Modeling and simulating the lightning phenomenon:
aeronautic materials comparison in conducted and
radiated modes
JAZZAR Ali(*), CLAVEL Edith(*), MEUNIER Gérard(*), VINCENT Benjamin(*), GOLEANU Anca(*),
VIALARDI Enrico(+)
(*)
G2elab, BP 46, F-38402 Saint Martin d’Hères Cedex, France
Email: Ali.Jazzar@g2elab.grenoble-inp.fr
(+)
CEDRAT, 15 Chemin de Malacher – Inovallée – 38246 Meylan Cedex – France
Abstract- The composite materials are becoming more and more
used in aircrafts design. Their light weight and their excellent
robustness make them attractive compared to metallic materials
which have been widely employed till now (aluminum for
instance). However, an important drawback is their electric
conductivity which is quite weak compared to the metallic one.
Thus, in case of lightning phenomenon, the outside circulating
current is not evacuated in the same way as in aluminum
structures with possible damages to the on-board devices. The
objective of this article is to compare the performances of two
cylindrical samples made of composite and aluminum
respectively. The PEEC (Partial Element Equivalent Circuit)
method is applied to model their electrical behavior in terms of an
equivalent circuit, which is then supplied with the standardized
lightning current in order to evaluate its impact upon the
structure. The conducted and radiated EMC modes are both
investigated by means of two different test-cases. Conclusions
concerning the level of currents, frequency range involved and
EMC performance are then drawn.
Keywords: PEEC method, lightning, eddy currents, conducted and
radiated current density.
I.
equipotential parts seem to be critical problems via electric
network function.
In this context, another parameter has to be taken into
consideration: the current in the composite itself. Since these
currents can cause local heating and degradation, they have to
be very well controlled. It is also necessary to model the
behavior of the entire composite structure power including
frames and other conductive parts, in order to be able to
characterize current circulating in the skin [6-12].
The aim of this article is to show that a representation with a
global equivalent electrical circuit of the 3D studied device as
well as its environment could be used to evaluate the
partitioning and the distribution of the lightning current in the
different elements of the electrical architecture.
This paper is focused on one of the most critical parts of an
aircraft: the nacelle where jet engines are hosted (Fig. 1) and
where some cables are routed inside or outside the cylindrical
structure. That’s why the studied test-case is constituted by an
open (in the sense that is devoid of the bases) cylinder and
some rectilinear conductors.
INTRODUCTION
The last forty years have shown a progressive increase in the
percentage of composite CFR (Carbon Fiber Reinforced)
materials used in the aircraft structures. These materials weight
is less than metals and provide better stiffness and mechanical
strength. In addition, composite structures last longer due to a
greater time-to-failure and their resistance against corrosion.
For all these reasons, composite structures promise longer
periods between maintenances and less fuel consumption, so
they become interesting for aircraft manufacturers and airline
companies. However, since their electrical conductivity is
weak compared to the metal’s one, they cannot evacuate
lightning current as well as aluminum [1-2].
So for the new aircraft systems, the evaluation of a new
electrical architecture is required in order to lead to engender
an optimal protection against lightning.
The development of the embedded electrical network in the
aircraft taking into account this new electromagnetic
environment has raised fundamental questions concerning the
protection of on-board devices through this electrical network:
its behavior during lightning and the identification of
Fig. 1: Real aircraft configurations to study the lightning effect
In section II, the geometry and the electrical configuration of
the studied cases are detailed. The modeling approach is then
presented in the section III. For the conducting parts, the PEEC
method is used to obtain an electrical equivalent circuit. The
principles of this method are also briefly recalled.
To model the lightning waveform, the data given by
standards are exploited and the time-domain definition of the
lightning current is shown. Results will be analyzed in section
IV. Not only is the global current inside the structure evaluated
but also the current density in the cylinder and the equivalent
impedance of the entire study case. A precise modeling via
adapted simulation tools will be presented taking into account
this complex electromagnetic environment. The use of a circuit
solving process makes it possible to evaluate the time-domain
waveforms of current inside the structure. The advantages of
this modeling approach will be detailed as well as the results.
The Vth section underlines the main advantages of the
modeling process for aeronautic purpose as well as the further
works which are in progress.
II.
THE STUDY CONFIGURATIONS
A. The geometry of the studied cases
The geometry of the studied cases is a cylinder of thin
thickness whose material can be aluminum or composite.
Indeed, one of the aims will be to identify the physical
phenomenon of the current distribution in this cylinder
correlated with its material. Some cables are added to this
geometry to define different electrical configurations. A
graphical sketch of the geometry is presented in Fig. 2 and 3.
The geometrical parameters of this study are the following:
• the length of the cylinder and the cables is one meter:
length of maximal size in the aim to simulate (reducing
unknowns number), without furthering the side effect;
• the cylinder diameter is one meter;
• the cylinder thickness is 2 mm;
• the cables section is 25 mm²
B. The electrical configurations
As depicted in Fig. 2 and 3, a current source, representing
the lightning strike, is used to supply the cylinder: it represents
the lightning strike. The current return is ensured using a cable,
which is connected between the load and the source.
For the first studied case, the conducted mode is evaluated.
Thus another cable A is directly connected to the cylinder (Fig.
2).
The objective of the second studied case is to evaluate the
radiated mode. The same cylinder with the same current
injection is used, but two aluminum cables are added, one
outside the cylinder, the other one inside. They are connected
to each other so that the evaluation of the induced currents on
these cables (Fig. 3) can be performed.
For these two studied cases, the current distribution is a key
point in order to identify which part is overloaded according to
the cylinder material and the electrical configuration.
Fig. 2: Electrical configuration to study the conducted mode
Fig. 3: Electrical configuration to study the radiated mode
The different physical parameters of this study are following.
• the composite conductivity is 5000 S/m
• the aluminum conductivity is 4E7 S/m
• the frequency range is from 100Hz to 10MHz
In this study, the composite material is considered
homogenous.
Since the objective of this study is to compare the two
materials in different configurations, exact values are not
necessarily expected. Behavior trends enabling us to
understand their impact are searched. So the values for the
resistivities of composite and aluminum are voluntarily chosen
so distinct in order to emphasize the differences. In reality, we
know that according the composite material which is used, the
factor between the two values can vary a lot.
III.
MODELING METHOD
The aim of this paper is to predict the current distribution
inside an electrical structure after a lightning phenomenon. So
the best suitable model is an electrical one. Thus, an electrical
equivalent circuit of the conducting parts of the studied device
has to be found. Moreover, the lightning phenomenon has also
to be modeled in order to supply the previous model with it.
A. The conductors model
For Power Electronics applications, the PEEC method [8-910-11-13] has proved to be very efficient. This is an integral
method which allows a precise and complete approach of the
phenomenon, without presenting the weight of the finite
elements method because it does not require meshing the
surrounding air.
When applying the PEEC method, the current density inside
the conductors must be uniform. But, for the studied
application, the frequency range needs to take into
consideration the skin effect as well as the proximity effect. So
the current density is not uniform inside the conductors. A
conductors meshing must then be applied. To be efficient,
equivalent of keeping a reasonable number of PEEC elements,
the meshing of conductors is directly linked to the possible
assumption upon the current way.
So a unidirectional conductor means that current goes one
way (Fig. 4) whereas a bidirectional conductor is a thin
conductor where current flows along two directions. For a
unidirectional conductor, the meshing concerns the cross
section and leads to PEEC elements of lower cross section for
which current density is supposed to be uniform. Each element
of the meshing is modeled by an R-L series equivalent circuit.
All partial inductances are coupled together by means of
mutual inductances. All circuits are associated in parallel so
that a simple R-L series equivalent circuit is sufficient to
translate electrical behavior of a unidirectional conductor (Fig.
4). This meshing has been used for the cables.
For the cylinder case, a 2D mesh has to be used because for
this conductor, the assumption of only one current direction is
not possible (Fig. 5). Moreover, two skin effects are involved
when frequency increases. The first one, which is the most
important, is modeled using a surface meshing as presented on
Fig. 5. The second one, which occurs in the thickness of the
conductor, has been neglected in this study but it has to be kept
in mind to refine the model.
In the case of AC steady-state analysis without magnetic
material, the use of PEEC method will consist in calculating
the value of the partial resistances, partial inductances and all
mutual inductances between them from the geometrical
characteristics of each element of the meshing.
The A-type temporal shape of the lightning current is
represented on Fig. 6. The current is bi-exponential as the
following form in (1) with α = 11345 s-1, β = 647265 s-1 and
I0=200 kA:
i (t ) = I 0 ( e
−α t
−e
−β t
)
(1)
The Fourier transform is applied (2). It can be noted that the
great part of the energy of the lightning signal is concentrated
in the low frequency range, up to 10MHz (Fig. 7). This allows
justifying the non evaluation of parasitic capacitive effect.
 1
1 
(2)
I ( jω) = I0 
−
α
j
ω
β
jω
+
+

Fig. 4: The principle of the unidirectional meshing
Fig. 6: Model of the current wave associated to the lightning
Fig. 5: The principle of the bidirectional meshing
This electrical model is suitable for quite low frequencies.
Parasitic capacitances should have to be added in order to
model the high frequency behavior and resonance phenomena,
as it has been achieved in [14-15]. For the studied cases, the
first step presented in this paper consists in taking into account
only the inductive behavior and in concluding upon the truth of
this assumption.
Once the complete and quite complex equivalent circuit is
evaluated, it is necessary to add the supply source and all other
components (load…) and to solve the circuit equations
associated to this circuit.
This illustrated PEEC method is implemented in the
InCa3D® software [7] that is used in this study.
B. The lightning model
The aim of this study is to reproduce faithfully the current
distribution when a lightning strike occurs on the aircraft and
to evaluate the consequences on the on-board equipments.
Lightning is a natural dangerous phenomenon whose
influence on electrical systems can go from the dysfunction of
equipments to their destruction.
Lightning is not just light between two clouds or inside one
cloud. It is produced many kilometers up in the sky and makes
every airplane in this zone vulnerable.
Since it is not easy to predict a lightning occurrence, the
objective of scientists is to predict and control its impact on the
electrical equipments.
As presented in standards, the waveform of the lightning
current is defined as an electrical arc wave which has precise
characteristics (intensity, time, di/dt). Several waves’ shapes
according to the studied phenomenon are associated [3-4-5].
Fig. 7: Fourier transform of the current wave associated to the lightning
IV.
RESULTS
A. Modeling of the studied cases
The previous geometries have been described into InCa3D
and simulated.
The available data at the end of the first phase of solving are
an electrical equivalent circuit with great numbers of elements
(according to the meshing assumptions). Then a source is
added to supply the system and to evaluate the current density
distribution in each conductor. In order to obtain the total
current inside the cable or at the inputs of the cylinder a simple
sum of phases is made.
Another important output provided by InCa3D is the
equivalent impedance of the studied device from its inputs and
outputs.
In the following these different results are detailed for the
studied cases in the two electrical configurations.
B. Current density in the cylinder
The current distribution on the surface of the composite
cylinder is drawn on Fig. 8 at the frequency of 10 kHz. This
computation is performed by injecting a current of 200 kA
between two opposite sides of the cylinder and no cables are
included in the simulation, in order to estimate the distribution
of current in case of a lightning phenomenon.
The current is very high at the injection points and quickly
decreases from this point. So according to the position of the
internal cables compared to these points, the induced effect due
to the lightning will have more or less influence on electrical
equipments.
circulate on the metallic surface of the airplane (Fig. 10). A
low quantity circulates in the internal elements (cables…). The
current in the cylinder structure is the same for the whole
frequency range and it is equal to the injected current.
2. Radiated mode
In the case of the radiated mode (Fig. 3), the lightning
current inside the cylinder implies a magnetic field all around
the structure. According to the electrical circuit and its
geometry, induced currents can appear and damage the
electrical equipments.
For the studied cases, the induced current in the cable has
been evaluated and is presented in Fig. 11.
A first analysis shows that this current is almost the same for
the two cases of material for the cylinder.
Fig. 8: Current distribution at the surface of the cylinder at 10 kHz
C. Global current distribution
The most important consequence of using the composite
material is the redistribution phenomenon: the circulation of
the lightning current on a composite material airplane differs
from the metallic traditional airplane.
In general, the lightning current flows into the less
impedance parts of the aircraft, i.e. those being the less
inductive in high frequencies and the less resistive in low
frequencies.
So the highest frequencies of the lightning circulate
preferentially on the nacelle, composite or metallic. And the
lowest frequencies of the lightning circulate on the parts that
are less resistive. They are distributed on the nacelle and the
cables, proportionally to their resistance.
1. Conducted mode
In the case of the composite airplane, the low value of the
conductivity of the nacelle leads to the major part of the low
frequency lightning current circulating in the internal metallic
elements which are better conductors. This is the current
redistribution phenomenon: in case of a lightning, the internal
currents can present a high intensity and a longer duration that
exceeds those of the lightning phenomenon (spectral content at
low frequency), and also a high energy.
On Fig. 9 and 10, global current in the cable and the cylinder
is drawn for the metallic and the composite cylinder, in the
case of conducted propagation mode (Fig. 2). In the case of
composite material, one quarter of the current flows into the
cable (aluminum) for low frequency. When the frequency
increases the current in the cable decreases until it becomes
null. Conversely, the cylinder carries the other three quarters of
the lightning current at low frequencies and the all of it at high
frequencies (Fig. 9). So the use of a composite material can
lead to problem in case of lightning at low frequencies.
In the case of an entire metallic airplane, the resistance of the
fuselage is weak, and the majority of the low frequencies
Fig. 9: Redistribution of the current in the aluminum cable and the composite
cylinder (conducted mode).
Fig. 10: Redistribution of the current in the aluminum cable and the aluminum
cylinder (conducted mode).
Fig. 11: Induced current on the cable A in the case of cylinder made of
aluminum or composite (radiated mode).
According to Fig. 11, the same induced current in the
aluminum cables is observed in both cases of material for the
cylinder. The resistive effect appears for low frequency, then as
the frequency increases, the predominant effect is inductive.
D. Equivalent impedance
InCa3D is also able to reduce the complete equivalent circuit
given by the solving in order to evaluate the impedance of the
cylinder between the two points of the current injection. These
two points are defined on Fig. 12.
Fig. 14: Inductive part of the equivalent impedance of the cylinder.
Fig. 12: The two points to evaluate the equivalent impedance of cylinder.
Fig. 13: Resistive part of the equivalent impedance of the cylinder.
Resistive and inductive parts of the equivalent impedance are
drawn for both composite and aluminum cylinder in Fig. 13
and Fig. 14.
The mesh density is important to fully capture the skin
surface effect (in relation with increasing frequency). The
figures shown here correspond to "sufficiently meshed"
geometries ( the values are stabilized despite the increasing
mesh density).
Nevertheless, the range of value is respected.
To easily simulate the time variation of the current
waveform, the resistance and inductance of the equivalent
electrical circuit of the cylinder have to be constant across the
frequency range of the injected current (Fig. 7). For our study
case and with composite materials (Fig. 13), the resistance and
the inductance are constant up to 100 kHz. After which the
resistance starts increasing due to the skin effect, contrary to
the inductance part which decreases.
This behavior is quite different for the aluminum case,
where the skin effect occurs for lower frequencies. A meshing
of only the surface of the bidirectional conductors seems not to
be sufficient to give accurate results. A finite elements model
using Flux® software [7] is under work as well as development
of new meshing techniques for PEEC method.
E. Time domain simulation
With using of the PEEC method via the present version of
InCa3D, only a harmonic analysis can be undertaken as
previously presented. But the lightning is a time phenomenon
as shown on Fig. 6. Thus, a time simulation could be very
useful to conclude on its effect on electrical on-board
equipments.
To reach this pertinent information for the industrial
aeronautics, an equivalent electrical circuit of the studied
structure is extracted from InCa3D at a given frequency. This
frequency is chosen from the previous results. In fact the
variation of equivalent impedance with frequency is not
significant and this parameter has very little impact on the
results.
An equivalent circuit can be extracted from InCa3D and
imported into electrical software. For this study, Portunus® [7]
has been chosen because it is automatically linked with
InCa3D. Then the lightning current is described with the data
of standards and the effect on cables can be evaluated.
This modeling process has been achieved on the structure
presented on Fig. 15 where several aluminum cables inside the
composite cylinder have been described.
The first results of the cylinder with many cables inside are
shown on Fig. 16. It can be noted that according to the cable
and its position, in relation with the injection of the lightning
current, the current is different. So a great attention has to be
paid to the cabling inside the aircraft because according to its
position and its geometrical parameters, the impact of a
lightning on the electrical equipments could be different.
We observe that during the first microseconds and during the
transitional regime (high frequency), the current flows further
in the composite material (less inductive). However, when time
passes (low frequency), the current tends to flow only in
aluminum (less resistive).
limit the computation time. Research works in that way are
currently in progress [14-15].
Further works are in progress to also evaluate the magnetic
field near the electrical equipments since the values of induced
currents are then known using the proposed modeling. The
induced phenomena via magnetic couplings are supposed not
to be negligible.
The final aim is in fact to propose some rules to better cable
some areas in the aircraft. Since a parametric description is
possible inside InCa3D analysis, the best position of cables
could be found, using optimization process. The most critical
areas are those where lightning often occurs.
ACKNOWLEDGMENT
Fig. 15: Cylindrical structure with many cables inside
This work is a part of a great French research program called
PREFACE. Authors want to thank the sponsors of this project
which are ASTECH: Hispano-Suiza, AESE: Safran
Engineering Service, PEGASE: Eurocopter.
REFERENCES
[1]
[2]
[3]
[4]
[5]
Fig. 16: Time response of the current in the cables in case of a lightning.
V.
CONCLUSIONS
In this paper, a modeling approach has been proposed to
predict the influence of a lightning impact on an aircraft or on a
part of it, the nacelle for instance. A PEEC method and a timedomain solving have been jointly used to evaluate the current
waveforms inside the cables routed near the injection points. A
simple structure of a cylinder with some cables has been used
as an example to show the different behavior of composite
material compared to aluminum on the current distribution in
case of conducted or radiated mode. For composite structures,
the major problem remains for low frequencies, where a great
quantity of current flows in the cables with possible damages
to the on-board equipments. Conversely, for high frequencies,
the influence of the structure material is less important since,
the current redistribution phenomena are leaded by the
geometrical sizes.
The works presented in this paper have also proven the
pertinence of the PEEC method for the analysis of the indirect
lightning effects on aeronautic structures. Nevertheless, some
improvements, like the modeling of the skin effect inside the
cylinder, seems to be required if more precise results are
expected from the PEEC computations. Such enhancement of
the methodology is strictly related to the use of specific
mathematical techniques, like the Fast Multiple Method
(FMM), able to reduce the required RAM memory space and to
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
S. Baldacim, N. Cristofani,C. do Nascimento Santos, J. Lautenschlager,
"Study of lightning Effects in Aircraft", SAE Technical Paper, 2001.
D. Heidlebaugh, W. Avery, S. Ulrich, "Effects of lightning Currents on
Structural Performance of composite Material", SAE Technical Paper,
2001.
Plumer, Perala, Fisher, “Lightning protection of aircraft”, Lightning,
2°edition 1999
J.J DiNicola, “lightning Induced Voltage and current Measurements on a
Mooney scale test bed”, Lightning technologies, INC, 200
NormeRTCA/DO-160E Section 22, “Environmental conditions and test
procedures for airborne equipment - Lightning induced transient
susceptibility”, Dec. 2004.
Krietenstein, B.; Schuhmann, R.; Thoma, P.; Weiland, T, “The Perfect
Boundary Approximation technique facing the challenge of high
precision field computation”, Proc. of the XIX International Linear
Accelerator Conference (LINAC’98), Chicago, USA, pp.860-862, 1998
www.cedrat.com
J. Aimé, T. S. Tran, E. Clavel, G. Meunier, “Magnetic field computation
of a common mode filter using Finite Element, PEEC methods and their
coupling”, ISIE International Symposium on industrial Electronics,
Cambridge: United Kingdom, June 2008.
V. Ardon, J. Aimé, E. Clavel, O. Chadebec, E. Vialardi, “EMC analysis
of static converters by the extraction of a complete equivalent circuit via
a dedicated PEEC method”, ISIE International Symposium on. Industrial
Electronics, 2007
J. Aime, J. Roudet, E. Clavel, O. Aouine, C. Labarre, F. Costa, J.
Ecrabey, “Prediction and measurement of the magnetic near field of a
static converter”, ISIE International Symposium on Industrial
Electronics, Jun. 2007
A.E. Ruehli, “Equivalent Circuits Models for three Dimensional
Multiconductor Systems”, IEEE Transactions on Microwave theory and
Techniques, Vol. MTT 22, N°3, March 1974.
E. Clavel, J. Roudet, Th. Chevalier, D.M. Postariu, “Modeling of
connections taking Into Account Retum Plane: Application to EMI
Modeling for Railway”, IEEE Transactions on Industrial Electronics,
March 2009
G. Antonini, “Full wave analysis of power electronic systems through a
PEEC state variables method”, ISIE International Symposium on
Industrial Electronics, 2002
V. ARDON, J. AIME, O. CHADEBEC, E. CLAVEL, J-M. GUICHON,
E. VIALARDI, “EMC Modeling of an Industrial Variable Speed Drive
with an Adapted PEEC Method”, IEEE – Transactions on Magnetics,
Vol. 46, N°8, August 2010, pp 2892-2898
V. ARDON, J. AIME, E. CLAVEL, O. CHADEBEC, E. VIALARDI, JM. GUICHON, P. LABIE, "EMC analysis of static converters by the
extraction of a complete equivalent circuit via a dedicated PEEC
method", 8th International Symposium on Electric and Magnetic Fields
EMF’09, Mondovi, Italy, 26-29 May 2009.