Eclipse Solar

Balance

On Jet

Centre-line.

a rudimentary steam engine working on a j e t reaction p r in c ip le andl c o n sistin g o f a r o ta tin g steam driven device operating on the same "basis as many present-day lawn sprinkler s^*^# I t was regarded by

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Hero as a curious toy rather than a u se fu l machinev ^ « In the tw elth or th irteen th century an improvement o f the foot-d riven bellow s o f the Egytians appeared in Europe (probably imported by returning C rusaders), in the shape o f furnace bellow s driven by water wheels#

During the fifte e n th century, the Rennaissance brought with i t a gradual change in thought from the purely p h ilosop h ical to observational science# Perhaps the most im pressive o f the early proponents o f t h is approach was Leonardo da V inci (1452-1519 Amongst h is many achievem ents, he made a sig n ific a n t contribution

to the development o f hydraulics in h is c o lle c te d w ritin g s fDel moto

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e misura d e llfacqua* • Included in the phenomena o f which he was the f i r s t to sketch or d escrib e, i s that o f the p r o file s o f free jets#

Early in the seventeenth century, E vangelista T o r r ic e lli, in h is work * de moto gravium* proposed a hypothysis r e la tin g to the e fflu x o f a flu id from an o r ific e # In an attempt to prove b is h yp oth esis, he conducted several experiments u sin g water jets#

In 1686, M arriotte*s work 1 T raite du movement des eaux e t des au tres corps f l u i d e s * w a s published. I t included in the sectio n

d ealin g w ith the * equilibrium o f flu id bodies by w eigh t1, a s e r ie s o f r u le s d escribing the d e fle c tio n o f a j e t by a.normal surface# He also produced analyses o f the parabolic tr a je c to r ie s o f j e t s

discharged at d iffe r e n t in clin a tio n s#

Isaao Newton (1642-172?) was a lso in te r e ste d in the pi'oblem o f e fflu x from an o r ific e .' In h is hypothysis p ostu lated in h is I 687

(Yi) ed itio n o f ‘P rin cip ia Mathematica P hilosophise H atu ralis' ,.ih io . computed r a te o f e fflu x d iffe r e d from th at a c tu a lly measured by a

fa cto r approximately equal to the square root o f two# In the second e d itio n , published in 1713, he a ttrib u ted the error to the

con traction o f the jet#

The tr e a tis e 1 Hydro dynamics1, by Daniel B ern o u lli, was published in 17385 a sectio n was devoted to Vthe v e lo c ity o f e fflu x

( ^2)

and e fflu x under constant headtv . He orig in a ted the idea o f j e t propulsion for sh ip s, although he was thinking only in terms o f the

reaction produced by the e fflu x o f water from a tank* F ifty years

la te r th is idea was to be improved upon by an American named James fiumsey. He employed the newly-developed steam engine to propel a boat on the Potomac River by u t ilis in g the reaction o f a j©^ of

water produced by a steam driven p isto n pump*

In 1766 Borda published a tr e a tis e e n title d 'Memoire sur 1* ecoulement des flu id s par le s o r if ic e s des v a s e s ' i n which he sought to remove certain d iscrepancies in B e r n o u lli's and d'A lem bert's an alyses o f the e fflu x problem. B esides introducing the conoept o f elementary stream tubes, he also showed that not only the contraction o f the j e t , but also a lo s s o f energy, must u su a lly be taken in to account in form ulating the discharge rate*

The year 1854 ©aw the p u b lication o f a paper by G.H.L. Hagen 'Ueber den E in flu ss der Temper a tur auf d ie Bewegung des Wassers in R o h r e n ';^ ^ , ^ which he d ealt w ith the e ffe c t o f temperature upon the r e sista n c e to flow through pipes* In the course o f h is

experim ental work he n o ticed that the appearance o f an e fflu x j e t v aried with temperature, remaining 'immovable as though i t were a

s o lid g la ss rod*, a t low temperature and ex h ib itin g 'very n o tic a b le

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flu c tu a tio n s o f short period*, as the temperature r o se ' ^ . He went on to introduce sawdust in to water flow ing through g la ss tubes and observed sim ilar phenomena to those described by Osborne Reynolds in the la t t e r 's famous paper o f 1 8 8 3 ^ ^ . The laws o f in s t a b ilit y o f stream line motion and the fundamental fa c ts o f turbulent f lo w ^ ^ , as proposed by Reynolds, have provided one o f the major con trib u tion s to contemporary flu id mechanics*"One o f the e a r lie s t papers

published by Reynolds was concerned with the suspension o f a b a ll by

a j e t o f water

The early part o f the tw entieth century saw the beginning o f in crea sin g ly system atic and d e ta ile d in v e stig a tio n s in to j e t flo w s. In te r e st in the f ie ld was heightened by a growing awareness o f the p o te n tia l o f j e t propulsion p a r tic u la r ly w ith regard to a ir c r a ft The development o f the j e t engine, and r e la te d research in to j e t flo w s, was accelerated by the m ilita ry im plications* The exten t o f research in th is f ie ld i s such as to go beyond the scope o f th is study. The ensuing account w ill now be mainly confined to d escrib in g -in v e s tig a tio n s r e la tin g to plane j e t flow s.

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j e t was carried out 1)7 Forthmann' ' in 1934 when he made a number o f measurements o f the mean v e lo c ity o f a j e t issu in g in to s t i l l air* Over the next two decades other sim ilar in v e stig a tio n s were

made - Kuethe^ 7 ^ in 1935$ Albertson e t a l.^ ^ in 1948, and

A bram ovich^ in 1957 -* most o f them being concerned w ith the development o f phenomenological expressions for the p red ictio n o f the mean v e lo c ity d istrib u tio n and the spread o f the jet* A number o f th e o r e tic a l models were proposed over th is p eriod , ranging from Schlichting* s approximate so lu tio n o f a laminar j e t ^ ^ , to be

la te r developed by B ick ley' , to various analyses o f the turbulent j e t . Prominent amongst the la tte r were those o f follm ien and G ortler, employing d iffe r e n t approaches u t ilis in g Prandtl*s momentum tra n sfer

theories^ Howarth, u sin g Taylor1 s v o r tic ity -tr a n s fe r theory, and

K eichardt, employing a m olecular analogy theory. D eta iled d escrip tio n s o f th ese stu d ies can be found in standard t e x t s ^ ^ ^ ^ ^ In the

o

la te f i f t i e s , a further advance in the knowledge in the nature o f ' (22)

the turbulent j e t was made by M iller and Comings' , who

in v e stig a te d i t s s ta tic pressure d istr ib u tio n , and B.Ge van dor Hegge Z ijn e n ^ ^ ^ * ^ $ who in v e stig a te d both-the.m ean-and the flu c tu a tin g v e lo c ity d istr ib u tio n s.

The la s t decade has seen research d irected towards the establishm ent o f the actual structure o f the j e t ^ (38)(39 ) in v e stig a tio n o f such phenomena as in term ittan cy, se lf-p r e se r v a tio n and the behaviour o f the j e t in a co-flow in g strea m ^ yhe in v e stig a tio n s have been very much a sso cia ted with the la rg e eddy

f PO )

hypothesis proposed by Townsend v a l i d i t s ensuing development.

The a n a ly tica l work that has been carried out over t h is p eriod has mainly been concerned with the solu tion o f d iffe r e n tia l transport equations o f various turbulent q u a n tities. Such so lu tio n s have

employed approximate numerical methods, notably the F in ite D ifference method, in conjunction w ith the e lectro n ic d ig ita l oom p u ter^ ^ .

This top ic i s discussed further in Chapter Four. 1 .6 Summary

The aim o f th is chapter has been th ree-fold j f i r s t l y , to d elin ea te c le a r ly and lo g ic a lly the problem to be considered in

t h is study, and, secondly^ to introduce, and where necessary d efin e, the “basic parameters to he encountered in the succeeding chapters* To th is end, the c la s s ific a tio n o f Jet flow s has “been d iscu ssed , the topology o f the problem domain has been o u tlin ed , and the mechanisms and corresponding flow c h a r a c te r istic s have been considered# f in a lly , a review o f the h isto ry o f J e ts, and a chronological account o f th eir more recen t in v e stig a tio n have been given# The q u a lita tiv e element in th is chapter i s to be substantiated more q u a n tita tiv e ly , a lb e it in a somewhat sim p lifie d manner, in Chapter Two which con tain s the r e s u lts o f an exploratory experimental in v e stig a tio n o f the plane Jet#

CHAPTER 2

AH EXPERIMENTAL STUDY 2*1 Introduction

The experim ental work in th is chapter should be viewed in the lig h t o f the scope and the o b jectiv es o f th is study. The study i s e s s e n tia lly concerned with the development o f a numerical

p r e d ic tiv e technique for j e t flow s, A f u ll experimental in v e stig a tio n in v o lv in g , for example, the measurement o f the d istrib u tio n o f the flu c tu a tin g components o f v e lo c ity , i s not proposed* E stablish ed data o f t h is nature may be found in the relevan t lit e r a t u r e ^ ^ ’^ ^ ' ^ ^ ^ * The p rin cip a l o b je c tiv e o f th is in v e stig a tio n was to fa m ilia r ise the author w ith the p h ysical c h a r a c te r istic s o f the plane j e t . The

experim ental work was conducted in the F luid Mechanics Laboratory a t the C ity U n iversity employing the a ir j e t apparatus belonging to the Department o f C iv il IShgineoring*

2,2 Experimental Apparatus

The apparatus used in the in v e stig a tio n was an adaptation o f a standard p iece o f equipment designed and b u ilt by P lin t and Partners Ltd,^^*^ to demonstrate the main a ir j e t c h a ra cteristics* I t i s illu s t r a te d in Figure (10) and b a sic a lly c o n s is ts o f a n o zzle mounted h o rizo n ta lly on a horizon tal p la te . The a ir was supplied to the n o zzle by a cen trifu g a l fan which discharged in to a plenum chamber containing a smoothing gauge. The discharge v e lo c ity was co n tro lle d by a th r o ttle valve and the pressure in the plenum chamber was in d icated by a se n sitiv e manometer. The v e lo c ity

t *

d istr ib u tio n in the j e t was measured by a to ta l head tube cai’r ie d on a graduated s lid e capable o f traversin g across any sectio n o f the j e t .

The use o f a to ta l head tube im p lies that the s ta tic

pressure i s constant throughout the j e t , W hilst t h is i s not s t r ic t ly