The document summarizes a study on the effect of jet configuration on transverse jet mixing. Direct numerical simulations were performed to analyze the effect of jet velocity profile and exit shape. Results show that a parabolic velocity profile enhances mixing over a top-hat profile due to slower vortex breakdown. For exit shape, a circular jet exhibits the most efficient mixing while triangular jets display two counter-rotating vortex pairs that increase entrainment and mixing.

1. Effect of Jet Configuration on Transverse
Jet Mixing Process
Sin Hyen Kim, Yonduck Sung, Venkat Raman
Department of Aerospace Engineering and Engineering Mechanics
The University of Texas at Austin

2. Outline
• Introduction
• Objectives
• DNS of Jet in Crossflow
• Results and Discussion
➡ Effect of Jet Velocity Profile
➡ Effect of Jet Exit Shape
• Conclusions

3. Introduction : Transverse jet
• Transverse jet consist of crossflow and main jet
Crossflow
stream
Jet
➡ Can be found in many engineering applications
- Combustion chamber, chemical reactor
➡ How do we enhance mixing using transverse-jet?

4. 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
T.H.New et al, “Elliptic jets in cross-flow”, J of Fluid Mech. (2003), vol. 494,

5. Complexity of Vortical Structure
772 Phys. Fluids, Vol. 13, No. 3, March 2001 Lim, New,
FIG. 3. Authors’ interpretati
finally developed vortex stru
JICF. a The sketch shows
‘‘arms’’ of both the upstream
Crossflow lee-side vortex loops are me
stream the counter-rotating vortex
Cross sectional views of a
various streamwise distanc
their close resemblance with
cross sections of the jet de
Fig. 5.
Jet
Initiation of CVP
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
upstream vortices and the lee-side vortices, respectively.

6. 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?

7. 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

8. DNS of Jet in Crossflow

9. Schematic view
• Velocity ratio = V /V
jet crossflow = 1.52
• Laminar crossflow
Vcrossflow
• Rejet = 3000
u∞
Crossflow s
y
z x
Jet
Vjet
D

10. Fig. 1 shows a schematic of the problem. The incompressible flow
s a Fig. 1 showstheschematicThethe problem.The continuity and are solve
schematic of a conserving numerical scheme. The incompressible flow
energy problem. of incompressible flow equations momentu
Governing Equations scheme. momentum equations are giv
erving numerical scheme. The continuity andThe continuity and moment
energy conserving numerical
∂uj
∂uj =0
=0 ∂xj
∂uj
∂ui ∂xji uj
∂u 1 ∂P ∂x ij= 0
∂τ
∂ui ∂ui uj 1 ∂P + ∂τ = − + j ,
∂t ∂xj
ij ρ ∂xi ∂xj
Incompressible Navier= ρ∂u−+ ∂ui uj j 1 − ∂P + ∂τij ,
∂t
+
∂xj i
∂xi
+
∂x =
,
where ui is the velocity ∂t
Stokes Equation component, jρ is the constantifluid∂xj
∂x ρ ∂x density,
he velocity is the viscousρ is the constant fluid density, P is the local pressu
component, stress tensor.
2 ∂uk
s stress tensor. the velocity component, ρ is the− µ
where ui is τij = constantijfluid density
δ + 2µSij ,
2 ∂uk 3 ∂xk
is the viscous stressijtensor. µ
τ =− δij + 2µSij ,
here µ is the constant fluid viscosity. To study 1mixing+in these jets
3 ∂xk 2 ∂u∂ui ∂uj
k
τij = −= µ ∂x ij +∂x ij ,
S
ij 2 δ 2µS,
olved along with the flow equations. ∂uj
1 ∂ui 3 ∂xk j i
Sij = + ,
2 ∂xj
∂φ ∂uijφ=
∂xi 1 ∂ ∂ui ∂φ
∂uj
Passive scalar transport + Sj = + ,
∂t ∂xj 2∂x∂xjD ∂x i ,
∂x
equation j j
here φ is the scalar mass-fraction and D is the scalar diffusivity, wh

11. 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 y
x
➡ ≈130 Gb of data per simulation
jet

12. Grid convergence test
• Tested three grid set to validate
the result from 512x256x256
➡ 256x128x128
➡ 512x256x256
➡ 1024x512x512
y
x
jet

13. Mean passive scalar field
256 1 rsd = 0.5 sec
2 rsd
512 1024
2 rsd ~0.65 rsd

14. Grid convergence
Passive scalar
x/D = 3
256
512
1024

15. Grid convergence
U
256
512
x/D = 0.75
1024
4 4
3 3
y/D
y/D
2 2
1 1
0 0
-0.5 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8
U Urms

16. Computational cost comparison
256 512 1024
grid 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

17. Results and Discussion
1. Effect of Jet Velocity Profile
2. Effect of Jet Shape

18. Effect of Jet Velocity Profile
• For circular jet
➡ Parabolic velocity profile
u∞ ➡ Top-hat velocity profile
Crossflow s
• With the same boundary condition
y
z x
Jet
D ➡ Equal volume rate from the jet
➡ Laminar crossflow
➡ Fully developed laminar velocity profile
with the Vmean = 1.52 m/s
Parabolic Top-hat

19. Jet Evolution Dynamics
• Contour of passive scalar
http://www.youtubeloop.com/v/5eTsmNMJ9RQ
Top-hat
Parabolic
• Top-hat velocity profile exhibits large-scale vortical structures
➡ Vortex break-down is slower
➡ Hence, mixing is slower

20. Mean Trajectory
• Mean trajectory based on mean velocity field
Mean trajectory Mean passive scalar contour

21. Trajectory Comparison
6
5
4
y/D
3
2
Parabolic
1
Top-hat
0
5 10 15
x/D
• Parabolic velocity profile has higher trajectory
➡ Less interference with the boundary layer downstream of the jet exit

22. Mixing along centerline trajectory
• Passive scalar along the mean trajectory
Mean passive scalar along the trajectory Variance of mean passive scalar along the trajectory
1
0.15
Parabolic Parabolic
Top-hat Top-hat
0.8
0.1
0.6
0.4 0.05
0.2
0
5 10 15 20 5 10 15 20
x/D x/D

23. Evolution of vorticity
http://www.youtubeloop.com/v/1LD-tO20hiM
Parabolic Top-hat
Evolution of iso-surface of vorticity, contoured by passive scalar
Interaction between the jet flow and the crossflow The vortex ring disturbs the jet flow as it comes out
cause this thin “vortex shield” to increase in magnitude Deflects the jet flow as soon as it comes out
= LOWER TRAJECTORY

24. Coherency bet ween Eddy break-up and Turbulent Mixing
http://www.youtubeloop.com/v/1LD-tO20hiM
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

25. Effect of Jet Exit Shape
• Four different geometries were chosen for comparison
u∞
Crossflow s
Triangle Triangle
y
Circle D Square
1 2
z x
Jet
D
• 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

26. Jet Evolution Dynamics
• Contour of passive scalar
http://www.youtubeloop.com/v/5eTsmNMJ9RQ http://www.youtubeloop.com/v/mrfaa8bzk4s
Triangle
Circle 1

27. Circle (p)
Coherent structures
Circle
http://www.youtubeloop.com/v/1LD-tO20hiM http://www.youtubeloop.com/v/Wx3A73QGSNE
Vorticity Q-criterion

28. 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
T.H.New et al, “Elliptic jets in cross-flow”, J of Fluid Mech. (2003), vol. 494,

29. Circle (p)
Coherent structures
Circle
http://www.youtubeloop.com/v/Wx3A73QGSNE http://www.youtubeloop.com/v/xJcsHYU8Et8
Hanging
vortex
Wake
Q-criterion Mixture fraction

30. Square
Coherent structures
Square
http://www.youtubeloop.com/v/AQ65AaIPKH4 http://www.youtubeloop.com/v/jkC7BZ7Y2GE
Hanging
vortex
Q-criterion Mixture fraction

31. Triangle 1
Coherent structures
Triangle
1
http://www.youtubeloop.com/v/F5t68NWPe4U http://www.youtubeloop.com/v/jkC7BZ7Y2GE
Hanging
vortex
Q-criterion Mixture fraction

32. Triangle 2
Coherent structures
Triangle
2
http://www.youtubeloop.com/v/1Q6sh9TBcjk http://www.youtubeloop.com/v/_-QIzG3zxGw
Hanging
Horseshoe vortex
vortices
Q-criterion Mixture fraction

33. SquareCONTROL WITH N
FLOW
Comparison with free jet
999.31:239-272. Downloaded from arjournals.annualreviews.org
of Texas - Austin on 09/30/09. For personal use only.
Square jet in crossflow Square jet without crossflow
Figure 14 Interacting ring and braid vortices for low-AR
Instantaneous visualizations at two consecutive times based
lines. (Grinstein DeVore 1996)
Grinstein et al, “Dynamics of coherent structures and trasitioin to
turbulence in free square jets”, Phys of Fuild (1996),Vol. 8, pp 1244

34. 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.

35. Triangle 1
Coherent structures
Triangle Triangle
1 2

36. Trajectory Comparison
6
5
Trajectory 4
y/D 3
2
Circle
Square
1 Triangle 1
Contour of passive scalar with mean trajectory Triangle 2
0
0 5 10 15
x/D

37. Mixing along centerline trajectory
• Passive scalar along the mean trajectory
Mean passive scalar along the trajectory Variance of mean passive scalar along the trajectory
1.00 0.10
Circle Circle
Square Square
0.80 Triangle 1 0.08 Triangle 1
Triangle 2 Triangle 2
0.60 0.06
SC-ZMIX
Var
0.40 0.04
0.20 0.02
0.00 0.00
0 5 10 15 0 5 10 15
x/D x/D
Near-field Far-field

38. Near-Field Flow Evolution
• Mean passive scalar contour
Triangle
Circle 1

39. Near-Field Flow Evolution
• Mean passive scalar contour
One source of CVP Two sources of CVP
Triangle
Circle 1

40. Near-Field Flow Evolution
• Mean passive scalar contour
More entrainment by the leading vortex
Triangle
Circle 1

41. Near-Field Flow Evolution
• Mean passive scalar contour
Two vortices merged
together
Triangle
Circle 1

42. Statistical measure of mixing
• Mean of mixture fraction
• Variance
• Intensity of segregation

43. Circular (parabolic)
Circle
Mean of mixture
fraction
Variance
Intensity of segregation

44. Circular (tophat)
Circle
Mean of mixture
fraction
Variance
Intensity of segregation

45. Square
Square
Mean of mixture
fraction
Variance
Intensity of segregation

46. Upstream Triangle
Triangle
1
Mean of mixture
fraction
Variance
Intensity of segregation

47. Downstream Triangle
Triangle
2
Mean of mixture
fraction
Variance
Intensity of segregation

48. Mixture fraction
14 1
Circle(parabolic)
Circle(tophat)
0.9 Square
12 Tri1
0.8 Tri2
Mean of Zmix within the jet boundary
10 0.7
0.6
8
A/Ao
0.5
6
0.4
4 0.3
Circle(parabolic)
Circle(tophat) 0.2
2 Square
Tri1 0.1
Tri2
0 0
0 5 10 15 0 5 10 15
s/D s/D
Area variation (Zmix0.05) Mean of mixture fraction

49. Variance
3
x 10
3 0.06
Circle(parabolic) Circle(parabolic)
Circle(tophat) Circle(tophat)
Square 0.055 Square
Tri1 Tri1
2.5
Tri2 0.05 Tri2
Mean of Var within the jet boundary
0.045
2
0.04
A/Ao
1.5 0.035
0.03
1
0.025
0.02
0.5
0.015
0 0.01
0 5 10 15 0 5 10 15
s/D s/D
Area variation (Var0.01) Mean of variance

50. Intensity of segregation
- shows level of variance normalized by its maximum at given mixture fraction
40 0.35
Circle(parabolic)
Circle(tophat)
35 Square
0.3 Tri1
Tri2
Mean of Int of Seg within the jet boundary
30
0.25
25
0.2
A/Ao
20
0.15
15
0.1
10
Circle(parabolic)
Circle(tophat)
Square 0.05
5
Tri1
Tri2
0 0
0 5 10 15 0 5 10 15
s/D s/D
Area variation (Int. Seg0.01) Mean of intensity of segregation

51. Summary of effect of jet geometry
• There are some differences in the near-field behavior
➡ Triangle 1 had the highest trajectory and the most Triangle
1
entrainment
➡ Core of triangle 2 had the slowest jet breakdown Triangle
2
• 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

52. 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