jet in crossflow mixing

Effect of Jet Configuration on Transverse Jet Mixing Process

Sin Hyen Kim, Yonduck Sung, Venkat Raman

Department of Aerospace Engineering and Engineering MechanicsThe University of Texas at Austin

Outline• Introduction

• Objectives

• DNS of Jet in Crossflow

• Results and Discussion

➡ Effect of Jet Velocity Profile

➡ Effect of Jet Exit Shape

• Conclusions

Introduction : Transverse jet

• Transverse jet consist of crossflow and main jet

➡Can be found in many engineering applications

- Combustion chamber, chemical reactor

➡ How do we enhance mixing using transverse-jet?

Crossflowstream

Jet

T.H.New et al, “Elliptic jets in cross-flow”, J of Fluid Mech. (2003), vol. 494, pp 119

Flow Structure in a Transverse Jet

• Transverse jet involves complex flow interaction

• Four major vortical structures

➡Counter-rotating vortex pair (CVP)

➡Horseshoe vortices

➡Jet shear layer vortices

- Leading-edge vortices

- Lee-side vortices

➡Wake vortices

Complexity of Vortical Structure

upstream vortices and the lee-side vortices, respectively.

These vortices resemble a ‘‘daisy chain’’ of interlocking

loops, which are similar to the buoyant jet structures ob-

served by Perry and Lim.41 What is interesting about these

loop vortices is that they were not produced by the bending

or folding of the vortex rings, as some researchers were led

to believe. In fact, there is no evidence of vortex rings in any

of our studies. This observation has also been made by Yuan

et al.27 in their large eddy simulation of a round jet in cross

flow.

To better understand how these loop vortices evolved,

video images of the flow field were replayed in slow motion.

They show that as soon as the cylindrical vortex sheet !seealso Fig. 1" emerged from the nozzle, it immediately folded

up on its edges to form a CVP. This finding is consistence

with the experimental observation of Kelso et al.,15 and the

large-eddy simulation of Yuan et al.27 Furthermore, it was

found that the CVP played a significant role in preventing

the cylindrical vortex sheet, which contains ‘‘circular’’ vor-

tex lines, from rolling up into vortex rings. This is in contrast

to the free jet, where the absence of CVP allows the vortex

sheet to roll up ‘‘axisymmetrically’’ into vortex rings. In the

case of JICF, the vortex sheet can roll up freely only at the

upstream and the lee-side of the jet column since the CVP

suppresses similar roll up at the two sides. This scenario

gives rise to two rows of loop vortices separated by the CVP

at the sides. Close examination shows that this formation

process is similar to the buoyant jet structures observed by

Perry and Lim,41 although the details are different. During

the folding of the vortex sheet, the fluid that originated from

the nozzle remained within the cylindrical boundary, and

there was no indication of holes or openings in the original

vortex sheet. This feature is clearly illustrated in Fig. 2,

where the jet fluid, which had been premixed with fluores-

FIG. 3. Authors’ interpretation of the

finally developed vortex structures of

JICF. !a" The sketch shows how the

‘‘arms’’ of both the upstream and the

lee-side vortex loops are merged with

the counter-rotating vortex pair. !b"Cross sectional views of !a" taken atvarious streamwise distances. Note

their close resemblance with the laser

cross sections of the jet depicted in

Fig. 5.

FIG. 4. Detailed sketches of the proposed model. !a" The sketch shows howthe vortex loops give rise to the resultant Section B-B. !b" Section E-E alongthe deflected jet centerline in the streamwise direction. This sketch repre-

sents the laser cross section of JICF depicted in Fig. 2.

772 Phys. Fluids, Vol. 13, No. 3, March 2001 Lim, New, and Luo

Downloaded 13 Nov 2008 to 146.6.102.83. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp

Lim et al, “On the development of large-scale structures of a jet normal to a cross flow”, Phys of Fuild (2001), Vol. 13, pp 770

Crossflowstream

Jet

Initiation of CVP

Jet Mixing Control Parameter

• Velocity ratio results in higher trajectory and more efficient mixing

• Thicker crossflow boundary layer results in higher trajectory, but less efficient mixing

• What is the effect of jet configuration?

Objectives• How to enhance mixing by simple modification

➡Effect of jet velocity profile

➡Effect of jet geometry

• Methodology

➡Perform direct numerical simulation (DNS) of passive scalar mixing process in a transverse jet

DNS of Jet in Crossflow

Schematic view

• Velocity ratio = Vjet/Vcrossflow = 1.52

• Laminar crossflow

• Rejet = 3000

z x

y

u∞

Crossflow

Jet

s

D

Vjet

Vcrossflow

Governing Equations

Figure 1: A sketch of a crossflow jet system.

The motivation for this work is the optimization of a crossflow chemical reactor. The reactants,contained in the two jets, react with infinitely fast chemistry. However, the product can further reactwith one of the reactants to produce secondary unwanted products. Optimization of this systemwill require minimization of the secondary reactions caused mainly by the recirculation producedat the lower-wall. Consequently, the main jet velocity compared to the crossflow jet should be highenough to ensure that the product trajectory is high above the lower boundary flow, and shouldcarry sufficient momentum to ensure rapid mixing. However, this increased velocity will alsoincrease the power requirements and pressure losses thereby increasing the operating costs. Theobjective of this study is to determine if modifiying the jet exit shape can enhance mixing rates atlower velocity ratios while still limiting the secondary reactions. Two different jet exit shapes, asquare and circular shape, are compared to determine mixing patterns.

B. Direct numerical simulation of crossflow jets

Fig. 1 shows a schematic of the problem. The incompressible flow equations are solved using anenergy conserving numerical scheme. The continuity and momentum equations are given by

∂uj

∂xj= 0

∂ui

∂t+

∂uiuj

∂xj=

1

ρ

�−∂P

∂xi+

∂τij

∂xj

�, (1)

where ui is the velocity component, ρ is the constant fluid density, P is the local pressure, and τij

is the viscous stress tensor.τij = −2

3µ

∂uk

∂xkδij + 2µSij, (2)

Sij =1

2

�∂ui

∂xj+

∂uj

∂xi

�, (3)





∂uj

∂xj= 0

∂ui

∂t+

∂uiuj

∂xj=

1

ρ

�−∂P

∂xi+

∂τij

∂xj

�, (1)



3µ

∂uk


Sij =1

2

�∂ui

∂xj+

∂uj

∂xi

�, (3)





∂uj

∂xj= 0

∂ui

∂t+

∂uiuj

∂xj=

1

ρ

�−∂P

∂xi+

∂τij

∂xj

�, (1)



3µ

∂uk


Sij =1

2

�∂ui

∂xj+

∂uj

∂xi

�, (3)where µ is the constant fluid viscosity. To study mixing in these jets, a passive scalar was also

evolved along with the flow equations.

∂φ

∂t+

∂ujφ

∂xj=

∂

∂xj

�D

∂φ

∂xj

�, (4)

where φ is the scalar mass-fraction and D is the scalar diffusivity, which was assumed to be the

same as the fluid viscosity.

The above equations were solved using a finite-volume projection-based solver. The convection

terms in the momentum equations were discretized using a second-order energy conserving central

scheme. The convection term in the scalar transport equation was discretized using a third-order

upwind-biased scheme. This upwind bias was necessary to reduce unphysical oscillations in the

scalar transport equation. The viscous and diffusion terms were discretized using a second-order

central scheme. The time advancement is based on a semi-implicit predictor-corrector algorithm.

The computational domain spans 26D× 13D× 13D, where D is the diameter of the main jet. The

jet Reynolds number was fixed at 5000 while the main flow Reynolds number was set to 1500,

yielding a velocity ratio of 1.52. This particular ratio was chosen so that direct comparison with

prior experiments could be carried out for validation purposes. To resolve the smallest length-

scales in the flow, over 30 million computational points (512 × 256 × 256) were required. To

capture the near-field dynamics, the grid was clustered in all directions close to the jet entrance.

The focus of this study is the effect of jet exit shape on mixing. For this purpose, both the incoming

crossflow and the main jet were assumed to be laminar. The crossflow boundary layer thickness

just before the main jet entrance was approximately equal to the jet diameter for all the studies

considered. For the square jet, the inlet area was set such that the mass flow rate is equal to that of

the circular exit case.

All computations were carried out on massively parallel computers. A domain decomposition

strategy using an MPI-based distributed computing paradigm was used. Separate studies demon-

strated that the code scales efficiently up to 512 processors. The simulations performed here used

between 128 and 512 processors and were carried out on the Lonestar computing system operated

by the Texas Advanced Computing Center (TACC). Each simulation took roughly 20 hours from

start to completion for over the five residence times.

C. Results and Discussion

The discussion below is based on steady state profiles obtained from the two simulations involving

a circular jet and a square jet. The simulations were carried out long enough to ensure that statistics

were stationary. Here, the flow behavior is analyzed using the vorticity and passive-scalar evolution

fields.

Fluid vorticity provides an excellent measure of the large-scale fluid circulation in turbulent flows.

Here, the vorticity is computed from the steady-state three-dimensional velocity fields. Essentially,

this Reynolds-averaged computation of vorticity will indicate the regions of large-scale recircula-

tion that are responsible for jet breakup and mixing. This vorticity field is shown in Fig. 2 for both

jet exit shapes. All crossflow jets exhibit a horseshoe vortex pattern, seen in Fig. 2, on the floor

from which the main jet is issuing. This feature represents the strong curvature of the crossflow

Incompressible Navier Stokes Equation

Passive scalar transport equation

jet

yx

Computational Detail

• Domain : 512 x 256 x 256

• Domain size ~26D x 13D x 13D

• Low Mach-number flow solver with energy conserving method

• Massive parallel computation

➡ MPI based parallelization

➡ 512 CPUs and 24 hours

➡ ≈130 Gb of data per simulation

jet

yx

Grid convergence test

• Tested three grid set to validate the result from 512x256x256

➡ 256x128x128

➡ 512x256x256

➡ 1024x512x512

Mean passive scalar field256

512 1024

1 rsd = 0.5 sec

~0.65 rsd2 rsd

2 rsd

Grid convergence

2565121024

x/D = 3

Passive scalar

Grid convergence

2565121024 x/D = 0.75

U

Urms

y/D

0 0.2 0.4 0.6 0.80

1

2

3

4

U

y/D

-0.5 0 0.5 1 1.50

1

2

3

4

Computational cost comparison

256 512 1024grid cells 4 million 33 million 268 million

data size 0.170 Gb 1.3 Gb 11 Gb

CPU 16 512 512

hours ? 24 150 hrs

SU’s ~1000 ~12,000 73,600

Results and Discussion

1. Effect of Jet Velocity Profile

2. Effect of Jet Shape

Effect of Jet Velocity Profile

z x

y

u∞

Crossflow

Jet

s

D

• For circular jet

➡ Parabolic velocity profile

➡ Top-hat velocity profile

• With the same boundary condition

➡ Equal volume rate from the jet

➡ Laminar crossflow

➡ Fully developed laminar velocity profile with the Vmean = 1.52 m/s

Parabolic Top-hat

Top-hat

Jet Evolution Dynamics

Parabolic

• Top-hat velocity profile exhibits large-scale vortical structures

➡ Vortex break-down is slower

➡ Hence, mixing is slower

• Contour of passive scalar

http://www.youtubeloop.com/v/5eTsmNMJ9RQ

http://www.youtube.com/watch?v=5eTsmNMJ9RQ


Mean Trajectory• Mean trajectory based on mean velocity field

Mean trajectory Mean passive scalar contour

x/D

y/D

5 10 150

1

2

3

4

5

6

Parabolic

Top-hat

Trajectory Comparison

• Parabolic velocity profile has higher trajectory

➡ Less interference with the boundary layer downstream of the jet exit

x/D

5 10 15 200

0.05

0.1

0.15

Mixing along centerline trajectory

x/D5 10 15 20

0.2

0.4

0.6

0.8

1

Parabolic

Top-hat

• Passive scalar along the mean trajectory

Mean passive scalar along the trajectory Variance of mean passive scalar along the trajectory

Parabolic

Top-hat

Evolution of iso-surface of vorticity, contoured by passive scalar

Parabolic Top-hat

Evolution of vorticity

The vortex ring disturbs the jet flow as it comes outDeflects the jet flow as soon as it comes out => LOWER TRAJECTORY

Interaction between the jet flow and the crossflowcause this thin “vortex shield” to increase in magnitude

http://www.youtubeloop.com/v/1LD-tO20hiM



Coherency between Eddy break-up and Turbulent Mixing

Parabolic Top-hat

Evolution of iso-surface of vorticity, contoured by passive scalar

• Parabolic velocity profile has higher and efficient mixing because of vortex “shield” at the leading edge

• Top-hat velocity profile entrains larger amount of the crossflow, forming large vortical structure at earlier stage

➡ Vortical structure break down more slowly

http://www.youtubeloop.com/v/1LD-tO20hiM



z x

y

u∞

Crossflow

Jet

s

D

Effect of Jet Exit Shape• Four different geometries were chosen for comparison

• With the same boundary condition

➡ Equal volume rate from the jet

➡ Laminar crossflow

➡ Fully developed laminar velocity profile with the Vmean = 1.52 m/s

Circle SquareTriangle

1Triangle

2D

Jet Evolution Dynamics

CircleTriangle

1

• Contour of passive scalar

http://www.youtubeloop.com/v/5eTsmNMJ9RQ http://www.youtubeloop.com/v/mrfaa8bzk4s





Coherent structuresCircle (p)

Circle

Vorticity Q-criterion

http://www.youtubeloop.com/v/1LD-tO20hiM http://www.youtubeloop.com/v/Wx3A73QGSNE





T.H.New et al, “Elliptic jets in cross-flow”, J of Fluid Mech. (2003), vol. 494, pp 119

Flow Structure in a Transverse Jet

• Four major vortical structures

➡Counter-rotating vortex pair (CVP)

➡Horseshoe vortices

➡Jet shear layer vortices

- Leading-edge vortices

- Lee-side vortices

➡Wake vortices

Coherent structuresCircle (p)

Circle

Q-criterion Mixture fraction

Wake

Hanging vortex

http://www.youtubeloop.com/v/Wx3A73QGSNE http://www.youtubeloop.com/v/xJcsHYU8Et8





Coherent structuresSquare

Square

Hanging vortex


http://www.youtubeloop.com/v/AQ65AaIPKH4 http://www.youtubeloop.com/v/jkC7BZ7Y2GE





Coherent structuresTriangle 1

Triangle 1

Hanging vortex


http://www.youtubeloop.com/v/F5t68NWPe4U http://www.youtubeloop.com/v/jkC7BZ7Y2GE






Triangle 2

Hanging vortexHorseshoe

vortices


http://www.youtubeloop.com/v/1Q6sh9TBcjk http://www.youtubeloop.com/v/_-QIzG3zxGw





Comparison with free jetSquare

Square

P1: NBL/mbg/spd P2: NBL/ary QC: ARS

November 16, 1998 17:1 Annual Reviews AR075-07

FLOW CONTROL WITH NONCIRCULAR JETS 265

Figure 14 Interacting ring and braid vortices for low-AR rectangular free jets with AR= 1.Instantaneous visualizations at two consecutive times based on vorticity isosurfaces and vortex

lines. (Grinstein & DeVore 1996)

Strong interactions with braid vortices and other rings can inhibit axis rotations

of nonisolated rings, which do not recover shape and flatness after the initial

self-deformation.

In the square jet case (Grinstein & DeVore 1996), for example, braid (hair-

pin) vortices induce flow ejection at the corner regions and flattening of the

ring portions left behind after the initial ring self-deformation (Figure 14), and

this mechanism leads to the second axis rotation of the jet cross-section. This

is in contrast with the self-induced axis-rotation dynamics of isolated rings, a

process in which ring shape and flatness are approximately recovered. In terms

of jet spreading along characteristic directions, axis rotations first require faster

growth on the flat sides (s-direction) and shrinking along the vertex direction

(d-direction) so that crossover of jet widths along ‘s’ and ‘d’ is possible. The

self-distortion of the corner regions of the vortex ring is the mechanism under-

lying the initial shrinking along ‘d,’ depending directly on the local azimuthal

curvature C and thickness σ (according to Equation 1). The dependence of

An

nu

. R

ev.

Flu

id M

ech

. 1

99

9.3

1:2

39

-27

2.

Do

wn

load

ed f

rom

arj

ou

rnal

s.an

nu

alre

vie

ws.

org

by

Un

iver

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of

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as -

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stin

on

09

/30

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or

per

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al u

se o

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.

jet in crossflow Square jet without crossflow

Grinstein et al, “Dynamics of coherent structures and trasitioin to turbulence in free square jets”, Phys of Fuild (1996), Vol. 8, pp 1244

Instability caused by collision of vortices• Head-on-collision of two vortex rings

Lim, T. T. & Nickels, T.B (1992). Instability and reconnection in the head-on collision of two vortex rings. NATURE, Vol. 357.


Triangle 1

Triangle 2

x/D

y/D

0 5 10 150

1

2

3

4

5

6

CircleSquareTriangle 1Triangle 2

Trajectory Comparison

Contour of passive scalar with mean trajectory

Trajectory

• Passive scalar along the mean trajectory

x/D

SC-ZMIX

0 5 10 150.00

0.20

0.40

0.60

0.80

1.00


x/D

Var

0 5 10 150.00

0.02

0.04

0.06

0.08

0.10


Mean passive scalar along the trajectory Variance of mean passive scalar along the trajectory

Near-field Far-field

Mixing along centerline trajectory

Near-Field Flow Evolution

CircleTriangle

1

• Mean passive scalar contour

One source of CVP Two sources of CVP

CircleTriangle

1

Near-Field Flow Evolution• Mean passive scalar contour

More entrainment by the leading vortex

CircleTriangle

1


CircleTriangle

1

Two vortices merged together


Statistical measure of mixing

•Mean of mixture fraction

•Variance

• Intensity of segregation

Circular (parabolic)

Variance

Intensity of segregation

Circle

Mean of mixture fraction

Circular (tophat)

Variance


Circle


Square

Variance


Square



Upstream Triangle

Variance


Triangle 1

Downstream Triangle

Variance


Triangle 2


Mixture fraction

0 5 10 150

2

4

6

8

10

12

14

s/D

A/A o

Circle(parabolic)Circle(tophat)SquareTri1Tri2

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s/D

Mea

n of

Zm

ix w

ithin

the

jet b

ound

ary


Area variation (Zmix>0.05) Mean of mixture fraction

Variance

0 5 10 150

0.5

1

1.5

2

2.5

3x 10 3

s/D

A/A o


0 5 10 150.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

s/D

Mea

n of

Var

with

in th

e je

t bou

ndar

y


Area variation (Var>0.01) Mean of variance

0 5 10 150

5

10

15

20

25

30

35

40

s/D

A/A o


0 5 10 150

0.05

0.1

0.15

0.2

0.25

0.3

0.35

s/D

Mea

n of

Int o

f Seg

with

in th

e je

t bou

ndar

y


Intensity of segregation- shows level of variance normalized by its maximum at given mixture fraction

Area variation (Int. Seg>0.01) Mean of intensity of segregation

Summary of effect of jet geometry• There are some differences in the near-field behavior

➡ Triangle 1 had the highest trajectory and the most entrainment

➡ Core of triangle 2 had the slowest jet breakdown

• In the far-field, all jets behave identically

• Jet shape effect is confined only to the near-field

➡ Even in the near-field, the jet shape effect is not as much significant as the one in free jet

Triangle 1

Triangle 2

Conclusion• Effect of transverse-jet geometry was studied

➡Jet exit geometry cause minor impact on overall mixing process

➡For circular jet, velocity profile affects both trajectory and mixing condition

- Parabolic jet has higher trajectory and develops more favorable condition for turbulent mixing by interacting with the crossflow

- Top-hat jet entrains the crossflow earlier in near-field, but mixing is slower

jet in crossflow mixing

Business

transverse jet transverse

jet fluid

round jet

jet column

main jet

free jet

effect of jet configuration

vortex loops