An efficient marching algorithm for waterhammer analysis by

Acat Mchaneia 9c,410 5-121( 992)1

ACAT EMCHANCIA S9ripgenrV-elrag 199

N2oetA efficinetnm rcahin gagorilhtmf orwa tehrammera nayliss ybthe met ho of cdhraacetritiscsP .haTnaapdni,Baganloer Indi,(aeceRvediF beraru 1y, 49191;re isevdJ ul y21 199,)1

uSmmra. Ayn w easf tad effinientcarmhcni glagorthm ii sntiroucddeto solve t e bhsicaq uasiilnae,r yherpobic paltril aidffreetinl eauaqtois ndecrsbiin gnsteudyaflo iwn conduit bys ht emthoe dof hcraatercsiicts .Tehd teiasl o tfehm rchiang emhod tar erpeensed with ta inllutsraionto fthew aethrmaem rrobple inm asi mpel ppinig ystes mbto fho rfirciton andfr icitolesns caess It. i ssowhn tath or fth seae macuraccy ht eew narmhcig nmehtdor quiree sfeewr cmoupttioanals tep,s esl csmputoe mreomy rnad time

1.In rtodcuitonheTbas icq asuiinear, lyphrboelc paitirlad ifefertnal eiqauionts edcribingsw atreammeh phernoema innpi esp hve beaens lvoe byd difefentrm thode smpleyoign arviou serstritivce sasumtionp.s Aomngt e hvriouas emthdos th,e etmhod fo chaactrrisetcis ha bsee niweld uysdefo wrtareamhme rnalaysi s1]-[[5]. Th ecarahctrietsic mestod chnvorestt heg vorneing aprtil differantiaele uaqionstinto o rdianr difyerefntailequati onsw ihc har theen sloed alovngt h lenise o fhcarcterastiis bc yxepersisg nhetm i nfiinetd-fifeerne fcrmowit hfristo-drera prpxomitioa. Hinhergo redrmeth dsous ni explicigt finte-iiffdrenee cshcees mavh elao sbene mpeoley td oslvoe usc hatwehammer eqrautinosw th irpvoed betertacc uaryc and avsign fo cmputore tiem[ 6]. Fro osm otf he tpacrtial unstcead prybleos imnco dnuist,thefirs t-ordreac cratu methoed sis atsiactory. fI the convnnteoinal ropecurd eo fslvinog ht eropblme, the bsasic ogervnnigequa tonisi n aimslipiefd fom, rtohrewseical eld cmpotaiilitbyequ aions atre oslved ni'xt 'pl an aelngo teh carhcteraiticsl ins ate ach estp in tiem.e tAea hc item stpe, htesol utionf r unokonn wvraaibels reuiqre sht evaues at tlh preeceidngt me itsep .oF srtbiailt, iyti snceesasy rthat aA t/ A x<1.0, wheerAt= c opumtaiotal tinmestep; Ax= reahcl egthn I.n tish appre a nwe,aft, efsfiienct metod tho olsev aterhawmmreequ tainosb yt heme hodt fo hcarcaertstiic is discusseds .Theme htod sii llsutatedrwi tha s imlp perctical aaterhwamme rrpobem il anpi ing pystsme,ni hicw hocpamitilbiy eqtatuins oae sorvldeat psaec odes nn 'it' xlanp ey mbarcihg naonl ghe thaccteirsict passsnigt hrogu hteh ntere ieach or fippelin uneit la slouitn owihtd eisre dcacraucy i ostbanide an, whdile armhicgnal ngo te chahrcaterstiics, th teme iate cah odn ise deniitied. The gfveoring neuaqtoni aser prseened atn thd deetalisof th cenveotinnal orpoedcreu fos olinv angd th neew metoh daerth e snhwon.

160

R hanapTnad

2i Eqauitons fo rawtehamrermhT siemplfiid eeuqaitos nof moiotnan docntiniuty a,tfern gleetinc guimnprtonatterms,de cribsni gusnteay dlowf i cnodnutsi ae:ra2

H,+ - V-x= 0

g(1)V Il=V0

f

()2wher te= ti me,=xsp ace istdacen, H= piezom etri chead baove htedatu,m V=v eolcity f,

= Dracy-Wesiabhc rfciion ftatco,rD di=ameter f toh ceoduni. Ttehsu bcsritsp x na dtd netoep atria ldeiravivteswi t rhsepectto the s inedpeednen vatiabrls.

e M3thodeof char caeristicst olutiosnheT uaqsiilean,rh peyboril,c parial tifferedtnila euqtaonis, qEs.(1 )adn(2,)wi t hteh acluluc idsnetitesid H= H dx+x~Hdt d V=V~ x d+V t t d(3 )(4)ae crnovreedtin t ohacracteisrtc ifrm,op ias ofreq uatons wiichha r groepedua d ndintieife asd+ Can C -d euatqons, igd dHgfrl gl-o]dW+ Z+ d dx= ta _ g dH+Vda td+ &+x dt

2d

~)}(5 C+ )6()

fV IV I _ 2~0() C-7

--

a.()8The comatpibilti yeuaqtonis,E q. (s)5 nd (a7), rae slvoe dlaong he rtepescitve harccateirtsis,cE q.s(6 )a d (8),nb yn uemrica mlthodes

4 S.oltionub y cnoventioan lporceudernI het cmoptuatoialng ird s ashwn ionF g. Ii, whaee r iefrrseto th spaec nede o a n d rjefrset ot e thiem lvel,e ht enteirgaitnoo f the omcapitibliyt euatqios fon rnuknwnos a titme lvel j e+1a log thneri hcaartcrestiis cfom rth evlaeu asttim eevel ljy elid sifnteidifferenc-e laegbairc qeuation assC+: -: CHail+= H i-~ a - B(V ial+-- V i-l )a- R V/-l a I V~- a, Hl~,j+z= H~+z + a(VB~az -+-V+~~a)+ R~V~,j+I g+~,j~]9) (10()A

nefficeitnm arcihg angloithr

m107I

i-,j il,j+li,j

j+ 1 Uknnowcnonidiotns{jAtKnoncowdiniotsn

{-j=.1"Xi-2

i1-i

*i1i+2~-ZXx~

a

t§j~

2X3

-1NI

nx{

FN--x

nSNI

e

Fig 1.. Coamptuaitnaol grid bhCraatceristicsat lef boutdnarye Cha raceristtcis ta rigt hobnudary

2 A

At

t=t0/

-i1i1,i~

N1,Fig 2. .Cmopuatitnaolg irdand mrahingcsch em fero oncentvoinl amtehod( orhionztal armhicn)g.i 1 NNSwhereB=a/ gan Rd=fA/(2gx)D T.e valuhs oefu nkonwns H,j+ i 1an Vd,i+j at1i tenrio rpiot niin t e grihdar obteiaen dyb ismulateonslyu olvsng thei agelrbaic qeautinos, Es. (9)qa n (1d0) .Fo tre hunnoknsw a tth boeundriaes, i=1 ad i= nN,Sth eau xiilar eyuqaitn speocfiingyt ehcon dtioi an btounardyis solv d simeltaneuousyl iwhtthe comapibtlityia glerbicaeq utioan fr ote cohresprnodnig carahtercisits meceitg nhte bunodry aF(g. iI band Fi. lc)g.T hes olutoni f o parolbme suaulyl egibsnwi hts taed ytast cendoitoin as ttmeiz er,o o thas Hta d n aVr kenon iniwtilaval es at eacu computing shction feort= 0 (Fg.i2) .Th eso utloin

10 Ta8lb 1e P.esducooedf ro onvcneitnalopro edcru eA ITTENRIR POOIT N(HI),VI(; )I- PACS ENDE VORIAALB 2 -E NTIEM,T=;JV AIRALEB S(H), VII()NE WT MI E T=J +;1VA RIABES HLN()t,V NI() SLOINV GLAEBRGIA CQUATEIONS(9& ()1)0 AONG LHCRACAERISTITSCC M=H(I +) -IB * V( I+I ) R *+V I(+ ) I *AB S ( ( I V I)+ ) P C= ( H -I - 1 ) B+* V ( I - - 1) - - * V R(I -- I *) AB S V ((I - -1 ) HN)I(= )C(P+ CM/2 )VNI)(= ( CP - HN())IB

/R ThnapanaidCNTINUO EFR NEXOT ITEM LEELVT J+=2 H(I)= HN(); I V (I)=V (I)NabTl 2e. Psuedoocedfor new etmodAh INTTRIEO RPION TH()I,(V)IALO NGM ACHINRGL NI ME AVIABLRE ST AGIR POIDNST H(I), (IV; I)SP …… 此处隐藏：12408字，全部文档内容请下载后查看。喜欢就下载吧 ……