experimental and numerical examination of confined laminar opposed jets part ii. momentum balancing

P e r g a m o n

Int. Comm. Heat Mass Transfer, VoL 27, No. 4, pp. 455-463, 2000 Copyright © 2000 Elsevier Science Ltd Printed in the USA. All rights reserved

0735-1933/00IS-see front matter

I ' l l S0735-1933(00)00128-7

E X P E R I M E N T A L AND N U M E R I C A L EXAMINATION OF CONFINED LAMINAR OPPOSED JETS

PART II. M O M E N T U M BALANCING

David A. Johnson Department of Mechanical Engineering,

University of Waterloo Waterloo, Ontario, Canada N2L 3G 1

(Communica ted by J.P. Hartnett and W.J. Minkowycz)

ABSTRACT Impingement of laminar fluid jets in a confined cylindrical chamber is examined using steady and unsteady three dimensional finite volume numerical simulations using boundary fitted non- orthogonal coordinates. The results presented here deal with modifying an existing flow imbalance and suggest alternative momentum arrangements to improve the flow characteristics. Unequal flow cases in an opposed two jet configuration indicate an asymmetric flow field with significant downward recirculation from the region away from the nozzles to the nozzle region and a jet-to-jet impingement point very close to the low flow rate nozzle. Large areas of recirculation in the flow direction of the chamber will lead to poor mixing due to the possibility of unmixed fluid leaving the chamber and the increase in the residence time of the mixing fluids. © 2000 Elsevier Science Ltd

I n t r o d u c t i o n

Due to the flow configuration or mixture requirements flow imbalance is a common occurrence in

applications involving opposed jet impingement. Alternative schemes are proposed to reduce the negative

aspects of flow imbalance such as an impingement point near the weaker jet exit, a high pressure gradient

near the weaker nozzle exit due to the impingement position and significant flow along the chamber

boundaries leading to high thermal gradients in heat transfer applications and an axially extended mixing

zone. Schemes are proposed which alter the jet diameters while preserving the flow rate ratios in two jet

configurations and a three jet configuration is examined.

For all specified problems, a fluid flows from a nozzle into a chamber of enlarged area and flows from

the chamber. In the directly opposed configuration a jet, formed when fluid issues from the nozzle on one

455

456 D.A. Johnson Vol. 27, No. 4

side, impinges onto a jet formed when fluid issues from the opposed nozzle. Upon impingement, the flow

field is created which forces the fluid from the chamber. The particular focus of this study is the

characterization of the fluid mechanics of the flow field under unequal flow conditions where the imbalance

may cause plugging of the weaker jet and significant flow along wall surfaces. A flow visualization study

using water in two model mix chambers with equal jet flows is reported by Akaike et al. [1] who found stable

flow when Re d < 200, an unstable impingement surface for 200 < Re d < 500, and a stable impingement

surface for Re d > 500. An important consideration is the development and subsequent impingement of the

jets issuing from the nozzles. Akaike and Nemoto [2] have made measurements of the initial development

region of an unbounded laminar jet and found parameters such as jet spreading and maximum velocity decay

to agree well with the boundary layer analysis presented in Rankin et al.[3]. Steady two-dimensional

simulations of jet to jet impingement by Hosseinalipour and Mujumdar [4] show a steady increase in axial

distance to a uniform temperature profile with increasing jet Reynolds number. At lower values of Red there

may be a similarity between the jet to jet impingement process and isolated jets impinging on solid surfaces.

Deshpande and Vaishnav [5] have numerically examined laminar jet impingement on a solid surface two

nozzle diameters from the nozzle for Re =1 and 1000. They present plots of maximum velocity decay as a

function of axial distance to the solid surface.

Several flow imbalance cases are examined for the two jet opposed configuration (2J) using three

dimensional steady and unsteady numerical simulations. Visualization of these confined flows has indicated

a three dimensional flow field exists for all values of R%. In Part I a two jet (2J) unequal flow, equal nozzle

diameter case was evaluated showing an impingement region very close to the weaker jet exit. To overcome

the shortcomings of that configuration while maintaining the identical mass flow ratios the following

alternatives are proposed: l) a 2J model where the weaker jet diameter is reduced by one half, 2) a 2J model

where the weaker jet diameter is reduced by one quarter, and 3) a three jet (3J) model where the higher flow

jet is divided into two original diameter jets which are equally spaced with the weaker jet around the

periphery of the chamber. The goal of these proposals are to attain a more centrally located impingement

point avoiding an impingement point near the weaker jet and the associated pressure gradient, to reduce the

axial recirculation length, and reduce flow along the axial wall boundaries.

Numerical Simulations

The flow domain considered is similar to that described in Part I (D* = 10, H* = 5, L,*=95, parabolic

inlet profile) with the exception that in these cases some alteration to the inlet nozzle diameters is examined.

Two grid densities were used, a 23 x 21 x 70 (x,y,z) grid for the 2J configurations (Figure 1) and a 33 x 27

Vol. 27, No. 4 CONFINED LAMINAR OPPOSED JETS, PART II 457

x 70 grid for the 3J configuration to allow for equal numbers of grids in each jet as shown in Figure 2.

Two 2J cases were examined for numerous values of Re d for a mass flow imbalance of 2.1 : 1 . In the first

case the cross sectional area of the lower mass flow jet was reduced to one half of the stronger jet (2Ja)

which to maintain identical mass flow conditions as in part I required the jet exit velocity to be increased by

a factor of four and in the second case the cross sectional area of the lower mass flow jet was reduced to one

quarter of the stronger jet (2Jb) which required the jet exit velocity to be increased by a factor of sixteen for

similar mass flow conditions. Using these mechanisms the effective jet momentum of the weaker jet is

increased by the same factor. As well, a 3J case is developed where the higher mass flow jet is divided into

2 equal jets and with the weaker jet they are spaced 120 ° apart. The original full je t diameter is utilized as

in part I and in this way all the jets have approximately the same exit conditions (Part I examines the case

of 2.1 to 1 flow ratio). For the unsteady calculations reported here, a first-order implicit (backward)

dimensionless time step of 0.01 was used beginning with either a converged steady state or transient solution

at the highest available Reynolds number. Calculations continued until periodic solutions were obtained.

FIG. 1 Computational mesh XY plane 23 x 21 (x,y) Two Jet cases 2J

FIG. 2 Computational mesh XY plane 33 x 27 (x,y) Three Jet cases 3J

Results

Unsteady calculations were required for 3J and 2Jb cases for values of R% > - 100. The 2Ja case did

not require unsteady calculations and a converged steady solution could be obtained for all Re d values. For

each case and Red where unsteady solutions were required 9 representative unsteady solutions were used to

obtain an average. The representative time steps were taken by examining a plot of dimensionless velocity

versus dimensionless time obtained at (X*,Y*) = (0,0) above the point of impingement at Z* = 6 and dividing

the range of oscillation into equal time intervals. Figure 3 shows typical results from unsteady time step


solutions for the highest 3J Re d examined (Re d = 217 left jet, Re d ~ 229 remaining two jets), The

impingement region remains stable in the 3J case although the radial jets formed as a result of the

impingement oscillate in the region between the jets.

FIG. 3 Three jet configuration (3J) XY plane at Z=0 three different time steps (jet at left Red=217)

Impingement Region

Velocity vectors in the geometric plane of impingement are shown in Figure 4 for the maximum R e d

studied for the three cases examined (2Ja, 2Jb, 3J). The location of the impingement region as indicated by

a U velocity of zero on the jet-to-jet axis (Y=0) are plotted in Figure 5 as a function of R% including the data

from part I. The geometric center of the chamber is located at (x,y,z) = (0,0,0). The 3J configuration is not

indicated on the figure as a centrally located impingement point (X* = 0) was found for the entire range of

Re d studied. For the 2Ja case the impingement point is seen to steadily move toward the lower flow jet as

Re d is increased and approach the impingement locations found in the equal jet diameter case examined in

part I. The values indicate a plateau value is reached at R% = 300. The 2Jb case indicates a impingement

point close to the geometric centre of the chamber as Re d increases and some movement in the impingement

point is indicated by the bars at Red = 200 and 400 as found in different time step results.

FIG. 4 Velocity vectors in impingement plane (Z = 0): left side 2Ja case, center 2Jb case, right 3J case. 2J cases: left jet Red = 458 right jet Red = 217 3J case: left jet Red = 217 other jets R% = 229 Dimensionless unit vector U* = 1


Comparable data in the literature is scarce although results for unequal flow rate turbulent free a]r jets

have been detailed by Ogawa et al. [6] who found for a flow rate ratio U,vgl/Uav~2 of 0.935 the impingement

point was located at X" = -1.61 (-2.15 > X* < 2.15) and for a flow rate ratio Uav~t/Ua~gz of 1.044 the

impingement point was located at X ' = 1.32 (d = 35 mm, L/D = 4.3, Re d = 5.61X104). Although the flow rate

ratio is smaller, their results indicate that the relationship between flow rate ratio and impingement point is

not linear and flow rate ratio may not solely be used to determine the impingement point. Unsteady

simulations reported by Ho [7] in a cylindrical chamber (D" = 10) for a flow rate ratio of 1:1.5 found the

impingement point to be located at X* = -3.5 (-5. > X* < 5.) Uavg~/U,vg 2 = 1.5, and for the flow rate ratio of

1:2 found the impingement point to be located at X* = -4.3 (-5. > X* < 5.) Uavg~/U,vg ~ = 2 which is in good

agreement with these results. These values are in reasonable agreement considering the unsteady nature of

the flow field at these Re d and the technique used to ascertain the impingement point. A typical characteristic

of the impingement region is the high pressure gradient due to the stagnation conditions as seen in Figure

7 for Red = 100. In the 2Ja case the larger jet is seen to impact the smaller jet at the point of impingement

near the smaller nozzle exit and also to impact the wall surfaces due to the cross sectional area imbalance.

The 3J case shows a centrally located impingement region.

5.0

4m5 i

4.0

3.5 •

3.,0 m mm

2.5

2.0

).5 ,Ik-

0.5

i i i I00

., ,• &

mm m

. !

200 300 400 500 P~

FIG. 5 Impingement Position for all 2J cases studied. X* = 0 indicates the geometric center of the chamber at Z* = 0 • 2Ja case, • 2Jb case , , 2J part I case

30

25

20

~4 ~5 A

1 0

5

, I 1 0 ( )

• A • Ira,

• !

I , I , I ~ I 200 300 400 500

Ro

FIG. 6 Highest axial location of -W* velocity. Z* = 0 indicates the geometric center of the chamber at (X*,Y*) = (0,0) • 2Ja case, • 2Jb case, • 3J case


FIG. 7 Pressure (P*) contours XY plane at Z = 0 Rea= 100. Left 2Ja case, center 2Jb case, right 3J case Contour values 0.025,0.05,0.1,0.15

Axial Velocity_

An estimate of the size of the mixing zone may be made by determining the highest z plane that contains

negative W* flow. This is comparable to the complete mixing criterion used by Hosseinalipour and

Mujumdar [4] where temperature is used as a mixing indicator. Fluid from this plane may flow back down

to the impingement region. The highest axial Z* plane where negative W* velocities were found is shown

on Figure 6. Generally, the highest negative W* velocities increased with Re d. There is some scatter in the

data although the alternative schemes do not show a significant reduction in negative W* flow as the equal

diameter jet simulations in part I show unidirectional flow occurring after Z* = 22.3. The 3J configuration

at the highest Re d studied showed the last negative values of W* at Z* = 26.3i 1. l an average of the unsteady

time step solutions. This value is significantly higher than the Z* = 10.75 value found in 2J balanced flow

cases (Johnson et al.[8]).

Jet Development

In an effort to classify the opposed jet configuration comparisons were made to laminar jet development

and laminar jet impingement studies in the literature. Figure 8 shows the decay of dimensionless maximum

jet velocity Urn* with dimensionless distance X c for the 2Ja case. This arrangement lead to a collapse of all

the data for 50 < Red < 150 0 < X~< 0.06 as would be predicted by boundary layer assumptions [2],[3] for

unbounded submerged laminar jet development. Jets similar to these have been shown to be fully developed

at Xd* > 4 [8] and Xd* = 6 [2],[3]. As the impingement point is approached the shape of the Urn* vs X~ curve

changes significantly showing a rapid drop in the maximum jet velocity. For values of Re d > 150 Urn*

decays very rapidly and does not approach the curve describing the boundary layer assumptions suggesting

that the jet does not develop and remains underdeveloped before the effects of impingement are seen. The

data that do approach the development line 50 < Re d < 150 may be predicted using an exponential decay as


0.8

0.6 L i t I i ~ I. i ~ I 1 I

0.4. r- i i

r i ~

02L ii _ i I

i j

i t

i' i I il

il i I i j

I,, I 0.05 0.1 0.~5 0,2

X o

FIG. 8 Decay of maximum jet velocity with distance: 2Ja case Lines plotted are from the right : Red =50,75,100,150,250,300,350,400,458

Exponential fit to velocity decay - - Data from [6] . . . . Data from [5]

shown on the figure. Also shown on this figure are the results of numerical examination of laminar jet

impingement on a surface from Deshpande and Vaishnav [5] (Re d = 1000) where the nozzle is located two

jet diameters from the surface. This plotted result suggests that the opposed jet values will asymptote to

these values as Re d is increased. This would suggest that lower values of Re d show effects of jet development

and impingement while higher values of Red are influenced more strongly by the impingement surface.

C o n c l u s i o n

The effects of unequal flow on the velocity field of confined impinging jets has been examined through

numerical simulations. Unequal flow rate ratios were found to alter the flow field significantly by moving

the impingement point toward the lower momentum jet and stabilizing the flow field to some extent.

Modification of the two jet opposed nozzle cross sectional areas to decrease the flow area of the lower flow

rate nozzle and increase the jet momentum was shown to move the impingement point (as measured using

zero U* velocity and pressure contours) toward the geometric centre of the chamber however the mixing

volume (distance to uni-axial flow) was not reduced. A three jet arrangement which divided the higher mass

flow jet into two equal jets was found to orientate the impingement point at the geometric centre of the

chamber. Unsteady simulations were required for the smallest opposed jet case 2JB and three jet 3J case for


Re d > 100 due to oscillations in the radial jets formed in the impingement region. For Red < 150 the higher

mass flow jet was seen to develop as a submerged axisymmetric jet until the impingement region. The

improvement in the location of the impingement position with the alternative schemes will reduce the

negative aspects of an imbalanced flow field such as nozzle plugging for the mixing of reactive fluids or a

high pressure region near the lower momentum jet outlet.

Acknowledements

The author gratefully acknowledges the support of this research through grants fro m the Natural Sciences

and Engineering Research Council of Canada.

Nomenclature

d

D

D'

H

H*

Lc*

P

p*

Red

Uavg

U,V,W

Umax

Um ~

U',V',W'

x,y,z

x~

X* Y',Z"

Xd*

Xc

nozzle opening diameter (mm)

main chamber diameter (ram)

dimensionless chamber diameter, D/d

head length (nozzle centre to closed chamber end) (m)

dimensionless head length, H/d

dimensionless length of chamber above nozzle centre/d (95)

pressure

dimensionless pressure P/(pUZavg)

Reynolds number

average fluid velocity leaving the nozzle (m/s)

velocities in x,y,z direction (m/s)

maximum jet velocity in any y plane (m/s) (subscript 0 indicates exit condition)

Uma x/U max(~

dimensionless velocities, U/Ua.g, V/U.v ~, WAJa.g

distance (ram)

distance from jet exit (ram)

dimensionless distance, x/d, y/d, z/d

dimensionless distance from jet exit (x/d)

dimensionless distance from jet exit (x/d)/R%

1.

References

Akaike, S., M. Nemoto and R. Ishiwata, Flow Visualization of Coaxial Impingement of Opposing Jets in Mixing Chamber, Proc. Fourth Int. Symp. Flow Vis., pp. 527-532, Aug 26-29, Paris, France, 527 (1986).


2. Akaike, S.M. and Nemoto, M., ASME J. Fluids Eng., 110, 392 (1988).

3. Rankin, G.W., Sridhar, K., Arulraja, M., Kumar, K.R., ASME~ Fluid Mech., 133, 217 (1983).

4. Hosseinalipour, S.M. and Mujumdar, A.S., Int. Comm. Heat Mass Transfer, 24, 27 (1997).

5. Deshpande, M.D., and Vaishnav, R.N.,ASMEJ. Fluid Mech., 114, 213 (1982).

6. Ogawa, N., H. Maki and K. Hijikata, JSMEInt. J Set. II, 35, 205 (1992).

7. Ho, A.S.K., The Effects of Flow and Geometrical Parameters on Impingement Mixing for Reaction Injection Molding, M.Eng. Thesis, McMaster University, Hamilton, Canada (1992).

8. Johnson, D.A., Wood, P.E., Hrymak, A.N., Can. ~ Chem. Eng., 73, 40 (1996).

Received April 7, 2000

experimental and numerical examination of confined laminar opposed jets part ii. momentum balancing

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