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Mechanics of Wall Turbulence

Mechanics of Wall Turbulence. Parviz Moin Center for Turbulence Research Stanford University. Classical View of Wall Turbulence. Mean Velocity Gradients  Turbulent Fluctuations Predicting Skin Friction was Primary Goal. Classical View of Wall Turbulence.

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Mechanics of Wall Turbulence

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  1. Mechanics of Wall Turbulence Parviz Moin Center for Turbulence Research Stanford University

  2. Classical View of Wall Turbulence • Mean Velocity Gradients  Turbulent Fluctuations • Predicting Skin Friction was Primary Goal

  3. Classical View of Wall Turbulence • Eddy Motions Cover a Wide Range of Scales • Energy Transfer from Large to Smaller Scales • Turbulent Energy Dissipated at Small Scales

  4. Major Stepping Stones • Visualization & Discovery of Coherent Motions • Low-Speed Streaks in “Laminar Sub-Layer” • Kline, Reynolds, Schraub and Runstadler (1967) • Kim, Kline and Reynolds (1970) • Streaks Lift-Up and Form Hairpin Vortices • Head and Bandyopadhyay (1980) Large Eddies in a Turbulent Boundary Layer with Polished Wall, M. Gad-el-Hak

  5. Low-Speed Streaks in “Laminar Sub-Layer”Kline, Reynolds, Schraub and Runstadler (1967) y+ ≈ 4 • Three-Dimensional, Unsteady Streaky Motions • “Streaks Waver and Oscillate Much Like a Flag” • Seem to “Leap Outwards” into Outer Regions

  6. BurstsKim, Kline and Reynolds (1970) • Streaks “Lift-Up” Forming a Streamwise Vortex • Near-Wall Reynolds Shear Stress Amplified • Vortex + Shear  New Streaks/Turbulence

  7. Major obstacle for LES • Streaks and wall layer vortices are important to the dynamics of wall turbulence • Prediction of skin friction depends on proper resolution of these structures • Number of grid points required to capture the streaks is almost like DNS, N=cRe2 • SGS models not adequate to capture the effects of missing structures (e.g., shear stress).

  8. Early Hairpin Vortex ModelsTheodorsen (1952) • Spanwise Vortex Filament Perturbed Upward (Unstable) • Vortex Stretches, Strengthens, and Head Lifts Up More (45o) • Modern View = Theodorsen + Quasi-Streamwise Vortex

  9. Streaks Lift-Up and Form Hairpin VorticesHead and Bandyopadhyay (1980) Reθ = 1700 • Hairpins Inclined at 45 deg. (Principal Axis) • First Evidence of Theodorsen’s Hairpins

  10. Streaks Lift-Up and Form Hairpin VorticesHead and Bandyopadhyay (1980) • For Increasing Re, Hairpin Elongates and Thins • Streamwise Vortex Forms the Hairpin “Legs”

  11. Forests of HairpinsPerry and Chong (1982) • Theodorsen’s Hairpin Modeled by Rods of Vorticity • Hairpins Scattered Randomly in a Hierarchy of Sizes • Reproduces Mean Velocity, Reynolds Stress, Spectra • Has Difficulty at Low-Wavenumbers

  12. Packets of HairpinsKim and Adrian (1982) • VLSM Arise From Spatial Coherence of Hairpin Packets • Hairpin Packets Align & Form Long Low-Speed Streaks (>2δ)

  13. Packets of HairpinsKim and Adrian (1982) • Extends Perry and Chong’s Model to Account for Correlations Between Hairpins in a Packet; this Enhanced Reynolds Stress Leads to Large-Scale Low-Speed Flow

  14. Major Stepping Stones • Computer Simulation of Turbulence (DNS/LES) • A Simulation Milestone and Hairpin Confirmation • Moin & Kim (1981,1985), Channel Flow • Rogers & Moin (1985), Homogeneous Shear • Zero Pressure Gradient Flat Plate Boundary Layer (ZPGFPBL) • Spalart (1988), Rescaling & Periodic BCs • Spatially Developing ZPGFPBL • Wu and Moin (2009)

  15. A Simulation MilestoneMoin and Kim (1981,1985) ILLIAC-IV

  16. A Simulation MilestoneMoin and Kim (1981,1985) LES Experiment

  17. A Simulation MilestoneMoin and Kim (1981,1985)

  18. Hairpins Found in LESMoin and Kim (1981,1985) • “The Flow Contains an Appreciable Number of Hairpins” • Vorticity Inclination Peaks at 45o • But, No Forest!?!

  19. Shear Drives Hairpin GenerationRogers and Moin (1987) • Homogeneous Turbulent Shear Flow Studies Showed that Mean Shear is Required for Hairpin Generation • Hairpins Characteristic of All Turbulent Shear Flows • Free Shear Layers, Wall Jets, Turbulent Boundary Layers, etc.

  20. Spalart’s ZPGFPBL and PeriodicitySpalart (1988) • TBL is Spatially-Developing, Periodic BCs Used to Reduce CPU Cost • Inflow Generation Imposes a Bias on the Simulation Results • Bias Stops the Forest from Growing!

  21. Analysis of Spalart’s DataRobinson (1991) • “No single form of vortical structure may be considered representative of the wide variety of shapes taken by vortices in the boundary layer.” • Identification Criteria and Isocontour Subjectivity • Periodic Boundary Conditions Contaminate Solution

  22. Computing Power 5 Orders of Magnitude Since 1985! Advanced Computing has Advanced CFD (and vice versa)

  23. DNS of Turbulent Pipe FlowWu and Moin (2008) 256(r) x 512(θ) x 512(z) 300(r) x 1024(θ) x 2048(z) Re_D = 5300 Re_D = 44000

  24. Very Large-Scale Motions in PipesWu and Moin (2008) DNS at ReD = 24580, Pipe Length is 30R (Black) -0.2 < u’ < 0.2 (White) Log Region (1-r)+ = 80 Buffer Region (1-r)+ = 20 Core Region (1-r)+ = 270

  25. Experimental energy spectrum Experiment, using T.H. Perry & Abell (1975)‏ Energy Wavelength

  26. Energy Spectrum from Simulations Experiment, using T.H. Perry & Abell (1975)‏ Simulation, true spectrum del Álamo & Jiménez (2009)‏ Energy Wavelength

  27. Artifact of Taylor's Hypothesis Experiment, using T.H. Perry & Abell (1975)‏ Simulation, true spectrum del Álamo & Jiménez (2009)‏ Energy Simulation, using T.H. del Álamo & Jiménez (2009)‏ Wavelength

  28. Artifact of Taylor's Hypothesis Experiment, using T.H. Perry & Abell (1975)‏ Aliasing Simulation, true spectrum del Álamo & Jiménez (2009)‏ Energy Simulation, using T.H. del Álamo & Jiménez (2009)‏ Wavelength

  29. Simulation of spatially evolving BLWu and Moin (2009) • Simulation Takes a Blasius Boundary Layer from Reθ = 80 Through Transition to a Turbulent ZPGFPBL in a Controlled Manner • Simulation Database Publically Available: • http://ctr.stanford.edu

  30. Blasius Boundary Layer + Freestream Turbulence t = 100.1T t = 100.2T 4096 (x), 400 (y), 128 (z) t = 100.55T

  31. Isotropic Inflow Condition

  32. Validation of Boundary Layer Growth Blasius Monkewitzet al Blasius

  33. Validation of Skin Friction Blasius

  34. Validation of Mean Velocity Murlis et al Spalart Reθ = 900

  35. Validation Mean Flow Through Transition Reθ = 200 Reθ = 800 Circle: Spalart

  36. Validation of Velocity Gradient Circles: Spalart (Exp.) Triangles: Smith (Exp.) Dotted Line: Nagib et al. (POD) Solid Line: Wu & Moin (2009)

  37. Validation of RMS Through Transition Circle: Spalart Reθ = 800 Reθ = 200

  38. Validation of RMS fluctuations circle: Purtell et al other symbols: Erm & Joubert Reθ = 900

  39. Validation of RMS Fluctuations Circle: Purtell et al Plus: Spalart Lines: Wu & Moin

  40. Total stress through transition Plus: Reθ = 200 Solid Line: Reθ = 800

  41. Near-Wall Stresses Total Stress Circle: Spalart Viscous Stress

  42. Shear Stresses Circle: Honkan & Andreopoulos Diamond: DeGraaff & Eaton Plus: Spalart

  43. Immediately beforebreakdown t = 100.55T u/U∞ = 0.99

  44. HairpinPacket at t = 100.55 T Immediately Before Breakdown

  45. Winner of 2008 APS Gallery of Fluid Motion

  46. Summary • Preponderance of Hairpin-Like Structures is Striking! • A Number of Investigators Had Postulated The Existence of Hairpins • But, Direct Evidence For Their Dominance Has Not Been Reported in Any Numerical or Experimental Investigation of Turbulent Boundary Layers • First Direct Evidence (2009) in the Form of a Solution of NS Equations Obeying Statistical Measurements

  47. Summary-II • Forests of Hairpins is a Credible Conceptual Reduced Order Model of Turbulent Boundary Layer Dynamics • The Use of Streamwise Periodicity in channel flows and Spalart’s Simulations probably led to the distortion of the structures • In Simulations of Wu & Moin (JFM, 630, 2009), Instabilities on the Wall were Triggered from the Free-stream and Not by Trips and Other Artificial Numerical Boundary Conditions • Smoke Visualizations of Head & Bandyopadhyay Led to Striking but Indirect Demonstration of Hairpins Large Trips May Have Artificially Generated Hairpins

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