wan hao jiang - sim numerical 3dim lightning based on dbm (2010)

7/31/2019 Wan Hao Jiang - Sim Numerical 3dim Lightning Based on DBM (2010)

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TDmsl Nmcl Smlt f Lt Dsc Bs DBMMl

Wn Ho-jng, We Gung-u, Cen QngInstitute ofElectrostatic &Elecomagnetic Prtecon

OrceEngineering College,Shijiauang, China

E-mal:

Absact-The modeling nd imulon of lighing dihrgere very imporn for he lighing proeion engneeringnd lighning reerh. In hi pper, wih he hunderloudeleroi model nd poenil equon in he pe, hreedimenionl(3D) numeril imulon of lighing dihrge 50m roluon w preened. The diele rekdown

modelBM) ed on fl heory nd idireionl lederindden delop mehnim were employed o imulehe lighng leder progreion. The effe of proliyeonen nd inernl Eeld Ein long he hnnel on heonground Eeld diuon were nlyzed repevely. Thereul how h he diriuion of Eeld he ground levelelow he epped leder i imilr o Gu diuion. Thepek vlue of he Eeld he ground level inree wih heproiiy exponen nd inel Eeld long he hnneldereing.

Kos-DBM; thudercoud model; ghtg smuo;dbu ofEld; parame of mod

I. NTODUTIONLightning is a tical damagng source in the nate.Especially with the quick increase of micreleconic devicesused in the stems, e probility of lightning dageincreases accordingly [1], [2]. However, reseches onlightning dischge ulizing natal lightning are quitedicult to cry out because of the rndomicity ddesuctive eect of lightning dischges. Therefore, themodeling d silation of lightning discharges are valuablefor the lighing proction engineering. In the late 1980s,the DBM model was inoduced by Niemeyer et al. [3],which was n developed and used in the simulation oflightning discharges. Nevertheless, the DBM model wasmostly employed win the connes of 2-D simulation, or

3-D simulation wi a low resolution, which can't presently e 3-D chacteristics of lightning discharges [4]-[7].In the present work, thrugh he combination of athundercloud elecostac model wi 3-D DBM model, ae resolution 3-D numericl simulation of lightingdischge was presented according to acl theory dbidirectional leders independent develop mechism.Mewhile, considering at he disibution ofE-eld at thegrod level below e stepped leader will determine thepoints of strike to a great extent , the eects of probilityexponent d inteal E-eld on e on-grod E-elddisibuon were also analzed respectively.

9784445549//$6. IEEE

II. THE ASI OF 3-D ATAL IMULATION OFIGHTING ISHGE

The 3-D cl smulation of lightning discharge in ispaper is derived om e macrscopic phenomenon of

lightning dischges and do not deal wi the microscopicprocesses of breadown. Based on Laplaces equation (orPoissons uation) d the bodary condions, hepotential disibution in the interested region is xed. Thenthe 3-D simulation of lightning dischge is realizedaccording to actal theory and bidirectional leadersinddent develop mechism. The prgression of thelightning leaders is deteined by these factors such ashundercloud model, DBM model, peter settings d soon. The concrete applicaon of each factor is discussed asfollows.

A. TundercloudModel

The initial boudary conditions of the nterested regionare deteined by e sucte of e thundercloud model inthe simulation. In e traditional dipole d multiple-dipolemodels, as a result of oversimplied point concenations oflarge disibutions of chges, the geometrical viables inquestion can signicantly inuence the calculation of the

E-eld [8]. us, a hree-level set of chged circular discsrepresenting a generic cell recommended by Amorso dLattlo [8] is used n is paper, as shon in ig. 1. is

model, e local non-uniformity in the chge disibution ofthe thundercloud is neglected. Ting into accout of themirroring action of e ground which is assumed to be aperfect conductor, e on-grond E-eld on he obsvationpoint c be represented as follows:

(1)

in which S is the srface where the chge of each layerlocated, Ui is the unit vector of each surface, is the volumecharge density deposited on the sfaceS, is the distancebetween e elementary surfacedS d To ech discsrce, the surface integral is given by


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dS= 2[-(1-e')h+rdE(p)

r 2a2 _R2 h2 aR

+K(p)+-(p,m)]rd rd a+R

(2)

where a is e radius of e chged circular disc, R is thehorizonl distce om e observation point to e centreof e disc, h is e height of e disc, =-1, 0, 1 whenR isless than, equal to, eater a, reectively,

rd = +h2 , K(p) , E(p) and (p,m) arecomple elliptic integrals of e rst, second and ird kind,respectively, where p = 2.;/rd and m = 2.;/(a + R) .Thus, underclouds of dierent characristics c beobtained throu seosition of dierent cell stems.

z

u

I a

u

Figure Tee-level charged discs model

Considering at e on-axis eld of thdercloudincreases parolically with ascending of the heightapproximately, the eld distribution in the space c beobtained by the method of pabolic crve ting based onthe on-ondE-eld data. Then, the potential disibution inthe interested region can be determned as = f d Andthe potential disibuons on e bondary of the interestedregion see as e nitial boundy conditions of the

numerical simulation.

B. DBMModel

In the actal simulation, the prgression of e leaderdepends on DBM model principally. There are to tes ofcommonly used DBM models: NPW model d WZ model[9], [10]. NPW model, presented by Niemeyer et al. in 1980s,assumes that e selection of the dischge point and edischge direction during the leader pgression is random,and considers e prbility of e leader progression is thebiggest along e direcon where e elecic eld intensity

1

is the greatest. However, NPW model supposes e leaderchannel is equipontial, and neglects the critical eleciceld threshold for propagation, which are nrealistic.

Therefore, WZ model developed by Wiesmn d Zelleradds a critical electric eld reshold for propagationand an nal electric eld in e leader channel basedon the NPW model. The ppagaon probility of WZmodel c be expressed as

(3)

where = (qj q )/M is the magnitde of the eleciceld beteen the th point of the channel and the adjacentnon-chnel points, is the distce beteen e twopoints, probability exponent denotes e intensity ofaaday eect, which would inuce the actal dimension.Results of research have shown that the channels visualizeas bush te for1, but "brnched te for ?3.

e WZ model, if e reference potential of the initialbredown point is the potential of the h channel pointc be obined as

(4)

where

LM is the disnce along the channel beteen the

initial bredon point and ei chnel point.In he 3-D DBM model, e leaders prpagate st-by

sp om an inial breadon point. ig. 2 shows the 18adjacent non-chnel ponts ound the bredown point.The extension probabilities of the possible channel pointsin e next step d e prpagation pbabilities of the18 adjacent non-chanel points ound the selected channelpoints c be calculated om Eq. (3). Then, e breakdopoint on e channel d e dischge direction are selectedby Monte Cl Mehods.

--:--0----I ,'1

"--'- : , ,

p a -

Figre 2 18 adjacent non-channel points aund the breakdown point.Solid sphere indicates the breakdown point. Hollow heres indicate the

possible new breakdown point.


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C Pameter SettingsConsider a medium-sized undercloud in this paper.

The coesponding pareters e set as follows: e disc

radius of e thundercloud is =2km, the charge dsities ofthe positive discs d e negative discs are =0.5nCm,=-0.5nCm, respectively, the height of the upper posivelayer, the intermediate double layer and the lower negativelayer e set to 10km, 5.5km, 1.5km, resptively.urthermore, additional 05-km radius positive layer with=0.1nCm is embedded in he centre of e lowernegative layer. Considering at the stped leaderstically advance n segments on the order of 50m, hence50-m spatial resolution is adopted in the simulation. Basedon e previous works, e critical eld threshold for theleader initiation is set to be 200kYm, and is chosen tobe 150kYm

III. LENTATION OF 3-D FATAL SIMULATIONBased on the peters set above, the ow chart of 3-Dactal simulation of lightning dischge is sho in ig. 3.Thou e breakdown phsics mechanisms ae diert forpositive d negative leader propagation, both tes ofleaders e eated in the se way in is simulation. Theleaders nitiate at a point, which is chosen at (0, 0, 3.0) inthe per, while e electric eld magnitude in a cerinregion exceeds e reshold Then the bidirectionalleaders develop indendently.

Cc b cs

Cc sb

C

cs

Cc ; sc bw c

Cc ?p sc sc c

II

DBM

III

L__________ ____________ 1

J w s c b

Figre 3. Flow chart of simulation

ig. 4 shows a negative cloud-to-od \CG) lighingdischgediagram wi =3 and =-17kYm , n which themain channel of e bidireconal leaders is visible dbranches of e leaders e plic.

SOOO

45

4

35

3

25

2

5

5

0

5

y/ 2

Figure 4 G lightning diharge aam

E-IELD ISTIBUTIONS T HE OUND EVELELOW HE EADES

TheE-eld disibuon at e ound level is determinedby e thdercloud d e leaders togeer. Moreover, thedowd stepped leader plays important role in e

selection of e point of sike when e leader has peneatedup to a height of hdreds of meters. Here, represents thetip height of e downwd leader above e ground. Theeects of the peter settings on the on-grund E-elddisibuon were analed by king exple for =500m asfollows.

A. ect of Probabli xontThe pbability exponent can inuence the actal

dimension. The ear the value of is, e less e actaldimension is. It means at while e value of is enlged,the branches of the leders will decrease, which will decreasethe E-eld at the grund level contributed by e leadersmulneously. By remaining the parameters as specied in

Section II and setting =-17kYm, numerical simulationsof lightning dischge for =1, 2, 3, 4 e coed, and hecorreonding E-eld distributions at the ground level areobtained. The results show that e on-grond E-elddisibution below the stped leader is simil to Gaussdisibution, as shown n ig. 5. And the peak values of the

E-eld calculated om our simulations va with theprobability exponent, as listed in Table I. When is lger,e peak value of e E-eld at the ground level is smaller.Alhough there are some statistic eors because of therdomicity of e leader development, the calculated resultsare consistent with e above-mentioned results of eoryanalysis.


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E -100l

y/(m) 2000 2000 x(m)

20

Figre 5. On-ground electric eld distribionwhn =3

TABLE I. AK ALUS OF ONGROUND E-FORDFRNTALUSOF

2 3 4

Peak vaue of the-240.8 -213.9 -198.2 -153.6

o-groud -ed(k'm)

B. ect ofthe Inteal Field

In order to ensure the extensibility of the main lightningchannel d e prolic brched suctre in e CGlightning simulation simultaneously, e probilityexponents for e prbabilities d e considered

indepdently. Set =3 for the extension prbility d= I for e prpagation prbability By some discretevalues of , the relation between e pe values of the onodE-eld and e ntealE-eld is obtained, as shownin Table II. The pe value of the E-eld increases wi einteal E-eld decreasing. This is because at themagnitde of intealE-eld along the channel is n relaonto the chnel current. The less intealE-eld is, e higherchannel current is. Thus, the contribution of the chnel toe on-grund E-led is greater in he sitation of e seactal dimension.

TABLE II. AK ALUS OF ONOUND E-FORDFFRNTALUSOF in

(km) -17 -1 -5 0

Peak vaue of theo-groud -ed(k'm)

-191.9 220 9 252 6 2943

V. CONLUSIONS

In this paper, a 3-D numerical simulation of lightningdischge at 50-m resolution was presented based on thethree-level elecostatic model of a thderstorm cellrecommended by Amorso and Lattulo. Then, king thedownwd leader tip height =500m for exple, e eectsof probility exponent and inteal E-eld on e ongrod E-eld disibution were disussed according to the

simulation, respectively. Results show that he disibution ofon-ound E-eld is simil to Gauss distribution, and thepe value of e E-eld at e grund level increases with

the pbability expont and intealE-eld decreasing.KNOWLEDGNT

This paper is supported by Equipment Exploration dResech Program uder Grt No. 7130933.

REFEENES

[1] Golde R H, Pysics of Litning. London: Academy Press Inc, 977.

[] Ma Ming, L Wei-tao, Zang Yi-jun, et a., 'aracteristics of litningexposure in Cina om 997 to 200," Joal of Applied MeteorologicalScience, vol. 9,August 200,pp. 9-400.

[3] Niemeyer L, L Pieonero, H J Wiesmann, 'ractal dimension of dielectricbreakdon," Pys. Rev. Let, vol. 2,94, pp. 0-0.

[4] Jemy A Riousset, Victor P Pasko, Paul R Krebiel, et a., redimensional actal modeling of inacloud litning discarge in a NeMexico undstorm d compison it ligtning mappingobservations," Journal of Geopysical Reserc, 2007,pp. 2.

[5] Tan Yongbo, Numerical simulation of te relationsip of te liingdiscarge it e ace cge and po ttial disibution n undcloud,Hefei: University of Science and Tecnology of Cina, 200.

[6] Xueei Zg, Lin Don Jnliang He, et a., Study on te eectiveessof sngle ligtning rods by a actal approac," Jornal of iingesec, vol. ,2009,pp. -.

[7] Fu Jin SiMa Wen-xia, Li Jian-biao, et a., 'stimation on litningsielding peoance of e transmission lines based on te actaltheory," High oltage Engineerng, vol June 2009 pp 1274-127

[8] Amoru Y, Lattalo F, ''Tundcloud presoke elecostaticmodeling," Journal of Electrostatics, vol. ,2002,pp. 2-27.

[] Gu Cen, an Ping, Sao Tao, et a., Fractal simulation of reakdon in

dielectric," Hig oltage Engi neerng, vol. 2,Jury 200,pp. -4.[1] Ed R Mansell, Donald R MacGo, Conrd L Ziegler, ''Carge

sucture d litning sensitivity in a simulated multicell tunderston,"Joual of eopysical esec, 2,pp. 0.

wan hao jiang - sim numerical 3dim lightning based on dbm (2010)

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