Lightning Effects and Structure Analysis Tool (LESAT)

Lightning Effects and Structure Analysis Tool (LESAT)

Steve [email protected]

What Is LESAT?

• LESAT - Lightning Effects Structure Analysis Tool– Computational methodology implemented in MATLAB

to analytically predict actual transient current levels and voltages on aircraft wiring and structural elements.

– Assists designers in protecting aircraft against the indirect effects of lightning strikes.

– Implements the methodology used successfully for MH-47 lightning analysis.

Outline

• Motivation• Objectives• Methodology• Results• Conclusions and Future Work• Questions?

Motivation

• Lightning is a severe threat (up to 200 kA peak).• More reliance on electronic systems.• Technology evolution from metallic aircraft

structure to composite structure.• High cost aircraft-level testing and hazardous

aspect of experiments in laboratories.

Objectives

• Input system geometry in a CAD format.• Circuit analysis approach - apply Kirchhoff’s

laws to obtain linear equations that can be solved in matrix form.

• Predict induced currents and voltage drops on wiring and structural elements.

Lightning Indirect Effects Waveform• MIL-STD-464C Severe Stroke in both Time and Frequency Domains

1

1

0

tt0s

s647265

s11354

A218810I

)ee(II

Why Kirchhoff Rather Than Maxwell?• Since the source frequency is very low, we have a

Quasi-static (near steady state) situation.• Dimensions of the conducting network are much

smaller than the wavelength.• Tool gives good results for aircraft dimensions up to ¼

the wavelength of the maximum frequency.

mMHz

smx

f

c

fc

3001

/103 8

Drawing not to scale

m30010

1

Code Analysis MethodologyRead Geometry

& Electrical Characteristics

From Mesh Files

Break UpStructure Into

Linear Segments

Compute System of

LinearEquations

CalculateFrequency DomainImpulse

Response forEach Branch

Calculate Time-DomainSolutions (Induced

Currents and Voltages)

Plot Results

ComputeResistances

CalculateSelf & MutualInductances

ComputeImpedance

Matrix

Calculate Laplace

Responses

Input Geometry

• Input system CAD geometry as a series of mesh files used to represent skins, pylons, and other routed cabling and electrical equipment inside the aircraft.

Example Mesh Geometry Input for a Structure

BULK RESISTIVITY Ω-m

LENGTH (L), WIDTH (W), THICKNESS (H)

Fundamental Resistance Data

SKIN RESISTIVITY Ω/□

LENGTH

RADIUS

Line/CableResistivity Ω/m

1. Lines/Cable Resistivity is measured in Ohms per meter ρ – to get Ohms use: Rc = ρL

2. Skin/Mesh Resistivity is measured in Ohms per square ρ – to get Ohms use: Rskin = ρL/W

3. Bulk Resistivity is measured in Ohm-meters ρ – to get Ohms use: Rbulk = ρL/(WH)

4. Equivalent resistance for a branch use:

R = Rbulk X Rskin/(Rbulk + Rskin)

Attachment Points

lightningdetachmentpoint

lightningattachmentpoint

Model• Circuit Approach: The airframe is represented by an

equivalent R,L circuit network.

k

210)()(

nnknknnnEEIMjILjR

R2

R3

L2

L3

L4

L1 R1

R4

M12

M34

M23

M12

k node to

connected b

0bkI

Kirchhoff’s Laws are enforced:

Piece of the meshhas 5 nodes and 4 branches.

x

B

y

I1 I2

A C

DM12

z 3D representation

Each branch is a resistive, mutually inductive circuit element.

Code calculates mutual inductances

Five-Branch Four-Node Circuit Example

.0

, -

,0

,

,0 ZZZZZ

,0 ZZZZZ

,0 ZZZZZ

,0 ZZZZZ

,0 ZZZZZ

541

43

532

21

42555445335225115

43545444334224114

32535434333223113

21525424323222112

41515414313212111

III

III

III

III

EEIIIII

EEIIIII

EEIIIII

EEIIIII

EEIIIII

s

s

E1

Is

Is

E3

E4 E2

Z11I L1(jω)

I L2(jω)

I2I1

I4 I3

I5

Z44 Z33

Z22

Z55

System of linear equations

Matrix Notation

Topology

TopologyT

0

Z I

=

E

0

I s

Input

Output

s

T

IE

IZ 0

0topology

topology Ax = b

Physics(squarematrix)

Number ofBranches

Number ofNodes

Number ofBranches

Number ofNodes

A x b

bxA

1

0

0

0

0

0

0

0

00000100

00000010

00000001

000

000

100

010

001

3

2

4

5

4

3

2

1

Z Z Z Z Z

Z Z Z Z Z

Z Z Z Z Z

Z Z Z Z Z

Z Z Z Z Z

5545352515

4544342414

3534332313

2524232212

1514131211

E

E

E

I

I

I

I

I

0

Is

0

Is

0

0

0

0

0

000011001

000001100

000010110

000000011

1010

1100

0110

0011

1001

4

3

2

1

5

4

3

2

1

ZZZZZ

ZZZZZ

ZZZZZ

ZZZZZ

ZZZZZ

5545352515

4544342414

3534332313

2524232212

1514131211

E

E

E

E

I

I

I

I

I

Reduction To Transformed Currents

System reduces to:

branches – (nodes – 1)

transformed currents.

35

34

5545

4544

Z

Z

Z Z

Z Z

5

4

I

I

Solution for Multiple Frequencies

Solution for a specific branchcurrent at each frequency.

Branch Current Laplace Transform – represents the frequency-domain Transfer function between the Injected lightning current and the current of the “victim” component.

)()()(SImRen

jjSjSjagnalnk

currentsbranch of # 1 n

241 k kkf 2

sj

m

nm

nm

o sc

sbas

1)(S

n

t

o

t

oeIeItI )(

s

I

s

IdtetIs oost

0)()(I

m

nm

nm

n sc

sbs

1a )(S

o

)(SI Jn

sssn

Lightning Time Dependence

Lightning Laplace Transform

Frequency Domain Transfer Function

Branch Current Laplace Response

1

a)(S)(I)(Jonn

m

nm

nmoo

sc

sb

s

I

s

Isss

Time-Domain Solution

nmc

t

m

nm

o

nm

o

nm

nm

m

nm

nm

o

t

om

nm

nm

o

t

on

ec

I

c

I

c

b

c

baeI

c

baeItJ

11

11)(

Note the addition of the purely resistive part ao

Branch Current Time Dependence

Cable Inside A Conducting Box• Rectangular

volume of material with dimensions (13.6m x 2.5m x 2.5m).

• Skin Thickness: 1.6mm

• Bulk Resistivity: 2.65x10-8 Ohm-meters

• Skin Parallel Mesh Resistivity: 1.35x10-4 Ohms/sq

• Skin Perpendicular Mesh Resistivity: 1.35x10-4 Ohms/sq

• Cable Resistivity: 1.728x10-15 Ohms/meter

• Cable Radius: 2.54cm

Results for Aluminum Conducting Box

• Blue curve represents cable current and voltage drop on cable for blue bolt strike location.• Magenta curve represents cable current and voltage drop on cable for magenta bolt strike location.

DrivingWaveform

Conclusions and Future Work

• Validation: compare calculated results to experimental data.

• Apply methodology to:– Ground systems– Buildings– Electromagnetic Pulse (EMP) excitation

• Relate predicted Lightning Effects to structural damage.

Questions?

Steve [email protected]

Lightning Effects and Structure Analysis Tool (LESAT)

Documents

Transcript of Lightning Effects and Structure Analysis Tool (LESAT)