Modeling of the Electric Arc Plasma Discharge Produced by a Lightning Strike Continuing Current

Abstract

Despite the superior properties of the carbon fiber reinforced polymer matrix (CFRP) composites, such as the high strength-to-weight ratio, low coefficient of thermal expansion, excellent corrosion and fatigue resistances, the susceptibility of such composites to lightning strike damage still remains a concern to the aerospace industry. Although CFRP composite is considered electrically conductive, its electrical conductivity is still substantially lower than that of the metallic materials. For example, the electrical conductivity that of carbon fiber is around 1e-3 times that of the copper. During a lightning strike discharge, the pulsed current can rise up to 30 ~ 200 kA with a duration of several microseconds and the continuing current can reach 200 ~ 800 A with a duration of 0.25 ~ 1 seconds. The low conductivity of the composite makes it difficult to dissipate the intense electrical energy, which can cause significant damage to the composite structure. This paper will be devoted to the study of the electric arc behaviors, including the electric and magnetic field evolutions, arc expansion, current density, and temperature distributions within the lightning arc using an electric arc plasma discharge model. Such a plasma model was developed through the coupling of Maxwell’s equations, the energy balance equation, and the laminar flow equation, and implemented with COMSOL Multiphysics. The model was employed to study the behaviors of the electric arcs produced by a lightning strike continuing current between a tungsten cathode and a solid anode material in argon and air mediums. The lightning-plasma-induced heat flux impinges on the anode material surface was also predicted. The model was validated through comparisons with experimental data and other numerical results reported in the existing literature. After the model was successfully validated, it was employed to study the effect of arc gaps on the lightning plasma behaviors. In addition, the effect of using different anode materials, i.e., copper, aluminum, and steel on the heat flux that flows from the plasma into the material surface was also investigated. Our next step is to use the current model to predict the current density and heat flux that flow into a CFRP composite anode material.

Full text

1
Modeling of the Electric Arc Plasma Discharge Produced by a Lightning Strike Continuing Current
Youssef Aider1, Yeqing Wang1*, Gasser F. Abdelal2, Olesya I. Zhupanska3
1Department of Aerospace Engineering, Mississippi State University, Mississippi State, MS, 39762 USA
2School of Mechanical and Aerospace Engineering, Queen’s University Belfast, BT7 1NN Belfast, UK
3Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, 85721 USA
*Corresponding author, email address: yw253@msstate.edu
ABSTRACT
Despite the superior properties of the carbon
fiber reinforced polymer matrix (CFRP)
composites, such as the high strength-to-
weight ratio, low coefficient of thermal
expansion, excellent corrosion and fatigue
resistances, the susceptibility of such
composites to lightning strike damage still
remains a concern to the aerospace industry.
Although CFRP composite is considered
electrically conductive, its electrical
conductivity is still substantially lower than that
of the metallic materials. For example, the
electrical conductivity that of carbon fiber is
around 1×10-3 times that of the copper. During
a lightning strike discharge, the pulsed current
can rise up to 30 ~ 200 kA with a duration of
several microseconds and the continuing
current can reach 200 ~ 800 A with a duration
of 0.25 ~ 1 seconds. The low conductivity of the
composite makes it difficult to dissipate the
intense electrical energy, which can cause
significant damage to the composite structure.
This paper will be devoted to the study of the
electric arc behaviors, including the electric and
magnetic field evolutions, arc expansion,
current density, and temperature distributions
within the lightning arc using an electric arc
plasma discharge model. Such a plasma model
was developed through the coupling of
Maxwell’s equations, the energy balance
equation, and the laminar flow equation, and
implemented with COMSOL Multiphysics. The
model was employed to study the behaviors of
the electric arcs produced by a lightning strike
continuing current between a tungsten cathode
and a solid anode material in argon and air
mediums. The lightning-plasma-induced heat
flux impinges on the anode material surface
was also predicted. The model was validated
through comparisons with experimental data
and other numerical results reported in the
existing literature. After the model was
successfully validated, it was employed to
study the effect of arc gaps on the lightning
plasma behaviors. In addition, the effect of
using different anode materials, i.e., copper,
aluminum, and steel on the heat flux that flows
from the plasma into the material surface was
also investigated. Our next step is to use the
current model to predict the current density and
heat flux that flow into a CFRP composite
anode material.
ACRONYMS AND SYMBOLS
Acronyms:
CFRP:
Carbon fiber reinforced polymer
matrix
DC:
Direct current
FEA:
Finite element analysis
FEM:
Finite element method
LTE:
Local thermodynamic equilibrium
RANS:
Reynolds-averaged Navier–Stokes
Symbols:
A:
Magnetic vector potential
B:
Magnetic flux density
Cp:
Specific heat capacity
D:
Electric flux density
E:
Electric field
H:
Magnetic field intensity
I:
Identity matrix
J:
Current density
n:
Normal vector to the cross-
sectional surfaces
P0:
Atmospheric pressure
PA:
Absolute pressure
r:
Radial direction of the cylindrical
coordinates
sym:
Symmetric boundary condition
T:
Temperature
t:
Time
u:
Velocity field
V:
Electric potential
z:
Axial distance of the cylindrical
coordinates
γ:
Ratio of specific heat
ρ:
Density
ρv:
Electric charge
øe:
Effective work function

2
I. INTRODUCTION
The lightning strike on composite structures
cannot be ignored, especially for composite
aircraft skin and wind turbine blades [1-4]. The
low electrical conductivity of the composite
material makes it difficult to dissipate the
intense lightning strike energy, and thus leads
to appreciable lightning strike damage [5-9].
The lightning electric arc can even puncture
straight through the composite surface layers,
exposing vulnerable electric cables and
hydraulic tubes directly to the extreme
environment. As an example, the Fairchild
metro 3 passenger airplane crashed in 1988
after it got struck by lightning. It caused a major
electrical system failure, that lead to the loss of
19 passengers’ and 2 crew members’ lives [2].
Lightning damage to the composite material
can be very difficult to repair and may result in
replacing a large section of the damaged part.
In some cases, the lightning damage to the
composite material, such as the delamination
of internal laminate layers, can be invisible and
may just look like paint peeling on the surface.
Examples of lightning strike damage on CFRP
composites are shown in Fig 1. In particular,
Fig 1a shows the lightning strike damage on a
horizontal stabilizer of a Boeing airplane, while
Fig 1b shows a lightning strike damage on a
woven CFRP composite sample in our lab after
it got struck by a pulsed lightning strike with a
peak current of 97 kA. In both examples, fiber
breakage, delamination, matrix cracking, and
fiber charring can be visually observed.
Similarly, lightning strikes to glass fiber
reinforced polymer (GFRP) composite used in
wind turbine blades can be even worse due to
it being electrically non-conductive. Even
though lightning receptors are used as a safety
measure to avoid a direct strike to the blade’s
surface, lightning may still strike the electrically
nonconductive skin if the electric field exceeds
the dielectric breakdown strength of the
composite wind turbine blade. This will lead to
damage that can be described as pin holes or
punctures in the composite structure [3].
The aim of this paper is to simulate the lightning
electric arc using a finite element (FE) method
using the commercial software COMSOL. The
lightning strike continuing current is considered
in this simulation. The heat flux and current
density at the surface of the anode are
predicted. The predicted information will be
further used as loading boundary conditions for
modeling the damage of the composite material
subjected to lightning strikes.
Figure 1: (a): Lightning strike damage on a horizontal
stabilizer from Boeing lightning protection manual
[10], (b): lower image shows the lightning strike
damage on a woven CFRP composite sample in our
lab after struck by a 97 kA pulsed lightning strike
current (courtesy of the High Voltage Lab at the
Mississippi State University).
The first challenge of this work is the modeling
of the electric arc. An electric arc can be
regarded as a thermal plasma in Local
Thermodynamic Equilibrium state (LTE) [11-
18]. Modeling the electric arc requires solving a
coupled system of equations, mainly Maxwell’s
equations, the heat transfer energy balance
equation, and the fluid flow Navier-Stokes
equations. The other challenge comes from the
numerical implementation of the model due to
the extreme short duration of the lightning
strike. Waveforms A, B, and D (Fig 2) are
typically in microseconds and reported to be
very challenging to simulate due to the fast rise
of the electric current in a very short duration of
time [11, 12]. In this paper, we attempted to
study the electric arc due to a lightning strike
waveform C. Such a waveform can be regarded
as a steady or direct current (DC) case [19].
(a)
(b)

3
The model is validated by comparing the
simulation results for a free-burning argon arc
with the experimental data.
Figure 2: Idealized aircraft lightning current
waveforms (not to scale) [9].
After the model was successfully validated, it
was employed to study the effect of arc gaps on
the arc behaviors, including the heat flux,
plasma temperature, and arc expansions. Such
a study is also important to shed light on the
difference of the arc behaviors between those
generated in the laboratory conditions with an
arc gap of about 3 mm and those produced in
the nature with arc gaps of more than 3000 m
[1, 3, 4].
II. NUMERICAL MODELING
To simulate the generation of the electric arc,
two models were used. The first model is a 200
A DC current with argon gas as the plasma
medium. This model is used to validate the
numerical results. The second model is a 400
A DC current with air as the plasma medium.
The current intensity is chosen based on the
lightning current suggested by the standard
waveform C (see Fig 2).
In the second model, the electric current is
applied at the cathode root. The heat transfer
equation is solved at both the fluid and the
electrode domains. The heat sources include
the Joule heating and enthalpic heating. The
radiation loss is considered as a subtraction of
a volumetric heat source, which is a function of
the net-emission coefficient and the
temperature, under the assumption of an
optically thin plasma [11, 12, 14-16, 18-21]. The
flow of the electric arc plasma is simulated by
solving Navier-Stokes equations. The plasma
flow is modeled as a laminar flow, which proved
to give good results with the argon arc model,
although a modified k-ε RANS model can also
be used for better results of air thermal plasma
modeling [22]. Furthermore, the driving force of
the fluid flow is the Lorentz force, which is
calculated from the magnetic flux density vector
by solving Maxwell’s equations. To simplify the
calculation, in this study, the lightning arc is
assumed to be a thermal plasma in the LTE
condition [11-18]. The plasma is assumed as
an incompressible laminar flow. Gravity and
heat dissipation due to viscosity effects are
ignored. Such assumptions have also been
used in many other related studies [11-16].
1. Mathematical equations
The mathematical equations for the model are
documented in COMSOL user’s guide [23].
Here, we provide a brief overview.
Electric potential and current density equations:
The electric current density and hence the
electric potential can be solved using the
current conservation equation:
  ,,
JV
Q
J
(1)
where
J
is the current density vector, and
,
JV
Q
is the rate of change of the electric current
charge density with time, for a direct current
(DC) arc,

,0
JV
Q
.The electric field
E
can be
solved from the equation


  
,
t
e1
D
J E J
(2)
where
e1
J
is the externally generated current
density, in our case, it is the induced current
from the magnetic field. The induced current
density is only effective if we were simulating a
time-varying current. Since the current of
waveform C is constant with time, the magnetic
vector potential will also be constant with time.
Thus, the induced current in our case can be
neglected.

0,
r
DE
(3)
where
D
is the electric displacement or electric
flux density,
E
is electric field, and the electric
potential is calculated using the equation

4
  .EV
(4)
Magnetic field equations:
The magnetic field is solved from the modified
Maxwell’s equations:
  ,HJ
(5)
  ,BA
(6)
,

    e2
J E v B J
(7)
,
t

 
A
E
(8)
where
H
,
B
,
v
, and
A
are the magnetic field
intensity, magnetic flux density, conductor’s
velocity, and magnetic potential, respectively,
e2
J
is the externally generated electric current
density and
.V

  
e2
J
Heat transfer energy equations:
The heat equation is coupled with the electric
current equations, written as:
 
,
pp
T
C C T k T Q
t

      
u
(9)
where
Q
is the volumetric heat source, which
includes the enthalpic transport, Joule heating,
and radiation loss, and expressed as:
 
54,
2BN
kT
QT
Tq



     

J E J
(10)
where

,,
Cp T
and
u
are the gas density,
specific heat capacity, absolute temperature,
and velocity vector, respectively,
N
is the net-
emission coefficient of the gas, which was
interpolated from the literature data [20] for air
and [21] for argon,
B
k
is the Boltzmann
constant, and
q
is the electron charge.
Fluid flow equations:
The fluid flow is modeled as a laminar flow. The
first main equation for flow modeling is the
continuity equation:
 

   
0,
t
u
(11)
which represents the conservation of mass.
The second equation is the conservation of
momentum equation and written as:
 
  

        

,
P
t
uu u I F
(12)
where
F
is the volume force vector. In our
case, it is the Lorentz force and expressed as,
.F J B
(13)

in Eq. (12) is the viscous stress tensor and
 
  
   
2
23
S u I
, with
S
being the strain-
rate tensor written as
 

   
1
2
T
S u u
.
2. Numerical implementation
The above mathematical equations were
implemented using finite element analysis
(FEA) using a triangular mesh of 8375
elements for the free-burning argon model, and
14275 elements for the 3 mm arc gap air
plasma model. The mesh was refined near the
cathode and anode regions.
Even though the free-burning DC arc (200 A
model) can be solved in a steady state mode,
in newer versions of COMSOL, both models
are solved using a time dependent study for a
better numerical stability [24]. The physics used
here are: (i) the heat transfer “ht” in both the
fluid domain (i.e., electric arc plasma flow) and
the solid domain (i.e., the cathode and the
anode); (ii) the magnetic field “mf” physics
which solves for a full field and in-plane vector
potential; (iii) the electric current “ec” interface
with a normal current density boundary
assigned at the cathode root, and a ground
boundary condition at the anode root area; and
(iv) the laminar flow “spf” interface with inlet and
outlet boundaries of zero pressure as shown in
Tables 1 and 2. The multiphysics coupling used
here are:
 Equilibrium heat source: electric current 
heat transfer.
 Lorentz force: magnetic field  laminar flow.
 Static current density: electric current
 magnetic field.

5
 Temperature coupling: heat transfer 
electric current, magnetic field, laminar flow.
 Equilibrium discharge boundary heat source
electric current  heat transfer.
It is worth noting that all the above described
physics can be coupled manually by calculating
the coupling variables using the COMSOL local
& global variables.
III. MODELLNG THE 200 A FREE-BURNING
ARGON ARC
1. Model setup
The first model is to simulate a 200 A
continuous current free burning argon arc. This
model is based on the simulation and the
experiment setup from Refs. [13] and [14].
Although the geometry is simple, it has been
used as a benchmark that is well validated by
the experimental data. In this section, such a
model is replicated to validate our proposed
model using the COMSOL Multiphysics. Here,
the model geometry of the cathode domain in
Fig 3 is not included in the heat transfer
calculation and assigned with a constant
temperature of 3500 K at the surface boundary
of the cathode.
Figure 3: Calculation domains and boundaries for a
200 A argon model based on the simulation setup
from Ref. [13].
The current density is applied to the boundary
AD (i.e., a fictions line boundary, not an actual
physical boundary), as shown in Fig 3, using an
exponential function [13]
   

max exp ,
r br
JJ
(14)
max
J
and
b
are constants, defined as:


max 2,
h
I
Jr
(15)
where
h
r
= 0.51 mm is the radius of the hottest
part of the plasma for a 200 A arc,
b
is solved
from the self-consistent integral
 

0
2,
c
R
I r rdr
J
(16)
where
c
r
= 3 mm is the cutoff radius of the arc
along the horizontal boundary DA (see in Fig 3)
and
I
= 200 A is the electric current. The
boundary conditions for the model is described
in Table 1 below.
Table 1: Boundary conditions for the 200 A free-
burning argon arc model.
AG
BC
EC
EF
AF
AD
U

  
  
V

  
  
P


 

 
T

(17)
 

 

 

J

    
  
CH
GH
T
  
  
φ
    
  V
2. Results
The simulation results for the 200 A free-
burning argon arc model, are taken at t=0.149
s when the current density data at the anode
surface reaches a peak value of 6.9259×106
A/m2. As one can see in Fig 4, the predicted
current density is in good agreement with the
numerical predictions reported by ONERA [14]
and Lowke & Tanaka [16].
The temperature of the model has reached a
maximum of 19000 K at t=0.149 s. The
temperature contour is shown in Fig 5. The
temperature profile of the plasma produced by
a free-burning argon arc shows a bell shape,
which is well known to the research community.
The data is taken at t=0.149 s, which in our
case, the electric arc has reached the steady
state. For the temperature distribution at the
axial line, we compared the predicted results
with the experimental data reported by Ref. [13]
in Fig 6.

6
Figure 4: Current density at the anode surface
compared with data from literature [14, 16].
Figure 5: Predicted temperature contour plots within
the plasma flow.
Figure 6: Plasma temperature vs. the axial distance:
comparison between the prediction and the
experiment data reported by Ref. [13].
It can be seen that the temperature distribution
along the arc center line (symmetry line in our
model) gives good agreement with the
experimental data by Ref. [13], bearing in mind
that the accuracy of the LTE calculated material
properties and net-emission coefficient can
also affect the temperature predictions.
IV - MODELLNG THE 400 A LIGHTNING
CURRENT OF WAVEFORM C
1. Model setup
In the previous section, a 200 A continuous
current was used in the simulation for a free-
burning argon arc. The reason for choosing 200
A as the value of the current is to compare the
results with experimental data of a 200 A TIG
welder [13]. For simulating the lightning arc, the
current is chosen to be 400 A as suggested by
the standard waveform C (see in Fig 2). The
lightning current is assumed to ramp up to a
steady state value of 400 A within 2 μs. Here,
the reason for ramping the current is that it
makes the calculation and convergence much
easier. A sharper rise of the electric current will
require more refined mesh and thus leads to
unaffordable computational cost [11, 12].
The total charge produced during a typical
lightning strike waveform C is about 200 C, i.e.,
the integral of electric current over the time [19].
Here, the charge considered in the current
simulation with a 400 A electric current is
 

  
0.5 /0.001
0400 1 199.6 C
t
q e dt
.
The current density applied to cathode root is

2.
in
i
I
JR
(17)
The model domains and boundaries are
illustrated in Fig 7.
The cathode length is 15 mm for an arc gap of
10 mm and 22 mm for an arc gap of 3 mm.
Between the electrodes and the plasma, there
exist a thin sheath layer that is assumed to be
in non-LTE. This discontinuity is usually
simulated as a fixed temperature of 3500 K at
the cathode surface (for tungsten, an additional
thin layer of 0.1 mm is added [11, 12, 18]). This
layer has a material property similar to that of
the plasma except for the electrical
conductivity, which is considered to be the
same as that of the electrodes. Furthermore,
additional heat sources are added to the
Radial distance [mm]
0 2 4 6 8
Current density [A/(m2)]
0
2e+6
4e+6
6e+6
8e+6
Current Model
Lowke & Tanaka
ONERA Simmulation
Axial Distance (Arc Length) [mm]
0246810
Temperature [K]
5000
10000
15000
20000 Current Model
Hsu. experimental data

7
electrodes surface boundaries. The heat
source at the anode is:
  
      4,
anode pl a a B
q q T
n n J n
(18)
where
a
,
a
, and
B
are the emissivity,
anode work function, and Stefan-Boltzmann’s
constant respectively. The cathode surface
heat flux is modeled by the equation:
  
       4,
cathode pl i i e c c B
q q J V J T
nn
(19)
where
c
and
c
are cathode work function
and emissivity respectively,
i
J
and
e
J
are the
ion and electron currents, respectively, and are
expressed as [16]:





2exp .
e
rr
B
q
J AT KT
(20)
 
 
  

   


0,
0
rr
e
r
J if J
Jif J
Jn
J n J n
(21)
   ,
ie
JJ
Jn
(22)
Where,
r
J
and
r
A
are respectively, the
Richardson’s current density and constant.
Heat sources’ equations are taken from Ref.
[11, 12, 16, 18].
Figure 7: Model Domains and boundaries.
The boundary conditions for the 400 A model
are similar to those of the 200 A argon case,
except that the domain of the tungsten cathode
(Fig 7) is now taken into the computation. Due
to the lack of the experimental data about the
electric current and electric field distributions
within the tungsten cathode, adding a physical
cathode with realistic material properties takes
care of this problem. The material properties of
the tungsten cathode are taken from the
COMSOL material library. The argon transport
properties are taken from Ref. [25]. The
temperature-dependent material properties of
the air plasma (e.g., transport properties) are
taken from Ref. [26].
Table 2 : Boundary conditions for the 400 A air
thermal plasma model.
AB
BC
CD
DG
HB
AF
U
  
  
  

V
  
  
  

P

 

 
T
 

 





J
  
  
 
  
 

DE
EF
T
    
  
φ
    
  V
2. Results
It can be seen from Fig 8 that the temperature
of the plasma reaches a maximum value of
19000 K at t=0.5 s near the tip of the cathode.
Figure 8: temperature Contour for the 400 A
waveform C model.
The radiation loss and current density
dissipation contribute to the decrease of the
temperature as the arc approaches the anode
surface. The temperature at the anode is
mainly controlled by the boundary sources,

8
which differs from one material to another. For
copper, the temperature at the anode, as we
can see in Fig 9, rises to 2100 K at the center
of the arc of and gradually becomes smaller as
we go further away from the center point to the
boundary CD at a temperature of 1000 K.
Figure 9: Temperature at the anode surface.
In addition, the heat flux follows the same
pattern, where a peak point is reached at the
center of the anode surface, i.e., the point near
the axisymmetric line of our model. The heat
flux gradually becomes smaller as we move
away from the center, as shown in Fig 10.
Figure 10: Heat flux at the anode surface, compared
with data from Nestor experiment [15].
The heat flux at the anode reaches a maximum
of 1.1x108 W/m2 for a 3 mm arc length (see Fig
10). The comparison between our predictions
and the experimental data (Nestor Data in Fig
10) reported by Ref. [15] shows that our
prediction is satisfactory.
Simulating multiple arc gaps shows that the
heat flux at the anode reduces as the distance
increases between the cathode and the anode
material (see Fig 11). However, it can be
noticed that there is potential for a convergence
of the heat flux intensity for distances higher
than 7 mm.
Figure 11: Heat Flux comparison between different
arc lengths.
The heat flux reaches a maximum of 2.4×108
W/m2 for the case with an arc gap of 1 mm, and
4.98×107 W/m2 for the case with an arc gap of
10 mm. The intensity of the heat flux reduced
almost one order when the gap increased about
one order. At the same time, the arc expansion
differs with different arc gaps as we measure
the anode radial distance at an isothermal
contour line of 1500 K. Figure 12 shows a
comparison of the final arc radii corresponding
to different arc gaps.
Figure 12: Arc expansion with relation to the arc
gap, taken for gaps of 1, 3, 5, 7, and 10 mm.
We can see that the arc expansion reaches a
convergence point as we go above an arc gap
of 5 mm. We should also note that the anode
area and the boundary condition at the edge of
Radial distance [mm]
0 2 4 6 8 10 12 14
Temperature [K]
1000
1200
1400
1600
1800
2000
2200
Radial distance [mm]
0 2 4 6 8 10 12 14
Heat flux [W/m2]
0.0
2.0e+7
4.0e+7
6.0e+7
8.0e+7
1.0e+8
1.2e+8 Current Model
Nestor Data
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10 12 14 16
Heat flux [W/m2]x 108
Anode radial distance [mm]
1 mm
3 mm
5 mm
7 mm
10 mm
12 mm
Arc gap along z [mm]
0 2 4 6 8 10 12
Radial distance along r [mm]
1.8
2.0
2.2
2.4
2.6
2.8
3.0
Arc expansion

9
the plasma domain may also influence the point
of convergence in this simulation.
In order to see the effect of different materials
on the heat flux, additional simulations were
carried out using different anode material
properties (i.e., copper, steel, and aluminum).
The material properties are temperature
dependent and available in COMSOL’s
material library.
Figure 13: The heat flux flow from the plasma to
different materials.
In Fig 13, we can see that different materials
lead to different magnitudes of heat flux that
flows from the plasma into the material. Copper
tends to have a higher absorptivity to the
lightning electrical energy, while aluminum has
the lowest absorptivity to the lightning electrical
energy. In the future, we will use the current
model to predict the current density and heat
flux that flow from the plasma to a CFRP
composite anode material.
V. CONCLUSION
Our proposed COMSOL FE plasma model of
the electric arc discharge has been validated
through comparisons of the electric current
density, heat flux, and plasma temperature with
the existing experimental data and other
numerical results for a 200 A constant current
argon plasma benchmark problem.
The validated model was employed to
investigate the effects of different arc gaps (i.e.,
from 1 to 12 mm) and different anode materials
(i.e., copper, steel, and aluminum) on the heat
flux and arc expansion for a lightning strike
electric arc plasma of 400 A. It was found that
the heat flux at the anode generally decreases
as the arc gap increases. However, when the
arc gap is larger than 7 mm, the decrease of the
heat flux becomes insignificant, which indicates
a possibility of using a laboratory generated
electric gaps of a few centimeters to represent
the actual lightning electric arc thousands of
meters long in nature. Furthermore, it was
found that using different anode materials will
lead to varying heat fluxes that flow from the
plasma to the anode material. Among the
materials we tested, the copper shows the
highest absorptivity to the lightning electrical
energy, whereas the aluminum shows the
lowest.
For future work, the predicted electric current
density and the heat flux will be further used as
lightning strike loading conditions and passed
to other FEM codes (e.g., ABAQUS) to model
the material response and damage of the
CFRP composite materials.
ACKNOWLEDGMENT
Y. Aider and Y. Wang wish to thank the High-
Performance Computing Center Collaboration
(HPCC) at Mississippi State University for
providing the licensing and computational
resource needed in this project.
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