VIP . Formulas and Rules for designers and final users
Ing. Pierattilio Di Gregorio
Saes Advanced Technologies S.p.A.
Email: pierattilio_di_gregorio@saes-group.com
t
(atm)-(0)
Introduction. The design of a Vacuum Insulated Panel (VIP) is a multidisciplinary activity that implies a
close interaction between designer (or supplier) and final user. Differently from conventional insulation
materials, Vips are complex items
whose final performances are
 [mW/m.K]
resulting from a multi steps design
PUR
a-a

approach. Herein after the
foremost rules for shelf life
VIP
estimation and thermal design are

exposed. Moreover some practical
w
log10(p)
rules for proper usage are also
mentioned.
S
Busta
Getter
pext
V
T(x)
Working principle. In Fig.1 is
shown the general structure of a
(T)Pt/w[pext-p(t)]
VIP. It comprises an inner "core"
p(t)
made of an highly porous matrix
a-a
(with porosity  > 90%) having
x
low bulk thermal conductivity.
Core
Fig.1
 (T)S [pext-p(t)]
The core must have a completely
"open cells" structure. This means
that is forbidden the presence of any closed cell entrapping some residual gases. An outer envelope, or
"pouch", seamed all around, encloses hermetically the inner core. Pouches are manufactured with not
conventional and high tech packaging materials with ultra high barrier property.
In a conventional porous material, like PUR foam, overall thermal conductivity  is resulting from (see
eq. 1): bulk conduction  S , radiative heat transfer  R , and gaseous
conduction G . In isothermal conditions  R depends on cell average
diameter  and porosity  . In turns,  S is function of porosity , matrix
conductivity M and shape (a/b) of cells. Instead, G is monotonically
p
related to inner pressure p , to porosity and cell average diameter.

Gaseous conduction is the most important term , being responsible for
about 80% of overall thermal conductivity. Hence, if inner pressure is



reduced up to cancel
out G , overall
(1)   R ( ,  )  S ( , M , a / b)  G ( p,  ,  )
thermal transmission
Fig.2
will depend on solid and radiative terms only. Actually eq. (1) is
S
M
R
G
experimentally deduced, measuring thermal conductivity just in center of a VIP, as here the flow is
unidirectional. A relationship as (2) has been
 (atm, T )   (0, T )
found out where first term  (0, T ) is the sum
(2)  ( p, T )   (0, T )  
A
S  R , and second term is G . In Eq. (2) with
~
p
1   
 (atm, T ) we designate VIP thermal conductivity
 p
at high pressure, i.e. close to atmospheric value.
Instead, A is a shape factor generally very
close to 1. Obviously , for very low inner
Core type
 (0,24C)  (atm,24C)
pCR
pressure p , below a critical value pCR , Eq.
[mW/m.K] [mW/m.K]
[mbar]
(2) simplifies to  ( p, T )   (0, T ) .
PolyStyrene “open cells”
4.5-5.5
33
0.5
Experimentally has been founded that
PolyUrethane “open cells"
6-8
33
0.01-0.1
 ( p, T ) depends not only on inner pressure
Silica powder
3.5-5
22
1-10
p , but on VIP average temperature T too.
Glasswool
2.5-3
33
0.01
Some reference values for the most used
Tab.1
"core" are listed in Tab.1.
Shelf life estimation. However good may be barrier property of materials used for pouch manufacturing,
inner pressure p doesn't remain fixed to the initial value p evac , but slightly grow up over the time because
of permeation of external gases that are at pressure p est  p . The foremost permeation takes place
through the "all around" flanges where the upper face of pouch is sealed to the bottom one. As shown in
Fig.1, permeation depend on “permeability “  of sealing polymer (normally polyethylene), flange
perimeter P , width w and thickness t of seam. There is also a secondary permeation through the pouch
faces themselves. These faces come as multi-layers of plastic sheets (i.e. metallized PET ), eventually coextruded with a foil of solid aluminum having thickness   5m . As in Fig.1 permeation through faces
depends on "permeance"  and outer surface S . Permeance is close to zero if an aluminum foil is
embedded in the multilayer. However the drawback in using an Al foil is a leak of thermal effectiveness
(see later the problem of "edge
  H i 
effects"). Therefore multilayers
  H i 
 i   0i exp 


 i   0i exp 
made exclusively of aluminum
 RT 
 RT 
metallized polymeric films are
(3) dpi  RT   P  t     S ( p ext  p )
often preferred. Generally the
p est   piest
i
i
i
i
dt
 V 
i
  V  w 
number n of metallized layers
ranges between 1 and 3. Thickness
p evac   pi (0)
p   pi (t )
 of sputtered aluminum is
i
i
normally below 1000Å. Metallized
films avoid problems related to
edge effect even if to the detriment of a higher permeance. It's important to notice that  e  depends
on barrier material and are specific for the gas/vapor passing through. Moreover are exponentially related
to absolute temperature. If we know  and  for all the gases/vapors of the outer atmosphere, the panel
geometry (i.e. volume V , flange perimeter P , ….), as well as temperatures "seen" by each face and by
flanges, it's possible to estimate the growing of inner pressure p (t ) , by integration of equations (3). Once
the function p  p (t ) is known, by means of eq. (2) we can estimate the evolution over the time of
thermal conductivity  , and consequently, establish the amount of getters and dryers according to
cost/opportunity ratios. This allow us a fine control of the thermal performance of the VIP and in such a
way that it could evolve, with specified safety margins, from the requested value at beginning of life
(BOL) to the end of life (EOL) one. Careful examination of Eq.(3) leads to interesting conclusions. For
example it's a good rule to place the most permeable face of the panel in the colder area, because  , as
well as  , strongly increase with temperature,. Moreover, big panels, with high ratio V/S or V/P, are to
be preferred over small ones because the growing rate of inner pressure is directly related to this ratios
Thermal design. Now we put our attention to a flat VIP, having sizes LxWxT , thermal conductivity  ,
and an outer pouch of thickness s and flange thermal conductivity F . By formula (4), we can estimate
the overall thermal conductivity VIP of the VIP.
P
 2(W  L) s 
(4) VIP     F 
     F s
The second term of (4) is referred to as "edge
LW
A


effect" and models heat transmission through
peripheral flanges It depends on thermal
conductivity of flange F , ratio
Pouch with
 
“metallized” barrier  F   PM  n  AL  Po lim
perimeter/surface P / S , and pouch
s
thickness s . In turns (see Tab.2) F
Pouch with “Al foil”
depends on flange geometry (standard or
 
 
barrier
F    AL 1   PM
with folded-back flanges), type of
s
 s
multilayer (with Al "foil" or metallized
Hybrid pouch
2PM
film), thermal conductivity of barrier
F 
"metallized" and "Al
material  Al and  Po lim , pouch total

s   
foil"
1    PM 
thickness s , aluminum foil thickness  ,
    AL 
number n of metallized layers, and
Hybrid pouch
2PM
F 
 2PM
"metallized" and "Al
thickness  of sputtered aluminum.
 s  PM 
foil", with folded

1   
Typical values are  Al =270E+3,
back flanges
   2 AL 
 Po lim =240 mW / m.K , s =100,  =6,
Pouch with “Al foil”

3   
 
F    AL1   PM 
 =0.1 m , n=1-3.
barrier and folded
2  s 
 s

back flanges
Current tendency is to use hybrid pouch
Pouch with
and with folded back flanges. This
3
F   PM
“metallized”
barrier
solution allows the highest coverage ratio
2
and folded back
(see later), a negligible "edge effect" and
flanges
a low overall permeance, being limited to
Tab.2
the metallized face only.
TWALL
T
A
AWALL
Fig.3
Rapporto (lambda Wall / lambda Vip)
1
0
1.2
0.8
9
1.5
9
1.7
0.7
9
2.1
80
1.
8
2.1
Rapporto di Riempimento (T / T Wall)
0.9
0
1.4

VIP
0
1.4

FOAM
60
1.
Now we turn our attention to Fig. 3 in which is shown
a Vip foamed inside a wall using conventional
insulation foam, for example PUR foam. This case is
typical of RF/FZ industry. The thermal conductivity
of the entire wall can be estimated by means of
formula (5), where we've denoted with  the
"coverage ratio" A AW , i.e. the ratio between the Vip
and wall projected areas, with  the "fill ratio"
T T W , that is the ratio between Vip and wall
~
thickness', and with  the dimensionless ratio
 FOAM  VIP between thermal conductivity's of
foam and VIP.
~
  (1   )
(5) W all  VIP


   ~  1   1   


58
2.
0.6
In graph shown in Fig.4 are drawn the level curves
2.
00
of ratio W all / VIP , assuming  and  as,
2.
2.
21
98
0.5
respectively, the abscissa and ordinate variables.
~
Here the value of parameter  ranges from 3 to 7.
2.4
3.
3.
38
1
0.4
95
From Fig.4 we observe that to achieve maximum
3.7
7
4.
54
thermal efficiency,  should be as close as
5.1
3
0.3
possible to 1. This justify current tendency to use
0.5
0.6
0.7
0.8
0.9
1
Rapporto
di
ricoprimento
(A
/
A
Wall)
folded back flanges. Also  should be close to 1 ,
Fig.4
even if a gap TW all  T of 12-15 mm at least, is
necessary for proper foam flowing.
Conclusions. In the present paper we have touched the foremost rules and formulas for designing and
proper usage of VIPs. In particular has been underlined as mounting rules, component choice, flange
design, thermal analysis, and shelf life estimation are strictly interconnected. Has been shown as the use
of dimensionless ratios allows a fast and preliminary design of a vacuum panel. This is beneficial also for
final user, as he can understand the underlying phenomena and, hence, interact properly with
designer/supplier to optimize the VIP design.
7
2.7
36
3.