Deflexion of a submerged round jet to increase lateral spreading

HOUILLE BLANCHE / NO 6-1974

Deflexion

of a submerged round jet to increase lateral spreading

by s. ^{K. A. Naib}

B. Sc. (Eng.), Ph. D, ACGI, DIC, C. Eng., MICE Head of Department of Civil Engineering

North East London Polytechnic

Introduction

A jet or a stream of air blown into tfue atmosphere mixes with the latter and spreads out Enearly in aœordance with we]!! known laws. ln the case of a jet issuing from a nozzle or an orifice and is diwcted at an angle ta a plane Isurface, it is transformed into a thin stream with wide l'ateml boundaries at a short distance downstream of the outlet, as shown in Fig. 1. The increased surface of the jet becomes a:vai'lable for mixing and enel'gy dissipation which resu~ts faster reduction of the velocity and energy of the jet than in the 'case of the free jet. Between this stream and the ~urroundingftuid, a tUl'budent mixing region is formed havi,ng normal and Ilateml boundaries band 1.

The normaJ! velocity ,profile at any section consists of a wal'l boundary 'layer and an outer jet layer, whioh is similar in character to that of the wabl jet analysed by Gl1auert[1]

and the parrulael waH jet recenvly investigated by the author [2].

The behaviour of the deftected jet is of importance in many industfÏ.a1 designs, incluc1ing combustion 'chambers, fUrIl1llces, jet exhaust systems, sÜUing basins of pipe chutes and fish passes of the ,pool type. In the llast two cases if the pipe outlet or orifice is indined downwards, the ftoor of the paal takes the place of the deftecting plane and this leads to a more rapid velocity reduction than if the outlet or orifice is horizontaL This aHows for a shorter length of pool nhan that required with a horizontall outlet.

Another aspect of the inolined jet design is the steadying effect it has on the ftow in the stiUing basin of a pipe outlet.

It was observed that a round water jet discharging into a rectangular channel produces bath unsymmetrical and unsteady ftow. Fo,r semi-submerged ftow, the jet is sucked lateraUy and adheTes to one side of the channel, with a long circulation zone forming on the other side. At higher depthof suil>mergence, the jet changes into a state of

455

sustained osci'llatory movement from one side of the channel to another. Attempts to stabilize the ftow without altering its character were unsU\ccessfuil. However, reasonably stea- dy and symmetricall ftow was obtained when the jet was directed at 45° angle to the channel bed.

ELEVATION

Normal width

x

.1

La teral width

u

_ _ _zI-+_u",,"w--+-'-__

PLAN Near Sur fac e

1/

Flow in a deflecled round jet.

bct.xl.^ü2 to the distance x,

Where VI is the initial velocity of the jet, K is a constant for the jet, and d is the orifice diameter. The value of K has been foundexperimentally ta be variabile depending on the effect of the boundary layer in othe nozzle. Bascd on theoreticaJl and experimenta:J reslllts, Squire [12] recom- mends a mean vaIue of 6.5.

The anal)ësis aiso gives the outer bOllndary of the jet by the foHowing :

(1)

(2)

V d

= J (

VI X

the value of Cl is 0.214, whiroh makes the angle of diver- gence approximate1y 12⁰ with the jet axis.

Kuethe [13] extended T ollmien',S work to the case of a jet with a finite source and estrublished ,the length of potential core js about 5 diameters from the orifice. This relsult aJgrees with e~periments over a wide range of Reynolds numbers.

The flow ofa round jet impingin:g on a plane surface and spreading radia1'ly over it has been analysed by Glauert[1].

He termed the ilow as a radial wall jet for which he obtained approximate simi'lar soIutions in regions far down- stream of the 'point of impingement.

The ,analysis near the wall:l was based on Blasius law for pipe fiow, while P,randd's mixing-length hypothesis was used further out. An e~perimenta,1 invesügation of the radiaI wal'! jet has been carried out by Bakke [14]. Measu- rements of velocity profiles were made at distances lOto 20 limes the jet diameter. At these diistances, the profiles were similar, and rate of spreading and decay of the jet fol1owed power laws:

Experimental method

and from a 6.5 mm rectangular sIot of the same area which were directed o'ver a plane wooden surface. The jets were examined for eaoh ruperture with the plane set bath paraIlel ta the jet axis and at an impinging angle of 15° ta the direction of discharge. For the circu\oar ol'ifi ce, they found indination of the jet ta the surface ,causes the angle of boundary divergence across the surface ta increase from 50° ta 68°.

Nemenyi and White[4] investigated the design of fish passes with submerged orifices given a downward sIope of 45°. They found immediately aiter issue the jet flanned out ta 90° on the floor of the pool and ran up the side waJllls very smoothly, prachoaHythe whole of its excess energy being dissipated before irt reaohed the next orifice.

This produced a saving in Ilelllgth of pool of ,about 50 per cent.

Recently, theauthor has investigated the s'Preading and deveIopmentof turbulent jets and st,reams[5 ta 9] inoluding a round air jet 'Projocted paraneI ta a wall,l[2]. Experiments were carried out ta estab\>ish theS1hape of the velocity profiles, ,the decay of maximum velocity and the rate of growth of the jet. lt was found that the jet consistJs of an -inner half extending from the walol to the centre line of the jet where the flow resembles that along a fiat plate and an outer haM whi'ch is similar -in chamcter ta that of a free air jet dischargillllg into the atJffiosphere. In the outer half the rate

ot

spreading paraBel ta the wall isabout six ta e1ight times greater than that nOl1maI to it. 11he present reseaToh was undertaken ta extend thi,s work by studying the flow cha,racteristÏ!cs of the jet impi'll'ging at 15, 30 and 45 degrees ta a plane smooth surface.

A jet of air, 25.4 mm diameter, was produced by a blower witha Theostat for adjusting the slpeed of the fan.

The jet was dire'cted at different angles ta a smooth wooden smfwce. Except of the smaH boundary layer on the inside of the nozzle, the velocity profi['e was practicaHy uniform rucross the exit section.

A shielded pressure probe [10] with a centraI sting was used for ve'locity measmements. The probe has been found ta be insensitive ta direction changes thfO'ugh a range of angles ± 45 degrees for a 1 'Per cent e,rroT Iimit. Near the waH, the velocity profi'les alCross the surface were measoUred by a total-head tube 1mm imide dirumeter. Each probe was Icla,mped into a micrometer screw transversing mechanism graduated ta 0.05 mm.

Analysis of turbulent round jet

The theoreticaI aspects of the dispe'l'Sion of a round jet into the staüonary atmosphereare covered in numerous papers and only a brief survey is given here ta help eXJplaining the trends of the present experimental resuilts.

Tolillmien[11] u~i'lligPrandtl's mixing Ilength otheory, solved the fundamental equations of tUJ:1bulent motion of a round

These are in fair agreement with Glauert's predi<;tions.

Variation of maximum velocity

The variation of maximum velocity of the jet for different angles of deflection are plotted non-dimensionaNy in Fig. 2.

As for the parall\el wall jet[2] the veIœity for the 'Case of 15° deflection is seen ta be co'nstant over 2 diameters i'olJowed by a transition aI Icngth up to 8 di'ameters which joins ta a straight Ene Ulp to 30 diametersand this is fol1owed by another line of greater s'Iope. With increasing defiection angle the length of transition decreases from 8 to 6 dia- meters, and the velocity beyond this Ilenguh decreases Jinearly up to 40 diameters.

The 1ength of the potenüalcore is seen to be independent of the defiection angle and it ,is about 2 diametel'S 'Compared with 5 diameters for the {ree round jet. As expected, the presence of the wallon one side of the jet Î'ncreases IateraI mixing and hence reduces the length of the potential core.

However, the kngth of the transition region for the 15<

deflection is seen to be sU'ch ihat the linear distribution

S. K.A. NAIB 14

12

10

8 U,

U 6

=4~

V ~ ^~o

0(

/0

V ,/

/' ^/

lY ^1/

^,/'

V

7

^{x , /}

^/

^)---

^{/ ...< V}

^o·

^/

~ ^{/ V}

^I?'

^~

^...,.

/ .J"< --'~

~ ^{,.-x0 ~}

"'"

~ ~

^~

~~~

o

o

8 12 20 24 28

x/ci

32 36 40 48

2/

Decay of maximum velocities.

begi:ns ata distance of 8 diameters as for a free jet.

It seems that the impingement region is relatively small and the deflection of the jet is completed within the potential core.

The following relationshilps between maximum velocity and distance are derived:

with velocity decay charaeterisücs nearly the same as ID

Region IV of terminal f10w for the 15⁰ deflected jet.

Velocity profiles

The velocityprofiles in various regions of the f10w are plotted non-dimensionaHy in Figs. 3 to 8. Concerning the normal profiles along the centre plane of the jet, for regions 5

<

xl d

<

35 they lie nearly on one cmveand therefore are similar despite the different rates of decay of maximum velocity in the three regions of the jet. The profiles are also seen to be in sorne agreement with Glauert's ,profile for the radial wall jet, and thUSi the two f10ws are similar.

0.6

~

r~~ x

~~~

^{x x/(j x1j}

\

A. ^{x +x 25 4>~ 2520}

1\

\~

_x~

^•

^{0 1015 0}

^•

³⁰³⁵

~

¹

x vGlauert Profile

~

x

~~

0.8

2.4 2.0 1.6

0.8 1.2 0,4

3/

Normal velocity profiles for a.= 15°.

o o

1.0

0,4

u

u

0.2

ANGLE RELATIONSHIP DISTANCE

0° VI V_r = 7 dl(x

+

^2.5) 8<xld<33 VIVI = 5 dl(x - 8) 33

<

xld

<

53 15° VI V_r = 4 dl(x - 2) 8

<

xld

<

29 VIVI = 2.2dl(x-14) 29

<

xld

<

45 30° VIV r⁼ 2.8dl(x-2) 7

<

xld

<

40 45° VIV r⁼ 2.4dl(x-l) 6<xld<36

The ongln for each relationship was ilocated by extra- ,polating the straiJght line thus obtained to meet the x-axis.

As for the free air jet and the par~1'le.j wall jet, four regions of' f10w are apparent in lihe 15⁰ deflected jet:

(i) Region 1 of potential core extending about 2 diameters fuom the orifice; (U) Reigion II of transition flow that extends '\.Dp to 8 diameters and in which the velocity appa- rently varies parabolicaJly with distance; (iii) Region III of established f10w which extends to about 30 diameters and (iv) Region IV of terminal f10w in which the residual velocity decays rapidly as a re~mlt of 'large seale turbulence to that of the iSurrounding ·ai,r.

Because of the greater rate of spreading and hence mixing for the 30° and 45⁰ deflœted jets, the rate of decay of maximum velocity is mureh faster than for the other jets, ibeing about two and ,a half times that for the ,parallel wall jet. Also, -it aJppears that downstreaJm of transition Region II, there is only one region of fuJ'ly deveJoped flow

Ir

_J

^~x

^{x 2 A 20}

~~

_·~t\x

⁺

^{5 <Il 25}

\'

0 10 ^lJ 30

•

15

•

³⁵

•

u^{+ x}

~

Glauer! Pro file¹

"-

•

x_x

+~

7/

Lateral velocity profiles near the wall for 0.

=

^30°.

~

~

^{x 2 A 20}

. . .

₊ 5

•

²⁵

~

^VTa li mien Profile

.

^{0 1015}

.

^{0 3035}

~

^+x+

~

_~ ^{x+ x+}

u

u

0·8

0.6

0.4

0.2

o o

0.4 0.8 1.2 1.6 2.0 2.4

0·8

06 u

u 04

0.2

o

o ^0.4 0.8 16 20 2.8 3.2

4/

Normal velocity profiles for 0.

=

^30°.

f',~

I \ x % x/cJ

• . -

^{x 2 • 15}

\

_x ⁺_{o 10}^{5 l>}_{A 25}²⁰

\-

Glauert Profile^T ."'\

~

ce

~

xx +

8/

Lateral velocity profiles near the wall for 0.

=

45°.

2.8 3·2 2.0

0.8 0·4

I~

^{°° •A}

.

^{0 % YcJ}

K ⁰ 0 1

.

¹⁵

o~

^{x 2 o 20}

" + 5

•

²⁵

1/

^{Tolimien Profile} _° 10

oK

^o _• ^° _° ⁰x ⁰ +

~

_~^{+ + +x x}

o

o

0.4 0.6

0.2 0·8 1.0

u

u

2.0 1.6 1.2

>/b,

0.8

o 0.4

o

0·4

0.2 1.0

0·6 0.8

u

u

6/

Lateral velocily profiles near the wall for 0.=15°.

:~

Q. ~ 0

^%

1

.

^x/cj15

~

^{A ox 3.52 .. 25A 20}

~

Tollmien Profile + 5 o 30

A ⁰ 10 • 35

'~D

... ~":

_{0 + X}⁰ _~

~ <

⁺

^-

^{0 "\,}

5/

Normal velocity profiles for 0.

=

45°.

u

u 1.0

0.8

0.6

0.4

0.2

o

o

0.4 0.8 1.2 1.6 2.0 2.4 2.8

However, i,n the outer layer of the jet and near the position of maximum velocity, there is a difIerenlCe in the velocity profile hom that of the wall jet. This is ocaused primarily by thespreading efIect of the wal'l on the jet and the efIect of the inner wall layer on the outer layer. The lateral velocity profiles near the wal'l for 5

<

xl d

<

35 show some variation with distance eSJpecially at the outer edge of the jet, where it is seen that the velocity fedls more slowly ,than in the case of the free jet. It should be noted, however, that ·a large 'Part of this discrepency may be due to inaccuracy of measurements in this Tegion of flow.

The 'Profiles compare reasonably with Tol1mien's curve for the free jet.

Spreading of boundaries

The nOI1mal and ·.[atera:l widths of the jet for difIerent deflection angles are plotted non-dimens'ionally in Figs. 9 to 14. On impact the jet SIpreads out r,3Jpidly over the waH, rea,ching a wide 1atera'1 width 'lVat a short distance downsrream of the nozzle. Using smokeand fine strings as tra!cers, it was observed that at about 30° deflection angle the jet fans out to 90° on the surface of the wall

S. K.A. NAIB

11/ Lateral width of the jet for a

=

^45° 4 0

0 Full wldth lw

x Hait width tw,

/

y=0.14d

V

V

/

lY

V ^---- _V ^~

J

1 ^{/ ~ V}

~ ^V

0 Full width lw x Half width !w ,

)

il

y= 0.14d

/

y ^V

^p

/ V

V 17

/ ^/:

! ^{/ V}

7 ^V

/

^V

/

32

28

24

20

16

A

12

-Y'\

8

4

o

o

^{5 10 15 20}

X/cJ

25 30 35

36

32

28

24

~_it 20

~16

12

8

o

o

5 10 20 25 30

9/

Lateral width of the jet for a

=

^15°.

0 Full wldth tw

x ^{Hall wldth} tw , ^/

/

y = 014 d

/

> ^V

~ ~

~ ~l.,...----"

/

^~

~

L---' ^~

~

10/Lateral width of the jet for a = 30°.

0 Full width b

Hall width b, /'

x

.

^Boundary Layer thickness

7

/

/ V

/ ^V

^../

/v _V ^V V ^{y V}

. . /

--:;;:'

V

",/

~

^~1----

y ~

/

/

t - - -

v / _j - - 60

50

40

J\U

30

-Y\

20

10

o

o 5 10 20 25 30 35

4.0

35

3.0

2.5

l A~u

~ 2.0

~

..Cl

." 1.5

0.5

o

o

5 ^{10 15 20 25} 30 35

12/

Lateral width of the jet for a

=

15°.

15/ Flow in the jet for different angles of impingement.

.

Boundary Layer thicklless

. /

/

/ ^v

y

-~

~

/ '

/ . /

7 ^~

~

'CT^X ~ _:;

17/ Boundary layer growth in the jets.

35

30 35 30

25 25 20

15 20

%

15

la 10

5 5

.

^15'

x 30'

l ; 45'

..---

^,...-

- ~

~ ~

----

/ Il

d=

VI ^/

/ ^{1/ 00}

/ V/ _/

/ ^~v /

/ / ^V

^/

^/

Jj _{/ '} ^V y ^/

1

^{, /}

V

^V

/

^V

---

!

^{. /}

^/ _---- ^~

^Jet

^---

~ ^{~ ---}

aa

0.6

o o

0.2 8 20 28 36 40

12 32

16 24

~

16/

17/

- ^~ I~

(a) 0<'. =15' lb) oC- =30⁰

/

*

, -

\

15/ Ic) 0<: =45^{0 Id)}

ex::

=90·

30 35 30

25 25 20

15 20

x/d

15 x~

10 10

5 5

o Full width b x Hall wldth b,

/

'/

• Boundary Layer thickness

/

V /

1/ /

/ ^;/

V/

^V

/

~

" " - -

/ ^V -

~ ^V--

---

^~

-

o

16/ Comparison of lateral widths of the jets.

14/ Normal width of the jel for a.= 45°.

13/

Normal width of the jet for <J.= 30°.

3.6

3.2

2.8

2.4

<..-0,\"0 ^2.0

~"O 1.6

Ll

\"0 _1.2

Ll

0.8

0.4

0

14/

::-\2

Ll

o

13/ 0

S. K. A. NAIB

(Fig. 15). With increasing deftection angle upstream ftow occurs (Fig. 15c), until when the jet impinges vertically on the surface, it s'pmads out radial!y in al! directions (Fig. 15d) as in the case of the radia 1 wall jet. This explains the considerable increase in lateral width of the jet at impact for the 30" and 45° deftecti'On angles and may also account for the similarity of decay of maximum velo- city in both cases. Downstream of fiow Region II, the lateral width fol!ows a curve which then joins ta a straight line of large divergence angle. As expected, the divergence angles for the 30" and 45" deflected jets are the same, about 60°. The widths are compared 'Ailh that for the round free jet in Fig. 16, which shows the considerable increase in lateral width with increasing deflection angle.

The normal widths, b, along the centre plane are plotted in Figs. 12 to 14. It is seen in the impingement Region, the jet contracts slighuly and then spreads linearly with maximum slope cf about 13° for the 30" deftected jet.

The angles of normal and lateral boundary divergence

e

and <P in the regions of fully developed fiow are given in the table below.

Notation

The notation used is illustrated in Fig. 1 and IS given below.

b Normal width of jet.

b_l Normal half-width of jet.

d Jet diameter.

lw Lateral width of jet near the wall.

llOl Lateral half-width of jet near the wall.

K Constant defined by equation(1).

U1 Jet exit velocity.

U Maximum profile ve1ooity.

U_lO Maximum profile velo city near wall.

y Normal distance measured from the wall.

z

Lateral distance measured from centreline.

Xo Distance fwm point source to the exit section.

/) Boundary layer thickness.

e

Angle of normal boundary divergence.

<P Angle of lateral boundary divergence.

ANGLES OF DIVERGENCE

List of references

BOUNDARY

0°De- 15°De- 30°De- 45°De- f1ection f1ection f1ection f1eclion

Normal width b

...

4.75° 5.2° 12.7" 7 ° Normal half-width b_l

..

2.3 ° 2.6° 4.4" 4.9"

Lateral width lw

...

28 37 ° 59.5" 59.5"

Late.ml half-width llOl

..

14 17.5° 20 ° 34 °

The value of Dhe constant isconsiderably !css than the average value of 0.067 found eX!perimentally for the 'plane

WalJil jet [15]. This is a further illustration of the deflection effect of l'he solid surface in transforming the jet into a very wide shaHow s,tream.

The .rate of spreadil1g paraUel ,to the wall is seen to be about 5 to 7 !tmes that normal to it. This is due to l'he effect of the waU in broadening the jet on impact and transforming it into a thin wide stream. The increased surface area of the stream becomes available for mixing which resuHs in faster redll!ction of velocities and greater eXipans.ion of l'he boundaries than in the ,case of the free jet.

The half-widths llOl and b_l aIS{) vary linearly with distance for the jets.

The development of the bounday layer, extending from the wal1 ta the point of maximUllll velocity in the profile, isshown in Fig. 17. The points lie dosely on a straight 'line passing through the oügin, which is represented by the folIowin:g equation:

[1] GLAUERT (M.B.). - The wall jet. J. Fluid Meeh., Vol. 1 p. 625 (1956).

[2] NAIB (S. K.A). - Spreading and development of the parallcl wall jet. Airera!t Engineering, Land., p. 30 (Dec. 1969).

[3] CHESTERS (J. H.), HOLDEN (c.) and ROBERTSON (AD.). - Pro- tection of Refractories by Moving Air Curtains. J. a! Iron and Steel Inst., Vol. 85, p. 177 (Feb. 1957).

[4] NEMENYI (p.) and WHITE (c.M.). - Report on hydraulic research on fish passes; Appendix of report of the Committee on Fish passes. Inst. Civil Eng., Land. (1948).

[5] NAlB (S.K.A). - Mixing of a Sllbcritical stream in a rectan- glllar channel expansion. J. IJ1St. Wat. E., Vol. 20, No. 3, p. 199 (1966).

[6] NAIB (S. K.A). - Stream bOllndaries of subcritical f10w in a trapezoidal channel expansio,n. Wat. & Wat. Eng., Vol. 73, pl. 155 (April 1969).

[7] NAlB (S. K.A.). - Flow patterns in a submerged liquid jet diffusing under gravity. Nature, p. 694 (May 14, 1966).

[8] NAlB CS.K.A.). - Photographie Method for Measuring Velo·

city Profiles in a Liquid Jet. The Engineer, Land., Vol. 221, p. 961 (June 24, 1966).

[9] NAIB (S.K.A.). - Unsteadiness of the circulation pattern in a confined liqllid jet. Nature, Vol. 212, p. 753 (Nov. 12, 1966).

[10] WINTERNITZ (F.A L.). - Single shielded total pressure probes.

Airera!t Engineering, Vol. 30, p. 313 (1958).

[II] TOLLMIEN (W.). - CalcllJations of turbulent expansion pro ces- ses, N.A.C.A., TM No. 1085 (1945).

[12] SQUIRE (H.B.). - Jet fiow and ils effects on aircraft. Airera!t Engineering, Vol. 22, p. 62 (March 1950).

[13] KUETHE (A.M.). - Investigation of the turbulent mixing regions formed by jets,J. Appl. Meeh., Vol. 2, p. A87 (1935).

[14] BAKKE (P.). - An experimenûal investigation of a wall jet.

J. Fluid Meeh., Vol. 2, p. 212 (1957).

[15] SCHWARZ (W. H.) and COSART (W. F.). - The two-dimensional turbulent wall jet. J. FIl/id Meeh., Vol. 10, Pt. 4 p., 481 (June 1961).

/) (X

(3)

d )

d =

0.012