Computer eriens n Fld y1ac The funda1�ental behavior of uis as traitiony bee se in anks an win tunnes. he capacities of he moern coputr ake it posse to o subter expriments on the cO�puter aone y Francis H. Harlow nd Jaco
T
he naturl phlosophers of ncint Greece liked to do experiments n their heds. Centuries lter Gli leo developed the "thought experment into a frutful method of nquiry nd n our own time the method ppeled strongly to such men s Albert Einsten nd Enrico Ferm Now the rrvl of the modern electronic computer has mde the method immensely more pow erful nd verstile The computer mkes it possible to simulte nture with nu mercal models nd to nvestigte it in wys tht he never been prctcble before Physcl processes of enormous complexity re being exmned minute ly nd wth considerble relism New hypotheses re beng proved true or flse In physis, engineering economics nd even anthropology the computer hs beome a revoionary tool One of the gret attrctions of exer ment by computer is that it cn vod some of the uncertinties of mesure ment Moreover, it provides technique tht cn be clssed as both theoreticl nd experimental It s theoreticl be cuse it deals wth bstrct (tht s, mthematicl) sttements of how things relte to one nother It is experimentl beas the computer is given only dat speifying the initial state of a systm ad set of rules for calculting its state at some time in the future. The com pter worer has no more ide how this ftre stat will unfold than has the trditional worr who conducts com prabe experim experiment ent in an ctul labor labor tory To donstrte te power of com puter experiments we have chosen single examle involving the dynmic behvior of uids The partculr ex periment is a study of the ow of ir pst rectngulr rod. At rst thought te use of computer for calulating this ow my seem to be nedlessly roundabout procedre
From
Would t not be simpler and more enlghtening to put the rod in wind tunnel nd observe how r contining lments of smoke ows rond it? Ac tlly it would not. For mny of the qestions to be nvestigted the physi cl exprimen exprimentt woul woul re re com plicted nd costly, nd t wold not
provide as muh formation s the ex periment by computer. For an example one pont to the problem of redesigning the Tcoma Narrows Brdge fter it hd been shken to peces by wnd-induced vibrtions soon fter it was built For the rebuild ing of the brdge many elaborte modl
VORTEX EXPERIMENT with a uid is compared with a similar computer experiment using a mathematical model In a tank dark lnes of dye within a movin body of water (top) ow past a cylndrca obstacle; the ater's velocity s rea enouh o disrupt lami.
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wee mde nd tested gn and agn befoe sfe esign ws nally deel oped. Wthout doubt much of the ost nd tme spent on the poblem could e been sed by computer calul tons f the computers nd ppropate numericl techniques hd then been ailble. periments wth numericl models cn show the ntection of winds nd bdge in detl nd poduce answes n far less time than t takes to pepae physcl epement. The Soiet physicst A. A Dorodntsyn has emrked bout such poblems that computer clculton "can gie solu tion tht is not only moe apd nd cheper but lso moe ccute than the physcl eperment itself. permenttion by computer so alows the nestgton of mn phe nomen that re either nccessible to direct study o inole fctos that can not be mesured ccurately. In the ow poblem tht we shll discuss, for e mple, it s dcult to mesue directly n wnd tunnel the tempetue dis tibuton in the complcted downsteam
wake. omuter epeimnts, owee, n yiel relale escpton of the temeatue dstibuton. Anote benet of computer eper ment is that t usually aods fa better contol of the epeimental conditons than s ossible in a physical epement. In win tunnel studies, for instance, the epeimenter mut modfy hs in tepetations to inlude the consdea tion of suh eets s those due to the compressiblty of the workng uid, aiatons n uid isosity nd uncer tnties in ow elocity. In compute epeiment such propeties often cn be ecluded or ncluded at will. Moreoe, the computer pogam n isolte cru cal featues for emintion, cn elm nte elent factos nd cn often ssess te epemental uncertintes. Finally, nd most mpotntly, eper ments by omputer poide a test of the ppliability of theory to the compli ctd phenomena under nestgtion. Do te equatons of ud dynmics rel ly epesent the coect theoeticl de scrpton when pled to phenomen
ar /ow ad eerae a characersc doue row o vorces n he compuer experme (bottom) comparae marker es are smulaed smulaed ad her moos are recorded recorded o mcrom; mcrom; ahouh
s compcted, sy, s the osclltoy ow that deelops n the wake of rec tngular rod? For such problems the mthemtician would lke to obtin wht h calls n nlyticl solutonthe knd of ect solution tht cn be ob tined by the processes of mthemtial nlysis. Fo problems n ud dynamics, hoeer, the necessry mthemtl technques for obtning the complete soluton hae not yet been deelope. The detled esults poided by com puter can ctully help in the deelop ment of nlytcl solutions to the basic equtions of uid dynamcs. Usully in the mthemticl model of comple poblem some of the fctors cn only be ppromated, nd obtinng rel stic soluton depends on nng out whch fetues re crucil for reason ble representton. ith the help of compute epeiments one ties to dis coer workble ppoimtons that wll simplify the mathemtics needed to soe complicted problemin ths case poblem in oscillatory uid ow. The ree wll nd the "comute
he osace s a recae raher ha a cyder, he rea ad mode paers show cose areeme The dye·e experme was perormed Aexader Tho o he Uversy o Oxord
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rpidy through the ir nd for the whine of ship's rigging in the wind It ws resonnt vibrtion produced by the wnd tht cused the Tcom Nrrows Bridge to brek nd f into the bay As te ir speed increses, the vorties in the vortex street become more nd more rged nd evetuy brek up into tiny eddies whose motion is most entirey rndom At this stge fuy deveoped turbuence hs been reched The known ptterns of ir moton past n object, then, give us certin de nite phenomen to ook for in the com puter experiments If the computer re produces vortex street nd, t ater stge, turbuence, it wi show tht the theoretic understnding of uid dy namics is ccurte nd therefore cn be reied on to predict wht wi en wen uid ows pst objects of vri ous shpes nd t vrious speeds o set up the ccution exeri ment we must rst trnste te
CLSIC PRBLM in i ynis is to prict th proreson fro orrly linr o pst n obstcl t slo sp (top illustration to totl turbulnc t hih spee crcil ipoint in this prorssion is rcd whn vortics for ltrntly t opposit s of th obstcl middle and bottom illustrations nd thn r sh ownstr
wind tunne experiment esier to fo ow if we consider briy how uid beves when it ows round xed object such s rectngur rod At ow speed the irow is smooth nd stedy, condition described s inr ow At certain critic speed, whic depends on te siz o the rod, the minr ow reks down For rod one inch in height the critic speed in ir is bout one inch per second; the smer the rod, the higher te speed t which turbuence begins If the uid is more viscous thn ir minr ow is more esiy ntined nd the critic
speed for turbuence becomes higher Above the critic spee the air strem breks up into vortices tt re simir to the sm whirpoos seen when cup of coee is stirred. These vortices re sed ternatey from the top nd bottom of the object pced in the irstrem This osciting wk was rst extensivey studied by the erody nmicist Theodor von Krmn nd is known s "von Krmn vortex street h osciting wke sends out puses tht rect bck on the object itsef The vibrton so produced is responsibe for the sound mde by gof cub swung
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physic sitution into the nuge of numbers for the computer For book keeing purposes the exeriment rea in the computer wind tunne is divided into mny squre ces, which form the bsic computing mesh A typic mesh reuires t est 49 ces in the direc tion of orizont ow nd 24 ces in the vertic dimensio, for tot of 1,176 ces Ech ce must contin two numbrs representing the components of verge ir vocity in two directions, together with other numbes represent ing such vribe quntities as "vortic ity, "strem function nd, if het ow is desired, temperture s we Fin y, the computer must be supied with set of opertig instructions, or "code, tht spes out in deti excty how the computer mut mnipute every num ber in every ce in order to ccute how the ow congurtion wi chnge from instnt to instnt It cn require biions of mthemtic opertions nd nywhere from few minutes to few hours of computing time to crry out th ccutions needed to represnt the ow of ir for time interv of sever minutes In our studies we hve used iter n IBM 709 computer or the somewht fster mchine, so buit by the Interntion Business Mchines Corportion, known s Stretch The ctu dveopment of success fu code is timeconsuming process nd is crried out in three steps The rst invoves the testing of detied numeric methods nd is strewn with ps It is no tric, for exmpe, to invent methods tht deveop numeric instbiity: the computer resuts rpidy
IC CMUTIG MEH fr thl n tunnl s r f 7 nul lls, rry n rs lls ln an lls Th bstl, t s hh s t s p, s lat lls y fr th nput w t th lft rn f h sh t h srt f n xprnt h ll s prr th a nu f tw nubrs, whh rprsnt th hrzntl n vrtal pnnts f th ar ar l t tht pnt n
sp T lls n ls b prr nn nurl nts fr nl rbls suh s h , ry n sr funn Drn th run f luln h pur s rry u bllns l prns n rr t rn h th w nrn rs In s xpl th w f r p h bsl hs rh rh th rl sp t hh lrntn rs r fr see strton on opposte pge).
IMULTED MTI F IR pst an bstl extreme left tht s sttnr th rspt t th bsrr prus a plt f swrln strlns Th urs f h ln prllls th r tn f th ajnt r urrnts w; th nrrwr th spn bwn lns, th hhr th sp Ths s n f fur plts tht sw rnt ta fr th s nstnt n a snl xprnt
IULTED MTI F BTCLE hruh by f sll r, lhuh thtlly ntl th th sun llus trt t th lft, prus qu rnt strln plt In ths nstn th r ss rhr hn th bsl s stnr th rspt t h bsrr; th ptrn f rts tr by th strlns rsbls th turbuln n th k f pssn shp
TREKLIE PLT s a thrd knd f nuratn pssbl n pur xprnts In ths s, ntr nubrs tht nt pl n prt n th w alulatns hav bn nsrtd n fur lls f th putr sh at th rar f th bstl Ths nubrs b "putatnal prtls that tra ut th n n s n strks, as sk lnts n a wnd tunn
THERM PLT prs a furh xpl f h t that n b bn b ns f putr xprnts s f tpr· tur lus suln t b hs bn sr n th ht lls ln th rr f th bstl s th r passs wn n h pur luls th rt t hh th ht s n dut th lns nnt pns f ul rutn n tprtur
© 1965 SCIENTIFIC SCIENTIFIC AMERICAN, AMERICAN, INC
4
6
3
DEVELOPMENT OF A VORTEX STREET is documented in six consecutive streamline stream line plots (left and center illustrations, top to changes to a bottom) The laminar ow at the outset 1) quickly changes stable pair of eddies behind the obstacle 2 The stability ends
run askew nd led to complete non sense. Like physicl experiments, com puter experiments re lso subject to interference by gremlins Just s the vibrtion of a motor my produce ex traneous turbulence in wind tunnel, so te numericl pproximtions fed into computer my led to eqully n wanted "trunction trbulence
when one or another of the edies begins to grow. The large r eddy shifts position both downstream and toward the center ine, thus pushing the smaller, upstream eddy out of its normal position (3 and 4. The upstream edy is now exposed to acceleration both by
The second step is to prepare a full scle code For our problem in uid dynmics this required required mny months, most of the consumed by "debug ging, or ferreting out errors in, the step-bystep instructions. instructions. Such a code is written with with sucient generlity so tht it cn be sed sed to solve a wide vri ety of roughly siilr problems. Tus
SEQUENCE OF STREAK LIES traces the transformation of a je of air as turbuence progressiely increases (jo steps from left t
good code cn be used for yers n will often be source of inspirtion for workers in other lbortories The third step is to formlate the code in terms of speCic problem. In our oscillatingwke study n important part of the formultion ws to determine the "initil and "boundry conditions. The initil condition describes the state
ight. I his experime computationa partices are inroduced hrough a igle cel hriznta streaks as hough squirting
08
© 1965 SCIENTIFIC SCIENTIFIC AMERICAN, INC
nto the computng egn n wy tht ceted a minimum of mathematical is ubnce. he computng pocess itself can be ompaed to the making of a motion ctue. Stating with the initial cn dtons pescbed f ech of the 7 cellss in "fame cell "fame No the the compute compute follws the coded instuctins to de temine the conditis in each cell a bief instnt f time late theeby ucng fame No 2 f the m Ech successive fame is smilaly geneate on the bass f numeical data cm puted f the peceding fame he fastest compute availble t us Stetch can geneate abut 0 fmes a minute. hen the calculatin has oceeded f enough the esults e gtheed up f study.
b
esults cn be pe Thesentedcompute's in any of sevel dieent
he main sream and by he reverse currens f he dwnstream eddy () and beins rw in it urn n he rwin upstream eddy pinches he dwnsream ne, which is hen shed as a vre whie a new eddy frs behind he bstace 5 and 6 he sreakine pts "a, "b and " a rih utine he frmatin f he vrices urin saes , 5 and 6.
of the a t the stt of the comput tion e could hve ssumed fo ex mple that the ai was at est coes pnding to the conditon n a eal wind tunnel befoe the fn s tuned on. e found that t ws simple howeve to stt with the ud behvng as if it wee wing pst the od n a smple min mnne without viscosty
he ounday cnditins efe to wht s happening at the edges of the cmputtiona mesh. Ou decisin was to have the tp and bottom edges e esent the wlls of the wind tunnel an to have the left edge epesent n ai nput of unifom w. he ight edge gve us moe tuble but we nlly nged fo the uid to ow out nd bck
cred waer in a cear ank he je f air is unsabe and sn breaks in epandin irreuar vrices ie hse ehibied by a
fms One fom of pintout cnsists of ll the numbes descbing the n each fame Usually this fm f intout is esticted t samplings taen at selected ntevls because the cm plete data fo evey evey one of the hun hun deds o thousands of cycles n an expement would be f to much f n nalyst to digest to say nthing of stoing the eams of pape Smetimes the cmpute s pogmmed to pint cetain calculations that suply paticu paticu la points f infmto such as the amount of a dag caused by the ob stacle at specic wind speeds. he most useful nd ppul type of pintut hweve is the actual pltting of the w in pctoil fom he compute itself can geneate plots of the w congutions nd pu them n lm by means of a mclm ecode Sevel selected fames fom such ecdings exactly as they cme fom the cmpute ae among the llus ttions on this pge and pecedig pges of this ticle he sequence of all the fames of n expeimet combined n lm stip nd un though motn
pume f sme imiar bu far mre cmpe eperimens can be sed es heries abu aircraf je enine nise suppressin
9 © 1965 SCIENTIFIC AMERICAN, INC
y ZZ h
he Damic adgraph f xplsvel Drv tals
The application of a pulsed radation beam produced by a hig current lctro accelerator (PHERMEX) to te studies o te dyamic beavor and proprts o tr te svere envronmt of explosve dtoatios, wre prsurs may be measurd n mgabars. Te radiograpic diagnos o sock wave itractions in mtas as well as atur of t etonation wavs i te xlosve drving carges ar of prtcular intrst T sigicace o suc paramtrs s tsle strengt ad viscosity, i t ig-sped dynamic ralm s sout Te ormtio prors d ects o mtallic jt are bsrvd ad studd 6-
/alazos F B V
q U z q
10 © 1965 SCIENTIFIC SCIENTIFIC AMERICAN, AMERICAN, INC
ictue ojecto gives a vey vvi ictue of the eveoment of votices an othe featues as uid ows oun an obstace Fom the numbes descibing the ow in ech ce of the comuting mesh the comute geneates steamines that show both the iection an the see of ow thoughout the spce The seed is indicate by the spacing between the steamines whee the ines e cose togethe the ow is fst; whee they e fathe aat the ow is sowe The compute can show the steamine ttens n ethe of two wys as if came wee photogphing steam o i owing past it o as if the camea wee moving ong wth the steam The atte view shows the tte of votices in cea deti Te compute cn even simute the motion of mkes often used to make ow visibe such s aments of smoke in i o of ye n wate In the com pute the makes consist of "comu ttion ptices At cetain esie oints in the comutation these atices e thown in (the magic of the com pute aows thei ceation anywhee at wi) n theeafte they e cae aong wheeve the ow of ai goes Thei pths of motion pouce ies ced steak ines The steak ines gen eate by the comute give a emak by faithfu impession of the behvio of smoke o ye mets Pehs te most stiking of these compute con stctions is the congution of steak ines emeging fom a jet it ooks ike a ament of cigaette smoke Usuay the comute is gamme to funish seve ieent congua ton ots showing featues of the ow fm vaious oints of view These ae by no means meey an inteesting a bum of pictues They show the quaita tive featues of the eveoment of the ow an povide pecise quantittive infomation bout the ow t evey oint In many cses the comute e veas impotat detais that wou be extemey icut to obtin fom physi ca expeiments The exampe we hve escibe of a copute technique fo investigating ui ow is ony one of mny success fu eots that hve been mae to cay out comex expeiments by compute Othe wokes hve used compute to te in eti what is gong on insie a nuea eacto nd to ssess in n in stant the pogess of ocket soing ito spce Tomoow the compute my give ccute foecsts of the wethe of te futue of the economy nd of the state of man' heth
Let m e explain why All-B All-Brradl is of utmost' •
Over the last quae centuy, Alle-Badey's hot moded compsiion esisos in a aings ae estab ished thei epuaion f being f unifomy cnsiset quaiyo even appaced by ay oe moded esiso on he maket. Neie yeas of seice, no yeas of oy shef ife wi aec tis unifomiy wiin the aing unde wich he uis wee oiginay puchased. Aen-Badey fees tha i as a esonsibiiy to is muiude of cusomes a oe te wod, ha wen hey de Aen-Badey esiss hey hae e condence ased o yeas of expeiencehat e quaiy and de edabe pefmace wi be e same as befoe! No ide deiains in chaaceisicseen i isoaed e sisoscan cause quesiabe pefomace in you equipmen. Caasopic faiues ae an impossibiity wih A- moded esisos Pehaps Ae-Baey doesn desee cedi fo such unifomiy becase i esus fom auomaic maciney whic cmpeey eiminaes e uma eeme Vaia tios ae oeaed by is maciney. Besides, if Ae-Baey had succumbe e pice agumen and ad paced n e make a we quaiy esis, hw wud you be abe to e em apa wihou haig is cost you exa money? Hw abou e wog esiso accidentay geing into he ong ace?
ga sisto pocy ou This coud oy be discoveed on a estand cec g such caeess misakes is expensie. D you eay save money he you buy an infei make of esis??? Leading eleconic manufacues ae fund i eay ays sandadize on Aen-aey uaiy esiss you wi, oo. F compee specicains, pease wie f Tecnica Buein 5050: Aen-adey C., 10 S Tid S., Miwaukee, Wiscnsin 530 In Canada: Ae-Badey Caada d, Ga, naio.
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© 1965 SCIENTIFIC SCIENTIFIC AMERICAN, AMERICAN, INC
