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(c)2001 American Institute of Aeronautics Astronautics or Published with Permission of Author(s) and/or Author(s) ' Sponsoring Organization.

V I I V I V I

A01 16838

AIAA 2001-1049

Num erical Investigations of M ulti

Turbulent Jetsin a Cross Flow

T. Ohanian and H.R. Rahai

California State University, Lo ng Beach

Long Beach, C alifornia 90840.

39th

A I A A

A erospace S ciences

Meeting

Exhibit

8-11January 2001/Reno,NV

For

permissionto copy or republish, contact the AmericanIns tituteof Aeronautics and Astronautics

1801 Alexander Bell Drive,Suite 500, Reston, VA 20191


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( c )2 0 0 1 A m e r i c a n I n s t it u te o f A e r o n a u t i c s A s t r o n a u t ic s o r P u b l is h e d w i th P e r m i s s i o n o f A u t h o r ( s ) a n d / o r A u t h o r ( s ) ' S p o n s o r i n g O r g a n i z a t io n .

AIAA2001 1049

NUMERICAL INVESTIGATIONS OF MUTI TURBULENTJETSIN ACROSS-FLOW

T.Ohanian*and

H . R .

Rahai+

Mechanical Engineering Department

California

State

University,

LongBeach

Long Beach, Ca. 90840.

Abstract

Numerical

Investigations of tw o turbulent

planerjets

in a cross flow are performed. The investigations are

performed for the

jetsvelocity ratios

of 0 . 5 , 1 . 0 , and 2.0

and

jets

spacing

of d, 2d, and 3d. Here d is the jet

diameter. Results show

that

th ejets coupling disappear

when

the

jets spacing

is 3d. For

Jets spacing

of d and

2d, increasing the exhaustmom entum ofdow nstreamje t

above th e free stream and

upstream

je t

velocities,

increases

the

throw

distance

in the cross

flow

beyond

the

wall

boundary

layer

thickness,

before

it is tilted in

the direction of the free stream flow. There is an

increase in the

turbulent kinetic energy

due to the

jets

coupling, which should enhance the mixing and

diffusion

processes.

1.

Introduction

Many engineering applications

involve

jets incross

flows.

These applications include smokestack pollution

dispersion, film cooling

of gas

turbines,

an d

vertical

impinging

jets

in V/STOL

aircrafts.

Details of

flow

characteristics of a jet in

cross

flow depend on many

parameters

with the most

significant being

th e

ratio

of

jet to cross flow momentum. Gregoric et al (1982)

performed

experimental

investigations of

merging

buoyant turbulent jets in a cross flow. For their

experiments, salt-water

jets were

discharged

into

a

stagnant water in a tow tank as they were

towed

at

different speeds. Their experiments included

different

number

of ports ranging from 1 to 7. The ports were

placed in a r o w . Th e ratiosof jet to free stream velocity

were

0 . 2 , 0.5 and 1 . 0 . Th e

experiments

are

also

performed for three

different

orientation angles th e

angle between

the

cross

flow

an d

line

connecting the

ports) of 0, 45 and 90 degrees.

They used flow

visualization and

recorded

images to analyze the flow

field.

Their results show that as the number of the ports

increases,

the amount of

entrainment decreases.

When

the

orientation

angle is at 0 degree, a

vortex

pair is

formed

at the jet

discharge

and iseffective in increasing

the entrainment of the ambient fluid. At 45

degrees

orientation angle, thejetsare

rolled

in space alongthe X

axis and have the

lowest

entrainment. At 90

degrees

orientation angle, the vortex pair is

formed

only at the

lower

velocity ratios.

For 90 degrees orientation

angle,

they offered correlations for the jet

trajectory

an d

normalized area.

Andreopoulos (1982) performed

measurements of

velocity

fluctuation

statistics in the jet-pipe of a jet in a

cross

flow conditions

fo rratiosofjet-pipet ocross

flow

velocity

of

0 . 2 5

to 3. His

results show that when

velocity

ratios

are small,

strong

streamline curvature

affect

turbulence activities at the jet

exit

plane.

However, fo r large

velocity

ratios, the

pipe flow

is

weakly affected by the cross flow. These studies were

extended

b y

Andreopoulos

and Rodi

(1984)

where

they

studied

a

single round planer

jet in the cross

flow

at

three different velocity ratios of 0 . 5 , 1 . 0 , an d 2 . 0 . Their

results show

that when

the velocityratio is

0 . 5 ,

the jet is

dominated

by the

boundary layer

an d

does

no t

have

enough momentum to penetrate beyond the

boundary

layer

into

the

cross

flow.

However,

as the

momentum

flux ratio increases,

the jet

momentum becomes

strong

enough to penetrate the boundary layer an d into th e

cross flow and then it is deflected by the

free stream

flow. For large

velocity

ratios, they also

found

existence

of two

counter

rotating vortices

within

t he j e t .

Sterland and Hollingsworth (1975) performed

experimental

study of multiple square jets

directed

normal

to the

cross

flow fo r different je t spacing to

diameter

ratios. Their

results show

that

when

the jet

spacing to

diameter

ratio is

o n e ,

th e

jets have

the highest

penetration into the cross flow. A s

this

ratio increases,

the jet penetrations are reduced due to entrainment of

free stream fluid in the j e t ,

resulting

in

increased

jets

deflections. Similar trends ar e found by Ligrani et al

(1994a).

Comparisons between experimental results

for a

round

jet in a cross flow withcorrespon ding results for a

square

jet are

made

by

Quinn

an d

Militzer

(1988) an d

* Graduate

Student

t

Professor,corresponding author


3/10

(c)2001 A merican Institute

o f

Aeronautics

Astronautics

or

Published with Permission

of

Author(s)

and/or

Author(s) ' Sponsoring O rganization.

Quinn (1992),

under

similar upstream and exit

conditions. Theirresults showthat

in the

near

flow field,

the

rate

of spreading of the squarejet is

higher than

the

corresponding

value for the

round

jet, which indicates

higherrateof

entrainment

of the

surrounding

ai r

into

the

square jet. Similar

results are found by Haven and

Kurosaka (1997) .

Huang

et al

(1991)

performed

experimental

investigation of a heated roundj et

injected

into a

cross

flow

from

an elevated source in the form of a circular

tube.

Their

results

show

generation

of a

counter

rotating

vortices

at the downstream location of the jet at

approximatelyone initial diameter and the

existence

o f a

quasi-periodic

Karman-like

coherent structure

in the

wakeof the

jet.

Kelso

et al (1996)

performed experimental

investigation of a round jet in cross flow using flow

visualization techniques an d flying ho t

wire

measurements. In their study, the ratios of jet to free

stream velocity were 2.0 to 6.0.

Their results

show that

the

jets

in cross flow

contain many interdependent

vortex

systems. They discussed the importance and

contributions

of the

separation inside

the

pipe,

the

vortex ringsin the jet shear layer and

vorticity

from the

flat

wall

to the counter rotating vortex pair

appeared

downstream of the jet

These

results are presented as a

function of momentum flux

ratio

and jet Reynolds

number.

Smith and Mungal (1998) performed

experimental

investigations

of mixing of a round je t normal to a

uniform

cross flow, for a

range

of jet to

free stream

velocity

ratios,

r, of 5 to 25.

Their results

suggest

that

the trajectory and physical

dimension

of the jet

both

in

the

near

and farfields are

related

to rd

scaling. Here

d is

the je t exit

diameter. Taking

S as the down stream

distance,

it is

shown

that for all

momentum flux ratios,

the jet

initial

decay is

proportional

to

S~

1

3

, when

concentration decay

i s

plotted against SI r d .However,

at a location corresponding to S/r

2

d=Q.3, the

concentration decay for each jet branches out and they

slow down and reach a decay rate proportional to

S .

They indicate that these

results

ar e

valid

fo r

r=10

to 25 and not valid for r=5

where

wall effects

becomeimpo rtant.

He et al

(1999)

performed

numerical

investigation

of the

effect

of

Schmidt number

on

turbulent

scalar

mixing in a jet in cross

flow, using

Reynolds averaged

Navier Stokes

equations

with

the standard

k 8

turbulence model.

Their results

show

that when

th e

ratios

of

jet-to

cross flow momentum are small, the

turbulent Schmidt number

has a

significant

effect on the

prediction of species spreading

rate.

They found best

agreement with corresponding experimental data when

turbulent Schmidtnum ber i s equal 0.2.

2 .

C o m p u t a t i o n a l

M e t h o d

All numerical

analyses

ar e

performed

using the

C O M P A C T 3D program. The

C O P M A C T

program is a

general-purpose program

fo r

calculating fluid flow, heat

an d

mass

transfer, chemical

reactions,

turbulence, an d

related

processes.

It can be used with Cartesian and

cylindrical

coordinate systems. In addition, by blocking

ou tpartsof the comp utational domain, i t isalsopossib le

to represent

irregular

geom etries.

The

computational grid

(X Y Z) for the

present

investigations

ar e

either 50x10x15

or 100X20X 30.

Thwo

round p laner

jets

of 0.5

units

in

diameter

ar e

placed on the

bottom surface

of the computational

domain

at the mid

section,

in the

streamwise

direction.

The investigations are

performed

for thejets spacing of

d,

2d, and 3d and

jets

to free stream velocity

ratios,

Rj

=

U j

IU^

of

0.5,

1.0,

an d

2.0.

The

temp eratures

of the jets are set at 80 units and the free

stream

temperature

is at 30

units.

The analyses are perform ed

based on

these

dimensionless

units.

The standard

k

turbulence model

w as

used

for all the

calculations.

3.

Results

and

D iscussions

Figures 1.0-1.2 show axial

an d

transverse mean

velocities,

mean

temperature

and turbulent

kinetic

energy (TKE) for a single jet in a

cross

flow at a

constant free

stream

mean

velocity of 1.0

unit

and jet

mean velocities of 0.5, 1.0 and 2.0. These units are

chosen

for qualitative

purposes;

t o investigatethe

effects

of changing

jet

momentum

on its development in the

cross

flow

condition. As these

results show, with

increase

in the jet

momentum,

the

rate

of entrainment is

increased

with

a decrease in the

turbu lent kinetic energy.

Th e regions of high turbulent kinetic energy ar e

confined to the wall

boundary layer

near the jet

outlet.

These

results are similar to the

previous

investigations

of a round

turbulentplaner

jet in a

cross flow condition.

Figures 2.0-2.3

show

variation

of the

axial

an d

transverse mean velocities, the

mean

temperature and

the TKE for two

jets

in a

cross

flow

along the mid axial

plane,

with

jets spacing, dX,=d. When Rl and R2 are

0.5, the jets ar e coupled and the region of low axial

velocity is increased near the

surface. There

ar e

increases

in the

regions

of low

transverse velocity

an d

high

temperature

and TKE

near

the

jets planer

surface.

The coupled

jets

do not have enough momentum to

penetrate outside the surfaceboundary layer.


4/10

(c)2001 American Institute

o f

Aeronautics

Astronautics

or

Published with Permission

o f

Author(s)

and/or

Author(s) '

Sponsoring Organization.

WhenRl=land R2=0.5, results aresimilar withthe

coupled je t

having

a higher throw distance before it is

tilted in the streamwisedirection. The

coupled

jet is still

bounded

by the

surface

boundary

layer.

When

Rl=2 an d

R2=0.5,

there is a significant

increase in the throw distance of the coupled jet which

penetrate

beyond

the surface boundary

before

it is tilted

toward streamwise

direction. There is a

small

region of

lo w

transverse

velocity and large

regions

of high

temperature an d high TKE in the

vertical direction.

Th e

regions of high temperature an d high TKE are reduced

in the downstream direction due to increased

entrainmentan d

mixing

betweent he free stream velocity

and the coupledjet.

Similar results

ar e seen

when

R l = 2

an d

R 2 = l

with the

noted effects

being

more

pronounced.

Figures 3.0-3.3 results for the two jets in a cross

flow with dX=2d . When Rl and R2 are 0.5,

region

of

low

axial velocity

is near the surface and the

results

fo r

the

transverse velocity

show two

small

high

velocity

regions near the

surface.

Similar to the correspond ing

results when dX=d, the

regions

ofhigh temperature and

high TKE arecloseto the

surface with

higher spreads in

the axial direction.

WhenRl=l

an d

R2=0.5,

th e

region

of low axial

velocity

for the downstream jet is less than

th e corresponding

region

for the upstream

jet .

Results

fo r

the transverse

velocity show decrease

in the

transverse velocity

for the

downstream

jet and increase

in

th e transverse velocity for the upstream jet

near

th e

surface. The results for the temperature field

show

regions of high temperature near th e surface with

gradual coolingin the downstream

direction.

There is a

significant

reduction in the TKE

with

a

small high

TKE

region associated

with the downstream

jet

When

R l = 2

an d R2=0.5, results for the axial mean

velocity

show

p enetration

of the

coupled

jet beyond the

surface boundary, before

it is tilted in the

streamwise

direction. The transverse

velocity

field does no t

show

tw o separate regions of high velocity, but only one,

which

isexten e in the

vertical

direction.

The results for the

mean

temperature show two

regions of high temperature, which are joining outside

the

surface

boundary

layer.

The

high temperature

region

fo r th e

downstream

jet is less than the

corresponding

region for the

upstreamjet ,

indicating the

cooling effect

the upstream jet has on the

downstreamjet.

The results for the TKE show an expanded region

of

high temperature beyond

th e surface boundary layer.

Th e

high

temperature region is declined in the

downstream

direction

due to the high

entrainments

of

the free

streamfluid.

When

R l = 2

an d

R 2 = l , results

ar e similar to the

case

when

R l = 2

and R2=0.5, with expansions of

regions of low axial velocity, high

transverse velocity,

high

mean

temperature,and highTKE.

Figures

4.0-4.3

show variation

of the

axial

an d

transverse

velocities, the mean tem perature and the TKE

fo r th e jets when

dX= 3 d .

When Rl and R2 are

0.5,

similarto the previous

corresponding

results, the

regions

of low axial velocity, high transverse velocity, high

mean

temperature and high TKE are

located

near the

surface boundary. The je ts are not coupled.

Whi le

th e

two regions of low axial

velocity

ar e joined near the

surface due to the entrainments of the jets in the axial

direction, however, other

results show

clearly

th e

presence

of two

separate

jets. There are two regions of

nearly

identical high transverse velocity, two regions of

high temperature wherethe region for the upstream jet is

less

than

the

region

for the

downstream

jet due to the

higher cooling effect that

th e

upstream

jet is

experiencing, and two regions of relatively

high

TKE

withexpa nded region for the upstreamjet.

When

Rl=l and R2=0.5, similar

results

ar e

seen

as

the previous case, except the regions for low axial

velocity, high transverse velocity and

high

TKE are

reduced

significantly. There is an increase in the je ts

throw distances, but they are still

mostly

within the

surface

bou ndary.

When R l = 2 and R2=0.5, the

regions

for the

upstream jet dominate the flow

field. There

is a

significant increase in its

throw

distance, before it is

tilted in the axial

direction.

The regions of high

transverse velocity and

high

TKE are associated with

the upstream je t . The temperature field shows two

regions of high temperature, with the expanded region

fo r

th eupstreamjet.

When R l = 2 an d R 2 = l ,

results

ar e

similar

to the

case when R l = 2 an d R2=0.5, except that there are

expanded regions of low axial

velocity,

and high

temperature for the downstream

jet . There

are no

significant increases

in the transverse

velocity

and the

TKE for the downstream

jet.

4.

Conclusions

Numerical investigations of two round planer jets

placed in a cross flow are

performed.

Th e ratios of the

jet to free

stream velocities,

Rj ar e 0.5,

1.0,

and 2.0,

and the streamwise spacing between thejets, dX, are d,

2d, and 3d. Results show that when Rl and R2 are

0.5, for dX=d and 2d, the jets are coupled but mostly

bounded by the surface boundary and the regions of

high temperature,

high

transverse velocity, and high


5/10

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TKE are near the surface boundary. When dX=3d, the

jets are not coupled and there are two

separate

interaction regions

with the

mixing

of the two jets are

performed in the downstream direction. The upstream

jet has higher TKE and lower temperature regions than

th e

downstreamjet.

Increasing the momentum of the jets, increases the

corresponding throw distances,

and depending on dX

spacing, th e je ts may either coupled above the surface

boundary an d then diffuse in the

downstream direction

or

they

m ay tilt in the

streamwise

direction and then

coupled in the downstream direction. Depending of the

Rj values, the regions of high TKE , high

transverse

velocity or high temperature may be near the upstream

or

th e

downstream

jet.

The overall results show that th e

diffusion process

is

enhanced

when

the

jets momentums

are

high enough

to al low them to break through the surface boundary ,

before

they

ar e

tilted

in the streamwise direction.

5. References

A nderop oulos, J, 1982, Measurem ents in a

Jet-

Pipe Flow

Issuing Perpendically

Into a Cross Stream,

A S M EJ. of F luids Engineering,Vol.

104,

pp .

493-499.

Anderopoulos ,

J., and

Rodi,

W .,

1984,

Experimental Investigation of Jets in a Cro ssflow, J.

of Fluid

mechanics,

Vol . 138, pp.

92-127.

Briggs, G.A . Plume Rise from

Mult ip le

Sources,

Atmospheric Turbulence an d

Diffusion

Laboratory

Contribution No. 91(1974).

Broadwell, J .E. and

Breidenthal,

R.E., 1984,

Structure

an d

Mixing

of a Transverse jet in

incompressibleFlow, J.

Fluid

mech., 148,405-412.

Gregoric, M, L.R.

Davis,

and D.J,

Bushnell.

A n

Experimental

Investigation of

M ergingBuoyant

Jets in a

Crossflow , Journal of Heat Transfer Transactions

of

ASME 104:236-40(1982).

Haven, B., Kurosaka, M., 1997, Kidney an d Anti-

Kidney Vorticies in Crossflow

jets,

J.FluidMechanics,

Vol .352,

p p .

27-64.

He, G.,

Guo ,

Y., andHsu,A , 1999, The Effect of

SchmidtNumber on Turbulent Scalar Mixing in a

Jet-in-

Crossflow, International J. of

Heat

and Mass

Transfer,

Vol .

42, pp .

3727-3738.

Huang,

Z., Low,

M.S., Kawall, J.G.,

an d Keffer,

J.F., Structural

Feature of a

Heated Round Turbulent

Jet in a Cross

Flow,

Paper No.

25-1,

Proceeding of the

Eight

Symposium on

Turbulent Shear

Flows,

September9-11, 1991, Mu nich, Germany.

Kelso, R.M., Lim,

T.T.,

andperry,A.E, 1996, An

Experimental Study of Round Jets inCross-Flow, J. of

Fluid

M echanics,

Vol .306,p p. 111-144.

Ligrani, P.M., Wigle , J .M. ,

and Jackson,

S.W.,

1994a, Film-Cooling

Holes

with

Compound Angle

Orientations:Part

2-Results Downst ream of a

Single

Row of Holes

with

6d spanwise

spacing,

A S M E J .

Heat Transfer, Vol. 116,pp. 353-362.

Quinn,

W., and

Militzer,

J .,

1988, Experimental

and Numerical Study o f a

T urbu l en t

Free Square

Jet,

Physics of

Fluids ,

Vol. 31, No. 5, pp. 1017-1025.

Qu inn ,

W., 1992, Stream wise Evolut ion of a

Square

jet Cross

Section,

A I A A Journal,

Vol .

30, No.

12 ,

pp.

2852-2857.

Smith, S. and Mungal, M.G.,

1998, Mixing,

Structure

an d

Scaling

of the Jet in

Crossflow,

J. of

Fluid Mechanics,

Vol .

357 ,

pp.

83-122.

Sterland, P.R., and Ho llingsworth,M.A. , 1975, An

Experimenta l

Study

of Mult ipleje ts DirectedNorm al to

a Crossflow, Journal of Mechanical Engineering

Science, Vol. 17, No. 3, pp. 117-124.


6/10

(c)2001American Institute of Aeronau tics Astronautics or PublishedwithPermission of Author(s) and/orAuthor(s)' S ponsoringO rganization.

iii

Figure

I. A jetma

cross

flow, Ri=L0

IA A-sisgle ei IB afossl@w,

:

RI O.5

l


7/10


of Aeronau tics Astronautics or Published with

Permission

of Author(s) and/or Author(s) ' Sponsoring O rganization.

gure 2X Two jets in a

cross Sow.

R

jets

IB a.

cross flow.

and

dX=d.

6


8/10



Permission


Figure

3 0

Tw o jets in a cross

flow.

R l= 0 5 ,

R2=0.5,

a nd

dX=2d.

Figure 2.3.Tw o

jets

in a cross flow. R

1=2.0

R 2= 1 . 0 , an d d X= d .

Figure

3.1.Tw o

jets

in a cross

flow.

R

1=1.0,

R2=0.5,

and dX= 2d.


9/10

(c)2001

American

Institute


Permission


Figure 4.0.

Two je ts in a cross flow.

O.S,anddX=3d.


10/10

(c)2001American

Institute

of Aeronautics Astronauticsor Published

with

Permission of Author(s) and/or

Author(s)' Sponsoring

O rganization.

Figure

4.L Two jets IB a cross

flow.

R1=L0,

Figure

4.2.Tw o jets

in

a cross

'flow

Figure 4 3

Two

jets

in a

cross flow.

R

1=2.0

R 2 = 1 . 0 a nd d X = 3 d

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CFD Numerical Investigations of Multi.pdf