In an effort to understand pyrolysis of Kapton in solar arrays, a computational heat transfer program was developed. This model allows for the different materials and widely divergent length scales of the problem. The present status of the calculation indicates that thin copper traces surrounded by Kapton and carrying large currents can show large temperature increases, but the other configurations seen on solar arrays have adequate heat sinks to prevent substantial heating of the Kapton. Electron currents from the ambient plasma can also contribute to heating of thin traces. Since Kapton is stable at temperatures as high as 600 C, this indicates that it should be suitable for solar array applications. There are indications that the adhesive sued in solar arrays may be a strong contributor to the pyrolysis problem seen in solar array vacuum chamber tests

Morton, Thomas L.

English

NASA Technical Reports Server

N92-22370
Theoretical models of Kapton heating in solar array geometries
Thomas L. Morton
Sverdrup Technology
Lewis Research Center Group
Cleveland, OH 44135
ABSTRACT
In an effort to understand pyrolysis of Kapton in
solar arrays, a computational heat transfer program
was developed. This model allows for the different
materials and widely divergent length scales of the
problem. The present status of the calculation
indicates that thin copper traces surrounded by
Kapton and carrying large currents can show large
temperature increases, but the other configurations
seen on solar arrays have adequate heat sinks to
prevent substantial heating of the Kapton. Electron
currents from the ambient plasma can also contribute
to heating of thin traces. Since Kapton is stable at
temperatures as high as 600 Celsius, this indicates
that it should be suitable for solar array applications.
There are indications that the adhesive used in solar
arrays may be a strong contributor to the pyrolysis
problem seen in solar array vacuum chamber tests.
INTRODUCTION
During plasma compatibility tests of the SSF solar
array blanket, pyrolysis of Kapton ® (registered
trademark of E.I. du Pont de Nemours & Co., Inc.)
was seen.' While performing a dark test, the
experimenters biased the array to a positive voltage,
and read the current drawn from the ambient
plasma. At +450 volts, a large spike was seen in
the current. When the solar panels were removed
from the test tank, a 1/8 inch hole was seen to have
enlarged to about 1/2 inch diameter, with black char
marks on the Kapton surrounding the hole.
Kapton was developed by du Pont in the early
1950's, and commercialized in 1966. It has been
used extensively in the aerospace industry for 25
years with few problems. Various laboratory tests
indicate that it does not pyrolyze until the
temperature reaches at least 500 ° C. z'3
The objective of this paper is to determine possible
causes of the pyrolysis, and determine the conditions
under which they could be repeated. In addition,
questions were raised about possible concerns when
Kapton was used in the space environment. Under
what conditions would Kapton pyrolyze, and would
those conditions happen often?
METHOD OF CALCULATION
Cooer slide (2 mils)
Silicon (8 mils)
Copper 11.4 mils)
Kapton (4.4 mils)
Figure 1 - Cross Section of Solar Cell
To study this problem, a computational heat transfer
computer program was developed. A new program
was needed because of the unique geometry of this
problem. The solar cells are very thin, as shown in
Figure 1. The entire thickness is about 15 mils, while
the hole that was examined was 1/8 inch in diameter
(125 mils). This disparity in scales does not allow the
direction perpendicular to the surface to be treated in
the same way as the directions parallel to the surface.
A schematic of the calculation geometry is shown in
Figure 2. Both the hole, and the paths for heat gains
and losses are shown. For most of the calculations, it
was assumed that incident radiation was coming in
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from a 300 K source. In addition, resistive heating
was ignored for most of the calculations, since the Radiation Incident(gain & loss)
system modeled was a dark solar panel, that is, no -e.[.ectrons
current was present. _ I \I I
Thus, the heat sources and paths are as follows:
1. Energy transfer from incoming electron, set
equal to current times bias voltage.
2. Conduction of heat through copper, kapton,
and silicon.
3. Radiation heat gain from external source at
300 K.
4. Radiation heat loss from surfaces, equal to
_oT 4, where _ is the emissivity , tr is the
Stefan-Boitzmann constant, and T is the
absolute temperature at the surface.
5. Internal Joule heating of copper from I2R.
1 v I
Kapton v
Copper
÷
Conduction
Kapton
&
Silicon
Different materials were included in this calculation,
as listed in Table 1. The adhesives were treated as
Kapton, since their thermal properties are similar,
and could not be identified until late in the
calculation.
Figure 2 - Heat pathways
Parameter \ Material Kapton Copper Silicon
Density (g/cm 3) 1.42 8.96 2.33
Specific Heat (J/g K) 1.09 .385 .702
Thermal Conductivity .00155 4.01 1.49
(W/cm K)
Resistivity (_fl cm) l0 ts 1.69x lO g 640.
Emissivity .7 .65 not used
(oxidized)
The fundamental equation for heat transfer is
pc OT-K_T+(_
at
(1)
were treated with a control volume approach. That is,
the heat flowing into and out or a node from each
direction would change the temperature of that node as
if the node had the average properties of the materials
around it.
where p is the density, c is the heat capacity per unit
mass, and K is the thermal conductivity. Writing
a = K / (p C), the equations can be re-written as
aT_oc:T+ Q___ (2)
at pc
For this calculation, a finite difference approach was
chosen. Boundaries between difference materials
In finite difference calculations, the time step is limited
by stability requirements. If the calculation is done
explicitly, it is necessary to maintain a ratio
,,At <! where At is the time step, and Ax is the
pc(ax)2 2
distance scale. However, if the temperature at the
succeeding time step depends implicitly on the
surrounding temperatures, this restriction does not
hold. Implicit calculations in one dimension are
straightforward, but three dimensional calculations are
difficult. For this reason, the calculation was done
implicitly only in the z direction (i.e. perpendicular to
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the surface of the Kapton).
For an explicit calculation, the temperature at time
n+l is simply
+1 n _ xAt n n n
CtyAt n n +Tn -
j,
Ct At n n n
+r'J*-0+---0oc
(3)
where c_, = K,/(pc), i-x,y,z. If we do an implicit
calculation in the z direction, the formula becomes
+1 n tt xAt n n n
ttyAt n n n(T,..t.- 2T,,,,+T,,_,.)(
tZzAt,.,_+l _,-r,n+1 ,T,n+I O
(az)2t*,j,,x-z,_j,+,,j,_x)+
(4)
treated with a control-volume approach. That is, it
was assumed that heat was transferred between nodes
using an average of the transport properties of the
materials involved. That is, the finite difference
version of Eqn 1 becomes
(_"-ro") _,+
(pc),_ At
(T__ To) (6)
[ T_, '_,_ l
a,#ac,=_ (Ai) 2
where (pc).v is the average heat capacity per unit
volume for the central node, Km, is the average thermal
conductivity on the line joining an adjacent node to the
central node, and Ai is the distance between the two
nodes.
This method requires the boundaries between different
substances to lie on nodes in the grid. However, this
was rarely a strong restriction. The largest problem
from that constraint was that the modeled hole through
the Kapton was not circular. However, in light of the
agreement with experimental results, the restriction
was not found to be major.
TESTS OF THE CALCULATION
Separating temperatures at time n from time n+l,
we get
e--
pc
+d,(Ti"+,.j.,- 2 Ti._.,+Ti" ,,.,)
(5)
tt rat
where d i- _ i=x,y,z .
(Ai) 2
stability analysis requires that dx
There is no restriction on dz.
Von Neumann
< V2, dy < IA .
Since d, has the spatial increment in the
denominator, it is very useful to not restrict dz. For
these calculations, a At = .0001 seconds was used.
This keeps both dx and dy within the stability
requirements.
The boundaries between different substances were
The model was tested in two different fashions. The
original code was compared to analytic solutions to
heat conduction problems, many of which were listed
in Carslaw & Jaeger (1959). 5 The results were
compared to the calculation method to semi-infinite
solids with a circular heat source, infinite slabs of
different materials, and some cylindrically symmetric
solutions.
By the time the code had been compared with the
models, results from laboratory experiments were
available, and the program could be compared to
them .6 The agreement with experiment was excellent
(see Figure 3). The top of Figure 3 shows three
temperature contours for a 1 inch copper strip,
insulated by 1 mil of Kapton on each side. The hole
is 1/4 inch in diameter, about 1/2 inch from the end of
the copper trace. The middle contour is the
experimental result, while the one on the right is the
program. If the program includes the averaging of the
infrared camera, and accounts for the lower emissivity
of copper, the contour on the left is obtained. The
graph on the bottom shows the temperature as a
function of time for the one inch strip. Since computer
time was limited, most runs were stopped at two
712
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100-
80-
60-
40-
20-
0
0 i 2 :3 4. ,5 (_ 7 8 9 10
Figure 3 Time (seconds)
713
seconds of simulated time. The graph shows that the
temperature at ten seconds is about two to three
times the temperature at two seconds. It was
therefore deemed appropriate to extend the
calculation to models of solar cells.
The experiments covered a range of incident power
from .005 W/cm 2 up to 13 W/cm 2. The computer
program was able to duplicate the experimental
temperature rise over the entire range of incident
power. For the smallest copper strip tested,
pyrolysis was seen at about 13 W/cm 2.
Two different examples of solar array geometries
were examined. The first case modeled the
connection between different silicon arrays, and
consisted of a copper trace bounded on both top and
bottom by Kapton. The second modeled the trace
near the silicon, and included an electrical
connection to the silicon as a possible pathway for
heat to move. Since the original test was a dark
test, no resistive heating was included in these models.
The results are shown in Table 2.
The first part of the Table shows the temperature rise
for a solar cell copper trace, both theoretically after
2 seconds, and the experimentally after 10 seconds.
The calculated temperatures should be multiplied by
2 to get an expected temperature rise for 10 seconds.
The calculations show that even a small variation in
hole size can change the expected temperature rise. In
addition, three magnitudes of incident power are
shown, to show how linear the problem is. The
radiative heat term should generate a non-linearity, but
that effect is quite small.
The second part of the Table shows the temperature
rise expected for a copper trace near silicon. All three
are after 10 seconds. The two calculations show the
effect of a conductive pathway between the copper and
the silicon. This is to model the weld joint which
connects the copper to the silicon.
Table 2 - Model of thin trace embedded in Kapton
Incident power / 1.4 mil x 5/32 inch 1.4 mil x 5/32 inch Experiment
area 1/8 " hole 5/64" hole
Time 2 seconds 10 seconds
.1 W / cm z .7867249 K .4821346 K .55 K
1 W / cm z 7.8614550 K 4.8192897 K 7.5 K
10 W / cm 2 77.9610901 K 47.971920 K 80. K
Model of thin trace near Silicon
Incident power / Conductor from No conductor from Experiment
area Copper to Silicon Copper to Silicon
Time 10 seconds
1 W/cm 2 .8K 1.I K 2.2K
NASCAP/LEO, a space-charge analyzing computer
program, can predict the currents expected for a
biased hole exposed to the ambient Low Earth Orbit
(LEO) plasma. For 1/4 and 1/2 inch diameter holes,
these I-V curves are shown in Figure 4 for possible
voltages and densities expected on the solar array 7.
The highest plasma densities expected for LEO
orbits would be during Solar Maximum conditions,
when the density can reach 4 x 1012 ions per cubic
meter. At this density, the area of the solar array at
160 volts would collect 70 micro-amps of electron
current. The model predicts a temperature rise of less
than 1 degree Celsius for this incident power. This is
not enough to cause significant heating of the copper or
Kapton. For comparison, the laboratory test that saw
pyrolysis had about 1 amp at 450 volts.
During daylight, the solar arrays are generating current
through the traces. If resistive heating in the copper
trace is included, the Kapton achieves an equilibrium
temperature rise of about 10 degrees Celsius. In
addition, the sunlight heats the arrays to about 70
714
temperature rise of about 10 degrees Celsius. In
addition, the sunlight heats the arrays to about 70
degrees Celsius. Even an extra 1 degree Celsius
from plasma heating will still not achieve pyrolysis.
CONCLUSIONS
Pyrolysis of Kapton has been duplicated in a
laboratory plasma tank for a solar array type of
geometry.
The calculations confirm the experimental results
that the change in temperature observed in these
samples is proportional to the product of incident
current times the bias voltage. In LEO conditions,
it does not appear likely that Kapton will pyrolyze
due to incident energy from the plasma at Space
Station voltages.
ACKNOLOWEDGMENTS
This work was supported by NASA grant NAS3-
25266 with Dale C. Ferguson as monitor. Paul J.
Cavano provided many useful discussions at the
beginning of this calculation.
REFERENCES:
.
2
.
.
.
Felder, Marian, private communications.
Jellinek, H.H.G., "Degradation and
Stablization of Polymers", Elsevier, New
York, 1983.
Punderson, J. O. and Heacock, J. F., "Why
Long-term Performance Exceeds Some
Limited Laboratory Projections", 34th
International Wire and Cable Symposium,
Cherry Hill, NJ, November 19-21, 1985
Jaluria, Yogesh and Kenneth E. Torrance,
COMPUTATIONAL HEAT TRANSFER,
Hemisphere Publishing Corporation, New
York, 1986.
Carslaw, H.S. and J.C. Jaeger,
CONDUCTION OF HEAT IN SOLIDS,
Clarendon Press, Oxford, 1959.
"g"
e_
O
b
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-6
-8
-10
-12
-14
-16
-18
-20
a
_ _ E_) IQO I_0 I;0 160 180 200
-5
-10
0
b
"_ -I5
"I
-30
40-
Q. 20 _
-30
£ -4O
,_o
-60
7o
0
-90
-100
C
Voltage
Figure 4 - (a) Dotted line is NASCAP/LEO, solid is
lab result. (b) Current in space for densities of 106,
2 x 106, and 4 x l& electrons/cc, 1/8 inch hole.
(c) Current in space for densities of 106, 2 x 106,
and 4 x 106 electrons/cc, 1/4 inch hole.
. Grier, Norman T., "Experimental verification
of Kapton Pyrolysis", SOAR-91, Houston, TX
July, 1991.
, Morton, T. and R. Chock, "NASCAP/LEO
simulations of current collection by pinholes",
(unpublished).
715


Theoretical models of Kapton heating in solar array geometries

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