Chaos: Applications of Stirring and Mixing. Guy Metcalfe

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1 Three Stories from the Commercialization of Chaos: Applications of Stirring and Mixing Guy Metcalfe CSIRO Australia

2 Physics of Mixing

3 Agenda 1. (A) Industrial Mixing 1. (B) Heat Exchange 2. Reaction/Extraction Porous Media 3. Bounded Steady 3D Chaotic Flow (for delicate suspensions) In Use In Discussion Too New to Tell

4 Agenda 1. (A) Industrial Mixing 1. (B) Heat Exchange 2. Reaction/Extraction Porous Media 3. Bounded Steady 3D Chaotic Flow (for delicate suspensions) In Use In Discussion Too New to Tell Simplicity Periodic Reorientation and Symmetry Boundary Driven Flows and Energy Use Global l Optima over Control Parameters and Rapidity are Important Idiosyncratic

5 Low Reynolds Number Processing Re = V L inertia ν viscous

6 Low Reynolds Number Processing Re = V L inertia ν viscous Food, polymers, etc

7 Low Reynolds Number Processing Re = V L inertia ν viscous Food, polymers, etc Geology, shear sensitive

8 Low Reynolds Number Processing Re = V L inertia ν viscous Food, polymers, etc Geology, shear sensitive Microfluidics, some biological Applied Fluid Chaos in Complex Physical, Biophysical and Econophysical Systems, World Scientific Lecture Notes in Complex Systems (2010)

9 RAM Schematic

10 Rotated Arc Mixer Transverse Flow Analytic Computation Experiment solution

11 RAM parameters Example of a Periodically Reoriented Flow Ratio of rotational to axial timescales = L / U

12 Periodically odca Reoriented e Flow

13 Laboratory Scale RAM Mixers

14 Experiment View from Upstream

15 Global Chaos Flow direction

16 KAM Tubes Flow direction

17 Experiment - End View Laser sheet cut near RAM outlet Initial condition: Dyed plane of blobs at RAM inlet

18 Dye Advection N=0 N=2 N=4 N=6 N=8 N=10

19 Performance and Power Consumption pto AIChE J. 52 (2006)

20 Performance and Power Consumption pto P (RAM) = 1 P (mixer) 5 P (RAM) = 1 P (mixer) 30 AIChE J. 52 (2006)

21 Fat Pipes = Lower Power Consumption o P ax /L = 8Q 2 v πr4 μ 2R = 10 cm J. Food Eng. 95 (2009)

22 Fat Pipes for Heat Exchange? P ax /L = 8Q 2 v πr4 μ Energy reduction favours fat pipes, but a fat pipe has smaller surface to volume ratio. Is viscous heat exchange amenable to chaotic enhancement?

23 HEAT TRANSPORT Organized motion (stirring) of the flow; and, Disorganized motion (diffusion) of molecular agitation. T + v(χ ) T = 1 2T t n Pe P e pure advection Pe 0 pure diffusion Pe = UL D

24 HEAT TRANSPORT T t +v(χ ) T = 1 2T n Pe T = n a n ψ n (x, t)e σ n t T ψ 0 Persistent t Spatial Pattern Pierrehumbert (1994), Gollub et al (1999), Liu & Haller (2004)

25 The Global Parametric Solution Pe = 10 4

26 Symmetry-Locked Tongues τ Θ Pe = 10 4

27 Asymmetry as Stretching Increases Pe = 10 4

28 Periodic odc Stretching, Folding, od and Healing 0 /5 /5 /5 /5

29 Show Movie

30 RAM heat exchanger

31 Selected ected Patterns at some Peclet et numbers P e =

33 Temperature Homogenization Energy Consumption P/L Open Pipe RAM 1 1 P total Newtonian non-newtonian q max =

34 Geophysical Transport: Minerals, Geothermal Energy, Water Prommer & Stuyfzand, Enviro. Sci. Tech. 2005

35 Abstract From Field to Laboratory ato

36 Abstract From Field to Laboratory ato

37 Reoriented Potential Mixing (RPM) Flow (Metcalfe et al, Phil. Trans. Roy. Soc. A, 2010, Lester et al, Phys. Rev. E, 2009) Parallel Streamlines and Darcy flow:

38 Reoriented Potential Mixing (RPM) Flow Metcalfe et al, Phil. Trans. Roy. Soc. A, 2010, Lester et al, Phys. Rev. E, 2009) Parallel Streamlines and Darcy flow: Reorientation gives chaos governed by symmetry: Jones & Aref 1988 Evans, et al 1997 Stremler & Cola 2006 τ, Θ

39 Time-Averaged Streamfunction, or the unperturbed Hamiltonion H = 1 N R Φ dt τ,, Θ Flow Symmetry + Periodic Reorientation = Lagrangian Symmetry

40 Symmetry y Geometry symmetry coincides with time-reversed flow Applied Fluid Chaos in Complex Physical, Biophysical i and Econophysical Systems, vol. 9 World Scientific Lecture Notes in Complex Systems (2010)

41 Islands in the Stream: a Partially a Open Flow

42 Periodic Reorientation Induces Reversal Reflection Symmetry y Θ/2 x L

43 Periodic Reorientation Induces Reversal Reflection Symmetry y R 1(L) Θ/2 Θ/2 x L

44 Periodic Reorientation Induces Reversal Reflection Symmetry y R 1(L) Θ/2 Θ/2 φ(r 1(L)) x (r, Θ/2) L

45 Darcy acyflow Hele-Shaw ees Flow u(x,y) = -(K/η) P (x, y) u(x,y) = -(b2/(12η)) P (x, y) permeability ~ height

46 Stirred Hele-Shaw e Experiment e

47 Disk Exit-Time Distribution Without Stirring

48 Steady Flow Experiment: No reorientation time Simulations Experiments

49 Exit Time Distribution

50 Trapping Sub-Surface Fluid (Metcalfe et al, Phil. Trans. Roy. Soc. A, 2010, Lester et al, Phys. Rev. E, 2009, 2010) Experiment: Computation:

51 Island sa Existence

52 Island sa Existence

53 Periodically odca Reoriented e Dipole poe Mixing

54 Periodically odca Reoriented e Dipole poe Mixing

55 Periodically odca Reoriented e Dipole poe Mixing

56 Periodically odca Reoriented e Dipole poe Mixing

57 Periodically odca Reoriented e Dipole poe Mixing

58 Periodically odca Reoriented e Dipole poe Mixing

59 Periodically odca Reoriented e Dipole poe Mixing

60 Periodically odca Reoriented e Dipole poe Mixing

61 Homogenization Rate (Activate Entire Reservoir) Time Between Reorientations Reorientation Angle

62 Many Questions s on Path to Use Heterogeneity Regional Flows 3-Dimensional Effects Scale Up and Field Studies

$random fractal$ field which

63 Subsurface Stirring Heterogeneity is modeled by a random fractal permeability field which mimics uranium-bearing sandstone. Uranium concentration is negatively correlated with permeability. Log(conductivity) U concentration Injection wells Extraction wells

64 Constant and Stirred Pumping Protocols Constant pressure drop between the injection and extraction wells serves as a benchmark for testing the impact of stirring. The stirred protocol uses transient switching of pressure to invoke an oscillatory flow with the same energy consumption. P/ P constant P Consta ant P P/ P constant t/t cycle Injection wells Extraction wells Stirred t/t cycle

65 Constant Pumping Flow

66 Constant Pumping ISL Results

67 Stirred Pumping Flow

68 Stirred Pumping ISL Results

69 Stirred vs Constant Pumping Uranium Yield (%) Uranium Extraction Rate (%) # fluid volumes # fluid volumes Stirred pumping generates faster extraction of Uranium, with 75% of ore removed 60% faster. Haque [6] shows a 50% increase in extraction rate increases IRR of typical ISL operation from 40% to 68% More detailed modeling and laboratory/field testing is required [6] Haque et. al., Techno-Economic Evaluation of In-Situ Leaching of Uranium Deposits, CSIRO Internal Report, MDU Flagship, May 2009.

70 Geophysical Stirring w/ Background Flow

71 3D Flow Inside Spherical Shell w/ Sectorial Boundary Motion Type I Type II

72 3D Flow Inside Spherical Shell w/ Sectorial Boundary Motion Analytical Velocity Field Experimentally Realizable Type I Type II

73 Type I

74 Type II

75 Operate Steady State or with Periodic Reorientation

76 Conclusions cuso s Three examples of applications of stirring and mixing One example of chaos plus Different stages of commercial development and use Energy savings can be large over conventional. Everything may be known, but applications abound Users usually do not know they need physics of mixing. Science collaborators also may not know they need physics of mixing.

77 Physics of Mixing

78 Champaign pag Polidori et al, American Scientist 2009 (University of Reims, France)

79 Champaign pag Polidori et al, American Scientist 2009 (University of Reims, France)

80 Applications abound. The enterprising physicist of mixing should seize her chances.

81 Acknowledgements e A/Prof Michel Speetjens, TUE Prof Jeff Morris, CCNY-Levich Institute Dr Pandurang Kulkarni, UCSB Dr Andrew Brydon, Washington Uni, St Louis Prof Richard Manasseh, Swinburne Uni CSIRO Funding: Complex Systems Science Initiative Advanced Engineered Components Theme Minerals Down Under Flagship Dr Murray Rudman Dr Daniel Lester Dr Alison Ord Dr Klaus Regenauer-Lieb Dr Mike Trefry Dr Bruce Hobbs Dr Yonggang Zhu Dr Lachlan Graham Dr Karolina Petkovic-Duran Industry Funding: Advanced Manufacturing CRC VCAMM Tasweld Engineering

82 CSIRO Materials Science & Engineering Applied Fluid Chaos Dr. Guy Metcalfe Phone: +61 (3) Web: Thank you Contact Us Phone: or enquiries@csiro.au Web:

Moving walls accelerate mixing

Moving walls accelerate mixing Jean-Luc Thiffeault Department of Mathematics University of Wisconsin Madison Uncovering Transport Barriers in Geophysical Flows Banff International Research Station, Alberta