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Measurement of heat flow through vacuum insulating glass part 1: measurement area in direct thermal contact with specimen

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Non-uniformities in the heat flow through the support pillars in vacuum insulating glass (VIG) can lead to significant errors in the measurement of the thermal insulating properties of these devices. This paper discusses these errors in instruments for which the measurement area is in direct thermal contact with the glass sheets. The spatial non-uniformities of the heat flow in different VIG designs are modelled using the finite element method. For measuring areas with large dimension compared with the separation of the support pillars, the errors are unacceptably large for all practical designs of VIG when using guarded hot plate instruments. These errors are less for heat flow meter instruments due to the construction of the heat flux transducer.
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Glass Struct. Eng. (2023) 8:3–18
https://doi.org/10.1007/s40940-022-00182-0
RESEARCH PAPER
Measurement of heat flow through vacuum insulating glass
part 1: measurement area in direct thermal contact
with specimen
Cenk Kocer ·Antti Aronen ·Richard Collins ·
Osamu Asano ·Yumi Ogi s o
Received: 1 February 2021 / Accepted: 11 May 2022 / Published online: 18 July 2022
© The Author(s) 2022
Abstract Non-uniformities in the heat flow through
the support pillars in vacuum insulating glass (VIG)
can lead to significant errors in the measurement of
the thermal insulating properties of these devices. This
paper discusses these errors in instruments for which
the measurement area is in direct thermal contact with
the glass sheets. The spatial non-uniformities of the
heat flow in different VIG designs are modelled using
the finite element method. For measuring areas with
large dimension compared with the separation of the
support pillars, the errors are unacceptably large for
all practical designs of VIG when using guarded hot
plate instruments. These errors are less for heat flow
meter instruments due to the construction of the heat
flux transducer.
Keywords Vacuum insulating glass ·Vacuum
glazing ·Measurement ·Thermal insulation ·Support
pillars
Nomenclature
AArea [m2]
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
DDistance [m]
dDiameter [m]
HHeight of pillar [m]
hHeat transfer coefficient [W m2K1]
kThermal conductivity [W m1K1]
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 m2K1]
wDimension of measuring area [m]
xPosition coordinate [m]
Greek letters
δFraction [–]
ΔChange [–]
εEmittance [–]
λSeparation of pillars [m]
ζSpecific resistance of one pillar [K W1]
σStefan Boltzmann constant [W m2K4]
Subscripts
CCold
123
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4C. Kocer et al.
eExternal
gGlass
iInternal
HHot
mMean
pPillars
rRadiation
vVacuum
1, 2, 3, 4 Identifying surfaces of glass sheets
1 Introduction
Vacuum insulating glass (VIG), shown in Fig. 1,isa
thermally insulating glazing consisting of two sheets
of glass that are hermetically sealed together around
the edges, with a thin highly evacuated internal space
(Collins and Robinson 1991; Collins and Simko 1998;
Collins et al. 1995). The separation of the glass sheets
under the forces due to atmospheric pressure is main-
tained by an array of small support pillars. The pillars
are placed on a square grid separated by λp. We define
a unit cell of the pillar array as a square area of dimen-
sions λp×λp, with sides oriented parallel to the rows
of pillars and a single pillar at the centre.
Several processes contribute to the heat flow through
a VIG specimen: thermal conduction through the sup-
port pillars, radiation between the internal surfaces of
the glass sheets, thermal conduction through residual
gas, and thermal conduction along the glass sheets in
the vicinity of the edge seal. We define the heat flux
as the heat flow per unit area at any point, with units
Wm
2. The highly localised heat flow through the pil-
lars, and the heat flow along the glass sheets near the
edge seal, result in significant spatial non-uniformities
in the heat flux across the external surfaces of the glass
sheets of the VIG.
Since 1989, the University of Sydney has undertaken
a comprehensive program of research and development
on VIG science and technology (Collins and Robinson
1991; Collins and Simko 1998; Collins et al. 1995;
Ashmore et al. 2016). An essential part of this program
is the ability to characterise the heat flow through VIG
specimens. This is done using custom built guarded hot
plate instruments in which the dimension of the mea-
surement area is small compared with the separation
of the support pillars (Collins et al. 1993; Dey et al.
1998). The separate contributions to the heat flow due
to individual pillars, and radiation between the glass
sheets, are combined to give the total heat flow. Data
obtained with these instruments have been validated by
measurements on large area specimens in conventional
calibrated guarded hot box instruments (Simko et al.
1999).
Unfortunately, the small area guarded hotplate is not
a commercial instrument that is readily available. Stan-
dard commercial guarded hotplate and heat flux instru-
ments typically measure contributions from many pil-
lars. With such instruments, the measured heat flow
through a VIG specimen is, in general, dependent on
the position of the measuring area relative to the pillar
array.
This is the first (Part 1) of two papers that discuss
the measurement of the thermal insulation properties of
VIG specimens using large area instruments in regions
remote from the edges. This paper deals with configura-
tions in which the measuring area of the instrument is in
direct thermal contact with the glass sheets of the VIG.
In this situation, the heat flowing into the measurement
area can differ significantly from the average heat flow
through the VIG over an equivalent area because of the
pillars, leading to errors in the measurements.
The second paper (Part 2) considers a configura-
tion in which the spatial non-uniformities in the heat
flux entering the measurement apparatus are reduced
by inserting slabs of thermally insulating material,
referred to as buffer plates, between the glass sheets
and the apparatus. It is shown that, for square mea-
surement areas large enough to contain at least several
unit cells, highly accurate estimates of the average heat
flow through the VIG can be obtained for a wide range
of specimen properties and area dimensions. However,
the buffer plates cause effects associated with heat flow
through the VIG edges to spread across the surface of
the VIG. The measurement area must be positioned
far enough from the edges for such edge effects to be
negligible.
2 Background material
2.1 Use of thermal conductances and resistances
In the following, we use the convention of labelling the
external glass surface of the VIG on the cold side as 1
and the external glass surface on the hot side as 4, with
123
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Measurement of heat flow through vacuum insulating glass 5
Fig. 1 Schematic diagram of a vacuum insulating glass unit
the internal surfaces facing the vacuum gap labelled 2
and 3 in sequence.
To a good approximation, at points remote from the
edges, the average total heat flow Qthrough a large area
Abetween the glass sheets of a VIG is proportional to
Aand to the difference between the average surface
temperatures T4and T1of the glass sheets over that
area (Wilson et al. 1998):
QhvA(T4T1).(1)
The term hvin Eq. (1) is referred to as the thermal
conductance and has units W m2K1.
The separate contributions to the heat flow due to the
pillars and radiation can be characterised by similar
relations, with thermal conductances written hpand
hrrespectively. In well made VIGs, heat flow due to
residual gas is negligible, and is not considered further
in this paper. Should significant gas conduction occur,
however, it has the same effect as increasing the thermal
conductance due to radiative heat flow.
In all cases of practical interest, the heat flows due to
pillars and radiation can be considered independently
(Wilson et al. 1998). The total thermal conductance hv
between the glass sheets of the VIG can then be written:
hvhp+hr.(2)
The heat flow Qthrough area Abetween the sur-
rounding internal hot and external cold environments
at temperatures THand TCand the surfaces of the glass
sheets is also characterised (American Society of Test-
ing Materials 1991) by thermal conductances hiand he
123
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6C. Kocer et al.
respectively (also referred to as the heat transfer coef-
ficients):
QhiA(THT4)heA(T1TC).(3)
The heat flow through the VIG unit from the envi-
ronment on the hot side to the environment on the cold
side can then be characterised by an overall heat trans-
fer coefficient, hHC,(also referred to as the U-value
of the glazing), where:
1/hHC1/U1/he+1/hv+1/hi.(4)
In this paper, U-values are calculated using values
of heand hiof 23 and 8.3 W m2K1, respectively
(International Organisation for Standardization 1994).
It is also convenient to define the thermal resistance
of a unit area R(with units m2KW
1) associated with
individual or combined physical heat transfer processes
as the inverse of the relevant thermal conductance:
R1/h.(5)
The thermal equivalent circuits in Fig. 2a and b illus-
trate the relationships in Eqs. (1)to(5).
Figure 2c shows a more complete thermal equiva-
lent circuit that includes the thermal resistances of the
glass sheets on the hot and cold sides: 1/hgi and 1/hge,
respectively. In all practical cases, these thermal resis-
tances are less than 0.5% of that due to radiative heat
flow and can be ignored at this level of analysis.
In the measurement configuration discussed in
Part 2, the buffer plates positioned between the external
surface of each glass sheet of the VIG and the adjacent
isothermal surface are assumed to be identical plane
parallel slabs of material, with thickness tband ther-
mal conductivity kb. For such buffer plates, the heat
transfer coefficients heand hiin Eqs. (3) and (4)are
replaced by the heat transfer coefficient of the buffer
plate hb:
hehihbkb/tb(6)
The thermal resistances Rband Rvassociated with
the heat flow through a unit area of the buffer plates
and between the glass sheets are, respectively:
Rb1/hbtb/kb,(7)
Rv1/hv.(8)
2.2 Mechanisms for heat flow through a VIG
In most practical VIG designs, the pillar acts as a local
thermal short circuit between the glass sheets. The mag-
nitude of the heat flow through each pillar is therefore
determined almost entirely by the spreading resistance
associated with the heat flow in the glass sheets very
close to the pillar. In addition, the pillar diameter is very
small (typically 0.5 mm) compared with the thickness
of the glass sheets (typically 3 mm). The volume of
glass adjacent to each pillar for which significant tem-
perature non-uniformities exist is thus very small com-
pared with the total volume of glass, and the temper-
ature non-uniformities on the external surfaces of the
glass are quite small. This justifies the characterisation
of the heat flow due to the pillars in Eqs. (1) and (2)
using a thermal conductance and average temperatures
T1and T4of the glass sheets.
In most practical VIG units the magnitude of the
heat flow (in W) through a single highly conducting
support pillar Qon epil lar can be written (Wilson et al.
1998):
Qonepi llar 2kgrp(T4T1),(9)
where rpis the radius of the pillar, kgis the thermal
conductivity of the glass.
For this total heat flow, it is convenient to define the
specific thermal resistance of a pillar, ζonepil lar :
ζonepi llar 1/2kgrp.(10)
For some designs of VIG, the material of the pillar
itself can also have a small, but measurable effect on the
heat flow. In this case, to a very good approximation the
thermal resistance associated with the heat flow through
a single pillar is the sum of the spreading thermal resis-
tance given in Eq. (10) and the thermal resistance asso-
ciated with uniform heat flow through the pillar itself
(Collins and Fischer-Cripps 1991). In this approxima-
tion, for a pillar of height Hpmade from material of
thermal conductivity kp,Eq.(10) then becomes:
ζonepi llar 1/2kgrp+Hp/kpπr2
p.(11)
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Measurement of heat flow through vacuum insulating glass 7
Fig. 2 Thermal equivalent circuits representing heat flow through VIG remote from the edges
For VIGs with metal pillars, the thermal resistance of
the pillar material itself is negligible compared with the
spreading resistance in the glass sheets and is ignored
in the following discussion.
To a good approximation the heat flow through each
individual pillar is independent of the heat flow through
all the other pillars (Wilson et al. 1998). The heat flow
through area Adue to the pillar array Qpil larar ray can
thus be written:
Qpill ararr ay Qone pill ar A2
p.(12)
We can therefore write the thermal conductance of
the pillar array hpas:
hp2kgrp2
p.(13)
To a good approximation, the radiative heat flow
between plane parallel surfaces of area Aand hemi-
spherical emittances εhot and εcold at temperatures Thot
and Tcold is given by Zhang et al. (1997):
Qrεσ AT4
hot T4
cold .(14)
In this expression, σis the Stefan-Boltzmann con-
stant (5.67 ×10–8 Wm
2K4), and εis the effective
emittance of the two surfaces, given by:
1 [1hot]+[1cold ]1.(15)
As mentioned, in all practical VIG designs, the
non-uniformities in the temperatures due to the pillars
are spatially limited and have negligible effect on the
overall radiative heat flow (Wilson et al. 1998). Also,
as noted above, the thermal resistance for heat flow
through the glass pane is negligible compared with that
due to radiative heat flow, so the external surface tem-
peratures can be used to obtain a good approximation
of the radiative heat flow between the glass panes. We
can therefore define the mean temperature Tmof the
internal glass surfaces as:
Tm(T4+T1)/2.(16)
To first order we can then write:
Qr4εσ AT3
m(T4T1).(17)
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8C. Kocer et al.
Tabl e 1 Design parameters that lead to the largest non-uniformities in the heat flux in practical VIGs
Glass thickness (mm) 3 4 5 6
Pillar separation (mm) 25 33 40 50
Pillar diameter (mm) 0.5 0.5 0.5 0.5
Emittance of LowE coating 0.03 0.03 0.03 0.03
Glass-to-glass conductance (W m2K1)
Pillars 0.71 0.41 0.28 0.18
Radiation 0.15 0.15 0.15 0.15
Pillars + radiation 0.86 0.56 0.43 0.33
U-value (W m2K1) 0.75 0.51 0.40 0.31
The thermal conductance associated with radiative
heat transport hrcan thus be written:
hr4εσ T3
m.(18)
2.3 Practical limits on VIG design parameters
The absolute and relative magnitudes of the spatial non-
uniformities in the heat flux through VIGs are greater
for thinner glass sheets, more widely separated pillars,
larger diameter pillars, and lower emittance coatings. A
detailed discussion of the process for designing VIG is
beyond the scope of this paper. However, the designs of
current commercial VIG products, and results of earlier
design studies (Collins and Simko 1998; Kocer 2011;
Collins et al. 1999), can be used to make reasonable
estimates of the maximum pillar separation for differ-
ent glass thicknesses. For each glass thickness, VIGs
with these maximum separations have the lowest pos-
sible thermal conductances and exhibit the largest heat
flux non-uniformities. The designs and performance of
these VIGs with 0.5 mm diameter pillars, and low emit-
tance coating on one internal surface only, are shown
in Table 1.
3 Measurement and modelling of heat flow
3.1 Measuring heat flow: available equipment
and measurement procedures
The thermal insulation properties of uniform, plane par-
allel slabs of material are conventionally measured in a
guarded configuration (International Organisation for
Standardization 1991b). In this type of equipment, the
specimen is positioned between two isothermal sur-
faces at hot and cold temperatures THand TC, respec-
tively. In the measurement, the heat flow through an
area near the centre of one or both plates is detected.
The isothermal plates in the region beyond the mea-
surement area, referred to as the guard region establish
approximately plane, parallel isotherms in the insulat-
ing slab, resulting in nearly uniform heat flow over the
measurement area.
The two different guarded configurations that have
been used to measure the heat flow through VIGs are
the guarded hot plate apparatus and the heat flow meter,
shown in Fig. 3.
In the guarded hot plate apparatus (International
Organisation for Standardization ISO 8302, 1991a)
(Fig. 3a), the hot isothermal surface is separated into
two regions a central metering piece and a surround-
ing isothermal guard that is maintained at the constant
hot temperature. The coplanar faces of both pieces are
separated by a small gap and contact the hot glass sheet
of the VIG specimen. These two pieces are relatively
well thermally isolated apart from the thermal contact
through the specimen at the gap. The outer surface of
the other glass sheet is in good thermal contact with
a second isothermal surface at the cold temperature.
Heat flow occurs directly from the hot guard through
the specimen, and from the guard to the metering piece
and then through the specimen. This causes the tem-
perature of the metering piece to be slightly less than
that of the guard. Power is dissipated in the metering
piece increasing its temperature. When the tempera-
tures of the guard and metering piece are precisely
equal, the heat that flows between them is zero, and
all the dissipated power flows through the sample. An
123
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Measurement of heat flow through vacuum insulating glass 9
Fig. 3 Two different large area guarded measurement configurations: aGuarded hot plate, bHeat flow meter
absolute estimate of the thermal insulating properties
of the specimen can be obtained by assuming that the
effective area of the metering piece is defined by the
middle of the gap. The effective area of the metering
piece can be estimated to higher accuracy by measuring
a calibration sample.
In heat flow meter instruments (International
Organization for Standardisation ISO 8301, 1991b)
(Fig. 3b), each side of the specimen being measured
is in good thermal contact with a heat flux transducer.
In the following, the dimensions and properties of the
transducers are typical of those in some commercial
instruments. Each transducer consists of a ~ 1 mm
thick plane parallel slab of plastic material of ther-
mal conductivity ~ 0.25 W m1K1. The slab has an
embedded thermopile with many junctions that are dis-
tributed over a well-defined area. The side of each trans-
ducer contacting the specimen is covered with a thin (~
30 μm) copper foil. The respective sides of the trans-
ducers remote from the specimen are in good thermal
contact with hot and cold isothermal plates. The same
heat flow occurs through the specimen and transduc-
ers. The temperature difference across the specimen is
slightly less than the total hot-to-cold temperature dif-
ference and is determined from the measured tempera-
tures of the copper foils. The output of each thermopile
is proportional to the heat flow through it, and therefore
to the heat flow through the specimen. These measured
data can be used to determine the insulating properties
of the specimen by measuring a calibration sample.
123
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10 C. Kocer et al.
When these two types of instrument are used to
determine the thermal insulating properties of a VIG,
the measured heat flow depends on the position of the
measurement areas relative to the pillar array. In the
guarded hot plate apparatus at the null condition, the
contacting metering piece and guard are at the same
temperature. The spatial non-uniformities in the heat
flux through the metering piece and guard are there-
fore the same as when the external surfaces of the glass
sheets are isothermal. When using a heat flow meter,
the spatial distribution of heat flux in the glass sheets is
very similar because the temperature difference across
the heat flux transducers is a very small proportion of
the total temperature difference. However, significant
lateral heat flow occurs in the copper foils due to the
high thermal conductivity of this material. As a result,
the lateral variations in the heat flux in the thermopile
regions of the transducers are significantly less than at
the copper-glass interface.
The practical significance of this result is that the
maximum position-related errors in the measurement
of a VIG with a heat flow meter are less than for a
guarded hot plate apparatus. The extent to which these
errors are reduced depends on the detailed design of the
heat flux transducer, which is in general commercially
confidential. These two papers are therefore primarily
concerned with the maximum possible measurement
errors that could occur with a guarded hot plate due to
the localised heat flow through the support pillars in
VIGs.
Figure 4illustrates the origin of the errors when
determining heat flow through a VIG with a square
measuring area Aof dimension wthat is significantly
larger than λp.
In both types of instrument, contributions to the
measured heat flow associated with heat flow through
the VIG edge seal must be negligible. When the glass
sheets are in good thermal contact with isothermal sur-
faces (Fig. 4), this occurs if the closest point of the
measuring area is at least 5 glass thicknesses (~ 20
30 mm) away from the edges. In heat flow meters, the
heat flux transducer causes the edge effect to spread
slightly further across the surface of the glass sheets.
Part 2 presents analytic and finite element modelling
procedures for determining the spreading of the heat
flow through the edges when buffer plates are used.
These procedures can be applied to the geometry of
the heat flux transducer to show that the effect of this
spreading is negligible when the measuring area is at
least ~ 40 mm from the edges. In contrast, the measure-
ment area must be much further away from the edges of
the VIG in the measurement configuration with buffer
plates, as discussed in Part 2.
It is convenient to write win terms of the pillar sep-
aration λpas
w(n+δ)λp,(19)
where nis an integer and 0 <δ<1.
In this case, in area Athere are n2complete unit cells
of the pillar array that contribute a heat flow that is equal
to the average of the heat flow through the VIG. At the
edges of A, heat flow occurs from (2n+1
)incomplete
unit cells. The magnitude of the combined heat flow
through these incomplete cells is, in general, different
from the average heat flow through an equivalent area
of the VIG. This can lead to errors in the measurement.
3.2 Finite element modelling of heat flow
Finite element modelling is used to determine the spa-
tial distribution of heat flux in the VIG. As noted, to a
very good approximation the thermal conductance hv
(Eq. 2) of a VIG remote from the edges is the sum of
the separate thermal conductances associated with heat
flow through the pillars hpand radiation through the
evacuated space hv. It is important to highlight that
only the heat flux through the pillars varies signifi-
cantly with position in the VIG. However, radiative heat
flow reduces the magnitude of the relative variations in
the total heat flux to values obtained by multiplying
the relative variations due to the pillars obtained from
modelling by the factor hp/hp+hr. Although the
model discussed here can include radiative heat flow if
desired, most of the modelling data presented are for
the spatial distribution of this heat flux related to heat
flow through the pillars alone.
In this work the ANSYS 18.0 FEM platform
was used to perform simulations. The element types
SOLID70/SOLID90 and SOLID182/SOLID183 were
employed to model thermal behaviour, with the
CONTA174 and TARGE170 elements employed to
model the thermal contact between the glass panes
and the pillars. The classic Ansys Parametric Design
Language (APDL) was used to define the modelling
process where the scripting language enabled an effi-
cient parametric study. The scripts were executed on
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Measurement of heat flow through vacuum insulating glass 11
Fig. 4 Schematic diagram of a large area configuration for measuring the thermal insulating properties of VIG
a High Performance Computing (HPC) cluster, with
7,636 cores (CPUs), 45 TB of RAM, 378 TB of stor-
age, using a 56 Gbps FDR InfiniBand network.
In regions remote from the edge seal of a VIG, the
spatial dependence of the heat flux is periodic. Except
when including the edge seal contribution, it is there-
fore sufficient to use a 3D model of the square unit cell
of the pillar array with adiabatic boundary conditions
around all 4 sides of the cell. The heat flux is retrieved
from the FEM models at each node of interest. Since the
mesh dimension is a constant size of 0.5 mm ×0.5 mm,
the heat flow at each node is proportional to the heat
flux over the element area. The heat flow is obtained
by multiplying the node heat flux by the element area.
Appropriate weighting is applied to the contributions
to the heat flux at the nodes at the edge and corners
of the model. The heat flow is then summed over the
defined metering area at each position of the metering
area to determine the spatial variation in heat flow with
respect to the location of this area over the VIG surface.
Figure 5contains an illustration of the unit cell and an
image of the typical mesh layout at a pillar used in the
FEM simulation.
In the model, unless otherwise specified, the pillar
is a cylinder 0.5 mm in diameter and 0.2 mm high. The
thermal conductivity of the pillar material is 20 W m1
K1to simulate the metal commonly used for the pillars
in VIGs. The glass sheets are simulated as two paral-
lel square slabs of material of side λpand thickness tg,
having thermal conductivity kgof 1.0 W m1K1, and
separated by the height of the support pillars. The model
incorporates a high density of elements within the pil-
lar and in the adjoining regions of the glass sheets. The
element density was optimised to provide good con-
vergence of the model while minimising the required
computing time and resource.
When modelling heat flow with a heat flux trans-
ducer, additional slabs of material of appropriate thick-
ness and thermal conductivity that represent the heat
flux transducer are included in the model between the
glass sheets and the isothermal plates. In all simula-
tions, the temperatures of the hot and cold exterior
boundaries of the model are set at 17.5 °C and 2.5 °C.
The heat flux in the unit cell is maximum directly
above the pillar and decreases in the adjacent region
with near-circular symmetry. There are four saddle
points in the heat flux distribution at the midpoints of
the edges of the unit cell, and four minima in the heat
flux at the corners of the unit cell. To illustrate the great-
est variation in the heat flux, the data presented in this
Section are plotted along a diagonal of the unit cell.
In all practical VIGs, the pillar diameter is very
small relative to the glass thickness. The spatial dis-
tribution of the heat flux at the external surfaces of the
glass sheets is therefore essentially independent of pil-
lar diameter. Changing the pillar separation λpand the
glass thickness tgby the same factor does not affect the
proportional variations of the external heat flux with
respect to relative position across the unit cell. Mod-
elling was performed for values of λp/tgbetween 3 and
10 to cover all current and possible future situations of
practical interest.
Figure 6shows typical modelling data for the heat
flux along the diagonal of a unit cell with pillar sepa-
ration of 20 mm, and different glass thicknesses. In all
cases, the non-uniformities remain significant even for
glass sheets that are much thicker than would be used
in practical VIGs.
123
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12 C. Kocer et al.
Fig. 5 a Illustration of the unit cell; bimage of the typical mesh layout at a 0.5 mm diameter pillar used in the FEM simulations
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)
Fig. 6 Heat flux along a diagonal of a unit cell
123
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Measurement of heat flow through vacuum insulating glass 13
Consistent with earlier modelling and experimen-
tal measurements (Collins and Simko 1998), this mod-
elled heat flux is essentially independent of the pillar
diameter and agrees closely with the analytic result in
Eq. (9). The spatial distribution of the modelled heat
flux over the external surfaces of the glass sheets also
agrees very well with previous modelling data (Wilson
et al. 1998), and with measurements reported in the
literature (Collins et al. 1993; Dey et al. 1998). These
results provide strong validation of the model used in
this work.
4 Variations in the heat flow for large measuring
areas
4.1 Variations in the measured heat flow with position
of the measuring area
This Section presents data for measured heat flow as a
function of the position of a square measuring area rel-
ative to the pillar array in VIGs. The VIGs have specific
values of λpand tgchosen to represent the range of val-
ues of the parameter λp/tgin practical specimens. The
data are expressed in dimensionless form as a multiple
of the heat flow through a unit cell.
The largest and smallest possible heat flows through
a square measuring area of dimension woccur when
there are respectively the largest and smallest number
of pillars inside that area. As illustrated in Fig. 7, for odd
values of the integer ndefined in Eq. (19), the minimum
heat flow occurs when the centre of the measuring area
is directly above a support pillar, and the maximum
heat flow is when the centre of the measuring area is
mid-way between 4 pillars. Figure 7also shows that
these positions are reversed when nis an even integer.
The data presented are scans of the modelled heat
flow as the centre of the measuring area is moved along
a straight line between the positions of maximum and
minimum heat flow. The position of the centre of the
area along each scan is given in dimensionless form,
with x0 directly above a pillar, and x1 in the cen-
tre of four pillars, as shown in Fig. 7. The dimension w
of the measurement area is expressed in dimensionless
form as a multiple (n+δ)of the pillar separation λp,
as in Eq. (19).
Figures 8,9and 10 show scan data for VIGs with
the specified values of λpand tg. Each figure contains
three sets of scans, corresponding to values of nin
Eq. (19) equal to 1, 2 and 3. Each set has four scans
corresponding to values of δin Eq. (19) equal to 0, 0.25,
0.5 and 0.75. Obviously, greater heat flow in each set
of four scans occurs for larger values of δ. In each set
of data, the solid circles indicate the positions of the
centre of the measuring area when the measured heat
flow is equal to the average heat flow through the VIG.
For these normalised quantities, the accurately char-
acterised heat flow through each measurement area is
equal to (n+δ)2. Clearly, for given values of λp,tg
and δ, the positions of the centre of the measuring area
when the measured heat flow is equal to the average
heat flow are the same for all values of n.
ThedatainFigs.8,9and 10 show that large varia-
tions occur in the measured heat flow as the measure-
ment area is moved relative to the pillar array. In gen-
eral, there is no simple way of positioning the area so
that it will measure the average heat flow. There are,
however, two specific situations for which an accurate
measurement can be made. Firstly, the measured heat
flow is obviously independent of position when the
dimension of the measuring area is an integral mul-
tiple of λp[δ0inEq.(19)]. Secondly, when the
dimension of the measuring area is w(n+0.5)λp,
the heat flow through the measurement area is equal
to the average heat flow when the centre of the area is
midway between the two extreme positions.
4.2 Predicted errors in the measured heat flow
As noted, the largest and smallest heat flows through
the measurement area occur when the centre of the area
is at the ends of each scan in Figs. 8,9and 10. These
maximum and minimum heat flows can be combined
with the accurately characterised normalised heat flow
for each measurement area to calculate the largest pos-
itive and negative proportional errors that could occur
in any VIG design. Figure 11 shows these errors for the
cases presented in Figs. 8,9and 10 up to large values
of n.
The data in Fig. 11 between sequential integer val-
ues of nare smooth curve fits to values calculated for
8 evenly spaced values of δin Eq. (19) over the range
from zero to 0.875. For even values of n, the largest
positive errors occur when the centre of the measuring
area is above a pillar, and the largest negative errors
are when the centre is mid-way between 4 pillars. This
situation is reversed for odd values of n.
123
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14 C. Kocer et al.
Fig. 7 Illustrating the positions of the measurement area for maximum and minimum heat flow for odd and even values of nin Eq. (19)
Fig. 8 Heat flow through square measuring areas of different dimensions, as the centre of the area is scanned across a VIG from above
a pillar (x0) to a point midway between 4 pillars (x1). The VIG has a pillar separation λp20 mm and glass thickness tg3mm
123
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Measurement of heat flow through vacuum insulating glass 15
Fig. 9 As for Fig. 8for a VIG with pillar separation λp40 mm and glass thickness tg3mm
Fig. 10 As for Fig. 8for a VIG with pillar separation λp20 mm and glass thickness tg5mm
The data in Fig. 11 show that the magnitude of
the errors decreases approximately inversely with the
dimension of the measuring area. However, significant
errors can occur when measuring VIGs for all practi-
cal dimensions, even for large measurement areas. For
example, for a VIG with 3 mm thick glass sheets and
a pillar separation of 20 mm, the maximum errors are
> 17% for areas ~ 100 mm square (n5inEq.(19)),
and > 12% for ~ 200 mm square measurement areas
(n10). The data in Fig. 11 foraVIGwith5mmthick
glass sheets and a pillar separation of 20 mm show that
these errors are still significant when the glass sheets
are much thicker than commonly used in practice.
When radiative heat flow between the glass sheets
is included, the maximum possible errors are less and
are obtained by multiplying the values in Fig. 11 by
123
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16 C. Kocer et al.
Fig. 11 Largest positive and negative proportional errors in the measured heat flow for square measuring areas of different normalised
dimensions, for VIGs with pillar separation and glass thickness in Figs. 8,9and 10
the factor hp/hp+hr. The magnitude of this factor
depends on the detailed design of the VIG. In some
cases, radiative heat flow may be large enough to reduce
the measurement errors to acceptable levels. However,
these results show that the large area guarded hot plate
configuration illustrated in Fig. 3a is, in general, not
suitable for making accurate measurements of the heat
flow through a VIG.
As mentioned, the construction of the heat flux trans-
ducers in heat flow meters significantly reduces the
non-uniformities in the heat flux due to the pillars in
VIG. These reductions are reflected in smaller possi-
ble measurement errors with these instruments. The
magnitude of these reductions depends on the detailed
design of the transducers. Figure 12 gives an exam-
ple of the maximum positive and negative errors in the
measured heat flow for a VIG with pillar separation λp
20 mm and glass thickness tg3 mm. These data
are for a heat flux transducer having the design param-
eters discussed in Sect. 3.1 (1 mm thick plastic layer
and 30 μm thick copper foil).
The data in Fig. 12 show that the heat flux trans-
ducer reduces the magnitude of the errors by a factor
of about 8 for a VIG with pillar separation of 20 mm.
These reduction factors are less for more widely spaced
pillars, with values of approximately 4 and 3 for VIGs
with pillar separations of 30 mm and 40 mm respec-
tively. The reduction factors are essentially indepen-
dent of glass thickness. These reduced possible mea-
surement errors may still be significant, even for large
measurement areas and when the effects of radiative
heat flow are included. Work on this matter is continu-
ing.
As noted earlier, design data of the heat flux trans-
ducers in commercial heat flow meter instruments are
not usually publically available. In general, it is there-
fore not possible to make an apriorijudgement of
whether such an instrument will reduce the errors dis-
cussed above to acceptable levels. This can be deter-
mined experimentally, however, simply by using the
instrument to measure the heat flow through the VIG
specimen at the two extreme positions with the cen-
tre of the measuring area above a pillar, and mid-way
between 4 pillars.
5 Conclusion
The localised heat flow through the support pillars in
VIGs can lead to significant variations in the measure-
ment of the thermal insulating properties when using
large area instruments that directly contact the glass
123
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Measurement of heat flow through vacuum insulating glass 17
Fig. 12 Largest positive and negative proportional measurement errors with and without heat flux transducers for a VIG with pillar
separation λp20 mm and glass thickness tg3mm
surfaces. The maximum and minimum heat flows occur
(not necessarily respectively) when the centre of the
area is directly above a pillar, and directly above the
centre of a unit cell.
These variations can lead to errors in the measured
heat flow. In general, there is no simple way of posi-
tioning the measuring area relative to the pillar array
so that it measures the average heat flow through the
specimens. There are, however, two exceptions to this.
Firstly, the errors do not occur if the dimension of the
square measuring area is an integral multiple of the pil-
lar separation. Secondly, the errors are zero if the centre
of a measuring area of dimension equal to (n+0.5) times
the pillar separation (nan integer) is located midway
between the positions of minimum and maximum heat
flow.
The magnitude of the errors decreases approxi-
mately inversely with the dimension of the measuring
area due to the proportionally larger number of com-
plete unit cells that contribute to the heat flow. The
errors are also less for heat flow meters than for guarded
hot plates due to lateral heat flow in the heat flux trans-
ducers. The extent of this reduction depends on the
specific design of the heat flux transducer in this instru-
ment. The errors may be acceptably small for VIGs
with thick glass sheets and closely spaced pillars, and
for very large area heat flow meter instruments. It can
be determined experimentally if this is the case by mea-
suring the maximum and minimum heat flow through
the specimen.
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 in 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,
sharing, adaptation, distribution and reproduction in any medium
or format, as long as you give appropriate credit to the original
author(s) and the source, provide a link to the Creative Com-
mons licence, and indicate if changes were made. The images
or other third party material in this article are included in the
article’s Creative Commons licence, unless indicated otherwise
in a credit line to the material. If material is not included in the
article’s Creative Commons licence and your intended use is not
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18 C. Kocer et al.
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