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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. - PowerPoint PPT Presentation
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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
• Eddy Motions Cover a Wide Range of Scales– Energy Transfer from Large to Smaller Scales– Turbulent Energy Dissipated at Small Scales
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
Low-Speed Streaks in “Laminar Sub-Layer”Kline, Reynolds, Schraub and Runstadler (1967)
• Three-Dimensional, Unsteady Streaky Motions– “Streaks Waver and Oscillate Much Like a Flag”– Seem to “Leap Outwards” into Outer Regions
y+ ≈ 4
Bursts
Ki
m,
Kline
and
Reynolds (1970)
• Streaks “Lift-Up” Forming a Streamwise Vortex
• Near-Wall Reynolds Shear Stress Amplified• Vortex + Shear New Streaks/Turbulence
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).
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
Streaks Lift-Up
and
Form
Hairpin
Vortices
Head
and
Bandyopadhyay (1980)
• Hairpins Inclined at 45 deg. (Principal Axis)• First Evidence of Theodorsen’s Hairpins
Reθ = 1700
Streaks Lift-Up
and
Form
Hairpin
Vortices
Head
and
Bandyopadhyay (1980)
• For Increasing Re, Hairpin Elongates and Thins• Streamwise Vortex Forms the Hairpin “Legs”
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
Packets of HairpinsKim and Adrian (1982)
• VLSM Arise From Spatial Coherence of Hairpin Packets• Hairpin Packets Align & Form Long Low-Speed Streaks (>2δ)
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
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)
A Simulation MilestoneMoin and Kim (1981,1985)
ILLIAC-IV
A Simulation MilestoneMoin and Kim (1981,1985)
LES
Experiment
A Simulation MilestoneMoin and Kim (1981,1985)
Hairpins Found in LESMoin and Kim (1981,1985)
• “The Flow Contains an Appreciable Number of Hairpins”
• Vorticity Inclination Peaks at 45o
• But, No Forest!?!
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.
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!
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
Computing Power
5 Orders of Magnitude Since 1985!
Advanced Computing has Advanced CFD
(and vice versa)
DNS of Turbulent Pipe FlowWu and Moin (2008)
Re_D = 5300 Re_D = 44000
300(r) x 1024(θ) x 2048(z) 256(r) x 512(θ) x 512(z)
DNS at ReD = 24580, Pipe Length is 30R
Very Large-Scale Motions in PipesWu and Moin (2008)
Log Region (1-r)+ = 80
Buffer Region (1-r)+ = 20
Core Region (1-r)+ = 270
(Black) -0.2 < u’ < 0.2 (White)
Experimental energy spectrum
Wavelength
Energy
Experiment, using T.H.Perry & Abell (1975)
Energy Spectrum from Simulations
Wavelength
Energy
Experiment, using T.H.Perry & Abell (1975)
Simulation, true spectrumdel Álamo & Jiménez (2009)
Artifact of Taylor's Hypothesis
Wavelength
Energy
Experiment, using T.H.Perry & Abell (1975)
Simulation, true spectrumdel Álamo & Jiménez (2009)
Simulation, using T.H.del Álamo & Jiménez (2009)
Artifact of Taylor's Hypothesis
Wavelength
Energy
Experiment, using T.H.Perry & Abell (1975)
Simulation, true spectrumdel Álamo & Jiménez (2009)
Simulation, using T.H.del Álamo & Jiménez (2009)
Aliasing
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
Blasius Boundary Layer + Freestream Turbulence
4096 (x), 400 (y), 128 (z)
t = 100.1T
t = 100.2T
t = 100.55T
Isotropic Inflow Condition
Validation of Boundary Layer Growth
Blasius
Blasius
Monkewitz et al
Validation of Skin Friction
Blasius
Validation of Mean Velocity
Murlis et al Spalart
Reθ = 900
Validation Mean Flow Through Transition
Reθ = 200
Reθ = 800
Circle: Spalart
Validation of Velocity Gradient
Circles: Spalart (Exp.)Triangles: Smith (Exp.)Dotted Line: Nagib et al. (POD)Solid Line: Wu & Moin (2009)
Validation of RMS Through Transition
Circle: Spalart
Reθ = 800
Reθ = 200
Validation of RMS fluctuations
circle: Purtell et al other symbols: Erm & Joubert
Reθ = 900
Validation of RMS Fluctuations
Circle: Purtell et alPlus: SpalartLines: Wu & Moin
Total stress through transition
Plus: Reθ = 200Solid Line: Reθ = 800
Near-Wall Stresses
Circle: Spalart
Viscous Stress
Total Stress
Shear Stresses
Circle: Honkan & AndreopoulosDiamond: DeGraaff & EatonPlus: Spalart
Immediately before breakdown
t = 100.55T
u/U∞ = 0.99
Hairpin Packet at t = 100.55 TImmediately Before Breakdown
Winner of 2008 APS Gallery of Fluid Motion
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
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
Conclusion• A renewed study of the time-dependent
dynamics of turbulent boundary layer is warranted. Helpful links to transition and well studied dynamics of of isolated hairpins.
• Calculations should be extended to Re>4000 would require 3B mesh points. • Potential application to “wall modeling” for LES