Presentation

Wall Turbulence Parviz Moin
Stanford University
Classical View of Wall Turbulence • Mean Velocity Gradients  Turbulent Fluctua9ons • Predic9ng Skin Fric9on was Primary Goal Major Stepping Stones • Visualiza9on & Discovery of Coherent Mo9ons – Low‐Speed Streaks in “Laminar Sub‐Layer” • Kline, Reynolds, Schraub and Runstadler (1967) • Kim, Kline and Reynolds (1970) – Streaks LiT‐Up and Form Hairpin Vor9ces • 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) y+ ≈ 4 • Three‐Dimensional, Unsteady Streaky Mo9ons – “Streaks Waver and Oscillate Much Like a Flag” – Seem to “Leap Outwards” into Outer Regions Bursts Kim, Kline and Reynolds (1970) • Streaks “LiT‐Up” Forming a Streamwise Vortex • Near‐Wall Reynolds Shear Stress Amplified • Vortex + Shear  New Streaks/Turbulence Major obstacle for LES • Streaks and wall layer vor9ces are important to the dynamics of wall turbulence • Predic9on of skin fric9on depends on proper resolu9on 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 Models Theodorsen (1952) • Spanwise Vortex Filament Perturbed Upward (Unstable) - Vortex Stretches, Strengthens, and Head LiTs Up More (45o) • Modern View = Theodorsen + Quasi‐Streamwise Vortex Streaks LiT‐Up and Form Hairpin Vor9ces Head and Bandyopadhyay (1980) Reθ = 1700 • Hairpins Inclined at 45 deg. (Principal Axis) • First Evidence of Theodorsen’s Hairpins Major Stepping Stones • Conceptual & Quan9ta9ve Model Development – “Forests of Hairpins” and Reduced‐Order Models • Perry and Chong (1982) • Kim and Adrian (1999) • Smits & Dussauge (2005) Supersonic Boundary Layers • Seeing the Forest for the Trees Hairpin Interac9ons, Smith (1984) Forests of Hairpins Perry and Chong (1982) • Theodorsen’s Hairpin Modeled by Rods of Vor9city - Hairpins Scamered Randomly in a Hierarchy of Sizes • Reproduces Mean Velocity, Reynolds Stress, Spectra - Has Difficulty at Low‐Wavenumbers Packets of Hairpins Kim and Adrian (1982) • VLSM Arise From Spa9al Coherence of Hairpin Packets • Hairpin Packets Align & Form Long Low‐Speed Streaks (>2δ) Major Stepping Stones • Computer Simula9on of Turbulence (DNS/LES) – A Simula9on Milestone and Hairpin Confirma9on • Moin & Kim (1981,1985, 1986)Channel Flow • Rogers & Moin (1985), Homogeneous Shear – Zero Pressure Gradient Flat Plate Boundary Layer (ZPGFPBL) • Spalart (1988), Rescaling & Periodic BCs – Spa9ally Developing ZPGFPBL • Wu and Moin (2009) A Simula9on Milestone Moin and Kim (JFM, 1981,1985,1986) ILLIAC‐IV A Simula9on Milestone Moin and Kim (1981) LES Experiment Hairpins Found in LES Moin and Kim (1981,1985,1986) • “The Flow Contains an Appreciable Number of Hairpins” • Vor9city Inclina9on Peaks at 45o • But, No Forest!?! Shear Drives Hairpin Genera9on Rogers and Moin (1987) • Homogeneous Turbulent Shear Flow Studies Showed that Mean Shear is Required for Hairpin Genera9on • Hairpins Characteris9c of All Turbulent Shear Flows – Free Shear Layers, Wall Jets, Turbulent Boundary Layers, etc. Spalart’s ZPGFPBL and Periodicity Spalart (1988) • TBL is Spa9ally‐Developing, Periodic BCs Used to Reduce CPU Cost • Inflow Genera9on Imposes a Bias on the Simula9on Results • Bias Stops the Forest from Growing! Analysis of Spalart’s Data Robinson (1991) • “No single form of vor9cal structure may be considered representa9ve of the wide variety of shapes taken by vor9ces in the boundary layer.” • Iden9fica9on Criteria and Isocontour Subjec9vity • Periodic Boundary Condi9ons Contaminate Solu9on Compu9ng Power 5 Orders of Magnitude Since 1985! Advanced CompuJng has Advanced CFD (and vice versa) DNS of Turbulent Pipe Flow Wu and Moin (2008) 256(r) x 512(θ) x 512(z)
Re_D = 5300
300(r) x 1024(θ) x 2048(z)
Re_D = 44000
Very Large‐Scale Mo9ons 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)+ = 80 Buffer Region (1‐r)+ = 20 Core Region (1‐r)+ = 270 Simula9on of spa9ally evolving BL Wu and Moin (2009) • Simula9on Takes a Blasius Boundary Layer from Reθ = 80 Through Transi9on to a Turbulent ZPGFPBL in a Controlled Manner • Simula9on Database Publically Available: hmp://ctr.stanford.edu Blasius Boundary Layer + Freestream Turbulence t = 100.1T
t = 100.2T
4096 (x), 400 (y), 128 (z)
t = 100.55T
Isotropic Inflow Condi9on Valida9on of Boundary Layer Growth Blasius Monkewitz et al Blasius Valida9on of Skin Fric9on Blasius Valida9on of Mean Velocity Murlis et al Spalart Reθ = 900 Valida9on Mean Flow Through Transi9on Reθ = 200 Reθ = 800 Circle: Spalart Valida9on of RMS Through Transi9on Circle: Spalart Reθ = 800 Reθ = 200 Valida9on of RMS Fluctua9ons Circle: Purtell et al Plus: Spalart Lines: Wu & Moin Immediately before breakdown
t = 100.55T
u/U∞ = 0.99
Hairpin Packet at t = 100.55 T
Immediately Before Breakdown
2008 APS Gallery of Fluid Motion
Summary • Preponderance of Hairpin‐Like Structures is Striking! • A Number of Inves9gators Had Postulated The Existence of Hairpins • But, Direct Evidence For Their Dominance Has Not Been Reported in Any Numerical or Experimental Inves9ga9on of Turbulent Boundary Layers • First Direct Evidence (2009) in the Form of a Solu9on of NS Equa9ons Obeying Sta9s9cal 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 Simula9ons probably led to the distor9on of the structures • In Simula9ons of Wu & Moin (JFM, 630, 2009), Instabili9es on the Wall were Triggered from the Free‐stream and Not by Trips and Other Ar9ficial Numerical Boundary Condi9ons • Smoke Visualiza9ons of Head & Bandyopadhyay Led to Striking but Indirect Demonstra9on of Hairpins Large Trips May Have Ar9ficially Generated Hairpins Conclusion • A renewed study of the 9me‐dependent dynamics of turbulent boundary layer is warranted. Helpful links to transi9on and well studied dynamics of of isolated hairpins. • Calcula9ons should be extended to Re>4000 would require 3B mesh points. • Poten9al applica9on to “wall modeling” for LES Re=2000