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Lightning strikes on ships: an initial application of the similarity theory through scaled experiments E. P. Nicolopoulou, V. T. Kontargyri, I. F. Gonos,

G. J. Tsekouras, E. C. Pyrgioti, I. A. Stathopulos


Electric Power Quality (PQ) problems in Ship Electric Energy Systems (DEFKALION)

Research Activities  Investigation of PQ problems due to shaft generator operation  Investigation of PQ problems due to thruster operation  Investigation of PQ problems due to pod operation  Analysis of impact of earthing (grounding) on PQ phenomena  Analysis of PQ phenomena due to lightning strikes  PQ Measuring and Monitoring System 2


Lightning strikes (WP 6): Work Process Data Collection Investigation of the relevant regulations and standards Study of the behavior of the hull during a lightning strike (theoretical analysis and simulations) Tests in the premises of the High Voltage Laboratory of NTUA with a scaled ship model (experimental investigation)

 

3


Scaled models: Preliminary measurements 

Dangers arising from lightning strikes on ships: Overvoltages, Overcurrents, Induced currents to electronic equipment

Rapid distribution of the lightning current into seawater through the highly conductive body of a metallic ship 1. Former conceptions: a metal hull would face no problems during a lightning strike 2. Nowadays: Discontinuities in the hull structure, The All Electric Ship (sensitive electronic equipment)

Investigation of the behavior of the ship hull during a lightning strike (voltage and current distribution): an initial approach is the concept of the ship metal hull as a “grounding electrode”.

Limitations of experiments in a controllable laboratory environment (Laboratory space, electrode dimensions, excitation parameters of the impulse current) lead to the design of scaled experiments based on the Similarity Theory and the Dimensional Analysis

Verification of the validity of this analysis through measurements of the impulse grounding resistance of strip electrodes embedded in an electrolytic tank for various electrode dimensions and water conductivities. Simulation of the full scale phenomenon with the scaled model:  Sea surface  Ship metal hull  Lightning strike 4

metal tank filled with saline water solution metal strip electrode with scaled down dimensions injection of impulse current produced by an impulse generator


Scaled models: Theoretical Background Similarity Theory: a method applicable on scaled-model experiments (in various scientific fields: naval engineering, telecommunications, high voltage engineering etc.) which allows the derivation of scale laws for the physical quantities of a problem based on the principle of physical similarity. Physical similarity between model and prototype can be acquired through: 1. geometrical similarity and 2. the application of Dimensional Analysis

Formation of dimensionless products (Πi parameters) from the magnitudes that appear in the governing equations of the problem: Πi model = Πi full scale (Buckingham Πi Theorem)

Advantage: the method does not require the knowledge of the exact relationships that describe the problem, only the physical magnitudes that appear. 5


Dimensional Analysis

1. 2. 3. 4.

5.

6

Specification of the r variables of the problem and their dimensions Definition of the dependent and independent variables Description of the dimensions of each variable based on a unit system formed by fundamental magnitudes Formation of the dimensional matrix (rank n ) and selection of the dimensionally independent subset of variables Calculation of the dimensionless k Î parameters ( k = r - n )


Variables of the problem (I) For the purposes of the present analysis the following formula has been adopted for the calculation of the impulse grounding resistance Z:

Z  Ai  R (1) Where R is the steady state grounding resistance (Ω) Ai is the impulse coefficient taking into consideration both soil ionization (i.e. the reduction of grounding resistance due to the high value of the injected current) and inductive phenomena (i.e. effective length: dissipation of fast wavefront current from a fraction of the electrode length) Ai 

1  A 1 1 Im I g

(2)

I m = the peak value of the current (A) = the critical ionization current (A) Ig

7

Ig 

E0  2R 2

(3)

E= 0 the critical ionization field (kV/m) = soil resistivity (Ωm)


Variables of the problem (II) A is the impulse coefficient without the influence of ionization, defined as: A  1 l  leff A  al   l  leff

(4)

1  is the effective length a coefficients a,  are functions of the resistivity  and the current waveform rise time T1 leff 

  2l  ln  l  d 

For a grounding strip:

R

where l = length (m),

d= width (m)

(6)

(1)-(6)

8

Z  f d , l ,  , I m , E0 , T1 

(5)


Πi Parameters and Scale Factors 

Application of the Dimensional Analysis on the relationship Z  f d , l ,  , I m , E0 , T1  (unit system [M L T I], r=7 variables, rank=n=4, dimensionally independent subset [ρ, Im, l, T1], k=3) yields the following dimensionless Πi parameters:

Z l 1   

d 2  l

0  l 2 3    Im

According to the Buckingham Πi Theorem (Πimodel = Πifull scale) the scale factors for each magnitude ( K i ) must obey to the following equations under physical similarity conditions:

K Z  K   K l1 

Kl  K d

1 K  K l

K E0  K  K   K I m  2 l

9

K Im K


Experimental setup •

Impulse current generator 8/20μs up to 25kA

Electrolytic tank: 2m x 1m x 0.5m

Strip electrodes

Oscilloscope

Conductivity meter – Calibration solution

Temperature-, humidity-, pressure-meter 

4 conductivity levels :  0.08 S/m  1 S/m  2 S/m

 4 S/m

4 electrode dimensions:  20cm x 2cm  40cm x 4cm  30cm x 3cm  60cm x 6cm

IMPULSE CURRENT GENERATOR (EMC 2004 HILO TEST) POTENTIAL DIVIDER (50kΩ/50Ω)

STRIP ELECTRODE

ELECTROLYTIC TANK CURRENT SHUNT (1mΩ, 20ΜΗz)

TO OSCILLOSCOPE

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Measurement procedure 

Two measurement scenarios are implemented: 1 I. For the same conductivity level K  K E  comparison between electrodes of the measurements recorded under injected current conditions: K I  K l2 The scaling law to be verified in this case is: K Z  1 Kl II. For the same electrode Kl  1 comparison between conductivity levels of the measurements recorded under injected current conditions: K  K I  By adopting the assumption K  1 the scaling law to be verified is: K Z  1 K 0

m

m

E0

The waveforms of the injected current and the electrode voltage are recorded and the impulse impedance is calculated from the oscillogramms applying two alternative definitions: V and Z  V @ I max Z  max I max

I max

The deviations of the experimental ratios K Z values are calculated.

11

from the theoretically expected


Conductivity comparisons (I) Comparison between σ=4 S/m and σ=2 S/m ( Z 

theoretical Ι4 (Α)

Ι2 (Α)

200

experimental ΚΙ

deviation ΚΙ %

theoretical

ΚZ (a) 0.500

Ι4 (Α)

Ι2 (Α)

ΚΙ

100

200,4

99,4

2,016

0,805

300

150

297,4

150,0

1,982

-0,880

400

200

500 600 700 800 900 1000

250 300 350 400 450 500

2

Measured Kσ=1.919

V @ I max I max

402,1

198,8

2,023

1,127

489,4 589,8 689,8 780,5 891,8 988,2

250,4 302,0 351,6 401,6 450,4 500,0

1,955 1,953 1,962 1,943 1,980 1,976

-2,268 -2,358 -1,911 -2,829 -0,995 -1,184

average values

1,977

-1,164

ΚZ (b) 0.522

): 20cmx2cm electrode experimental

deviation

Ζ4 (Ω)

Ζ2 (Ω)

ΚΖ

ΚΖ % (a)

ΚΖ % (b)

1,389

2,435

0,571

14,123

9,346

1,402

2,448

0,573

14,515

9,722

1,377

2,523

0,546

9,137

4,569

1,370 1,381 1,371 1,388 1,413 1,401

2,518 2,511 2,494 2,522 2,544 2,496

0,544 0,550 0,550 0,550 0,555 0,561

8,813 9,977 9,948 10,064 11,091 12,226

4,258 5,373 5,346 5,457 6,441 7,528

0,555

10,959

6,314

average values

Comparison between σ=4 S/m and σ=1 S/m ( Z  V @ I max ): 30cmx3cm electrode

I max

theoretical

experimental

Ι4 (Α)

Ι1 (Α)

Ι4 (Α)

Ι1 (Α)

ΚΙ

deviation ΚΙ %

400

100

387,0

102,8

3,765

-5,875

800

200

786,6

198,8

3,957

-1,087

ΚΙ

4

theoretical ΚZ (a) 0.250

experimental

deviation

Ζ4 (Ω)

Ζ1 (Ω)

ΚΖ

ΚΖ % (a)

ΚΖ % (b)

1,033

3,767

0,274

9,754

5,651

1,023

3,847

0,266

6,386

2,409

900

225

896,3

224,8

3,987

-0,320

1,035

3,801

0,272

8,963

4,890

1600

400

1570,0

399,2

3,932

-1,703

0,991

3,717

0,267

6,669

2,681

1800

450

1779,0

448,0

3,971

-0,714

0,989

3,777

0,262

4,767

0,851

1,922

-1,940

0,268

7,308

3,296

Measured Kσ=3.817

12

average values

ΚZ (b) 0.262

average values


Conductivity comparisons (II) Comparison between σ=2 S/m and σ=1 S/m ( Z 

theoretical Ι2 (Α)

Ι1 (Α)

450 800 900 1350 1600 1800 2250 2400 2700 3200

225 400 450 675 800 900 1125 1200 1350 1600

experimental ΚΙ

Ι2 (Α)

Ι1 (Α)

ΚΙ

deviation ΚΙ %

2

441,6 801,6 900,8 1348 1600 1800 2260 2400 2700 3200

233,2 401,6 444,8 674,4 803,2 896 1112 1184 1358 1604

1,893 1,996 2,025 1,998 1,992 2,008 2,032 2,027 1,988 1,995

-5,317 -0,199 1,259 -0,059 -0,398 0,446 1,619 1,351 -0,589 -0,249

1,995

-0,214

Measured Kσ=1.883

average values

Comparison between σ=2 S/and σ=1 S/m (Z 

theoretical Ι2 (Α)

Ι1 (Α)

200

experimental ΚΙ

deviation ΚΙ %

Ι2 (Α)

Ι1 (Α)

ΚΙ

100

202,4

98,2

2,061

3,055

400

200

400,8

198,4

2,020

1,008

600

300

600,8

298

2,016

0,805

Vmax ): 60cmx6cm electrode I max

theoretical

ΚZ (a) 0.500

ΚZ (b) 0.531

experimental Ζ2 (Ω)

Ζ1 (Ω)

ΚΖ

ΚΖ % (a)

ΚΖ % (b)

1,2119 1,2155 1,2189 1,2195 1,2150 1,2067 1,2123 1,1983 1,1940 1,2025

2,2024 2,2151 2,1871 2,1738 2,1763 2,1696 2,1763 2,1993 2,2533 2,1621

0,5502 0,5487 0,5573 0,5610 0,558 0,5561 0,5570 0,5448 0,5299 0,5561

10,058 9,751 11,467 12,208 11,658 11,232 11,420 8,973 5,984 11,235

3,670 3,382 4,998 5,696 5,178 4,776 4,953 2,649 -0,167 4,779

average values

0,5553

10,398

3,9913

Vmax ): 40cmx4cm electrode I max theoretical

experimental Ζ1 (Ω)

ΚΖ

ΚΖ % (a)

ΚΖ % (b)

2,9369 2,9839 3,0121 3,0000 3,0008 2,9960 2,9795 3,0110 2,9988

0,5369 0,5324 0,5269 0,5333 0,5318 0,5296 0,5274 0,5272 0,5302

7,399 6,494 5,390 6,667 6,372 5,919 5,484 5,446 6,042

3,083 2,215 1,156 2,381 2,098 1,663 1,246 1,209 1,782

0,5306

6,1347

1,8703

800

400

2,000

0,000

998,4

499,2

2,000

0,000

600

1200

600,8

1,997

-0,133

700

1400

700,8

1,998

-0,114

1600

800

1600

798,4

2,004

0,200

2000

1000

2000

1000,4

1,999

-0,040

average values

2,011

0,531

average values

800

400 500

1200 1400

2

Measured Kσ=1.919

13

ΚZ (a) 0.500

ΚZ (b) 0.521

deviation

Ζ2 (Ω) 1,5770 1,5888 1,5872 1,6000 1,5960 1,5866 1,5714 1,5875 1,5900

1000

deviation


Electrode comparisons (I) 

V @ I max

For σ=4 S/m ( Z  I max

): 60cmx6cm – 40cmx4cm

theoretical Ι60 (Α)

Ι40 (Α)

225

experimental Ι60 (Α)

Ι40 (Α)

ΚΙ

100

220,80

118,04

1,871

450

200

446,08

192,64

2,316

2,916

675

300

664,00

295,12

2,250

-0,003

900

400

891,20

395,68

2,252

0,103

1125

500

1116,80

490,88

2,275

1,115

600

1324,00

594,08

2,229

average values

2,199

1350

ΚΙ

2.25

Kl=1.5 

For σ=2 S/m ( Z 

Ι30 (Α)

Ι20 (Α)

225

theoretical

experimental

deviation ΚΖ %

Ζ60 (Ω)

Ζ40 (Ω)

ΚΖ

0,5978

0,8404

0,711

6,705

0,6062

0,8949

0,677

1,600

0,6120

0,8620

0,710

6,502

0,6032

0,8896

0,678

1,713

0,5981

0,8638

0,692

3,873

-0,949

0,5740

0,8699

0,660

-1,022

-2,280

average values

0,688

3,229

-16,864

ΚZ 0.667

V @ I max ): 30cmx3cm – 20cmx2cm I max

theoretical

experimental Ι30 (Α)

Ι20 (Α)

ΚΙ

100

225,2

99,4

2,2655

450

200

450,4

198,8

675

300

674,4

302

ΚΙ

2.25

deviation ΚΙ %

theoretical

experimental

deviation ΚΖ %

Ζ30 (Ω)

Ζ20 (Ω)

ΚΖ

0,693

1,6163

2,4346

0,6639

-0,415

2,2655

0,693

1,6376

2,5231

0,6490

-2,642

2,2331

-0,751

1,6298

2,5113

0,6490

-2,645

1,6192

2,5219

0,6420

-3,691

1,6512

2,4960

0,6615

-0,766

ΚZ 0.667

900

400

899,2

401,6

2,2390

-0,487

1125

500

1124

500

2,2480

-0,089

1350

600

1350

599,2

2,2530

0,134

1,6148

2,4833

0,6502

-2,460

1575

700

1574

700

2,2485

-0,063

1,6416

2,5600

0,6412

-3,808

2,2504

0,019

average values

0,6510

-2,346

Kl=1.5

14

deviation ΚΙ %

average values


Electrode comparisons (II) For σ=0.08 S/m ( Z 

V @ I max ): 40cmx4cm – 30cmx3cm I max

theoretical Ι40 (Α)

Ι30 (Α)

7,1 14,2 16,0 21,3 … 184,9 192,0 224,0 256,0

4 8 9 12 … 104 108 126 144

experimental ΚΙ

Ι40 (Α)

Ι30 (Α)

ΚΙ

deviation ΚΙ %

1.78

7,70 14,00 15,64 21,80 … 182,30 189,90 221,40 251,80

4,74 6,84 9,10 11,76 … 103,40 106,80 124,90 143,30

1,624 2,047 1,719 1,854 … 1,764 1,778 1,773 1,758

-8,623 15,132 -3,324 4,273 … -0,779 0,009 -0,256 -1,131

average values

1,776

-0,104

Kl=1.333 

V @ I max

For σ=1 S/m ( Z  I max Ι30 (Α)

177,77 355,56 533,33 711,11 888,89 1066,67 1244,44 1422,22 1600,00 1777,78

100 200 300 400 500 600 700 800 900 1000

experimental ΚΙ

Ι40 (Α)

Ι30 (Α)

ΚΙ

deviation ΚΙ %

1.78

171,2 352 535,2 710,4 880 1062 1240 1420 1600 1784

102,8 198,8 300,8 399,2 500 600 699,2 800 897,6 1010

1,6653 1,7706 1,7792 1,7795 1,7600 1,7700 1,7734 1,7750 1,7825 1,7663

-6,323 -0,402 0,083 0,100 -1,000 -0,437 -0,243 -0,156 0,267 -0,644

1,7622

-0,876

Kl=1.333 , Measured Kσ=1.046

15

ΚZ 0.750

experimental

deviation

Ζ40 (Ω)

Ζ30 (Ω)

ΚΖ

ΚΖ %

25,1429 24,6286 24,8593 25,1009 … 25,4498 25,5687 25,2890 25,4130

40,0844 38,1287 36,5714 35,1701 … 34,9845 34,7500 34,7213 34,8409

0,627 0,646 0,680 0,714 … 0,727 0,736 0,728 0,729

-16,367 -13,876 -9,367 -4,840 … -3,006 -1,895 -2,888 -2,747

0,717

-4,401

average values

): 40cmx4cm – 30cmx3cm

theoretical Ι40 (Α)

theoretical

average values

theoretical

ΚZ (a) 0.750

ΚZ (b) 0.717

experimental

deviation

Ζ40 (Ω)

Ζ30 (Ω)

ΚΖ

2,7570 2,7000 2,7862 2,7027 2,7409 2,8060 2,7161 2,7696 2,7200 2,8341

3,7665 3,8471 3,8138 3,7174 3,7680 3,7200 3,8158 3,8400 3,7790 3,7624

0,7319 0,7018 0,7305 0,7270 0,7274 0,7543 0,7118 0,7212 0,7197 0,7532

ΚΖ % (a) -2,403 -6,423 -2,591 -3,062 -3,011 0,574 -5,092 -3,831 -4,030 0,436

ΚΖ % (b) 2,157 -2,050 1,960 1,468 1,521 5,274 -0,657 0,663 0,454 5,129

average values

0,7279

-2,943

1,592


Conclusions •

A comparison of the results shows an overall satisfying performance of the theory. Z

V @ I max I max

The definition provides in most cases smaller deviations and is thus considered more suitable both for comparisons between electrodes and for comparisons between conductivities.

For different electrodes and salinity levels the current risetime changes. Although T1 is eliminated by the Πi parameters it is taken into consideration by the second Z definition which accounts for the time-shift between voltage and current waveform.

Deviations in the exact value of the conductivity and in the electrode depth adjustment cause deviations from the theoretically expected Kz ratios.

The influence of the tank walls is observed for the big electrodes (40cm x 4cm, 60cm x 6cm) especially at high conductivity levels.

The accuracy of the recorded waveforms can be increased with the use of a differential probe and a current monitor.

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Future goals •

Injection of impulse current to a metallic scaled down ship model (based on an existing full scale model) placed in a bigger electrolytic tank, recording of the voltage and current waveforms on critical points of interest and reproduction of the corresponding full scale magnitudes from the scaled down measurements.

Further improvement of the presented scaling procedure: the Similarity Theory can alternatively be applied to Maxwell’s equations (Ampere’s Law, Faraday’s Law, constitutive relations etc.) to define the relationships between the scale factors.

Taking as a basis the experimental T1 and Im values of the impulse current generator and the corresponding parameters of real lightning strikes, the scale factors Kt, KI can be defined. Experimental results converted to full scale values will be compared to simulations carried out with the electromagnetic analysis software package CST Microwave Studio.

17


ACKNOWLEDGMENT THE

WORK PRESENTED IN THIS PAPER HAS BEEN DEVELOPED WITHIN THE

THALES-DEFKALION PROJECT. THIS RESEARCH HAS BEEN COFINANCED BY THE EUROPEAN UNION (EUROPEAN SOCIAL FUND – ESF) AND GREEK NATIONAL FUNDS THROUGH THE OPERATIONAL PROGRAM "EDUCATION AND LIFELONG LEARNING" OF THE NATIONAL STRATEGIC REFERENCE FRAMEWORK (NSRF) - RESEARCH FUNDING PROGRAM: THALES: REINFORCEMENT OF THE INTERDISCIPLINARY AND/OR INTER-INSTITUTIONAL RESEARCH AND INNOVATION.

FRAMEWORK OF THE


Thank you for your attention!

Lightning strikes on ships: an initial application of the similarity theory through scaled experimen  
Lightning strikes on ships: an initial application of the similarity theory through scaled experimen  
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