UNCLASSIFIED Nationaal Lucht- en Ruimtevaartlaboratorium

National Aerospace Laboratory NLR

Executive summary

Thermal analysis of wiring for weight reduction and improved

safety
Requirements review and validation of wire bundle model inside enclosure

Report no.
NLR-TP-2011-469

Author(s)
R.C. van Benthem
W. de Grave
F. Doctor
K. Nuyten
S. Taylor
P.A. Jacques
Problem area elevated air temperature due to
In SAE AS50881 wire (conductor) neighbouring bundles and/or limited Report classification
sizing is based on heat losses due to convection due to structural UNCLASSIFIED
the electrical resistance (when enclosures are not considered. Also
carrying a constant duty current) heat radiation is not taken into Date
and the maximum allowed account. It is therefore to be October 2011
temperature of a free wire cooled by expected that application of SAE-
ambient air convection. The AS50881 for aircraft bundle designs Knowledge area(s)
maximum free wire current in or ECSS-Q30-11A5 leads to Avionicatechnologie
ambient air is derated for altitude, Ruimtevaartinfrastructuur en
significant uncertainties in actual
-payloads
number of wires in a bundle, load wire temperatures or aerospace
conditions and air temperature. It is applications. Beside heavy harness Descriptor(s)
not a trivial matter to ensure that the designs this could lead to Thermal Analysis
end design conforms to the design unacceptable high bundle Wire Design Optimization
assumptions in such an integrated temperatures with respect to SAE-AS50881
system hence it is speculated that sensitive wire/cable content or ECSS-Q-30-11A
over-conservative derating factors structural parts subject to
are typically part of the system temperature limitations.
design e.g. at the maximum air
temperature, lowest pressure Description of work
derating factors are usually taken by The concept of thermal analysis was
the equipment suppliers e.g. at the demonstrated with the construction
maximum air temperature, lowest of a Thermal Design Model (TDM)
pressure and largest bundle size predicting wire temperatures in
under a maximum load. Poor bundles. Better knowledge of the
cooling conditions such as an wire temperature leads to improve

This report is based on a presentation held at the AIAA/ICES Conference, Portland,

Oregan, USA, 18-21 July 2011.

UNCLASSIFIED
UNCLASSIFIED Thermal analysis of wiring for weight reduction and improved safety
Requirements review and validation of wire bundle model inside enclosure

bundle design in terms of weight Extension of the validation range of

and safety. Several configurations the TDM1.0 for 5-35 mm bundles
of 14 mm to 16 mm diameter wiring in aircraft enclosures, other
bundle samples were tested under environmental conditions such as
representative air temperatures vacuum (space) or low pressure
between -55oC to +70oC and CO2 (Mars) and axial heat leak
pressure conditions between predictions is under investigation
120 mBar to 1 Bar (50.000 feet to for space applications.
sea level.
Applicability
Results and conclusions Design optimization of wiring
Evaluation revealed a temperature bundle designs for aerospace
prediction accuracy of +/-19oC (@ applications.
150oC) related to modelling and
manufacturing uncertainties.

Nationaal Lucht- en Ruimtevaartlaboratorium, National Aerospace Laboratory NLR

Anthony Fokkerweg 2, 1059 CM Amsterdam,

P.O. Box 90502, 1006 BM Amsterdam, The Netherlands
Telephone +31 20 511 31 13, Fax +31 20 511 32 10, Web site: www.nlr.nl
UNCLASSIFIED
 Nationaal Lucht- en Ruimtevaartlaboratorium
National Aerospace Laboratory NLR

NLR-TP-2011-469

Thermal analysis of wiring for weight reduction and

improved safety
Requirements review and validation of wire bundle model
inside enclosure

R.C. van Benthem, W. de Grave, F. Doctor, K. Nuyten1, S. Taylor1 and

P.A. Jacques2

1 Fokker Elmo BV
2 Open Engineering SA

This report is based on a presentation held at the AIAA/ICES Conference, Portland, Oregon, USA,
18-21 July 2011.
"This report has been reviewed by Ruel A. (Tony) Overfelt, Reed Professor of Mechanical Engineering,
Auburn University, and two other session attendees prior to the AIAA conference."

The contents of this report may be cited on condition that full credit is given to NLR and the authors.

Customer Netherlands Agency for Aerospace Programmes (NIVR)

Contract number 59919N
Owner NLR
Division NLR Aerospace Systems and Applications
Distribution Unlimited
Classification of title Unclassified
October 2011
Approved by:
Author Reviewer Managing department
R.C van Benthem J van Es P Dieleman
NLR-TP-2011-469

Summary

The concept of thermal analysis was demonstrated with the construction of a Thermal Design
Model (TDM) predicting wire temperatures in bundles. Better knowledge of the wire
temperature leads to improve bundle design in terms of weight and safety. Several
configurations of 14 mm to 16 mm diameter wiring bundle samples were tested under
representative air temperatures between -55oC to +70oC and pressure conditions between
120 mBar to 1 Bar (50.000 feet to sea level. Evaluation revealed a temperature prediction
accuracy of +/-19oC (@ 150oC) related to modelling and manufacturing uncertainties.

3
NLR-TP-2011-469

Contents

Summary 3

Nomenclature 5

Abbreviations 6

1 Introduction 7

2 Requirements review 9
2.1 Thermal equilibrium 9
2.2 Current derating factors 12
2.3 Heat transfer of bundles in free air and cylindrical enclosure 14
2.4 Estimation of current derating factor for multiple wires in a bundle 16

3 Thermal Analysis 17
3.1 Bundle modeling 18
3.2 Thermal Design Module (TDM) Software 19

4 Test Evaluation 21
4.1 Wire sizes 22
4.2 Test cases 22
4.3 Test Facility 23
4.4 Test Results 23
4.5 Model accuracy 24

5 Conclusion 25

Acknowledgments 26

References 26

4
NLR-TP-2011-469

Nomenclature

Ae = wire external surface area DeL m2

Ab = bundle external surface m2
cD = heat flux by air conduction W/m2
CD = heat transfer coefficient cylinder W/K per meter
De = external wire diameter Di+2t m
Di = internal (conductor core) diameter m
F = view factor (for IR radiation) -
h = heat flux by air convection W/m2
I = (design) current Amp
L = wire length m
MD = wire mass Kg
NuD = Nusselt Number -
P = transported Power W
Qc = wire cooling W
Qh = wire heating W
r = heat flux by IR radiation W/m2
R = wire resistance Ohm
t = insulation thickness m
T = temperature difference wire and air K
V = voltage drop Volt
(T1 - T24)
4 3
= IR radiation transfer ~4T T W/m2
= air expansion coefficient K-1
= IR emission coefficient -
= air conduction W/mK
-8
= Stephan Boltzmann = 5.67.10 W/m2K4
= material density Kg/m3
e = specific conductor resistance Ohm.m
= kinematic viscosity cm2/s
= contact conduction W/m2K

5
NLR-TP-2011-469

Abbreviations

AWG = American Wire Gauge

FEM = Finite Element Model
IR = Infra Red
TDM = Thermal Design Module
NIST = National Institute for Standards and Technology
NLR = National Aerospace Laboratory, The Netherlands

6
NLR-TP-2011-469

1 Introduction

M ass figures for wiring bundles required for distribution of electrical power and data for
aerospace applications, are difficult to obtain. A typical commercial aircraft with 150 seats
may contain over 1500kg of installed wiring harnesses, whereas commercial satellites could
have 50kg of wiring on board. Life cycle cost for an aircraft, or launch costs for a satellite,
could go up to >10.000 Euros per kilogram of wiring. Significant effort has been applied in the
aerospace industry for a reduction of the weight of wires and cables through application of
aluminum rather than copper as conductor material. Application of light weight dielectric
materials and high voltage designs also contribute to a reduction of the bundle weight.
However, not many electrical engineers realize that the weight of power bundles is related to a
thermal equilibrium. Wiring in
bundles produce significant Qnatural cooling =CD T
amounts of heat when
transporting a current (due to the V=IR
electrical resistance of its wires) R e
4L
M D L
2
Di D i
and need sufficient cooling to Di 2 4 I=P/V
control its temperature. Since
cooling is only available at the Qlosses=I2R=PV/V
outer surface of a wire by means
of natural convection and
infrared heat radiation, the
temperature of a wire (Figure 1) is Figure 1 Heating and cooling conditions for a piece of wire
controlled by sizing-up the
conductor core Di, controlling heat losses per meter and cooling area, at the cost of an increased
weight. Optimizing on voltage drop (V=IR) across a piece of wire transporting a current I and
power (P =IV) is often used by some aircraft manufactures to reduce weight. However, voltage
drop design only limits the total heat loss of a wire, hence the limiting factor for the current -
especially for short wire lengths- is also thermal. Now-a-days electrical engineers in the
aerospace industry around the world use the selection rules from SAE AS508816 or ECSS-30-
11A5 when designing wiring bundles for aircraft and space applications. However the
recommended design rules follow the successive series of MILW-5088s are basically
unchanged since the early 50s. The selection rules are based on a thermal balance between the
heat losses due to its electrical resistance of a wire and cooling by natural convection and heat
radiation. This results in a free wire current for which the maximum allowed temperature (Tmax)
of a single free copper wire in ambient air is given. Although several parameters contribute to
the heating and cooling of a wire the free wire current Ifwc is mainly related to the conductor size
Di, the temperature elevation above ambient T and the air pressure Pa. whereas the heat loss is
related to design parameters such as material properties, sizing and operating current, external
cooling of a wire is related to its local environment e.g. its application:

Ifwc = F(Di, De, e, , T, Pa) (1)

With e is the specific electrical resistance, the emission coefficient, and De the external
diameter due to dielectric insulation. To understand the implication of the thermal equilibrium
with respect to the wiring weight in Table 1 below an example is given for the free wire
currents allowed by the standards for a 120oC wire in a 70oC environment (T=50oC), under
several pressure conditions.

7
NLR-TP-2011-469

Free Wire Current [Amp]

SAE- AS508816 ECSS-Q-30-
11A5
Wire Gauge Core diameter Wire weight Ambient Air 60.000 feet Vacuum
(AWG) mm kg/km @ 1 Bar @ 0.072 Bar @ 0 Bar
24 0.59 2.7 7.5 5.6 3.5
20 0.97 6.8 13.5 10.5 7.5
16 1.45 14.6 20 15.6 13
12 2.18 31.3 36 28.1 25
8 3.85 90.0 75 58.5 45
4 6.35 215 132 103 81
120oC wire and 70oC environment (T=50oC)

Table 1 Wire properties related to size and free wire current for a single copper wire as
recommended by the aeronautical standards

The American Wire Gauge (AWG) 9,10, diameter is calculated by applying the formula
D(AWG)=0.127*92((36-AWG)/39) mm. This means that the American Wire Gauge every 6 gauge
decrease gives a doubling of the wire diameter, hence every 3 gauges doubles the weight. For
instance an industrial application in ambient air at sea level uses a single AWG 20 wire to carry
a current of 13.5 Amps. For a wire inside an aircraft flying at 60.000 feet, transporting the same
current, an AWG 18 (2 steps) is needed which is about 75% heavier. A spacecraft (vacuum)
needs an AWG 16 wire (4 steps) - which is more than 100% heavier. - at the same current. This
example illustrates that the application has a significant impact on bundle weight. Another way
to prevent overheating of wiring is to reduce the allowed current. The standards therefore
recommend a current derating factor d on the free wire current to compensate for a
temperature increase related to its environmental conditions.

Id=Ifwc d (2)

However, as illustrated above, current derating effectively means increase wire size &
weight'. Especially the high derating factors recommended for wires in bundles result in a
significant weight increase of bundles. Clearly for applications were weight is an issue
estimation of the current deration factors should therefore be as accurate as possible.

For practical reasons wires are usually routed together in bundles. The standards recommend
derating factors for core material, altitude, number of wires in a bundle and load conditions.
(See also section II 2.2) Since cooling of a wire in a bundle is largely blocked by its neighboring
wires, bundles are thermally worst case. The current derating factor for a wire in a bundle could
be as low as 0.1 corresponding to 16 gauges (example AWG 20 -> 4) resulting in a ca 64 times
weight increase. For weight optimization it may be better (however unpractical) to split large
bundles, keeping the number of wires per bundle low hence limiting the derating factors. Since
the maximum current is related to its application, manufactures, specify the maximum wire
temperature (rating). The wire rating (Table 2) is related to conductor plating and the applied
dielectric insulation.

8
NLR-TP-2011-469

Tmax oC Insulator Type(s) Conductor and plating

135 Fluoropolymer, FEP, PVF2 Tin coated copper
Fluoropolymer, extruded ETFE
150 Polytetrafluorethylene/polyimide Tin coated copper
Cross linked polyalkene
Fluoropolymer, TFE and
200 TFE coated glass, FEP, Silver coated copper
Fluorcarbon polyimide

260 Fluoropolymer, extruded TFE Nickel coated copper

Table 2 Wire ratings for several wires types as specified in SAE-AS508816

With increasing weight and complexity of wiring bundles in aerospace applications, the need
is felt to get a better understanding of the thermal conditions and related current derating for
wiring bundles, for optimization of the bundle weight and to prevent overheating.
Environmental cooling is limited by neighboring bundles, application of insulating braids,
routing through poorly ventilated channels and the use of composite structural materials which
are not considered in the standards at all. This justifies thermal modeling of the local conditions
of wiring bundles beyond the assumptions in the aeronautical standards. This paper investigates
the physical background of the wiring selection rules in section II and proposes a Thermal
Mathematical Method (TMM) comparing the results with the aeronautical standards in section
III. This led to the construction of a Thermal Design Module (TDM) that generates a thermal
model of wires in a bundle. In this stage the focus was the modeling of the heat transfer of a
bundle and wire configuration. The TDM is partly validated by testing of six 15-17 mm bundle
samples inside a temperature controlled low pressure facility simulating enclosure condition.
The test results are described in section IV. The work on the TDM is continuing by extending
its validation range for bundles between 5-35 mm and towards more complex enclosures
interactions estimated with Finite Element Analysis (FEM).

2 Requirements review

Starting point for the aerospace standards is the cooling conditions of a single wire provided
at the outer surface by natural convection in ambient (sea level) air. For space applications
without air, cooling of a wire is reduced to heat radiation. When cooling is limited, for instance
at high altitudes or due to neighboring wires in a bundle, the temperature of a wire increases and
current derating factors should be applied e.g. to prevent overheating at the cost of a increased
weight. For SAE AS508816 the maximum free wire current is derated for altitude, number of
wires in a bundle, load conditions and air temperature. In ECSS-Q-30-11A7 only the number of
wires at a 100% load is taken into account for derating the currents.

2.1 Thermal equilibrium

Both SAE AS508816 and ECSS-30-11A5 take the current versus temperature of a single free
copper wire as the starting point for the wire section rules. The heat loss Qh of a wire section L
when transporting a current I is related to the specific electrical resistance of the conductor
material e and its cross-section Di2 according to Ohms law:
4L
Qh I 2 R I 2 e (3)
Di 2

9
NLR-TP-2011-469

From this function it is evident that the heat loss of a wire with a fixed length L can be
reduced by using a material with a low specific resistance e (such as copper or aluminum) or
by enlarging the conductor diameter Di at the cost of a weight increase.

MD
2
Di L (4)
4
Although the density of Copper is relatively high it is the preferred conductor material in
most cases due to its low specific resistance. Aluminum which has a somewhat higher specific
resistance which is compensated by a increasing the core diameter and is applied in the
aerospace industry for its lower density resulting in lighter bundles, however at the cost of an
increased volume. The heat flux h=Qh/Ai across the outer surface of a wire (Ai=DiL) is a
function of Di3 with:
Qh 4 I 2 e
h (5)
Ai 2 Di 3
The cooling of a wire is provided at its outer surface (Ae=DeL) limited by natural
convection of air (h=NuD/De) and Infrared (IR) radiation (r~(T4-Ta4), Ts the temperature of
the outer surface of a wire and Ta the air or enclosure temperature. See also section C for more
details. Since air is transparent for IR radiation for short distances as found in enclosures these
two contributions add up for the overall heat transfer coefficient CD.of a wire. The temperature
elevation (T=Ts-Ta) of the wire with respect to its ambient is then defined by:

Qc Ae (h r )T CD T (6)

For space applications, in the absence of air h=0 and wire cooling is provided by heat
radiation only. The overall cooling flux cD can be written as cD=h+r in W/m2K or CD = DeLcD
which is a function of the wire external surface area. The free wire current (Ifwc), the final
temperature elevation of a wire above ambient (T) is found when there is an equilibrium
between the heat losses and the available cooling thus Qh=Qc which is optimized by selecting
the conductor diameter Di. Note that the external diameter De of a finished wire is slightly larger
then the conductor diameter Di due to insulation thickness. For the calculation it has been
assumed that De= Di+2t~Di and that T does not vary along the wire length L.
4 e I fwc
2
2 h
T k D I fwc (7)
Di DeC D
2 2
CD
The temperature elevation is the ratio between the heat flux at the outer surface and the heat
transfer coefficient. The heat transfer coefficient CD of a cylindrical body (a wire or bundle) in
free air or inside an enclosure is calculated in section 2.3 using air properties as function of
temperature and pressure. When CD is implemented in a Thermal Mathematical Model (TMM)
this shows T versus the current for a free copper wire in 20oC ambient air. The TMM
produces straight lines for each wire size (Figure 2) when plotting T versus I on a log-log
scale. When including both convection as well as heat radiation the calculation fits well with
SAE AS508815 (Figure 3). When excluding convection, the TMM calculations also matches
with the currents provided by ECSS-Q-30-11A5 under vacuum conditions (see Figure 4). Small
deviations indicate that possibly insulation thickness variation is considered in ECSS-Q-30-
11A5. Conclusion is that function (7) produces results comparable with the standards.

10
NLR-TP-2011-469

Figure 2 Temperature difference as function of the current for a single free copper wire in
ambient air as specified in SAE-AS508816 in the range of wire size 26 up to size 4/0

For ECSS-Q-30-11A a similar graph (Figure 3) is constructed for a free wire in 20oC
environment only radiating heat. The result is slightly fitted to match the currents as found in
the specifications for T=50oC. In SAE AS50881 the ambient temperature is set as high as
possible (worst case) to determine the maximum current and from that point current derating
factors are given for the core material (e.g. copper or aluminum), air pressure, number of wires
in a bundle and load. However, other conditions affecting external cooling such as braiding,
neighboring bundles or (local) enclosure (materials) are not addressed. Note that derating the
free wire current to level off the wire temperature is done at the cost of an increased bundle
weight.

1000
T e m p e r a t u r e d if f e r e n c e [ K ] = >

TMM AWG 24
TMM AWG 20
100 TMM AWG 16
TMM AWG 12
TMM AWG 8
TMM AWG 4
SAE 50881 dT=30C
SAE 50881 dT=50C
SAE 50881 dT=100C

10
1 10 100 1000
Current [Amp] =>

Figure 3 Predicted temperature elevation versus current using TMM for a single free copper
wire as function of wire size 24 up to size 4 compared with SAE AS508816

11
NLR-TP-2011-469

Temperature difference [K] =>

100

TMM AWG 24
TMM AWG 20
TMM AWG 16
TMM AWG 12
TMM AWG 8
TMM AWG 4
ECSS Q30 dT=50C

10
1 10 100 1000
Current [Amp] =>

Figure 4 Predicted temperature elevation versus current using TMM for a single free copper
wire as function of wire size 24 up to size 4 compared with ECSS-Q-30-11A5

2.2 Current derating factors

Application of current derating factors are recommended in the standards to prevent overheating
of wires. Because the free wire current is calculated for a single copper wire in ambient air,
worst case derating factors in SAE-AS508816 must be applied for:
Aluminum conductor (d1 = 0.8) > ratio of the specific resistances of copper and
aluminum cu/al
Altitude (d2= 1-0.7) >See also altitude derating factor calculated with TMM (Figure 5)
for convection and heat radiation for wire size 4 and 24.
Multiple wires & load cases in bundles (d3= 1-0.25) > See Figure 6 and bundle
derating factors calculated with TMM (Figure 8)

12
NLR-TP-2011-469

1.1

0.9

0.8

0.7

0.6
Derating

0.5

0.4 SAE 50881

TMM AWG 24 conv + rad
0.3 TMM AWG 4 conv+ rad
TMM AWG 24 conv
0.2 TMM AWG 4 conv

0.1

0
0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
Height (feet)

Figure 5 Current derating factor as function of altitude in SAE-AS508816 (solid line) compared
with TMM predicted for wire size 4 and 24 using convective cooling with and without heat
radiation

The overall derating is defined as: d = d1xd2xd3. The design current for the selection of a
wire is then defined as: Idesign=dIfwc. For example the derating factor for a wire inside a bundle
with >33 wires is 0.8*0.85*0.26=0.17, for an aluminum conductor (d1=0.8) at a worst case
altitude of 40.000 feet (d2 = 0.85) and a
100% load (d3=0.26).This indicates that for
33 or more wires in a bundle, with a 100%
load, a current derating factor of 0.26 must
be applied. Note that in this example the
bundle composition gives the largest
contribution to the derating factor. When a
wire in air is allowed to carry 100A, it can
carry 26A when applied in a bundle with 33
or more wires at a 100% load. The derating
levels off to about 0.24 (@100%load) for
33 wires or more. The requirements for
space are fully comparable with SAE-
AS508816, however ECSS-30-Q-11A5
assumes a worst case 100% load and has Figure 6 Current derating factor for
split has been made between size 0-12
and size 14-32 resulting in derating factors between 0.32-0.25 for 33 or more wires. In section D
an analysis is done to calculate the bundle derating factor from the ratio between the sum of the
heat transfers of its wires related to overall heat transfer of a bundle.

13
NLR-TP-2011-469

2.3 Heat transfer of bundles in free air and cylindrical enclosure

The heat transfer coefficient of a bundle can be
estimated using empirical functions for convection,
T conduction and IR radiation of a bundle in free air or
inside a cylindrical enclosure which have been
Tb
D D validated by test. For more complex enclosure
conditions CD is evaluated using Finite Element
Qh Modeling (FEM). For a general approach of the heat
transfer coefficient CD assume a isothermal heated
cylindrical object (e.g. a bundle) with length L meter
Figure 7 Bundle in enclosure and size D in free air (D->) or inside an
(cylindrical) enclosure size D. See Figure 7. The final
temperature elevation of a bundle above ambient is found when there is an equilibrium between
heating and cooling conditions. The heat dissipation is the sum of the heat loss of N wires in a
bundle.
N
Qc CD T Qh in Rn
2
(8)
n 1

With T=T-Tb is the temperature difference between the (external surface of) the bundle and
the enclosure. CD is the overall heat transfer coefficient of the bundle which is the sum of air
convection and IR radiation to the enclosure. The heat transfer coefficient CD is a function of the
averaged air temperature Tavr=(Tb+T)/2 and bundle size that can be evaluated per meter bundle
length by taking L=1m.
3
C D (T ) LD ( Nu D 4 eff T F ) (9)
D

The Nusselt number NuD is the ratio between convective and conductive heat flow, a
dimensionless number >1 reflecting convective properties of air related to bundle diameter D
and also includes cylindrical enclosure diameter D. The convection heat exchange of an
isothermal horizontal cylindrical shaped body in free air can be written according to:

0.387 RaD 6
1

Nu D 0.6 8 / 27
9
1 (0.559 / Pr ) 16
(10)

(Free convection for horizontal cylinder, 10-5 < RaD < 1012, Churchill and Chu (1975)1)

The convective heat exchange of a cylindrical shaped body inside an enclosure can be written
according to Raithby and Hollands1 as:

1/ 4
1 2.425 Pr RaD
Nu D
1 D
D
3/ 5 5 / 4
0.861 Pr
(11)

(Convection in cylindrical enclosure, RaD < 107, Raithby and Hollands1)

14
NLR-TP-2011-469

With Reynolds Number RaD= g(Tb-T)D3/2 Pr and Pr(Prandlt)=0.707 for air. Air properties
(thermal expansion) and (kinetic viscosity) as function of pressure and temperature are taken
from NIST8. At low pressures the contribution of convection is poor and NuD=1 (air conduction
only) until the boundary layer becomes lager then the available space e.g. <(D-D)/2 in that
case NuD = 1/ln(D/D). In vacuum NuD=0, leaving heat radiation doing the cooling. F=1 is the
geometrical view factor for IR radiation between the bundle and the enclosure which assumes
and unblocked view to the enclosure. Note that due to the relatively small temperature
differences between the bundle and the enclosure (Tb ~T), IR radiation can be linearized by
taken T3 at the averaged temperature using:

3
(Tb 4 T 4 ) (Tb 2 T 2 )(Tb T )(Tb T ) 4 T T (12)

The effective emission coefficient becomes:

1
eff (13)
1 Ab 1
1

b A

When assuming b ~1 and ~1 an effective emission coefficient (eff=1) was chosen as a

starting point for the calculation. For free air A->. Below the heat transfer coefficient CD for a
L=1 meter bundle at 120oC in free air (Table 4 ) and inside a 200 mm cylindrical enclosure at
70oC (Table 4) is calculated using the above functions. For a 200 mm enclosure minor
deviations in heat transfer with respect to free air situation is found. However for improved
thermal analysis the deviations in heat transfer should be included for bundles inside enclosures.

BundleSize Ambient 50.000feet Vacuum

mm 1Bar 0,116Bar
5 0.40 0.23 0.14
10 0.69 0.42 0.29
15 0.95 0.61 0.43
20 1.20 0.79 0.58
25 1.43 0.96 0.72
30 1.65 1.13 0.86
35 1.87 1.30 1.01

Table 3 Heat transfer coefficient CD (W/K) for a cylindrical object

(L=1m) at 120oC in free air at 70oC

15
NLR-TP-2011-469

BundleSize Ambient 50.000feet Vacuum

mm 1Bar 0,116Bar
5 0.36 0.25 0.14
10 0.63 0.43 0.29
15 0.89 0.61 0.43
20 1.14 0.79 0.58
25 1.39 0.96 0.72
30 1.64 1.13 0.86
35 1.88 1.31 1.01

Table 4 Heat transfer coefficient CD (W/K) for a cylindrical object

(L=1m) at 120oC in a 200 mm enclosure at 70oC

2.4 Estimation of current derating factor for multiple wires in a bundle

Assume N equally sized wires size Di in a bundle. When assuming a good packing of these
wires the bundle diameter DB becomes approximately:
DB N Di (14)
The thermal equilibrium is found when the total heat losses of all wires in the bundle (including
a current derating factor d) should be in thermal equilibrium with the overall bundle cooling.

N N N
Qh (din ) 2 Rn d 2 in Rn d 2 Ci T CB T
2
(15)
n 1 n 1 n 1

The current derating factor d for a wire in a bundle is calculated from ratio between the sum of
the heat transfer coefficient of all the wires and the overall heat transfer coefficient of the bundle
assuming an equal temperature difference.
CB
d N
. (16)
C
n 1
i

The above estimation of the derating factor for all wires in a bundle gives a good match with
SAE-AS508816 for a 100% load case, the smallest sizes and assuming convection only. See the
TMM AWG 24 line (triangle) in Figure 8. Since radiation cooling is not considered this is worst
case. Also it is found that derating factors in ECSS-Q-30-11A5 (black line) neglect radiation
cooling (TMM AWG24-4 radiation only - tilted square). The size split for >20 wires only
makes sense when assuming convective cooling only. It looks like that deration factors of SAE-
SA508816 are copied into ECSS-Q-30-11A5 which in fact is too worst case under vacuum. Since
for space applications the current is already significantly derated up to 50% for vacuum
conditions additional bundle deration leads to an increase in weight.

16
NLR-TP-2011-469

0.9

0.8
ECSS AWG 0-12
0.7 ECSS AWG 14-32
SAE 50881 at 100% load
C u rre n t d e ra tin g fa c to r

0.6 TMM AWG 24 convection only

TMM AWG 4 convection only
TMM AWG 24-4 radiation only
0.5

0.4

0.3

0.2

0.1

0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105
Number of Wires (N)

Figure 8 Current derating as calculated with TMM in air and vacuum compared with SAE-
AS508816 and ECSS Q-30-11A5

Conclusion is that since heat radiation looks like to be neglected in both SAE-AS508816 and
ECSS-Q-30-11A5 the recommended current derating factor for wires in bundles is most likely
too worst case, leading to an increase in bundle weight. A detailed thermal analysis of an actual
bundle design is therefore recommended to investigate if a weight saving is possible when
including heat radiation cooling.

3 Thermal Analysis

Since a bundle in an aircraft enclosure is surrounded by a pocket of air most of its heat
generated is transported in radial direction due to natural convection, air conduction and heat
radiation. Cooling by conduction in axial/length direction (via the wire cores) and by air
ventilation is very limited and therefore neglected for the worst case analysis. Note that the
generated heat by a bundle is finally absorbed in the surrounding aircraft structure. The
enclosure temperature is related to the balance between the absorbed and conducted heat to the
thermal mass of the aircraft. The final temperature of a bundle with respect to the enclosure (air)
temperature stabilizes by having a thermal balance between the (time averaged) heating and
cooling contributions. The heat balance for a bundle segment in aircraft is therefore:

Qheat-dissipation = Qnatural-convection + QIR-radiation = Qabsorbed-enclosure + Qventilation +Qaxial (17)

Worst case, cooling by axial conduction or ventilation is usually neglected. At high altitudes
e.g. low pressure conditions, the contribution of natural convection reduces significantly,
leaving heat radiation and air conduction to do the cooling of a bundle. See Figure 9 below for
an example calculation of the airs velocity field around a bundle of 16mm diameter due to

17
NLR-TP-2011-469

natural convection dissipating 50W per meter inside a 60oC cylindrical enclosure (ID=200mm)
as function bundle temperature and pressure conditions. The result is that the bundle
temperature increases from 112oC (T=520C) to 123oC (T=630C) when transporting the same
currents for aircraft flying in low pressure air at an altitude of 50.000 feet.

CD=0.962 W/K CD=0.786 W/K

bundle

(cross section)
convection

air

Enclosure
IR radiation
wall
o
T=60 C

Figure 9 Example calculation (FEM) of natural air convection as function of pressure on the
temperature of a 16mm bundle inside a 200mm enclosure (velocity arrows colored with
temperature field, Oofelie:Multiphysics, Open Engineering)

3.1 Bundle modeling

A bundle is defined as a collection of wires. A mixed (power + data) harness design has been
considered as starting point for the modeling which is possible for current below 15 Amps. A
typical mixed bundle has more than 100 wires per bundle of which are:
ca 35% AWG 24
ca 40% AWG 22
25% < AWG 22
Ca 65% of the large wires (<AWG 22) carry a current and the remaining small > AWG 22
'passive' wires are ca 35% for data transmission. Clearly, the size, currents, number of cores in
wire, the position of a wire in a bundle, fixtures and supports, air temperature and pressure
determines the wire core temperature. For instance a wire in the centre of a bundle is hardly
cooled since it is in close contact with surrounding wires limiting cooling whereas a wire along
the perimeter is directly cooled by air convection. Thermal modeling of wires in a bundle
therefore should take into account:
Wire type, dimensions and number of cores (e.g. AWG size, single, double, triple, quad).
Insulation, shielding and jacket thickness (thermal resistance).
Wire core (conductor diameter and material).
Current (DC, AC, heat losses).
Bundle configuration e.g. contact conduction with neighboring wires or air convection at
the bundle perimeter.
Environmental conditions (air temperature, pressure, enclosure).

18
NLR-TP-2011-469

A major point of concern for the modeling is that the wire position inside a bundle is fluctuating
e.g. changes along the length of a bundle due to the manufacturing process. For instance a wire
starting in the centre of a bundle can be at the perimeter several meters down the line. The
above factors require general assumptions about the wire environment inside a bundle. Each
wire is represented by a single thermal node with a radial heat transfer to its local environment.
A cylindrical shape of cores, wires, bundles and enclosures.
Electrical resistance as function of temperature.
Radial heat losses only, axial conduction, bundle supports and fixtures are neglected.
Small temperature difference exists between wires in a bundle.
Wires are mainly cooled by 'contact' conduction; internal convection and heat radiation
is neglected
Mutual contact conduction between the wires is related to their contact angles.
Each wire is modeled as a single node; no internal temperature gradients due to the high
specific thermal conduction of the conductor material all cores carry the same current.
The influence of the ETFE insulation and shielding is represented by a thermal
resistance of a wire node to its environment.
A fixed wire distribution assumed e.g. each bundle configuration requires a new
calculation
External air convection and heat radiation at the outer surface of the bundle is evenly
distributed over the wires located at the bundles perimeter.
The influence of braiding can be included by an additional node representing the braid of
a bundle.

3.2 Thermal Design Module (TDM) Software

The Thermal Design Model (TDM) is a NxN nodes matrix solver (see Figure 10) that is
implemented in a software application. It is a standalone application developed in Java. The
main advantage of the development in the Java language is that the application is platform
independent and it only needs a java runtime environment (jre 1.5 or higher). The TDM
software needs the following three input files:
Wire database file. File with information about the individual wires as provided by the
manufacturer. Per wire the following information is used: The wire type number, the wire-
type (twisted shielded, twisted shielded
load cases
triple, twisted triple, twisted pair and & sizing

single wire are the types that are

supported by the TDM software), the Bundle Design wire data base
Worst Case(default); Optimal; Random
conduction-outer-diameter [mm], the
wire-outer-diameter [mm], wire-outer- Bundle
Configuration
diameter [mm], the wire-size [mm], the Heat transfer coefficient, C
D

number-of-leads and the jacket- Temperature

thickness [mm].
Air properties/vacuum
TDM
Pressure
Bundle composition file. This file
contains the wires of which the bundle Wire
Sizing?
is composed, including the design Temperatures

currents [A]. The configuration is

defined by the user. See figure 11 for Figure 10 Thermal Design Module to predict
the three preset configurations. wire temperatures in a bundle

19
NLR-TP-2011-469

Air-properties file. This file contains the following values: Altitude [feet], Air Temperature
[oC], Pressure [MPa], Density [Kg/m3] Thermal condition [mW/mK], Kinematic viscosity
[cm2/s], Prandtl Volume-expansivity [1/K]. The values have been generated using NIST8
information.

Figure 11 TDM Bundle configurations: (1) Worst Case (default), (2) Optimal or (3) Random

Next to the input-files the following user input is required: altitude, enclosure-temperature,
enclosure-diameter and the bundle-diameter for the calculation of the heat transfer coefficient
CD. The TDM1.0 software distributes the cables of the bundle according to a worst case
configuration, which means that cables with largest weight and currents are in the centre of the
bundle and cables with smallest weight and lowest currents are at the outside of the bundle. It
was found during the testing of the samples that the worst case configuration gives the highest
wire temperatures compared to the 'as manufactured' (random) case. The TDM software uses a
radial approach for the calculation of the heat transfer coefficient of a bundle and computes the
mutual contact conduction of each wire based on
contact angles and bundle configuration. TDM
computes for each wire the dissipation Pi, and its
temperature Ti. The predictions are provided in a
file or plot (Figure 12). The TDM version 1.0 is
validated for worst case, optimal and random
bundle configurations, enclosure dimension 200
40 mm, bundle sizes 16 2 mm, 40 to 100 wires
and a absolute temperature accuracy of 20oC at
150oC related to modeling and manufacturing
uncertainties.
Figure 12 TDM output plot of wires
temperatures in a bundle

20
NLR-TP-2011-469

4 Test Evaluation

The Thermal Design Model version 1.0 was validated using 6 samples (Figure 13 and Table
5) of a typical mixed aircraft wiring bundle design statistically equivalent with respect to
composition and sizing with a bundle in typical aircraft. Note that modern separation rules do
not allow mixing of power and date wire anymore, but this has no influence on the model
validation. Two main series of samples were tested:
A series using a standard design (bundle diameter ca 16 mm)
B series using a reduced design (bundle diameter ca 14 mm)

Figure 13 Sample layout

For each series three wire configurations (Table 6) with respect to the distributions of power
(current carrying) and data (no/low current) wires were constructed, resulting in a (small)
difference in the convection properties:
1 Worst case (power wires inside, data wires outside)
2 Optimal (data wires inside, power wires outside)
3 Random (manufacturing practice)
The wire temperatures are measured using thermocouples at the left, centre and right
position attached to the wires (for all wire size at least three) located in that particular cross-
section. Note that the terms "Optimal" and "Random" were used prior to the testing. It was an
unexpected result that the random configuration gave a 6 7oC lower averaged bundle
temperature than "Optimal". See also Figure 15. A possible explanation is that the random case
spreads out its heat in all directions either by convection or conduction to surrounding wires. In
the optimal configuration only wires at the surface loose heat, resulting in higher bundle
temperatures.

Sample no Bundle Diameter [mm] Bundle Configuration

A1 17 Worst Case
A2 17 Optimal
A3 17 Random
B1 15 Worst Case
B2 15 Optimal
B3 15 Random

Table 5 Samples used for the validation of the TDM

21
NLR-TP-2011-469

4.1 Wire sizes

See Table 6 for the definition of the test sample wiring and currents. The wires inside each
sample are defined in 4 power lines carrying a current and 2 passive data lines.

Line Sample A Sample B Number Type Raychem SPEC557

series series of wires
Power 1 AWG 12 AWG 14 1 Wire, twisted triplet, tin plated, light weight insulation

Power 2 AWG 16 AWG 20 3 Wire, twisted shielded jacketed triplet, tin plated, light
weight insulation
Power 3 AWG 20 AWG 22 5 Wire, tin plated, light weight insulation
Power 4 AWG 22 AWG 24 7 Wire, twisted pair, tin plated, light weight insulation
Data 1 AWG 22 AWG 24 13 Wire, twisted shielded jacketed pair, high strength copper,
tin plated, light weight insulation
Data 2 AWG 24 AWG 24 29 Wire, high strength copper, silver plated, light weight
insulation
57
Table 6 Wire & current definition for the samples

4.2 Test cases

The above combinations resulted in the construction of the six bundles: A1, A2, A3, B1, B2,
and B3. Each bundle was tested under three environmental conditions (hot, nominal and cold)
ranging from -50oC to +60oC and 0.1 Bar to 1 Bar. The pressure and temperature ranges were
chosen for correlation of the air convection properties at sea level and 50.000 feet:

Test Case Environment Temperature [oC] Air Pressure [Bar]

Hot 60 0.1
Nominal 15 0.7
Cold -50 1

Table 7 Test conditions used for the validation of the TDM

22
NLR-TP-2011-469

4.3 Test Facility

The following set-up (Figure 14) is used for the bundle tests.
The sample bundles were placed in a pressure
controlled cylindrical tube (ID=200 mm) with
sealed flanges to allow testing in low pressure
environments.
The large tube was placed in a temperature
controlled chamber.
The cylinder temperature is measured using
several thermocouples.
The averaged bundle temperature is measured
using several thermocouples located in the
centre cross-section of the sample. Figure 14 Photograph of the test
facility in the climate chamber

4.4 Test Results

It was been assumed that the averaged surface temperature of a bundle equals the
averaged wire temperature. The effective heat transfer Ceff (= P/dT) between the bundle and the
enclosure (cylinder wall) is calculated from the total
T
Hot
= 60 C enclosure
o dissipation per meter of the bundle and the
130
temperature difference dT between the averaged
bundle and the enclosure (facility wall) temperature.
Bundle Temperature [oC]=>

125

120
Note the bundle configuration has a slight effect on
115
the averaged bundle temperature. As can be seen in
110 Figure 15 were the average bundle temperature is
105 plotted for sample A1, A2 and A3 in the hot case.
100 The max temperature difference in the bundle
A1 A2 A3
Sam ple
averaged temperature between the bundle
configurations is in the order of 12oC. Interestingly
Figure 15 Average bundle the 'random' configuration gives the lowest averaged
temperature as measured for the A bundle temperature even better than the 'optimal'
samples during the hot case configuration. The 'worst case' configuration gives
indeed the highest temperature of +12oC above
'random'. An explanation is that in the random case wires Ceff

loose their heat in all directions either by convection or

conduction to surrounding wires evenly spreading out 0.90
Bundle Conduction [W/K]=>

0.80
heat, whereas in the optimal case only heat rejection 0.70
0.60
towards the external surface is possible. Since the worst 0.50

case bundle configuration gives the highest wires 0.40

0.30

temperatures this is taken as the default case for wire 0.20

0.10
temperature prediction in TDM1.0. A small difference of 0.00
A1 B1 A2 B2 A3 B3
ca 8-14% in the averaged overall conduction (Figure 15) Sam ple

is found between the sample configurations 1, 2 and 3 of

both the series A and B. As expected by its ca 12% Figure 16 Hot case heat transfer
smaller surface area the reduced bundles (B) give a ca coefficient CD as measured for
samples A&B
12% lower heat transfer value compared to the nominal
(B) samples. Within the error margins the sample measurements and TMM predictions
correspond very well (see Table 8) except for sample A3. The overall measurement accuracy is
estimated using an error of 5oC for the measurement of the temperature difference between the

23
NLR-TP-2011-469

bundle and the facility and a heat dissipation measurement error of 1W. The estimated
calculation accuracy ( 0.05) is related to the uncertainty in the measurement of the bundle
diameter (0.5-1mm) and overall bundle surface temperature ( 5-10oC). A3 has a heat transfer
coefficient which is slightly higher than measured & predicted for sample A1 and A3 in all
cases. This could be related to a deviation in bundle diameter and/or random variations in the
bundle surface temperature.

Hot Nominal Cold

Measured Predicted Measured Predicted Measured Predicted
Sample +/-0.15 +/-0.05 +/-0.15 +/-0.05 +/-0.15 +/-0.05
A1 0.742 0.712 0.739 0.754 0.676 0.661
A2 0.749 0.698 0.746 0.743 0.716 0.643
A3 0.838 0.678 0.872 0.719 0.815 0.623
B1 0.652 0.529 0.721 0.809 0.666 0.687
B2 0.670 0.597 0.753 0.759 0.692 0.672
B3 0.683 0.592 0.785 0.748 0.731 0.657
Table 8 Measured and predicted heat transfer coefficient [W/K] for the sample bundles inside a
200 mm enclosure

Since the focus of sample test was on the internal temperature distribution, the bundle diameters
and corresponding heat transfer coefficients only slightly varied. It is therefore recommended to
extend the validation range by testing larger and smaller sized bundles and also to include
enclosure size variations.

4.5 Model accuracy

When including the calculation of the bundles heat transfer the TDM1.0 predicts the wire
temperature with a temperature variations of 10.3oC between similar wires, related to the radial
position. Also the temperature difference between the averaged predicted and averaged
measured wire temperatures is about 8.2oC. Conclusion is that the worst case accuracy of
TDM1 is 18.5oC to predict a wire temperature, related to both the bundle manufacturing (e.g.
varying radial position) and modelling accuracy.

TTDM1 = Tmanufacturing + Tmodelling = |10.3oC| |8.2oC| = 18.5oC

Since this is a worst case estimation of the accuracy it is more convenient to use a relative
accuracy related to the temperature elevation T between the wire and ambient temperature.
With this approach the prediction accuracy of the model improves when the temperature
elevation reduces and worsens when the temperature elevation increases. For TDM1.0 this is
defined as TTDM1=T/60*20 (or T* with =1/3), meaning that for a temperature elevation of
60oC the TDM prediction accuracy is 20oC and for a wire temperature elevation of 30oC above
ambient the prediction accuracy becomes 10oC. It is therefore recommended to use the relative
accuracy related to the temperature elevation rather than a worst case accuracy for future
validation of the TDM.

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NLR-TP-2011-469

5 Conclusion

In this paper it is investigated that the physical background of wire selection rules in the
aeronautical standards are based on a thermal equilibrium which is fully understood by thermal
modelling in a TMM. Application of current derating factors to reduce wire temperature leads to
a significant increase in bundle weight. Since not all local factors limiting bundle cooling are
considered in the standards, this could lead to overheating of bundle or structural parts or to
over weight designs. Because heat radiation cooling is neglected in both SAE-AS508816 and
ECSS-Q-30-11A5 the recommended current derating factor for wires in bundles is most likely
too worst case, leading to an unnecessary increase in bundle weight. A detailed thermal analysis
is recommended to investigate if a weight saving is possible when including heat radiation
cooling.
A generic Thermal Design Model (TDM) was constructed to predict wire temperatures
inside bundles for three preset configurations. It appeared that the overall heat transfer
coefficient CD of a bundle to its enclosure due to air convection and heat radiation at outer
surface should be taken into account when calculating wire temperatures. Bundle heat transfer
coefficients can be approximated using empirical functions for convection and heat radiation in
free air or inside cylindrical enclosures. For more complex enclosure conditions the heat transfer
can also be estimated with FEM analysis. The TDM1.0 was validated with 2x3 representative
samples (14-16 mm) and was found to have a worst case accuracy of 18.5oC for the tested
range. This is the sum of the uncertainty in the modelling and the inherent uncertainty of the
variable radial position of a wire inside a bundle due to bundle manufacturing. TDM1.0 is now
validated for:
a generation of a worst case (default), optimal or random bundle configuration
enclosure dimensions: 200 40 mm
bundle sizes : 16 2 mm
40 to 100 wires (extrapolated from test results)
worst case accuracy 19oC (modeling uncertainty + manufacturing variations)
a temperature range between : -55oC and 60oC
a pressure range between 0.1 Bar and 1 Bar.
Since the accuracy and range of the TDM1.0 was too limited for practical use, work is
continuing extending the validation range to 5-35 mm diameter bundles and several enclosures.
A focus on the conditions found for the largest bundle segments in aircraft for the Fuselage and
the Wing is recommended. Proposed improvements of the thermal analysis for aerospace
applications are:
Implementation of more representative enclosure conditions using FEM
Implementation of bundle braids
Implementation of heat capacities & load profiles for power critical bundle designs
Implementation of axial heat leaks for delicate bundle designs
Implementation of vacuum or low pressure conditions (e.g. CO2 atmosphere on Mars)
for space bundle designs
10% less current derating is possible, saving bundle weight for space applications
Use a relative accuracy related to the temperature elevation T of =T/3 (e.g. 20oC
at 120oC).

25
NLR-TP-2011-469

When the TDM is extended towards more complex environmental conditions an improved
prediction of the thermal interaction between bundles and structural parts for aerospace
applications is possible. By using thermal analysis in the design phase, derating factors and wire
gauging can be optimized beyond the limitations of the aeronautical standards. Life cycle cost
(or launch cost) reduction with respect to the harness weight and improved safety are to be
expected

Acknowledgments

The investigation of the thermal requirements for aircraft wiring was initiated by Fokker
Elmo and sponsored by the Dutch Aeronautical Institute. Fokker Elmo was responsible for the
bundle design and installation requirements and for the manufacturing of the samples. NLR was
responsible for the requirements review, the construction of the thermal model and evaluation of
the validation testing. Open Engineering provided the FEM analysis for the prediction of the
bundle heat transfer coefficients inside enclosures.

References

Books
1
Bejan, Adrian, Heat Transfer, 2nd ed., John Wiley, New York, 1983, Chapters 7, 10
2
Incropera, Frank P, De Witt, John, Bergman, Fundamentals of Heat and Mass Transfer, 6th
ed., John Wiley 2006, ISBN-13 *978-0-471-45728-2

Papers
3
Francois, Sandrine and Namy, Patrick, Finite element analysis of wire heating due to
PoE/PoE+, proceedings of the COMSOL Conference 2010 Paris

Standards
4
National Bureau of Standards Handbook 100, Copper Wire Tables, February 1966
5
ECSS-Q-30-11A Space Product Assurance, 24 April 2006, Derating EEE Components,
section 6.32
6
SAE- AS50881, rev C (2006), former MIL-W-5088, Aerospace Standard, Wiring
Aerospace Vehicle

Specifications
7
Raychem SPEC 55PC wire, Light weight modified cross-linked ETFE polymer insulation, -
65 C-200oC, Boeing standard wire BMS 13-48 for 777 airliner
o

Air properties
8
National Institute for Standards and Technology, NIST, using REFPRO air properties

Internet
9
http://en.wikipedia.org/wiki/American_wire_gauge
10
http://www.powerstream.com/Wire_Size.htm

26