The objective here is to describe the lightning hazards to buildings and their internal environments using advanced formulations of Maxwell's Equations. The method described is the Three Dimensional Finite Difference Time Domain Solution. It can be used to solve for the lightning interaction with such structures in three dimensions with the inclusion of a considerable amount of detail. Special techniques were developed for including wire, plumbing, and rebar into the model. Some buildings have provisions for lightning protection in the form of air terminals connected to a ground counterpoise system. It is shown that fields and currents within these structures can be significantly high during a lightning strike. Time lapse video presentations were made showing the electric and magnetic field distributions on selected cross sections of the buildings during a simulated lightning strike

Collier, Richard S.

Mckenna, Paul M.

Perala, Rodney A.

English

NASA Technical Reports Server

.. 
EVALUATING LIGHTNING HAZARDS TO BUILDING ENVIRONMENTS USING 
EXPLICIT NUMERICAL SOLUTIONS OF MAXWELL'S EQUATIONS * 
Richard S .  Collier, Paul M. McKenna and Rodney A. Perala 
Electro Magnetic Applications, Inc. 
12567 West Cedar Drive, Suite 250 
Lakewood, Colorado 80228-2091 
U.S.A. 
(303) 980-0070 
ABSTRACT 
Lightning hazards to buildings and their internal environments can be described in terms of electric and 
magnetic fields (and their time derivatives) and the resulting direct and induced electrical currents which are found 
in and around critical locations of the building during a lightning strike. The space and time distributions of such 
fields and currents follow solutions of Maxwell's Equations providing that appropriate initial and boundary 
conditions can be supplied in the regions of interest and that a method of solution can be applied. 
Building environments can be electromagnetically complex, because they consist of a variety of 
inhomogeneous materials (e.g.. concrete with rebar) which may be either conducting or partially conducting. In 
addition, the structures usually have metallic penetrations such as electrical cables or plumbing, as well as a 
lightning protection system including an earth ground of some type. 
The objective of this paper is to describe the lightning hazards to such structures using advanced 
formulations of Maxwell's Equations. The method described is the Three Dimensional Finite Difference Time 
Domain Solution. It can be used to solve for the lightning interaction with such structures in three dimensions 
and include a considerable amount of detail. Special techniques have been developed for including wires, 
plumbing and rebar into the model. 
Some buildings have provisions for "lightning protection" in the form of air terminals connected to a ground 
counterpoise system. It is shown that fields and currents within these structures can be significantly high during 
a lightning strike. Time lapse video presentations have been made showing the eIectric and magnetic field 
distributions on selected cross-sections of the buildings during a simulated lightning strike. 
1.0 INTRODUCTION 
Lightning hazards to building environments can be described in terms of electric and magnetic fields (and 
their time derivatives) and the resulting direct and induced eiecaical c m n t s  which are found in and around critical 
locations of the facility during a lightning strike. 
The space and time distributions of such fields and currents follow solutions of Maxwells Equations 
providing that appropriate initial and boundary conditions can be supplied in the regions of interest and that a 
method of solution can be applied. 
This paper describes the results of a numerical computer model which applies Maxwells Equations to 
describe a specified lightning attachment to a specific building or facility. The result shows how electromagnetic 
fields and currents are distributed in space and time in and near the facility during a simulated lightning strike. 
Time lapse video presentations have been made showing these distributions on selected cross-sections of the 
buildings. 
* Work sponsored by Picatinny Arsenal Under Contract # DAAA21-894-0176 
Presented at: 1991 International Conference on Lightning and Static Electricity, April 16 - 19, 1991, Cocoa 
Beach, Florih 
115-1 
https://ntrs.nasa.gov/search.jsp?R=19910023419 2020-03-17T15:00:40+00:00Z
Examples are given; 1. For an earth covered storage igloo with iron rebar reenforced concrete walls, and 2. 
For a rectangular building with cinder-block walls and a metal roof. Both structures have provisions for 
"lightning protection" in the form of air terminals connected to a ground counterpoise system. It will be shown 
that fields and currents within these structures can be significantly high during a lightning strike. 
2.0 DESCRIPTION OF THE NUMERICAL MODELS 
The numerical model of the structure and surrounding environment is based upon a finite difference time 
domain solution of Maxwell's equations. The solution technique is explicit and accurate to second order in the 
time and spatial increments, which in these models correspond to the three dimensional Cartesian coordinate 
increments as obtained by Merewether and Fisher El] with further discussion by Collier and Perala [21. 
A problem space containing the facility and surrounding environment is divided into rectangular cells. Each 
cell has a staggered spatial grid, as shown in Figure 1, composed of the vector components of E and H. There are 
approximately one million cells in the lightning strike problem spaces discussed in this paper. The cell 
dimensions Ax, Ay and Az are 12"x6x6" for the igloo and 6"xl2"x12" for the building. The field components in 
each cell are calculated numerically via the finite difference form of Maxwell's Equations [I]. 
MAXWELL'S EQUATIONS 
- aH 
X 
p x + V x E  
- aE E-+ OE - V x H 
Y at 
- V * E   
L 
Figure 1 Staggered Spatial Grid 
In addition to the appropriate boundary and initial conditions, the material properties at each cell location 
must be specified. This consists of the magnetic permeability, 1.1. in equation (1); the conductivity, o, in 
equation (2) and the dielectric constant, E, in equations (2) and (3). If the material is homogeneous within the 
cell (for example, volumes of air, soil, concrete, etc.) then the appropriate values of p, o, and E are included in 
the time advance equations for the cell in question. 
If the material properties are inhomogeneous in each cell (detailed structure, etc.) then a decision must be 
made on how to represent the properties in each cell. In some cases average properties are sufficient and in other 
cases they are not Special considerations are available for rreating apertures in metal walls and also for pipes and 
thin wires (radii much smaller than cell dimensions) which may run throughout the problem space. These pipes 
and wires can be carriers of high current. 
The buildings and facilities of interest usually have a great deal of "thin wire" situations in the form of 
signal and power lines, rebar in reinforced concrete, pipes, plumbing, metal poles, the lightning protection air 
terminals, down conductors, counterpoise, etc. 
The thin wires and rods are implemented in a self consistent fashion by making use of the telegrapher's 
transmission l i e  equations. The telegrapher's equations (3, (6) are a one dimensional solution of Maxwell's in 
terms of currents, Iw. and voltages,V,, on the wires, which are required to have diameters less than cell size 
(spatial increment). The per unit length inductances and capacitances are defined (7), (8) with respect to the cell 
size and the wire diameter, 2a. 
115-2 
The One Dimensional Transmission Line Equations arc 
where Lw and Cw is the incell inductance and capacitance of the wire per unit length. 
L w = g d n ( z )  
Gw is the in-cell conductance from the wire to the surrounding conductive medium 
The wire resistance per unit length, R, is obtained by considering the surface conduction of the metal in 
question using the skin depth obtained for a frequency of 1 MHZ. The resistance for pipes, wire, iron rebar, etc., 
is normally on the order of lo9 Ohms/meter. In practice, the major results at early time seem to be relatively 
insensitive to variations of the resistance. 
In the computer code, the wires and pipes are embedded into the staggered grid and are driven by the electric 
field component (see equation (7)) calculated by the three dimensional solution of Maxwell’s equations. In order 
to maintain electrical charge conservation, this wire current must also be injected back into the driving electric 
field component as a source current via Maxwell’s Equation (2). At the interconnections, which are voltage 
nodes, Kirchoffs law is invoked. At locations where the wires are situated in the soil or concrete, the wires are 
in electrical contact with the soil or concrete with in-cell conductance given by Gw in equation (9). This is also 
true of the facility ground wire which is in contact with the so& 
Complex networks of thin wires (e.g., concertina or metal rebar mesh embedded in conducting concrete) are 
included in the model by a vectorized extension of the transmission line formalism. Vectorized average wire 
currents coincide with the electric field vectors in each cell and a corresponding average inductance and resistance 
is associated with each wire current vector. Six component tensors exist at the cell comers (nodes) describing the 
equivalent transmission line voltages, wire capacitance, and conductance to the embedding medium. A 36 
component connectivity tensor exists at each node describing the ways that wires are connected at the nodes. 
At the boundaries of the problem space, some termination condition must be applied to both the 
counterpoise extensions and the power and signal lines and metal pipes entering the problem space. The 
boundary condition is applied at current nodes and is the equivalent of the Mur boundary condition applied to the 
magnetic fields [2]. 
3.0 THE ~ ~ G H T N I ~ G  STROKE CURRENT WAVE FOR^ AND INJECTIO~ 
The’ problem is initiated by imposing a pre-determined lightning wave form from the top edge of the 
problem space to a specific point on the structure. In a typical computational case described below, the lightning 
C aveform is characteristic of a 1% stroke of negative lighming. The lightning current, I(t), is given as a 
function of time by 
115-3 
I(t) = 1.1 x 1 6  Sin2 A 
(10-6) 
0 t .5 x 10% 
- .J  x 10-6 
I(t) = 1 . 1 ~  16 sit$( -5  ) A 
5 x 10 
.5 x 10-6 < t 
which has a peak current of 110 kA occurring at .5 ps. The lighming current appears without propagation delays 
in a line of vertical elechic fields (E,) from the top of the computational volume to the attach point. The 
lightning current is injected into the electric fields by dividing the current by the cell area whose normal is 
parallel to the vertical direction. This becomes the source current density, J. in Maxwell's equation (2). A 
number of different parameters are studied: lighming stroke attachment location, soil electrical conductivity, 
structure w a i  rebar composition, and power box attachment at the walls and ceiling. These parameters are varied 
in order to provide environments based upon the range of situations which could be encountered. 
The computer model contains features of interest such as, soil, concrete, rebar, counterpoise, etc., which are 
included in the computer model in a modular form. These separate features may be included or excluded from the 
model by calling subroutines specific to the features desired. The compurations are performed on a CRAY I1 
computer. Typical run times are 1 hour of computer time for each microsecond of wal time. 
4.0 LIGHTNING STRIKE MODELS 
The analysis of the preceding sections has been applied to two smctutes: (1) an earth covered storage igloo 
with iron rebar reinforced concrete walls as shown in Figure 2 and, (2) a rectangular constructed building with a 
metal roof as shown in Figure 3. 
The igloo interior is completely surrounded with either metal or iron rebar which forms a "leaky" 
electromagnetic shield for the interior. A schematic drawing of the igloo vertical mid-cross-section is shown in 
Figure 4. 
The building is made of concrete block outer walls with no rebar, a metal roof, and concrete with rebar floor 
and inner walls with rebar. Thus the building cannot be considered as having a contiguous shielding effect. 
For both models the numerical computer output from a simulated lightning strike may be categorized as 
follows: 
1. 
2. 
3. 
4. 
5. 
Contour Plots - These are "snapshots in time" of the electric and magnetic field structures on a plane 
cross-section of the building at some time after the initiation of the strike. 
Time Dependent Plots - these are time dependent graphs of electric and magnetic fields at selected points 
in the problem space. Currents and voltages on thin wires and rods also have time dependent plots at 
selected points. 
Current Arrays - These are spreadsheet tabulations of wire currents in specific areas of the building. 
Field Maxima - These are computer searches at selected times to find the maximum electric and 
magnetic fields and the maximum time derivative of the magnetic field within a specified boundary 
inside the building. 
Time lapse video presentations showing the magnitudes of the electric and magnetic fields on specific 
plane cross-sections of the buildings. 
15-4 
Figure 2 Earth Covered Storage Igloo -- Lightning Strike Model 
.- 
Figure 3 Building - Right Side View With Window Screens and Lightning Protection 
System 
115-5 
Figure 5 shows a contour plot of the vertical mid-plane longitudinal cross-section of the igloo corresponding 
to the schematic in Figure 4. The electric field pattern outlines some of the prominent features of the igloo, Le., 
the z-cage, soil berm over the igloo, headwall, backwall, e& The vectors show the projection of the electric field 
vector at each cell onto the mid-plane at a time 1 after the initiation of the strike. The length of the vector 
is proportional to the logarithm of the electric field. The contour lines show lines of equal electric field 
magnitude labeled as powers of 10 of the field magnitude in volts per meter. For example, the line labeled 4.0 
represents field magnitudes of l0,OOO volWmeter. 
Figure 6 shows a contour plot on a vertical x-z plane of the building cutting through wire mesh on the 
window nearest the strike. The view is as if looking from the back of the building. The field patterns show 
essential geometrical features of the model, Le., roof, supporting I~beams, outer wall, efc, 
The window mesh, a wire grid covering the building windows, is being charged (note E-field vectors 
pointing away from the mesh) and appears tb focus the,elecmc field into the interior of the building. The field 
levels are very high within the building approachitrg 1 Megavolt/meter (contours are labeled as powers of 10 of 
the electric field magnitude). 
In this case, Figure 6, the lightning proteetion system is not connected to the metal roof. At .462 p, seconds 
the top of the roof is positively charged and the bottom of the roof is negatively charged. 
Figure 7 shows the effect of adding an I-beam (perpendicular to the contour plane) with a hanging metal 
cable hoist. The field at the bottom of the hoist is on the order of a few megavoltdmeter and represents a 
potential for arcing between the hoist and the floor rebar (or any other piece of grounded equipment). In this case 
the lightning protection system is in contact with the metal roof which is also in contact with the I-beam. 
Figure 8 shows time dependent plots, corresponding to Figure 7, of the lightning injection current (given by 
equations (12)), the electric field and wire voltage in the middle of the window screen, and the voltage between the 
hoist hook and the floor rebar. This is a case showing that connecting the lightning ptotection system to the 
building structure can enhance the hazard inside the building. 
5.0 TIME LAPSE VIDEO PRgSENTATIONS 
The video tape shows computer calculated electric and magtietic fields on two different vertical plane cross- 
sections of the igloo (see Figure 4). The presentation begins with a view of the right-hand side of a transverse 
cross-section and ends with a views of the longitudinal vertical mid-cross-section (see Figures 4 and 5 )  and a 
plane o€fset Erom the mid-cross-section. 
The data shown is calculated by a Cray 11 computer using a finite difference form of Maxweil's Equations. 
The resulting data pertinent to the video display is taken from the Cray I1 computet results and displayed on an 
IBM PC compatible EGA screen. These EGA screens have twice the resolution of the VHS video tapes. 
The graphic frames are displayed at a rate of about 3 frames per second. Each frame occurs in simulated real 
time in 50 nanosecond intervals. There are then 20 frames per I microsecond simulated real time showing the 
time development of the electric and magnetic fields for each typical computer run, The time is shown in the 
upper left-hand comer of the screen. 
The electric and magnetic field magnitudes are shown at each finite difference cell on the plane. The colored 
dots represent the field magnitude ranges at each cell. Vecsots centered on the dots also exist at each cell showing 
the direction of the field projection onto the plane. The scale of values are shown in the video tape. There are 
approximately 1 million fmim difference cells in the entire problem space. 
Thspeak magnitude of the lightning current is 110 KA and the rise time is .2 microseconds. The lightning 
attaches to the igloo on the rear lightning protection air tefminal near the vent chimney of the igloo. 
The charge collecting on the rebar may be noted by obsefving electric field vectors pointing away from the 
ceiling and back wall in both directions. 
115-6 
Figure 4 Igloo Vertical Cross-section at j = jm = 75 
Figure 5 Electric Field Vector and Magnitude Contour Plot for Vertical Mid-Cross- 
Section of Igloo 
115-7 
Supportlq 1-l)rra 
Counterpolre Concrete 
Floor 
Figure 6 Electric Field Vector and Magnitude Contour Plot for a VerticaI Plane Passing 
Through the Window Mesh o? the Building 
X-CIXIS ICtfTl - . . .  A r L n ~ ~ r n m o ~  Pj 
Figure 7 Electric Field Vector and Magnitude Plot for Building Showing the Effect of 
an Internal I-Beam and Metal Cable Hoist 
115-8 
1 20 
100 
80 
"60 
40 
20 
0 
9 
t- 
0: 
3 
0 . 1  .2 .3 .4 .S .6 .7 .8 
time uscc 
300 [[j 
250 
200 
< is0 
w L 
g 100 
so 
0 
-5a 
0 ,1  .2 -3  .4 .S .6 .7 .8 
tine uscc 
INJECTION CURRENT - HIR ir, j~,k-2 EX-FIELO 
iwl .  jff+B,ltr+14 FLOOR REEAR - INMR WL & 1-8EPN - CON 
,01 SOIL-.OOl CDH;RETE-OATRSETS MFPXK n i a u  a nim =EN 
120 
100 
80 > 
Y 
0 
0 .1 .2 .3 .4 .5 .S .7 .8 
Figure 8 Time Dependent Plots of Building 
2500 
2000 
2 lS00 
0 
Fields and 
o . I  .2 .3 .4 .s -13 .7 .a 
t i e  use 
HOIST HOM 
ir*17, jft+Z3,k+21 to 23 
MIS7 Hop[ 70 ROQZ 
Lightning Injection Current 
115-9 
It is noted that the largest fields are near the floor and are on the order of 100 Kvoltdmeter at 1 psec. This is 
due primarily to capacitive coupling of charge on the rebar which, again, is enhanced by electrical contact 
between the lightning protection system .and the igloo metal structure. 
6.0 CONCLUSIONS 
A numerical computer model of Ivkqwell's Equations has been applied to buildings typical of munitions 
storage and handling s t r u c ~ e s  to calculate potential hazards due to lightning saikes. It is seen that detailed 
electromagnetic field profiles and currents may be calculated which estimate in a realistic manner the hazardous 
areas in and around the facility. A time lapse video representation has been produced which shows the electric and 
magnetic field magnitudes on plane cross-sections of the building during a simulated lightning strike. 
7.0 REFERENCES 
1. Merewether, D.E., and R. Fisher, "Finite Difference Solution of Maxwell's Equations for EMF' 
Applications," Electro Magnetic Applications, Inc. Report, EMA-79-R-4, Final Revision, 1/15/82. 
2. Collier, Richard S. and Rodney A. P e d ,  "Evaluation of Lightning Hazards to Munition Storage Handling, 
and Maintenance Facilities with the use of Advanced Methods for Solutions of Maxwell's Equations," 
presented at the Twenty-Fourth DoD Explosives Safety Seminar, Adam's Mark Hotel, St. Louis, Missouri, 
28 - 30 August 1990. 
115-10 


Evaluating lightning hazards to building environments using explicit numerical solutions of Maxwell's equations

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server