Presentation on theme: "Mechanics of Wall Turbulence"— Presentation transcript:
1Mechanics of Wall Turbulence Parviz MoinCenter for Turbulence ResearchStanford University
2Classical View of Wall Turbulence Mean Velocity Gradients Turbulent FluctuationsPredicting Skin Friction was Primary Goal
3Classical View of Wall Turbulence Eddy Motions Cover a Wide Range of ScalesEnergy Transfer from Large to Smaller ScalesTurbulent Energy Dissipated at Small Scales
4Major 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 VorticesHead and Bandyopadhyay (1980)Large Eddies in a Turbulent Boundary Layer with Polished Wall, M. Gad-el-Hak
5Low-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
6Bursts Kim, Kline and Reynolds (1970) Streaks “Lift-Up” Forming a Streamwise VortexNear-Wall Reynolds Shear Stress AmplifiedVortex + Shear New Streaks/Turbulence
7Major obstacle for LESStreaks and wall layer vortices are important to the dynamics of wall turbulencePrediction of skin friction depends on proper resolution of these structuresNumber of grid points required to capture the streaks is almost like DNS, N=cRe2SGS models not adequate to capture the effects of missing structures (e.g., shear stress).
8Early Hairpin Vortex Models Theodorsen (1952) Spanwise Vortex Filament Perturbed Upward (Unstable)Vortex Stretches, Strengthens, and Head Lifts Up More (45o)Modern View = Theodorsen + Quasi-Streamwise Vortex
9Streaks Lift-Up and Form Hairpin Vortices Head and Bandyopadhyay (1980) Spanwise Separation of Hairpins λ+ ≈ 100 y+Hairpins Inclined at 45 deg. (Principal Axis)First Evidence of Theodorsen’s Hairpins
10Streaks Lift-Up and Form Hairpin Vortices Head and Bandyopadhyay (1980) For Increasing Re, Hairpin Elongates and ThinsStreamwise Vortex Forms the Hairpin “Legs”
11Forests of Hairpins Perry and Chong (1982) Theodorsen’s Hairpin Modeled by Rods of VorticityHairpins Scattered Randomly in a Hierarchy of SizesReproduces Mean Velocity, Reynolds Stress, SpectraHas Difficulty at Low-Wavenumbers
12Packets of Hairpins Kim and Adrian (1982) VLSM Arise From Spatial Coherence of Hairpin PacketsHairpin Packets Align & Form Long Low-Speed Streaks (>2δ)
13Packets of Hairpins Kim 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
14Major Stepping Stones Computer Simulation of Turbulence (DNS/LES) A Simulation Milestone and Hairpin ConfirmationMoin & Kim (1981,1985), Channel FlowRogers & Moin (1985), Homogeneous ShearZero Pressure Gradient Flat Plate Boundary Layer (ZPGFPBL)Spalart (1988), Rescaling & Periodic BCsSpatially Developing ZPGFPBLWu and Moin (2009)
15A Simulation Milestone Moin and Kim (1981,1985) ILLIAC-IV
16A Simulation Milestone Moin and Kim (1981,1985) Experiment
18Hairpins Found in LES Moin and Kim (1981,1985) “The Flow Contains an Appreciable Number of Hairpins”Vorticity Inclination Peaks at 45oBut, No Forest!?!
19Shear Drives Hairpin Generation Rogers and Moin (1987) Homogeneous Turbulent Shear Flow Studies Showed that Mean Shear is Required for Hairpin GenerationHairpins Characteristic of All Turbulent Shear FlowsFree Shear Layers, Wall Jets, Turbulent Boundary Layers, etc.
20Spalart’s ZPGFPBL and Periodicity Spalart (1988) TBL is Spatially-Developing, Periodic BCs Used to Reduce CPU CostInflow Generation Imposes a Bias on the Simulation ResultsBias Stops the Forest from Growing!
21Analysis of Spalart’s Data Robinson (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 SubjectivityPeriodic Boundary Conditions Contaminate Solution
22Computing Power 5 Orders of Magnitude Since 1985! Advanced Computing has Advanced CFD (and vice versa)
23DNS of Turbulent Pipe Flow Wu and Moin (2008) 256(r) x 512(θ) x 512(z)300(r) x 1024(θ) x 2048(z)Re_D = 5300Re_D = 44000
24Very Large-Scale Motions in Pipes Wu and Moin (2008) DNS at ReD = 24580, Pipe Length is 30R(Black) -0.2 < u’ < 0.2 (White)Log Region (1-r)+ = 80Buffer Region (1-r)+ = 20Core Region (1-r)+ = 270
25Experimental energy spectrum Experiment, using T.H.Perry & Abell (1975)EnergyWavelength
26Energy Spectrum from Simulations Experiment, using T.H.Perry & Abell (1975)Simulation, true spectrumdel Álamo & Jiménez (2009)EnergyWavelength
27Artifact of Taylor's Hypothesis Experiment, using T.H.Perry & Abell (1975)Simulation, true spectrumdel Álamo & Jiménez (2009)EnergySimulation, using T.H.del Álamo & Jiménez (2009)Wavelength
28Artifact of Taylor's Hypothesis AliasingExperiment, using T.H.Perry & Abell (1975)Simulation, true spectrumdel Álamo & Jiménez (2009)EnergySimulation, using T.H.del Álamo & Jiménez (2009)Wavelength
29Simulation of spatially evolving BL Wu and Moin (2009) Simulation Takes a Blasius Boundary Layer from Reθ = 80 Through Transition to a Turbulent ZPGFPBL in a Controlled MannerSimulation Database Publically Available:
30Blasius Boundary Layer + Freestream Turbulence t = 100.1Tt = 100.2T4096 (x), 400 (y), 128 (z)t = T
49Summary Preponderance of Hairpin-Like Structures is Striking! A Number of Investigators Had Postulated The Existence of HairpinsBut, Direct Evidence For Their Dominance Has Not Been Reported in Any Numerical or Experimental Investigation of Turbulent Boundary LayersFirst Direct Evidence (2009) in the Form of a Solution of NS Equations Obeying Statistical Measurements
50Summary-IIForests of Hairpins is a Credible Conceptual Reduced Order Model of Turbulent Boundary Layer DynamicsThe Use of Streamwise Periodicity in channel flows and Spalart’s Simulations probably led to the distortion of the structuresIn 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 ConditionsSmoke Visualizations of Head & Bandyopadhyay Led to Striking but Indirect Demonstration of Hairpins Large Trips May Have Artificially Generated Hairpins
51ConclusionA 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>4000would require 3B mesh points.Potential application to “wall modeling” for LES