cfd numerical simulation and experiments of jets in cross.pdf

8/10/2019 CFD Numerical Simulation and Experiments of Jets in Cross.pdf

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American Institute of Aeronautics and Astronautics

1

Numerical Simulation and Experiments of Jets in Cross

Flow

Z. Li., S. Murugappan, E. Gutmark, L.Vallet

Department of Aerospace Engineering and Engineering MechanicsUniversity of Cincinnati, Cincinnati, Ohio, 45221-0070

A numerical simulation was carried out to compute the penetration, mixing and

turbulence structures of a jet injected perpendicular into a free stream through different

circular nozzles. Six cases were studied, including 3 different jet diameters and 2 different

blowing ratios. The formation of the Counter rotating Vortex Pair (CVP) and the interaction

between the free stream and jet flow is discussed. The d, rd and r2d scaling parameters

associated with the centerline jet trajectory shows bifurcation into two separate branches.

The bifurcation was related to the different Reynolds numbers. Flow features related to

mixing, centerline velocity decay, size and shape of the recirculation bubble formed behind

the jet are discussed. Higher blowing ratios show higher velocity decay rate. Both timeaveraged flow field and turbulence are compared with 2D Particle Image Velocimetry (PIV)

data taken along the jet center plane. Good match between the experiments and

computation was observed.

I. Nomenclature

d = hydrautic diameter of nozzle

I = turbulence intensityk = turbulence kinetic energy

r = square of momentum flux ratio

Rey = Reynolds number based on the distance y to the wall

ReDH = Reynolds number based on the hydraulic diameter

ju = jet velocity

'u = fluctuating velocity

avgu = mean velocity

u = free stream velocity+y = dimensionless sublayer-scaled distance

x, y, z = streamwise, transverse and spanwise coordinate directions

= density of fluid

= dissipation per unit mass

= molecular viscosity

t = eddy viscosity

II. Introduction

ETS in cross flow (JICF) belong to classical flows that are found in many engineering applications, including:smoke issuing from chimneys, pollutant dispersal, turbine blade cooling, V/STOL aircrafts, fuel injection in

supersonic flows, dilution zones in gas turbine combustors and reaction control jets in rockets and missiles.J

44th AIAA Aerospace Sciences Meeting and Exhibit9 - 12 January 2006, Reno, Nevada

AIAA 2006-307

Copyright 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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Overall, there are four important vortical structures which have been well established in the studies of jets in

cross flow. These are: (a) Horse shoe vortices 1-3 which form upstream of the jet exit and wrap around the jet

column, (b) Jet shear layer vortices 1 which form at the interface between the jet and the cross flow, (c) Wake

vortices3which form on the lee-side of the jet and persist far downstream, (d) Counter-rotating vortex pair 4which

forms after the jet has been turned by the cross stream.The horseshoe vortex system is a result of the interaction between the wall boundary layer and the transverse jet

1-3 .The adverse pressure gradient formed at the injection wall forces the wall boundary layer to separate and form

the horseshoe vortex. This vortex system is then convected and stretched around the jet periphery like a necklace.This is analogous to the vortex system formed when an approaching boundary layer interacts with a cylinder

mounted on a wall 4. The horseshoe vortex system exhibits oscillating modes which correlate with the periodic

motions of the upright wake vortices1-3.The upright wake vortices have been identified by Fric and Roshko 1by means of smoke wire visualization. The

boundary layer of the cross flow has been observed to provide the main source of vorticity in the wake vortices.

Fric and Roshko 1have also identified separate events where the wall boundary layer forms vortices which attach

themselves to the lee-side of the jet and eventually form the wake vortex system. This finding is called an upright

wake vortex system since one end of the vortex string is connected to the jet and follows the jet trajectory whereasthe other end stays close to the cross flow wall, positioning the vortex in an upright orientation.

The counter-rotating vortex (CVP) pair has been observed to be the dominating structure in the far field region

of the jet cross section 5 with evidence of its initiation in the near field 6,7. Knowledge of the origin and growth of theCVP are critical to the control of vorticity generation and evolution which are primary factors in the mixing of a

transverse jet with cross flow. It is generally accepted that the fold and rollup of the jet shear layer near the jet exitcontributes to the formation of the CVP 3. Also, tilting and folding of the vortical structures contributes to the

vorticity in the far field which causes, on a time average basis, the formation of the counter rotating vorticalstructures.

Margason8provided an extensive review of past work before 1993 on jet in cross flow. In many of the studies,

the main interests are the trajectories prediction, the formation, evolution and interaction of the counter-rotating-

vortex-pair (CVP) and their respective applications. Both experimental and computational efforts were conducted to

investigate the details of different flow structures of JICF. The flow field of a vertical jet in cross flow is observedto be primarily influenced by the square root of fluid momentum ratio

21

2

2

=

cfcf

jj

u

ur

(1.1)

or a simplified effective velocity ratio cfj uur= for incompressible flows.

Different range of velocity ratio determines different flow regime. Typically, for r


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CVP strength. Yuan and Street12, Yuan et al13were among the first to use LES simulations to compute the flow

field. Among their results is a proposed mechanism for the formation of the CVP by means of breakdown of quasi-

steady vortices that extend upwards and downstream from the lateral edges of the jet. Muppidi and Mahesh14did

DNS Computation of the JICF. They identified a new scaling law which depends on the inlet jet velocity profile and

the cross flow boundary layer. They proposed an analytical expression for the new length scale which is a measureof the relative inertia of the jet and the cross flow. They observed that incorporating this length scale improves the

scaling the trajectories.

The focus of the current paper is compare simulation and experiments15for six different cases. The effects ofblowing ratio r on the jet trajectory scaling are studied. The flow field and mixing characteristics of the jet with the

free stream is discussed. Different parameters such as the Turbulent Kinetic Energy and centerline velocity decay

are evaluated for the six cases. The size, shape of the recirculation bubble and possible scaling with r and d isinvestigated.

II. Computation Set Up

Figure 1a shows a schematic of the JICF solved numerically using FLUENT 6.0.12. The jet begins as a turbulent

pipe flow which then issues into a flat plate boundary layer through an orifice that is flushed with the plane of the

flat plate. The coordinate system used in the current simulation is depicted in figure 1. The origin x=y=z=0 islocated at center of the circular orifice. Here x, y and z represent the streamwise, vertical and spanwise directions,

respectively. Six cases are studied in the current paper. Table 1 lists the jet diameter, D is the jet diameter, bulk jet

velocity, V, free stream jet velocity, blowing ratio (r ) and the Reynolds number based on jet diameter

VDD =Re .

Figure 1a Flow configuration schematic with 3D coordinate setting used in the simulation

Diameter Velocity of the jetvelocity offreestream

Blowingratio, r,

ReD

Case1 10m/s 8.45

Case2Nozzle1 10.922mm 84.46m/s

17m/s 4.9763165

Case3 13.6m/s 8.38


23m/s 4.9673917

Case5 22m/s 8.55


35m/s 5.3759849

Table 1. Computational Parameters

The computational mesh is mainly unstructured and consists of hexahedral elements. The use of unstructured mesh

near the jet exit and wake region provides easier handling of variation in mesh size and relatively higher

computational efficiency, provided by the finite volume method in FLUENT. The computation domain for case1 isshowed in Figure1b. It is a combination of square channel and a long cylinder pipe.Dimensions of the simulation

domain vary depending on the velocity ratio, r. For higher r simulations, size in y-direction is set larger as the jet

has a deeper penetration into the cross-flow. For lower r cases with less jet penetration vertical extent of the domain


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is reduced to minimize the memory requirement and CPU time. A total of 0.9~2610 control volumes are used to

discretize the domain, of which over 90% are placed within the near field at the jet exit. Coarse elements are mostly

located far away upstream and downstream from the jet exit in the free stream. The near wall regions are treated

with refined boundary layer grids as they approach the solid surface. The viscous sub-layer is not captured in the

current simulations due to the time constraints. The pipe cross-section is hybrid meshed with unstructured grid atcenter surrounded by structured fine grid in order to have a high grid resolution in the region of strong shear stress.

In core region of channel, unstructured girds are of approximately the same edge length and the mesh size increasesgradually in the radial direction. The block volume mesh is created by sweeping the mesh in y-direction from flat

plate surface and pipe inlet face. The mesh size varies from 0.0006d to 1.5d over the core computational domain.

Figure 1b: Computational domain of the channel and pipe

A segregated, 3D, implicit, uncompressible and steady solver is employed for all these simulations. A standard

k model is chosen for the initial iterations, and a renormalization group (RNG) k model is selected for thesuccessive iterations. In a standard k model, the turbulence kinetic energy, k, and its rate of dissipation, , areobtained from the following transport equations:

KMbk

jk

t

j

i

i

SYGGxk

xku

xk

t+++

+

=

+

])[()()( (2.1)

and

S

kCGCG

kC

xxu

xtbk

j

t

j

i

i

+++

+

=

+

2

231 )(])[()()( (2.2)

Gkrepresents the generation of turbulence kinetic energy due to the mean velocity gradients. Gbis the

generation of turbulence kinetic energy due to buoyancy. YMrepresents the contribution of the fluctuating dilatation

in compressible turbulence to the overall dissipation rate and can be neglected here.1C , 2C , and 3C are

constants. k and are the turbulent Prandtl numbers for kand , respectively. Skand S are source terms. In

RNG

k model, all k

t

+

term are changed as effk . And equation (2.2) is added an additional term

R given by:

kS

SS

Rk

kk

])(012.01[

)38.4

1()(0845.0

3

23

+

= .

This term produces negative contribution in regions of large strain rate, thus yielding a lower turbulent viscosity

than the standard k model.


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X

0

0.05

0.1

0.15

0.2

0.25Y

-0.03-0.02

-0.0100.01

0.02

Z

0

0.05

0.1 1

2

3

4

5

678

9

10

X Y

Z

The boundary conditions are set as follows. A uniform inlet velocity profile is specified at the entrance to the flat

plate. A turbulent boundary layer represented by a 1/7 power law approximation was imposed on the flat wall. It

has been observed in the LES of Yuan et al13and DNS of Muppidi and Mahesh14that the flow inside the pipe need

to be modeled in order to capture asymmetry in the jet profile at the exit and possible reverse flow inside the pipe. In

the current simulations the flow inside the pipe was modeled with a uniform inflow velocity profile. Length of thepipe is designed to be sufficiently long for the jet fluid to fully develop and velocity profiles were checked with

experiments for validation after the computation. At the span-wise boundary and the top boundary, a symmetry

condition is set. On the downstream outflow face, a zero-gradient pressure outlet was applied. The turbulenceintensity at the entrance to the channel was set to 0.04%. No heat transfer in considered in simulation.

Figure 2 Time-averaged contours of Y velocity and some characteristic streamlines on symmetry center plane

for case 3

(a) (b)

Figure 3. (a), Streamlines originating from the jet in the center plane (Z=0) for case 3. (b) Evolution of the

Streamlines originating from the jet flow.

III. Results

3.1Flow feature

Figure 2 shows the contours of velocity magnitude and some characteristic streamlines for case 3 on the Z = 0symmetry center plane. Upstream of the jet exit the cross flow fluid close to the wall appears to stagnate upon

encountering the jet, streamlines upstream of the jet and above the injection wall bend around the jet. Streamlines

downstream show strong entrainment of the cross flow into the jet stream. Downstream from the jet exit and above

the injection wall exists a node with positive divergence (x=0.11rd, y=0.05rd). The streamlines from this nodeindicate that the part of cross stream is entrained into the jet whereas the streamlines close to the wall follows the


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streamwise direction. The existence of nodes has been observed in the past by Kelso et al3, Hasselbrink and

Mungal16and Muppidi and Mahesh14.

(a) (b)

(c)

Figure 4. (a) Schematic showing the location, where the free stream fluid marker was placed along the

centerline Y=0 upstream of the jet; (b) The jet fluid (Red) and free stream fluid (Blue and Green)

represented in different colors; (c) Cross section at 4 different planes

Figure 3 a and b show the streamlines originating from the jet and their evolution at 10 different cross sectional

planes. The ten planes were sliced normal to the jet trajectory coordinate, s. The formation and growth of the counterrotating vortex pair is clearly evident in these slices. In order to better understand the interaction of the jet flow with

the cross stream, fluid originating from the jet and cross stream were tracked. Two different regions upstream of the

jet with cross stream flow were marked with tracers. One region was closer to the wall and the other was right above

the first region. Both these regions were 3.2d upstream of the jet and had an equal width z=2.35d (refer to figure

4a). The height of the lower and upper region was 0.62d and 0.53d. In Figure 4b, the jet fluid is represented in red,while free stream flowing through the upper region is denoted by blue, and free stream through the lower region is in

green. The shape of fluid flow is constituted by numerous streamlines that is uniformly distributed in the tworegions. The cross stream fluid originating from both the regions wraps around the jet fluid as they both come in

contact. x-z cross sections (not shown here) indicate that the blue region marked by the free stream fluid does not

penetrate the jet fluid until z=0.09. The free stream region marked in blue is convected along with the jet fluid andfollows the jet trajectory. The formation of the CVP provides a higher contact area between the free stream region

marked in blue and the jet fluid. This enhances mixing between the jet and cross steam. The free stream fluid

originating from the region closer to the wall has a different behavior. Interestingly, the free stream fluid marked ingreen flows around the jet, part of it is convected up into the jet and the other part diverges like a fan following the

3.2d


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0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6

X/d

Y/d

Case1 (r=8.45,d=10.92mm, Re=63000)

Case2 (r=4.97,d=10.92mm, Re=63000)

Case3 (r=8.38,d=9.398mm, Re=74000)

Case4 (r=4.96,d=9.398mm, Re=74000)

Case5 (r=8.55,d=4.648mm, Re=60000,Fr=00)

Case6 (r=5.37,d=4.648mm, Re=60000)

Yuan & Street(d=13.84mm, r=2,Re=2100, Fr=00)

Yuan & Street(d=13.84mm, r=2,Re=2100, Fr=10)

Yuan & Street(d=13.84mm, r=3.3Re=1050, Fr=00)

Yuan & Street(d=13.84mm, r=3.3,Re=2100, Fr=00)

Su & Mugal (r=5.7,d=4.53mm, meanturbulent, Re=5000)

streamwise direction behind the jet wake. Figure 4c shows the interaction of the jet and free stream at four constant-

x slices. The observations made in the figure 4b are supported by the y-z planes. The free stream region marked by

green shows one mechanism of mixing encountered in JICF where the free stream flow in the jet wake is convected

up into the jet fluid through wake-upright vortices. The other mixing mechanism involves the free stream fluid

which is carried along by the jet stream and follows the jet trajectory. As the CVP grow in size there is highercontact area between the jet and the free stream that enables molecular mixing between the two streams.

3.2 Trajectories

Different definitions have been used to track the jet trajectory in experiments. Depending on the flow diagnostictechnique either the local velocity maxima (Kamotani and Greber17) or the local scalar concentration maxima (Smith

and Mungal6). The latter definition is usually showed to have about 5~10% deeper penetration into the flow than

the former one (Haniu and Ramaprian18). Other definitions such as streamline originating from the center of the jet

exit on the symmetry plane have been used by Yuan and Street12and Muppidi and Mahesh14. They justify using this

definition, since both the maximum velocity and scalar concentration has multiple maxima at the jet exit. In thecurrent work, the jet trajectory is defined as locus of maximum velocity in the center plane. In Figure 5 a-c,

trajectories of all 6 cases are plotted with three different normalizations: d, rd and r2d. Trajectories from experiments

and simulations of other researchers are also compared. Figure 5a shows the jet trajectory normalized by d. The d-scaled plot shows that the jet penetrates deeper into the cross stream for cases 1, 3 and 5 where r ~8.5 when

compared to case 2, 4 and 6 with r~5. The data from Yuan and street 13 simulations at r=2 and 3.3, Su and Mungal 19at r=5.7 and Pratte and Baines9experiments are included. Two issues become clear from the d scaled plots: 1) the

data does not collapse for the different r and higher r is associated with larger jet penetration into the cross stream.Figure 5b shows the jet trajectory normalized by rd. The data curves seem to bifurcate. The difference between the

bifurcating branches arises from Re in both the present data and other previously published JICF trajectories. The

higher Reynolds numbers (Re>2500) show a larger jet penetration and follow on the top branch, while the lower set

of curves relate to Re


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0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.5 1 1.5 2 2.5 3

x/rd

y/rd

Su & Mungal PIV (r=5.7,d=4.53mm,mean turbulent, Re=5000)

Case1 (r=8.45, d=10.92mm,Re=63000)

Case3 (r=8.38, d=9.398mm,Re=74000)

Case2 (r=4.97, d=10.92mm,Re=63000)

Case5 (r=8.55, d=4.648mm,Re=60000)

Case4 (r=8.38, d=9.398mm,Re=74000)

Case6 (r=5.37, d=4.648mm,Re=60000)

Roth et al (r=6)

Roth et al (r=4)

Smith & Mungal (scaledcoefficient=1.4)

Smith & Mungal (scaledcoefficient=1.8)

Yuan & Street (d=13.84mm, r=2,Re=2100, Fr=00)

Yuan & Street (d=13.84mm, r=2,Re=2100, Fr=10)

Yuan & Street (d=13.84mm, r=3.3,Re=1050, Fr=00)

Yuan & Street (d=13.84mm, r=3.3,Re=2100, Fr=00)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.1 0.2 0.3

x/r2

d

y/r2d

Su & Mungal PIV (r=5.7,d=4.53mm, mean turbulent,

Re=5000)Case1 (r=8.45, d=10.92mm,Re=63000)

Case2 (r=4.97, d=10.92mm,Re=63000)

Case3 (r=8.38, d=9.398mm,Re=74000)

Case4 (r=4.96, d=9.398mm,Re=74000)

Case5 (r=8.55, d=4.648mm,Re=60000)

Case6 (r=5.37, d=4.648mm,Re=60000)

Yuan & Street (r=2,d=13.84mm, Re=2100,

Fr=00)Yuan & Street (r=2,d=13.84mm, Re=2100,

Fr=10)Yuan & Street (r=3.3,d=13.84mm, Re=1050,

Fr=00)Yuan & Street (r=3.3,

d=13.84mm, Re=2100,Fr=00)

(b)

(c)

Figure 5: Jet Trajectories with different scaling (a) d, (b) rd and (c) r2d.

3.3 Comparison between Experimental and Computational Results

2D time averaged flow field computed from PIV measurements on the Z=0 center plane are compared with the

computational results for all six cases. The data shows a good match in predicting the entire flow field. Details forCase 3 alone are shown in this manuscript. Side views on symmetrical center plane of the velocity magnitude

contours and streamlines are shown in figure 6 a and b. The simulations predict the entrainment of the free streaminto the jet flow, the existence of nodes and the stagnation region on the leeward and windward side close to the

injection wall. The potential core in the simulation was found to be 10% smaller in experiments when compared tothe simulations. This indicates that the jet centerline decays faster with experiments than simulations.


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-0.2

0

0.2

0.4

0.6

0.8

1

-0.12 -0.02 0.08 0.18 0.28 0.38

X/rd

V/Vmax

computation

experiment

-0.2

0

0. 2

0. 4

0. 6

0. 8

1

1. 2

-0.12 -0.02 0.08 0.18 0.28 0.38

X/rd

V/Vma

x computation

experiment

(a) (b)

Figure. 6 Side view of the velocity magnitude contour with streamlines on symmetrical center plane. a)

experimental; b) Numerical

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.2 -0.1 -0.1 0.0 0.1 0.1 0.2 0.2

X/rd

V/Vmax

experiment

computation

(a)

(b) (c)


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-0.1

0.1

0.3

0.5

0.7

0.9

-0.12 -0.02 0.08 0.18 0.28 0.38

X/rd

V/Vmax experiment

computation

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-0.12 -0.02 0.08 0.18 0.28 0.38

X/rd

V/Vmax

computation

experiment

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

X/rd

Y/rd

Case1 experiment

Case2 experiment

Case3 experiment

Case1 simulation

Case2 simulation

Case3 simulation

(d) (e)

Figure. 7: The Y velocity profile at jet exit vicinity region: a) Y=0, b) Y=0.13rd, b) Y=0.25rd, c) Y=0.38rd, d)

Y=0.51rd

Figure. 8: Comparison of Jet Trajectory from Experiments and Simulations

In order to validate the simulations, the flow field near the jet exit region is compared quantitatively between thecomputations and the experiments. Figure 7 shows a series of y velocities profiles at y=0, 0.13, 0.25, 0.38 and

0.51rd. The y velocity profiles are normalized by rd. The results show a good agreement with each other in the near

field. Further downstream, the peak velocity shifts to the right indicating that the jet begins to bend. Also evident in

these figures is the broadening on the leeward side of the jet along the vertical direction, since the jet begins to mixwith the cross stream. The jet trajectory is also compared for cases1-3. The simulations agree fairly well with the

experiments. Figure 9 shows the windward and leeward boundaries from the simulations. The boundaries of the jet

are identified as 40% of the maximum jet velocity. Case 1 and 3 shows very similar jet upper and lower boundarytrajectories, possibly due to the small variation between actual r and d between these cases. The trajectory in case 2

does not match with case 1 and 3. In all cases, the jet width becomes narrow until the end of the potential core

(y


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magnitude, Vmmax/Vm, as a function of the normalized distance. Two different regimes are noticed; the higher r

cases (case 1, 3 and 5) collapse on to one set and lower r (cases 2, 4 and 6) collapse onto the lower set. The slopes

were computed for both the curves in the regions (1.2


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Figure 12 displays the width of the jet boundary for case 3. The boundary was defined as 40% of the maximum

velocity on the jet trajectory, s, on the center plane. The width of the boundary is measured on the perpendicular to

the jet trajectory. The variation of the width of the boundary displays a converging-diverging tendency. Theboundary was found to converge until the end of the potential core; past the potential core the jet tends to spread.

The plot of turbulent kinetic energy (TKE) contour on the center plane is showed in Figure 14 for cases 2 and 3.

The TKE is scaled by the square of the jet exit velocity. The turbulence is most strong at the windward jet shearlayer at the nozzle exit in both the cases. The high turbulent intensity (TKE>0.025) apparently follows the

streamlines that pass at the vicinity of the jet exit edge. The high TKE produced on the windward shear layer arises

from the shear layer eddies created by the Kelvin-Helmholtz instability, and the impingement of the cross flowstream on the jet flow at the windward side. A plot of the turbulent kinetic energy along the jet trajectory is shown in

Figure14 for all 6 cases. The TKE is normalized by the square of the jet velocity and the distance, s, is normalized

by rd. The TKE reaches its peak at about 1 rd, and it rapidly decreases to very low magnitude after a distance of 2

rd. This is mainly because the trajectory (locus of maximum velocity) crosses over the highest TKE about Z=1rd

and then continues to remain be above the higher TKE trajectory.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.5 1 1.5 2

S/rd

Width/rd Case1

Case2

Case3

Figure 12. The width between leeward and rearward boundary variation along the trajectory, normalized by

rd for case3.

(a) (b)

Figure 13. Turbulent kinetic energy contour on the center plane(Y=0) with two streamlines passing the edges

of jet exit. (a) Case 2; (b) Case 3


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0

0.005

0.01

0.015

0.02

0.025

0.03

0 1 2 3 4 5 6

S/rd

TKE/UjUj

Case1, r=8.45, d=10.92mm, Re=63000

Case2, r=4.97, d=10.92mm, Re=63000

Case3, r=8.38, d=9.398mm, Re=74000

Case4, r=4.96, d=9.398mm, Re=74000

Case5, r=4.96, d=9.398mm, Re=60000

Case6, r=5.37, d=4.648mm, Re=60000

Figure 14. Turbulent kinetic energy variations along the trajectory, non-dimensionalized by rd

4.5 Recirculation bubble

Figure 15a-f describes the characteristics of the recirculation bubble that forms behind the jet in case 3. Figure 15a

shows the contours of static pressure on the center plane (Y=0). A high pressure region exists in front of the jet and

acts as a driving force to bend the jet . It also has a region of negative pressure behind the jet exit, generating a

reverse flow in the jet wake. This negative pressure region stretches into the jet nozzle when the blowing ratio issmall, extending the reversed flow into the nozzle. LES of Yuan et al13and DNS of Muppidi and Mahesh14also

observed reverse flow inside the pipe at low blowing ratio (r0 is calculated by integrating the cell volumes. The resultsindicate that, lower blowing ratio or higher free stream velocity generates smaller recirculation region. There is

almost an order of magnitude increase in recirculation bubble volume when the jet diameter is increased by a factor

of 2. This could be observed when we compare case 3and 5 at the higher blowing ratio or case 4 and 6 at the lowerblowing ratio.

Figure 15f, g gives a comparison of recirculation bubble in 2D for case 3 between experiment and numerical

simulation. In terms of X and Y range, this region is smaller in experiment possibly due to minor differences in the

blowing ratio and upstream flow conditions between computations and experiments.


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Table 2

r d(mm) Length/rdLength

(m) Width/rdWidth(m) Volume(mm

3

)

Case1 8.45 1.349 0.1245 0.331 0.03059 3.214E-05

Case2 4.9710.922

1.393 0.07561 0.4 0.02172 1.249E-05

Case3 8.38 1.328 0.1046 0.327 0.02574 2.168E-05

Case4 4.969.398

1.352 0.06303 0.406 0.01891 9.280E-06

Case5 8.55 1.318 .05221 0.412 0.01636 2.760E-06

Case6 5.374.648

1.212 0.03024 0.385 0.0096 8.350E-07

(a) (b)

(c) (d)


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(e) (f )

Figure. 15a-f , Structure of recirculation Bubble for case 3. (a) Static pressure contour on the center plane;(b) The relative position of 3D recirculation bubble in red color with in contrast with jet fluid in green color;

(c) 3D close view of the recirculation bubble; (d)The dimension to compare on the side view. 2D recirculation

bubble for case 3: (e) experimental result;(f) numerical result.

V. Conclusion

Numerical simulations of a turbulent circular jet exhausting into cross flow, were performed using commercialFLUENT Software. The simulations were conducted for a range of jet nozzle diameters and blowing ratio. The

computational results were validated by a quantitative comparison with corresponding 2D Particle Image

Velocimetry data.The time averaged flow field was analyzed using 3-D stream shape embodied by streamline of finite thickness.

The evolution of jet fluid and its interaction with the cross flow was clearly identified in these simulations. The free

stream fluid was found to follow two different trajectories depending on where it originates. The cross stream fluid

closer to the wall gets entrained from the bottom up into the CVP. The fluid stream originating above the wallboundary layer follows the jet trajectory and wraps around the jet fluid. The fanning motion of the free stream flow

originating close to the wall was also observed as noticed by many experimental observations (Fric and Roshko1,

Smith and Mungal6). The cross sectional slices along the jet trajectory indicate that the CVP convolute and grow in

size thereby increasing the interfacial contact between the jet and cross stream fluid which enable mixing betweenthe two streams.

The jet trajectory was normalized by d, rd and r2d. They are also compared with other published experimental

and computational data. All the three scaling laws causes bifurcation and the effect of Reynolds number seems to bean important factor that causes the split in scaling. An examination and categorization of the magnitude of Reynolds

number is therefore necessary to obtain better scaling law.

Velocity decay, jet width and turbulent kinetic energy along the trajectories were also studied. Under the

existence of cross flow, circular jet decays much faster than a free jet. The slope of the decay was found to be 44%

higher with larger r (~8.5) as compared to smaller r (~5). The TKE along the shear layer indicates that the windwardturbulence is higher than the leeward side.

The shape, size of the recirculation bubble behind the jet was also presented. Reversible flow upstream of the

jet and in the jet wake was identified. Negative flow velocities were also detected inside the pipe. The projected

X (rd)

Y

(rd)

0 0.2 0.4 0.60

0.2

0.4

0.6

0.8

U

-0.505806

-1.68742-2.86903-4.05065

-5.23226-6.41387-7.59548

-8.7771-9.95871-11.1403

-12.3219-13.5035-14.6852

-15.8668-17.0484-18.23

X (rd)

Y

(rd)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

U

-2-4

-6-8

-10-12

-14-16

-18-20-22

-24-26


16/17


16

length and width of the recirculation bubble was found to scale well with rd. The volume of the recirculation bubble

was found to increase with increasing jet diameter. The recirculation bubble was found be smaller with lower

blowing ratios or higher free stream velocity.

Acknowledgements

The authors would like to greatly appreciate R. DiMicco and R. Ogden for their support in laboratory; HerveMazieres from Fluent France for their help in CFD; Irene Ibrahim for sharing her experimental data.

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cfd numerical simulation and experiments of jets in cross.pdf

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