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Effect of Jet Configuration on Transverse            Jet Mixing Process     Sin Hyen Kim, Yonduck Sung, Venkat Raman       ...
Outline• Introduction• Objectives• DNS of Jet in Crossflow• Results and Discussion  ➡ Effect of Jet Velocity Profile  ➡ Eff...
Introduction : Transverse jet • Transverse jet consist of crossflow and main jet                      Crossflow            ...
Flow Structure in a Transverse Jet• Transverse jet involves complex flow interaction• Four major vortical structures  ➡ Cou...
Complexity of Vortical Structure772      Phys. Fluids, Vol. 13, No. 3, March 2001                                         ...
Jet Mixing Control Parameter • Velocity ratio results in higher trajectory and more efficient mixing • Thicker crossflow bou...
Objectives • How to enhance mixing by simple modification  ➡ Effect of jet velocity profile  ➡ Effect of jet geometry • Met...
DNS of Jet in Crossflow
Schematic view                             • Velocity ratio = V /V                                                jet   cr...
Fig. 1 shows a schematic of the problem. The incompressible flows a Fig. 1 showstheschematicThethe problem.The continuity a...
Computational Detail• Domain : 512 x 256 x 256• Domain size ~26D x 13D x 13D• Low Mach-number flow solver  with energy cons...
Grid convergence test• Tested three grid set to validate  the result from 512x256x256 ➡ 256x128x128 ➡ 512x256x256 ➡ 1024x5...
Mean passive scalar field             256                   1 rsd = 0.5 sec                                   2 rsd512    ...
Grid convergence                   Passive scalar                                    x/D = 3                              ...
Grid convergence                                                             U                            256             ...
Computational cost comparison                  256         512          1024   grid cells   4 million   33 million   268 m...
Results and Discussion  1. Effect of Jet Velocity Profile  2. Effect of Jet Shape
Effect of Jet Velocity Profile                                            • For circular jet                              ...
Jet Evolution Dynamics• Contour of passive scalar http://www.youtubeloop.com/v/5eTsmNMJ9RQ                                ...
Mean Trajectory• Mean trajectory based on mean velocity field       Mean trajectory           Mean passive scalar contour
Trajectory Comparison                         6                         5                         4                   y/D ...
Mixing along centerline trajectory      • Passive scalar along the mean trajectoryMean passive scalar along the trajectory...
Evolution of vorticity        http://www.youtubeloop.com/v/1LD-tO20hiM                                               Parab...
Coherency bet ween Eddy break-up and Turbulent Mixing    http://www.youtubeloop.com/v/1LD-tO20hiM                         ...
Effect of Jet Exit Shape  • Four different geometries were chosen for comparison              u∞  Crossflow               ...
Jet Evolution Dynamics• Contour of passive scalar http://www.youtubeloop.com/v/5eTsmNMJ9RQ   http://www.youtubeloop.com/v/...
Circle (p)Coherent structures                                               Circle    http://www.youtubeloop.com/v/1LD-tO2...
Flow Structure in a Transverse Jet• Four major vortical structures  ➡ Counter-rotating vortex pair (CVP)  ➡ Horseshoe vort...
Circle (p)Coherent structures                                                Circle     http://www.youtubeloop.com/v/Wx3A7...
SquareCoherent structures                                                Square     http://www.youtubeloop.com/v/AQ65AaIPK...
Triangle 1Coherent structures                                             Triangle                                        ...
Triangle 2 Coherent structures                                                   Triangle                                 ...
SquareCONTROL WITH N                                                                                                      ...
Instability caused by collision of vortices • Head-on-collision of two vortex rings Lim, T. T.  Nickels, T.B (1992).  Inst...
Triangle 1Coherent structures         Triangle     Triangle             1            2
Trajectory Comparison                                                        6                                            ...
Mixing along centerline trajectory          • Passive scalar along the mean trajectory  Mean passive scalar along the traj...
Near-Field Flow Evolution• Mean passive scalar contour                                Triangle            Circle          ...
Near-Field Flow Evolution• Mean passive scalar contour           One source of CVP    Two sources of CVP                  ...
Near-Field Flow Evolution• Mean passive scalar contour                                More entrainment by the leading vort...
Near-Field Flow Evolution• Mean passive scalar contour                                Two vortices merged                 ...
Statistical measure of mixing • Mean of mixture fraction • Variance • Intensity of segregation
Circular (parabolic)                              CircleMean of mixture   fraction                  Variance              ...
Circular (tophat)                             CircleMean of mixture   fraction                  Variance                  ...
Square                              SquareMean of mixture   fraction                  Variance                            ...
Upstream Triangle                                    Triangle                                        1Mean of mixture   fr...
Downstream Triangle                                    Triangle                                        2Mean of mixture   ...
Mixture fraction       14                                                                                                 ...
Variance                    3             x 10        3                                                                   ...
Intensity of segregation                - shows level of variance normalized by its maximum at given mixture fraction     ...
Summary of effect of jet geometry • There are some differences in the near-field behavior  ➡ Triangle 1 had the highest tra...
Conclusion• Effect of transverse-jet geometry was studied  ➡ Jet exit geometry cause minor impact on overall    mixing pro...
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Jet in crossflow mixing

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Jet in crossflow mixing

  1. 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. 2. Outline• Introduction• Objectives• DNS of Jet in Crossflow• Results and Discussion ➡ Effect of Jet Velocity Profile ➡ Effect of Jet Exit Shape• Conclusions
  3. 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. 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. 5. Complexity of Vortical Structure772 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 CVPLim et al, “On the development of large-scale structures of a jet normal to a cross flow”, Phys of Fuild (2001),Vol. 13, pp 770upstream vortices and the lee-side vortices, respectively.
  6. 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. 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. 8. DNS of Jet in Crossflow
  9. 9. Schematic view • Velocity ratio = V /V jet crossflow = 1.52 • Laminar crossflowVcrossflow • Rejet = 3000 u∞ Crossflow s y z x Jet Vjet D
  10. 10. Fig. 1 shows a schematic of the problem. The incompressible flows 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 giverving 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 jhere φ is the scalar mass-fraction and D is the scalar diffusivity, wh
  11. 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. 12. Grid convergence test• Tested three grid set to validate the result from 512x256x256 ➡ 256x128x128 ➡ 512x256x256 ➡ 1024x512x512 y x jet
  13. 13. Mean passive scalar field 256 1 rsd = 0.5 sec 2 rsd512 1024 2 rsd ~0.65 rsd
  14. 14. Grid convergence Passive scalar x/D = 3 256 512 1024
  15. 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. 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. 17. Results and Discussion 1. Effect of Jet Velocity Profile 2. Effect of Jet Shape
  18. 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. 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. 20. Mean Trajectory• Mean trajectory based on mean velocity field Mean trajectory Mean passive scalar contour
  21. 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. 22. Mixing along centerline trajectory • Passive scalar along the mean trajectoryMean passive scalar along the trajectory Variance of mean passive scalar along the trajectory 1 0.15 Parabolic Parabolic Top-hat Top-hat0.8 0.10.60.4 0.050.2 0 5 10 15 20 5 10 15 20 x/D x/D
  23. 23. Evolution of vorticity http://www.youtubeloop.com/v/1LD-tO20hiM Parabolic Top-hat Evolution of iso-surface of vorticity, contoured by passive scalarInteraction between the jet flow and the crossflow The vortex ring disturbs the jet flow as it comes outcause this thin “vortex shield” to increase in magnitude Deflects the jet flow as soon as it comes out = LOWER TRAJECTORY
  24. 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. 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. 26. Jet Evolution Dynamics• Contour of passive scalar http://www.youtubeloop.com/v/5eTsmNMJ9RQ http://www.youtubeloop.com/v/mrfaa8bzk4s Triangle Circle 1
  27. 27. Circle (p)Coherent structures Circle http://www.youtubeloop.com/v/1LD-tO20hiM http://www.youtubeloop.com/v/Wx3A73QGSNE Vorticity Q-criterion
  28. 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. 29. Circle (p)Coherent structures Circle http://www.youtubeloop.com/v/Wx3A73QGSNE http://www.youtubeloop.com/v/xJcsHYU8Et8Hangingvortex Wake Q-criterion Mixture fraction
  30. 30. SquareCoherent structures Square http://www.youtubeloop.com/v/AQ65AaIPKH4 http://www.youtubeloop.com/v/jkC7BZ7Y2GEHangingvortex Q-criterion Mixture fraction
  31. 31. Triangle 1Coherent structures Triangle 1 http://www.youtubeloop.com/v/F5t68NWPe4U http://www.youtubeloop.com/v/jkC7BZ7Y2GE Hanging vortex Q-criterion Mixture fraction
  32. 32. Triangle 2 Coherent structures Triangle 2 http://www.youtubeloop.com/v/1Q6sh9TBcjk http://www.youtubeloop.com/v/_-QIzG3zxGw HangingHorseshoe vortex vortices Q-criterion Mixture fraction
  33. 33. SquareCONTROL WITH N FLOWComparison 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. 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. 35. Triangle 1Coherent structures Triangle Triangle 1 2
  36. 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. 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 0.06SC-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. 38. Near-Field Flow Evolution• Mean passive scalar contour Triangle Circle 1
  39. 39. Near-Field Flow Evolution• Mean passive scalar contour One source of CVP Two sources of CVP Triangle Circle 1
  40. 40. Near-Field Flow Evolution• Mean passive scalar contour More entrainment by the leading vortex Triangle Circle 1
  41. 41. Near-Field Flow Evolution• Mean passive scalar contour Two vortices merged together Triangle Circle 1
  42. 42. Statistical measure of mixing • Mean of mixture fraction • Variance • Intensity of segregation
  43. 43. Circular (parabolic) CircleMean of mixture fraction Variance Intensity of segregation
  44. 44. Circular (tophat) CircleMean of mixture fraction Variance Intensity of segregation
  45. 45. Square SquareMean of mixture fraction Variance Intensity of segregation
  46. 46. Upstream Triangle Triangle 1Mean of mixture fraction Variance Intensity of segregation
  47. 47. Downstream Triangle Triangle 2Mean of mixture fraction Variance Intensity of segregation
  48. 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 8A/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. 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 0.04A/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. 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 0.2A/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. 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. 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

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