reatta｡｡e｡jetb｡tals｡ab｡｡tthet｡rb｡Ientproperties･ノ評･JnJn anAdjacen上FlatPlate

Res.Rcp.Fac･Eng･MieUniv･･Vol･12･pp･1‑20(1987)

OriglnalPaper

FlowCharacteristicsofaThree‑dimensional,Rectangular

JetReattachingto

anAdjacen上FlatPlate

(Department Of Mechanicaland Materials Engineering)

(Received September211987)

A three‑dimensional,incompressible jetissuing ^froma rectangular

nozzlewitha smallerheight(height:a)than the flowpassage(height:

H)oscillatesperiodicallywhenthe jetisissuedintoasuddenlyenlarged

flowpassage･=nordertoobtainsomebasicknowledgeonthisosci11atory

phenomenon‑reattaChmentpropertiesofathree‑dimensional･reCtangularjet

flowfromthenozzlewith a/Hく1toanadjacent flatplate･Side wall′

areexamined.Atheoreticalanalysis usingmomentumprincipleisdeveloped for the reattaChmentdistancer ^mean PreSSureWithin separationbubble‑etC･

The agreementWiththeexperimentalresultsis

fairlygood･MeasurementS

of velocity profileweremadenotonlyaboutthemeanproPerties of the

reatta｡｡e｡jetb｡tals｡ab｡｡tthet｡rb｡Ientproperties･ノ評･JnJn

andReynoldsshearstress･Thesetheoreticalandexperimentalresultsare

comparedwithones for ^a two‑dimensionalreattached jet･

Key Words:fluid mechanics･reattaCbed jet･three‑dimensionaljet･

rectangular nozzle,mOmentumprinciple′turbulent properties

1.工ntroduction

A three‑dimensional,incompressible jetissuing ^from rectangulaゝnozzle

with ^a smaller height(height:a}than ^{the flow} passage(height:H)

osci11ates periodically when the jetisissuedinto ^{a suddenly enlarged flow}

passagel)′2)･And′thestudyonthisphenomenoneXCeptingafewonesl)′2)can notbefound.工nthosestudies′theconditionscausingoscillationofajet･

the relation between oscillatory frequencY and configuration of flow passage

and etc.were made clear.In this case′the jetis ^calleda three‑dimensional

one becauseitisissuedfromarectangularnozzlewitharelativelYSmall

aspect ratio･Some studies3)･4)on ^a threedimensional･reCtangular･free jet

have been made andits flow characteristics ^are COnSiderably clarified･But,

thebehaviorofa three‑dimensionalrectangular jetissuingintoaconfined

flowpassagehasnotbeenclarifiedenough･ItisimportanttoClarifythis

T.SfIAKOUCHI

flow characteristics because of obtaining the detailed knowledges _on the above

mentioned oscillatory phenomenon･=n order to clarifY the flow characteristics

When such a jetisissuedinto a confined flow passage,the author6)have

Studied ^{the effect} of adjacent ^end plates.upper andlower plates(see,Fig.1),

On a reCtangular,three‑dimensionaljet ^{by using the detailed} measuring results

Of the velocity and pressure distributionsin the flow field.

In this paper,the reattachment of a three‑dimensionaljetissuing ^{from a}

rectangular no2:Zle with a/H ^{く1to an} adjacent ^{flat plate,Side wallin}

Fig･1′is discussed theoretica11y and experimentally･Theoreticalanalysis

using momentum principleis developed for the reattaching distance,the _mean

pressure within ^{a separation} bubble,etC｡

Many studies5)･6)on ^a three‑dimensional′reattaChed jethavebeenmade

after Borque&Newman7)and Sawyerlbut the study on a rectangular,three‑

dimensional.reattached jetissuing ^{from a} rectangular nozzle with a/H ^く1

has not been made.

2.Notations

a

b

C

D E E H h

Height of nozzle

Width of nozzle Pressure

coefficient[:(p‑pa)/(puA/2)]

Offset distance

Kinetic energY Of jet

Kinetic energy of jet ^{at the} no2:Zle exit

Height of flow passage

Distance between upper(orlower)lip ^{of nozzle and} upper(Orlower)end

plate

J :Jet momentum per unit span

J : jet momentum

Jl:Momentum flux proceeding downstream along a side wa11

J2: Momentum flux returned within a separation bubble at the reattachment

point

L : Distance along a side wa11

M : Momentum of ^a jet

Mo:Momentum of a jet at the nozzle exit

p : Pressure

pa:Ambient pressure

Pb:Mean pressure of a separation bubble

Prnin:Minimum pressure on the surface of a side wall

Q ^{: Flow} rate

Qc:Flow rateinto a separation bubble through the part between upper

0■

0■

0■

R R S e r O

(orlower)edge of a jet and upper(orlower)end ^plate

Flow rate entrained from _a separation bubbleinto jet

Flow rate returnedinto a separation bubble at the reattachment point

Flow rate of a jet at nozzle exit

Theoreticalradius of curvature of a reattached jet ^centerline

Reynolds

number(:umb/V)

Arclength

measured ^{from the} nozzle exit along a reattached jet center

Reattachment of a3‑dimensional,RectangularJet

sa:Valueofsatthepositionwheretheupper(Orlower)edgeofthejet

reattaches to the upper(Or10Wer)end ^plate

So ^: Distance from the nozzle exit to the hypotheticalorlgln Of a jet

u :Velocity a10ng the jet ^axis

uo:Maximum velocitY

um:Mean velocity at the nozzle exit

uo:Maximumvelocity at the nozzle exit

u.,V●lWt:Velocity fluctuations to s,yand ^z directions,reSPeCtively

,訂 盲1:Reynolds ^{shear stress}

x : Coordinate toward no2:Zle axis

xR:Reattachmentdistance ^ona Sidewall

y :C00rdinate perpendicular to jet ^axis

yr:See′Fig･2

21:Coordinate perpendicular to x‑y plane

α :Inclined angle of ^a side wa11

0 :Reattachment angle of a∋et ^{to a Side wa11}

p :Density

v : Kinematic viscosity

o : Spread ^parameter

3.TheoreticalAnalysis

when the jetissuesinto ^{a flow passage With a side wallin the}

neighbourhoodof thenozzleexitfromtherectangularnozzlewhichis setlower

than the height of flow passage′the rectangular jet･also ^{reattaches toa} side

walllikethecaseofa two‑dimensionalreattachedjet5)･7)･Butinthiscase･

itis seemed that the flow has three‑dimensionalproperties andits flow

characteristics ^are very complex.

=n this sectionlthe reattachment distance,Separation bubble pressure

etc.are predicted theoretically using momentum principlein order to clarify

the reattachment characteristics to a side wallof the three‑dimensional′

rectangular jet.

The f01lowing some assumptions are made:

(1)The flowisincompressible and steady･

(2)The centerline of a reattached jetis expressed approximat占1y ^by

arc of radius ^R.

(3)Separation ^{bubble pressureis uniform･}

(4)The ve10City.u,Of ^a reattached jetis ^expressed approximately ^by

Goertlerls profile8)for ^a two‑dimensionalfree jet･

ノす

〟=｢｢ _{p(5+ざ｡ドーー‖}^{sechし一里‑ざ+ざ○ …………(1)}

ois the spread parameter for a two‑dimensional･free turbulent jet and

Reichardt has obtained a result of o=7･67 experimentally･But,in this

case.the valueof ^o wi11be somewhatlarger than that because the jet also

T.SHAEOUCIiI

SPreadsin z direction and then the spreadin Y direction becomes smaller.

The applicability of this theoryis restricted to the _case of the upper

(orlower)edge of a jet reattaching to the upper(orlower)end plate until

the jet reattaches to a side wall.

When the jetissuing ^{from a} rectangular nozzle whichis setlower than the

flow passage reattaches ^{to a} side wall′a flow,Whose flow rateis Qc,enterS

the bubble through ^the part between the upper(Orlower)edge ^{of a} jet and ^the

upper(orlower)end platel)(see′Fig.1).

Qcis expressed as fol10WS･

￠c=Q.‑Qr

Where･Qe and Qr ^{are the flow} rate at which ^a jetis _entrained ^{from the} bubble

reglOn and the f10W rate Of return to the bubble at the reattachment point(

respectively･Qe and Qr are given as fo1lows at the reattachment point(s=

Sr′ See′ Fi9･1)･

￠･=〟Jニ功一圭血

=郎′(gr･ざ｡)/(4胡1′2一声血

￠,=g上''励

=〝(3J(ぶr+5｡)/(4J)♂))=(1‑り

′=ta血蓋･5｡=励3

yris the distance between the jet

(see,Fig.1).and cocorresponds to

From the above equations,We Obtain

号=♂(豊+〃)】′(3肋ト音

･･･(3)

………(4)

………(5)

Centerline and the reattaching streamline

the position of ^{y at u = 0.}

…………(6)

Reattachment of a3‑dimensional,RectangularJet

And the equation of the reattaching streamlineis glVen by

号=((豊+α)之/(3肋))ta血 1′

The following relationships ^can be obtained from Fig･1‥

即∂=ざJ(∂(α+の)

D/b=(R/b)(cosa‑COSe)/cosa‑1/2

xR/b=(R/b)sin(a+e)/cosa‑gJ(bsine)

……(7)

………(8)

…………(9)

…………(10)

where,R′D･XR and ^{O are the} theoreticalradius of the reattaching jet ^center

line,Offset dis･tanCe′ reattaChment distance and reattachment angle,

respectively.

Nowlapplying the momentum principlelocally at the reattachment point

(point flin _Fig.1)′ the fo1lowing relations ^are obtained･

Jc?Sβ=Jl‑J2,(J=〟)

Jl=gエp紬主‡〟(‡什‡′り J2=〝エーr曲=‡d′(号一汁‡̀3)

………(11)

…………(12)

…………(13)

where,O can be obtained from Eqs･(6)l(8)l(9)and(14)･

The reattachment distance,bubble pressure,reattaChing streamline,jet

centerline etc.were calculated for various shapes of no2:Zle and flow passage･

These calculated results willbe discussedlater comparing with the

experimentalones･

From Eqs.(11)〜(13)r ^a cubic equation can be obtained′and ^a significant

root among the three onesis glVen aS follows･

J=2cos((汀+の/3l

The pressure difference across the jetis

♪.一山=(α/〃)(〟斤)

………(14)

………(15)

where′ Pa and pb are the pressures outSide andinside the bubble reglOn,

respectively.

Qcis given approximately by

Q｡=l2(山一如)/p)1′2ざ.九 ………(16)

T.SH^KOUCfII

Where･Sais the value of s at the position where the upper(orlower)edge of

the jet ^{reattaches to the} upper(orlower)end plate.and the next relationis

Obtained experimentally when a side walldose not exist(only ^the upper and

lower end plates exist)6)

∫./∂≒3.3みル

The valuc of sa when the jet reattaches to _a side wallwi11be different from

the result of Eq･(17)･But,Eq･(17)is used approximatelyin the followin

The reattachment distance,XR′is

given as follows from Eqs･(7),(9),

(10).(15)and(16).

∫■=

(2β+∂)sin(α+β 2(cosα‑COS

) _α∂

3f〟2sinβ

×(4∫■九

COS a‑COS

∂〃2(2上)+占)cosα

+1)2

The results based _on the above mentioned theory would beindicatedin the

after chapter and discussed comparing with the experimentalresults.

4･ExperimentalSetup and Procedure

Figure2shows the test section of experimentalsetup･Air suppliedby

blowerissuesinto _a confined flow passage with upper andlower end plates and

a side wallfrom a rectangular nozzle′Whichis setlower thanthe height of

flow passage,through the coolerr flow meterlSettling chamber and

Straightener･The height of flow passage′Hland width of nozzlelb′are60mm

andlO mm′reSpeCtively･The height of no2:Zle′a,Can be varied from5rnm to

60mm by changlng the spacers･Offset distancelDlandinclined angle,α′Of a.

Side wallcan be set arbitrarily.

t165 500.…

】 l

N

ヽJ

l

y Edgeotjet

A.

T

A^r 巴

‖引

‖

■‑

lここニニニこここ=こ‑‑ここここ圭

t lα 1

■

㍉叫㌦/Pr:蒜慧誌佃s ^皿

Fig･2 Experimentalapparatus

Reattachment of a3‑dimensional,RectangularJet

static pressure on the upper part of the f10W paSSage WaS meaSured using

the upper end plate withpressure holes(diameter:1･O mm)in ^{aline at every}

lO mmin xdirection.This upper end plateis slidableinyandanydirections

with the airtight condition at contacting surface,SO that the pressure at an

arbitrary position ^can be measured･Pressure ^waS meaSured by using Betz‑type

manometer.pressure at half depth of the test̀section(X‑y ^{plane at z=0,}

see.Fig.1)was ^{also measured by the same} method ^{using a disk type static}

pressuretube(diskdiameter:6･Omm･holediameter;0･6mm)attached

to the

upper end plate･A side wallhas also pressure holesin aline at everylO mm

on the half depth ofit.

velocity distributionlulandlongitudinalvelocity fluctuation,ul,On

the horizontalplane at the half depth of the flow passage were measured using

the constant temperature hot wire anemometer andエーtype prObe(probe space:

2.O mm′ SenSOr SpaCe:1･O mmItungSten Wireof diameter 5mm used)whic

is set on the traverse device.Velocity fluctuations vllWIand Reynolds shear

stress 一丁Tweremeasuredbythemethod9)that turnaroundahotwireprobe

(Z‑type)about ^{the self axis at the measuring} point･The probewasinserted

into the flow field from _z direction using the access port of the upper end

plate which was arrangedindependently of the case of static pressure

measurement and from thelateraldirection.

R6attachment ^{point on a side wallwas determined by using a} flag(filament

aboutlO mmlong)attached ^{to a thin} sticklWhich ^was moved quasi‑Statica11y ^on

a side wall,becauseitindicates the boundary of forward and backward flows on

the side wall.On this occasion.the pressure distribution on the side wall

and the velocity distribution near the reattachment point were also referred･

Experiments covered the range of um=10〜40m/s【Re=umb/v;(0･96

■〜 2.75)xlO4,V:kinematic viscosity】′ ^{but the} difference of flow

characteristics ^can not be foundin this velocity range･Therefore,in this

paper,Only the results for um=20m/s ^are given･

5.Results and Discussion

工n this section,the experimentalresults for velocitY distribution,

pressure distributiont reattachment distance,etC･are Shown and they are

compared with theoreticalones･Flow characteristics of a three‑dimensional,

reattached jetissuing ^{from the} rectangular nozzle with a/H <1willbe

Clarified.

5.1Velocity distribution

Figures 3(a)Ib(C)show ^the approximate velocity profiles of ^the

reattached jet ^at z/H=O ^{for the case of} a/==1′ 2/3andl/2and D/b=

1.5.The mark△ shows the reattachment point(measured result),and ^{a thin}

dot̲Chainlineindicates the jet centerline(Calculated result)･From ^these

figurest an exact direction of the

velocity could ^{not be} recognized ^{because the}

hot wire probe(=‑type uSed)was ^traversed perpendicular to x axis･but the jet

issuing from _a rectangular noヱZle with a/Hく1also ^{reattached to a sid畠wal1}

1ike _a two‑dimensional′reattaChed jet ^{and the outlines of the} jet ^spreading

8 T.SEAEOUCE王

downstream areknown･Anditis recognized that ^the radius of,CurVatureof a

jet _centerline and the reattachment point ^moves downstream with ^{a decreasing}

no2:2:1e height a/H.

Figures 4(a)〜(c)show the velocitY prOfiles.u,at the various cross

SeCtions perpehdicular ^{to the} reattaching centerline and z/H=O ^{for the case}

Of a/H=1･2/3andl/2･Offsetdistance,D/b′andinclinedangleofaside

Wa11′a,arel･5andlOO′ reSpeCtively･Minus side of the abscissain ^the

figurei$the

reattached side,the separationbubble side･For theprofile

near the nozzle exit,the velocitY at the reattached side becomeslarger

because of the existence of separationbubblewithlowpressure.ztis

well

knownfromthesefiguresthatthejetspreadstoYdirectionunsymmetrically

With decreasing the maximum velocity･The spread ^rate and unsYmmetrY decrease

With decreasing nozzle height,a/H.This decrease of the spread rateis the

result ^{that the} jet ^can spread also to2:direction easily ^{when the} nozzle

height becomes small.

Figures 5(a)〜(C)repesent the velocitY.distributions by the

dimensionless quantities･u/uo ^and y/Y(uo/2}･getting ^{from the results of}

Figs･4(a)〜(c),reSpeCtively･ Where･uO _meanS the maximum velocity of a

VelocitYprOfileand y(uo/2)isthevalueof ycorresponding to uo/2･The

SOlidlinein each figureis Goertler.s velocity profile[Eq.(1)】for ^{a two‑}

dimensionalfree jet･Thedimensionless _profiles are fairly good agreement

With ^{Goertlerls one} except of a part of the separation bubble side.

Especially′ the profilesin the reglOn Of unattached side′ plus side of the

abscissa.are good agreement with Goertlerls profile.

Figures 6(a)〜(C)show the equi‑Velocity curves calculated from the

results of Figs･4(a)〜(C),reSpeCtively. From these figures,itis wellkn｡Wn

that the deflection

of a jet ^decreases and the decay of maximum velocity to

downstreamincreases with decreasing nozzle height,a/H.And.it seems that

the jet centerline can be expressed bY a Circular arc.

The half

width･y(uo/2)･at ^{Z=O to downstream for} D/b=2and α.=10｡

is shownin Fig･7･ The symboIs o,△′ ロ and ●′ ▲′■ Show the results at

unattached and attached sides,reSpeCtivelY･The dottedlinein the figure

shows the result bY PanilO)for ^{a free} jetissued ^from a square nozzle.

Fig.3Velocity distribution (D/b =1.5,Cl三100)

R戸TtttaChment oE a3‑dimensional,RectangularJet

l‑

▲

(a)

a/H=1十 l

l

▲

5 u

GQ●Ttl●r

∩

t】

l

8 ∩

‑3 8 5

ll

(b) a/11=2/5

･l l

■

■

5

▲F▲

●Jヽ

●●

Pロ詰も｡

ヽ▲▲

▲

▲ 1▲

8

‑3 8 3

T/T(U8/2I

9

Fig‑4Velocity distribution (u ^‑ y)

Y/†(uo/2l

Fig･5Velocity distribution

【u/u｡‑ y/y(u｡/2)]

10

y(uo/2)=0.097(Ⅹ/b)

T.SHAKOUCHI

(19)

The half widths at both sides･attaChed and unattached sides,Of jet

increaselinearlYWithincreasingsanddecreasewithdecreasingnozzleheight,

a/H･Andtheresults ^for a/H=1/2 approachtothatbypani.

Theequi‑Velocityprofiles,u′iny‑ZSeCtionatvariouspositions(S,

Were measuredin order to clarify the three‑dimensionalspreading _{of the}

reattachedjet･Theresultsfor a/H=2/3 areshowninFigs.8(a)〜(d).As theresultsofmeasurementweresymmetricwithyaxis,OnlythehalfreglOn

(plusregionof zaxis)is showninthefigures･Andtheminussideofthe abscissainthefigureisunattachedside･ThedottedlineinFig.8(a)shows

thecontourcorrespondingtotheconfigurationofnozzleat

z〉0.工tiswe11

reCOgnizedthatthesymmetricprofile _{near the}

nozzle exit with YaXis becomes

unSymmetric todownstream･Thedeflectionof _theprofile

tothe sidewall

､becomeslargerneartheupperendplate･Thisisthoughtthattheflownear

the upper end plate approaches to the side wallin order to balance the

Centrifugalforce′Which becomes smaller as the velocitYis small,With the

PreSSure difference at both sides of the jet.

5･2Spread rate to z‑direction

2.q＼(N＼｡ヱゝ

1･

一 芸≡=≡=F二== := ^､ ､､

‑

‑

■■‑■■■■‑■‑‑■

､■

＼

Fig･6 Equi‑Velocity curve

5

s/b

18

Fig･7Half width[y(u｡/2)/b‑S/b]

Reattachment of a3‑dimensional,RectangularJet 11

The spread rate to z‑directionis shown witD ^{sa for offset distance D/b=}

2 and ^α =100 in Fig.9. The edge of ^a jet ^{was determined by using the}

velocity profile measurements of z‑direction at various positions of s･ The

result for the case without side wa11is alsoindicated ^{by the} chainlinein

the figure･From this figure.we know

sa/bincreaseslinearly

Sa/b≒3･3(h/b)

1 0

y/b ^‑1

1 0

ー1y/b ^‑2

2 1 0 ‑1y/b ^‑2

Fig.8Equi‑Velocity curve(a/H=2/3,y‑Z SeCtion)

用 28

h/b ^3･0

Fig.9sa/b ^‑ h/b

12 T.SHAKOUCHI

andexponentiallywithincreasing h/bforthecasewithoutandwithsidewall.

respectively.

5･3Maximum velocitY

The variation of maximum velocity to downstreamis shownin Fig.10.The

alternatelongandtwoshortdashlinesin the ^figure shows theresult fora

tWO‑dimensionalfree jetissuing ^froma square nozzle,and the alternatelong

and short dashline,Short dottedline andlong dottedlineindicate the

results ^for nozzle height

a/H=1･1/2andl′3,reSPeCtivelY.Zn the _case of

the plane･free jetissuing ^froma square nozzle･the maximum velocity decays

mOre rapidly than the ^case of a confined jet asit sprea･ds not onlY tO y‑

directionbutalsoto z‑direction･And the ^decay of the maximum velocitY Of a

reattachedjetislarger ^than thecasewithoutasidewallbecauseofitslarge

･lossofflow･=nthedownstream,themaximumvelocityofatwo‑dimensionall

freejetdecaYSinproportionto(s′b)‑1/2 _andthatof theabovementioned

COnfined jets from the nozzle with smallaspect ratio decaysin proportion to

(s/b)‑1alikethecaseofafreejetfromasquarenozzle.

5･4Flow rate′mOmentumlkinetic energy

The variations of flow ratel

jet ^for a/H ⁼ 2/3,D/b =2 and cl=

result$ Of velocity measurements at

8 and12. The results are shownin

Flow rate,Q,mOmentum,M,and

the followin9 equations.

￠=仇み血

〟≡仇2̀砂 丘=÷爪3みゐ

8

■ヽ‑

1.Jコ＼コ臥

momentum and kinetic energy of a reattached

lOO to downstream _were calculated using the

Various section,y‑Z Plane,Of s/b;2,4.

Fi9.11.

kinetic energy′ E′ Were Calculated bY uSing

Fig･10Maximum velocity

S/b

.〇

5

.山､山..ミ三..〇､0

5 10

SJb

Fig･11q/q｡,M/M｡,E/E｡‑ S/b

Reattachment of a3‑dimensional,RectangularJet 13

Thedomainsofintegrations ^are from y=‑00(u=0}to ^{oo and from} z=‑H/2

to H/2.The ^{results for the} casewithouta sidewallindicatein the figure

for reference by the thinlines･

From this figuretitis we11known that the flow rateincreaseslinearly

andmomentumand ^{kinetic energy decrease} withincreasing s/b･Andit ^seems

that theloss of flow of the reattached jetislarger ^{than that for the}

case without ^a side wall.

5.5 Turbulent properties

In this section,turbulent properties of a reattached jetissuing ^{from a}

Figures12(a)〜(C)indicatethevariationofturbulentintensityJ戸′uo

profileof anreattached jet(D′b=2･α=100)todownstream ^for a/H=1･2/3

andl/2,reSpeCtively･The ^{minus side of the abscissa show}

the separation

bubble side.The profiles ^are unsymmetric with y‑aXis and spread to y‑

direction toward downstream with two maximum values･The positions of two

maximum values correspond to the shearlayer at both sides of the reattached

jet.And ^thevalueof JP/uo almost becomeslarger towarddownstream･

The equi‑turbulence profilesl ul,in y‑Z SeCtion at various positions,

8 2 ‑2

Fig･12Turbulence characteristics

(u‑2/u｡‑ y/b)

14 T.SHAKOUC甘Ⅰ

S･for a/H=2/3areshowninFigs･13(a)〜(d)･Theseresultscorrespondto

the casesin Figs･8(a)〜(d)･As the results of measurement were symmetric with

y axis,OnlY the half

region(plus regionof z axis)is showninthe figures.

The profile has two areas(A and Bin the figure)with _{maximum values at} both

Sides of the jet which correspond to the shearlayers･And their profiles

deflect ^toa side wallcorresponding ^{to the} velocity profiles(seelFig.8).

Figures14and15showtheturbulentintensityJP/uoinydirection andJP/uoinzdirectionfor

1 0

y/b ^‑1

8

1 0

y/b ^‑1

2 1 0

‑1y/b ^‑2

2 1 0

‑1y/b ‑2

Fig･13Equi‑turbulence curve(a/H= 2/3)

†2

ー2

Reattachment of a3‑dimensional,Rect8ngularJet 15

These values ^are smallcomparing

withJ罪′uo

that for

G/u｡.In

a/H:1andl/2,We alsoobtainedd the

same results.

Figures16(a)and(b)show ^the profiles of the ReYnOlds shear ^stress

‑Ⅳf｡r D/b=2,.α=100. ^{The value of}

‑す▼∇/uZ

unattached side(plus ^{side of the abscissain the} figure)of ^the jet ^and

becomeslarger toward downstream･ AndJit takes smaller value for the case of

a/H =1/2 ^{than for} a/H ^=1.

5.6 Pressure distribution

Figure17 shows the pressure distribution at the half depth(z ⁼ 0)of ^the

flow passage for a/H;1,D/b=2and ^cL =100.And Figs.17(b)and(C)give

the pressure distributions for a/H=1/2,D/b=2and ^{cL =100 at} 2:/H…O and

the surface of the upper plate(z/H ⁼ 0.5),reSPeCtively. ^The numeralsin the

figure show the pressure coefficient cp′and the markムglVeS the reattachment

point(measured results).工n ^{the case of} a/H:1.a､distinguished ^bubble

reglOnis formed between the jet ^{and the side} wallbecause the flowis two‑

0

0⊃＼.>‑コ1

〇.N

l

十2

Fig.16

‑u‑Ⅴリu喜 ^一y/b

Fig･17Pressure distribution

(D/bこ2,α;100)

16 T.SHAIくOUCHl･

dimensional.and a pressure rise occursin ^the neighbourhood of ^the jet

reattachment(downstreamof thereattachmentpoint)6).工nthe caseof a/H=

1/2and z/H=0[see,Fig･17(b)】′itis recognized ^{that the} bubble pressure

dose not decrease extremely and the reattachment point moves downstream because

a flowenteringthebubblethroughtheupperandlower _partof the jet ^{near the}

noz2:1e exit exists･ ^The shapes of equi‑preSSurelinesin Fig.17(b)is

COnSiderablY different ^from thatin Fig.17(a)(a/H:1)anditis thought that

their flow characteristics are different. 工tis noticed ^that the ^flow

COndition ^for a/H:1/2is three‑dimensional.because

the占rofiles ^{of the}

pressure distribution of Fig.17(b)(z/H ⁼ 0)and(C)(2:/H ⁼ 0.5)are

COnSiderablY different.

Similar results ^were obtainedin ^{the cases} of a/H=5/6,2/3andl/3.

Figures18(a)〜(C)indicate ^the pressuredistributions,ps′On ^{the side}

Wallfortheinclinedanglesofa sidewa11cL =00′100 and2001reSPeCtively.

The offset distance,D/b.equals ² andIJOf the transversalaxisindicates the

dis七ance along the side wa11･ps for

a/H ^{=1changes from negative to}

positiveas Lincreases′anditapproachestheatmosphericpressure(cp=0) after taking ^the maximum value,pmax･

The _same results were obtained for each case of a/H ^{く1.but the minimum}

pressure pminincreases.pmax decreases and the position Lo where the

negative pressure changes to positive one moves downstream with a decreasing

a/H･pmin ^{for cL=200is smaller than the} others(measurements ^{for cL} =00.

1SO were also carried).The ^{same results were obtained for each case} of D/b=

3′ 4.5 and ^6.

5.7 Reattachment distance

l●

L/b