 0.514 −0.308 −0.103
value of the integer nin Eq. (37):
QM,max/QM(2nP
L+[2n+1
]PC)/(2n+1
)2,
(44)
QM,min/QM(2nP
L+[2n+1
]PE)/(2n+1
)2.
(45)
Although the positions of maximum and minimum
heat flow are exchanged for odd and even values of n,
Eqs. (44) and (45) remain the same.
6.4 Examples of values of the parameters PC,PL
and PE
As noted above, the spatial distribution of the heat flux
due to the support pillars at the isothermal surfaces of
the measurement system is affected by tg,λp,Rband
tb. Table 2gives values of the parameters PC,PLand PE
in terms of these quantities for the examples in Figs. 8,
9,10 and 11.
The relative magnitudes and signs of PC,PEand PL
in these examples are consistent with the above qual-
itative description. In addition, there is a strong quan-
titative correlation between these three quantities. The
y = 0.093x2-0.6119x
y = -0.0465x2-0.194x
-1
-0.8
-0.6
-0.4
-0.2
0
00.511.522.53
PEand PL
PC
PE
PL
PE
PL
Fig. 13 Dependence of PEand PLon PCfor all combinations of
tg,λp,Rband tbin Table 2, including cases with no buffer plates
data points in Fig. 13 show how PEand PLvary with
PCfor all combinations of tg,λp,Rband tbin Table 2,
including cases with no buffer plates.
The lines in Fig. 13 are least square quadratic fits to
the data with the following regression relations:
PL−0.046P2
C−0.194PC,(46)
PE+0.093P2
C−0.612PC.(47)
Substituting these relations into Eqs. (44) and (45),
we obtain:
123
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Measurement of heat flow through vacuum insulating glass 35
0
0.05
0.1
0.15
0.2
0 0.5 1 1.5 2 2.5 3
h
p
/h
p
P
C
n=1 23
5
10
Δ
Fig. 14 Maximum error hp/hpas a function of PCfor different
values of n
QM,max/QM−0.094nP2
C+[1.61n+1
]PC/(2n+1
)2,
(48)
QM,min/QM−
0.094[n+1
]P2
C−[1.61n+0.61]PC/(2n+1
)2.
(49)
In all cases, QM,max is greater than
QM,min
.
Using Eq. (36), the maximum possible proportional
error in the measured heat flow through a VIG due to the
pillars for square areas of side (n+1/
2)λpis therefore:
hp/hp−0.094nP2
C+[1.61n+1
]PC/(2n+1
)2.
(50)
Figure 14 shows this maximum error as a function
of PCfor different values of n.
Obviously, the errors that may occur are larger for
smaller measurement areas (lower values of n). The
data in Fig. 14 show that values of PCslightly less than
0.1 can lead to significant errors with VIG specimens
and measurement equipment for which n1. In order
to cover all possible experimental configurations, the
PCdata presented in the next Section are therefore for
selected sets of parameters of tg,λp,Rband tbthat
give PCvalues above 0.01. PCdata for other values of
these parameters can be obtained by interpolation or
extrapolation.
0.01
0.1
1
10
345678910
Pc
Glass th ickness tg[mm]
No BP
0.01, 1
0.01, 5
0.01, 10
0.03, 5
0.1, 5
0.2, 5
λ
λ
p = 20 mm
Parameters: Rb(m2K W-1), tb(mm)
Fig. 15 Va l u e s o f PCas a function of glass thickness tg,fora
pillar separation λpof 20 mm, different values of buffer plate
resistance Rband thickness tb
0.01
0.1
1
10
345678910
P
c
Glass thi ckness t
g
[mm]
No BP
0.01, 1
0.01, 5
0.01, 10
0.01, 20
0.03, 5
0.03, 10
0.1, 10
λ
λ
p
= 30 mm
Parameters: R
b
(m
2
K W
-1
), t
b
(mm)
Fig. 16 Va l u e s o f PCas a function of glass thickness tg,fora
pillar separation λpof 30 mm, different values of buffer plate
resistance Rband thickness tb
6.5 Values of PCfor a wide range of VIG
and buffer plate parameters
The data points in Figs. 15,16,17,18,19 and 20 are
finite element modelling values of PCas a function of
glass thickness tg, for VIGs with pillar separations of
20, 30, 40, 50, 60 and 80 mm, respectively. The param-
eters for each set of 4 points are the various combi-
nations of buffer plate resistances and thicknesses that
give PCvalues of possible practical relevance. The lines
are smooth fits through the 4 data points for each pair
of parameters. The data are presented on a logarithmic
scale for clarity.
Figures 15,16,17,18,19 and 20 contain sufficient
PCdata to determine the magnitude of maximum pos-
sible measurement errors for all possible practical com-
binations of VIG designs and buffer plate parameters.
Several examples of the use of these data are given in
Sect. 6.7 below.
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
36 C. Kocer et al.
0.01
0.1
1
10
345678910
P
c
Glass th ickness t
g
[mm]
No BP
0.01, 1
0.01, 5
0.01, 10
0.01, 20
0.03, 10
0.1, 10
0.2, 10
λ
λ
p
= 40 mm
Parameters: R
b
(m
2
K W
-1
), t
b
(mm)
Fig. 17 Va l u e s o f PCas a function of glass thickness tg,fora
pillar separation λpof 40 mm, different values of buffer plate
resistance Rband thickness tb
0.01
0.1
1
10
345678910
P
c
Glass th ickness t
g
[mm]
No BP
0.01, 1
0.01, 10
0.01, 20
0.03, 20
0.1, 20
0.2, 20
λ
λ
p
= 50 mm
Paramete rs: R
b
(m
2
K W
-1
), t
b
(mm)
λ
p
= 50 mm
Paramete rs: R
b
(m
2
K W
-1
), t
b
(mm)
λ
p
= 50 mm
Paramete rs: R
b
(m
2
K W
-1
), t
b
(mm)
λ
p
= 50 mm
Paramete rs: R
b
(m
2
K W
-1
), t
b
(mm)
Fig. 18 Va l u e s o f PCas a function of glass thickness tg,fora
pillar separation λpof 50 mm, different values of buffer plate
resistance Rband thickness tb
0.01
0.1
1
10
345678910
P
c
Glass thi ckness t
g
[mm]
No BP
0.01, 1
0.01, 10
0.01, 20
0.03, 20
0.1, 20
0.2, 20
λ
λ
p
= 60 mm
Paramete rs: R
b
(m
2
K W
-1
), t
b
(mm)
Fig. 19 Va l u e s o f PCas a function of glass thickness tg,fora
pillar separation λpof 60 mm, different values of buffer plate
resistance Rband thickness tb
6.6 Including the effect of heat flow due to radiation
As noted in Eq. (5), to a very good approximation radia-
tive heat flow is uniform and unaffected by the heat
flow through the pillars. Radiation therefore does not
0.01
0.1
1
10
345678910
P
c
Glass thi ckness t
g
[mm]
No BP
0.01, 1
0.01, 20
0.03, 1
0.03, 20
0.1, 1
0.1, 20
0.2, 1
0.2, 20
λ
λ
p
= 80 mm
Paramete rs: R
b
(m
2
K W
-1
), t
b
(mm)
Fig. 20 Va l u e s o f PCas a function of glass thickness tg,fora
pillar separation λpof 80 mm, different values of buffer plate
resistance Rband thickness tb
contribute to the error hvin the measured thermal
conductance of the VIG, and we can write:
hvhp.(51)
Using Eq. (50), the maximum proportional error in
the measured VIG thermal conductance can therefore
be written:
hv/hvhp/hv×−0.094nP2
C+[1.61n+1
]PC/(2n+1
)2.
(52)
Thermal performance data for insulating glazing
units are conventionally presented as U-values, as this
is the relevant quantity for assessing performance in
practical installations. Following the same procedure in
the derivation of Eq. (39), the maximum proportional
error U in the measured U-value of the VIG is:
U/U(hv/hv)×(U/hv).(53)
Thus:
U/UUhp/h2
v×−0.094nP2
C+[1.61n+1
]PC/(2n+1
)2.
(54)
6.7 Maximum departures from average of measured
VIG U-value
Table 3presents numerical values of the quantities
involved in the determination of the maximum possible
proportional deviations U/Ufrom the average U-
value, for several specific designs of VIG and selected
123
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Measurement of heat flow through vacuum insulating glass 37
Tabl e 3 Examples of the maximum possible proportional deviation from average U/Uin the measured U-value for several VIG
designs
Case A Case B Case C Case D Case E Case F
VIG parameters
λp(mm) (Fig. 2)202030404040
tg(mm) (Fig. 2)333355
2rp(mm) (Fig. 2) 0.5 0.5 0.5 0.5 0.5 0.5
hp(W m−2K−1)(Eq.2) 1.25 1.25 0.55 0.31 0.31 0.31
Emittance of low E coating 0.03 0.03 0.03 0.03 0.03 0.03
hr(W m−2K−1)(Eq.3) 0.15 0.15 0.15 0.15 0.15 0.15
hv(W m−2K−1)(Eq.5) 1.40 1.40 0.71 0.47 0.47 0.47
U(W m−2K−1)(Eq.6) 1.13 1.13 0.63 0.43 0.43 0.43
hp/hv0.89 0.89 0.78 0.67 0.67 0.67
U/hv0.80 0.80 0.89 0.92 0.92 0.92
Uhp/h2
v0.71 0.71 0.70 0.62 0.62 0.62
Measurement instrument
w(mm) (Fig. 3) 110 110 105 100 100 100
n(Eq. 37)553222
Buffer plate properties
Rb(m2KW
−1) 0.01 0 0.03 0.03 0.03 0.1
tb(mm) (Fig. 2)505555
Measurement analysis
PC(Figs. 15,16,17,18,19,20) 0.35 2.3 0.46 0.82 0.51 0.19
hp/hp(Eq. 50) 0.036 0.15 0.053 0.133 0.084 0.032
hv/hv(Eq. 52) 0.029 0.13 0.041 0.089 0.056 0.021
U/U(Eq. 54) 0.023 0.11 0.037 0.082 0.052 0.020
buffer plate parameters. For each derived quantity, the
relevant equation or data source is given. The dimen-
sions of the square measuring areas are respectively
110, 105 and 100 mm for VIGs with pillar separations
of 20, 30 and 40 mm in order to satisfy the "worst case"
condition in Eq. (37). The different cases in this table
are chosen to illustrate the procedures and tradeoffs
required when selecting measurement parameters for a
wide range of VIG designs.
When measuring a VIG with 3 mm thick glass and
20 mm pillar separation using 5 mm thick buffer plates
of resistance 0.01 m2KW
−1(Case A), the largest
proportional deviations from average U/Uare quite
small (~ 2%). Reducing the buffer plate thickness to
1 mm increases PCto 0.065 (Fig. 16), resulting in a
deviation U/Uof ~ 4%, which may be significant in
some cases.
The deviations U/Uare significant (~ 4%) for
VIGs with 3 mm thick glass and 30 mm pillar sep-
aration using 5 mm thick buffer plates of resistance
0.03 m2KW
−1(Case C). For 40 mm separation and
3 mm thick glass (Case D), the deviations are unac-
ceptably large (~ 8%) with these buffer plates. Even
for 5 mm thick glass with 40 mm separation (Case E),
the deviations for this buffer plate resistance are still
significant (~ 5%). Increasing the buffer plate resis-
tance to 0.1 m2KW
−1reduces the deviation to ~ 2%
(Case F) which is probably acceptable for most mea-
surements. If a smaller maximum deviation is required
a further increase in the resistance would lead to sig-
nificant edge contributions to the measured heat flow.
In such a situation, it would be necessary to use thicker
buffer plates.
123
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38 C. Kocer et al.
For VIGs with pillar separations > 40 mm, the data in
Figs. 18,19 and 20 show that the values of PC, and the
associated maximum deviations from average U/U
in Fig. 14, are significantly larger. In such cases, higher
resistance and thicker buffer plates are needed to reduce
the deviations U/Uto acceptable levels. It may be
necessary to locate the measurement area further than
90 mm from the edge seal in order that the edge contri-
butions to the measured heat flow are tolerably small.
This could necessitate the use of larger VIG specimens
than discussed in Sect. 4.
If no buffer plate is used for a VIG with 20 mm pil-
lar separation (Case B), the maximum error U/Uis
unacceptably large (11%). This error would be approx-
imately halved using a 210 mm square measuring area
(n10 in Eq. 54). However, it is still significant. The
maximum deviations are larger for VIGs with more
widely spaced pillars. This result confirms the conclu-
sion in Part 1 that, in general, measuring the heat flow
through VIGs without using buffer plates will lead to
unacceptably large maximum deviations from the aver-
age measured U-value for measurement areas of "worst
case" size.
Obviously, these limitations on buffer plate param-
eters are less/more stringent for instruments with
larger/smaller measuring areas, and for VIGs with
higher/lower levels of thermal radiation, respectively.
In summary, for VIGs with pillars separated by
20 mm or less, the effect of non-uniformities in the heat
flow associated with the pillar array is quite small for
buffer plates with a resistance of 0.03 m2KW
−1and
thickness 5 mm. However, for glazings with pillars
separated by 30 mm or more, buffer plates of resistance
0.1 m2KW
−1and thickness > 5 mm should be used.
In general, the use of buffer plates with resistance >
0.1 m2KW
−1and thickness > 10 mm requires VIG
specimens of dimension > 300 mm in order that edge
effects are small.
7 Conclusions
The localised heat flow through the support pillars can
cause errors to occur during the measurement of the
thermal insulating properties of VIGs. The associated
non-uniformities in the heat flux at the measurement
apparatus can be significantly reduced with the use
of buffer plates. The thermal resistance of the VIG is
determined experimentally as the difference between
measurements with and without the buffer plates. This
paper analyses the errors that could occur in such mea-
surements when using an instrument such as a guarded
hot plate in which the measurement area is in direct
thermal contact with the buffer plate.
Compared with a guarded hot plate, the heat flux
transducer in a heat flow meter can reduce the non-
uniformities in the measured heat flux. The maximum
possible measurement errors that may occur with a heat
flow meter can therefore be less than those given by the
analysis in this paper.
The errors in the measured heat flow are affected
by 5 parameters: the dimension of the square measure-
ment area w, pillar separation λp, glass thickness tg,
buffer plate resistance Rb, and buffer plate thickness
tb. For all situations of practical importance, the maxi-
mum possible errors occur when the dimension of the
measurement area is w(n+1/
2)λp, where nis an
integer.
Buffer plates with higher thermal resistance cause
effects associated with heat flow through the edge seal
to spread further across the surface of the VIG. The
measurement area must be positioned far enough from
the edge seal to reduce these edge effects to tolerably
small levels. An analytic model is used to determine the
extent to which these edge effects influence the mea-
surement. For square measurement areas of dimension
100 mm and buffer plates with resistance up to 0.1 m2
KW
−1, the errors are likely to be tolerably small for
most practical VIG designs with the measurement area
positioned at least 90 mm from the edge seal.
The maximum possible measurement errors associ-
ated with the heat flow through the pillars for any VIG in
any measurement configuration can be characterised by
a single parameter PC. Values of PCobtained by finite
element modelling are given for all practically likely
combinations of λp,tg,Rband tb. An analytic expres-
sion involving PCis developed that gives the maximum
possible errors for square measurement areas of dimen-
sion (n+1/
2)λp, for all values of n.
Radiative heat flow between the internal surfaces of
the VIG reduces the magnitude of the maximum pos-
sible errors in the measured thermal conductance of
VIGs. A simple analytic expression is given for includ-
ing the effect of radiation on the measurement errors.
For most VIGs with pillar separation up to about
30 mm and 100 mm square measurement areas, accept-
ably small errors are obtained with buffer plates of
resistance up to 0.1 m2KW
−1. Achieving sufficiently
123
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Measurement of heat flow through vacuum insulating glass 39
small errors when measuring VIGs with more widely
spaced pillars may require higher resistance buffer
plates. In such cases, the measurement area should be
positioned at distances > 90 mm from the edge seal. For
very highly insulating specimens or when high accu-
racy measurements are needed, it may be necessary to
use specimens of dimension > 350 mm.
Acknowledgements The authors acknowledge the Sydney
Informatics Hub and the University of Sydney’s high-
performance computing cluster Artemis for providing the high-
performance computing resources that have contributed to the
research results reported within this paper.
Funding Open Access funding enabled and organized by
CAUL and its Member Institutions.
Open Access This article is licensed under a Creative Com-
mons Attribution 4.0 International License, which permits use,
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