Spanwise generalized Stokes layer and turbulent drag reduction - PowerPoint PPT Presentation

Turbulent drag reduction Laminar GSL Putting things together Spanwise generalized Stokes layer and turbulent drag reduction M.Quadrio 1 & P. Ricco 2 1 Politecnico di Milano 2 King’s College, London VIII Euromech Fluid Mechanics Conference Bad Reichenhall, September 14th, 2010

Turbulent drag reduction Laminar GSL Putting things together Outline Turbulent drag reduction with streamwise-travelling waves Laminar Generalized Stokes Layer (GSL) Putting things together

Turbulent drag reduction Laminar GSL Putting things together Outline Turbulent drag reduction with streamwise-travelling waves Laminar Generalized Stokes Layer (GSL) Putting things together

Turbulent drag reduction Laminar GSL Putting things together The travelling waves c 2h λ y z x Flow δ

Turbulent drag reduction Laminar GSL Putting things together Results from DNS (plane channel) Quadrio et al., JFM 2009 40 5 0 -10 2 36 41 43 45 45 46 44 5 -20 -20 -23 -23 -22 -17 -10 -2 0 2 40 0 0 0 1 20 23 8 0 4 15 38 41 44 46 45 36 6 -15 -18 -20 0 38 46 -16 -21 4 0 1 31 42 45 47 -20 - 24 45 13 0 3 40 46 -15 -18 2 1 0 15 41 -8 -17 8 15 30 k x 47 30 45 47 33 -16 -2 17 0 0 20 1 0 - 4 2 18 21 29 35 43 45 46 46 32 -7 -14 3 0 0 16 40 20 2 44 46 48 48 34 10 -14 21 30 33 40 0 45 46 47 40 8 1 -8 -10 13 24 0 31 1 21 34 37 41 45 45 47 39 31 18 10 3 -3 -6 -9 -9 -1 7 14 19 26 24 16 33 36 40 42 42 42 36 14 1 -7 1 24 28 20 10 0 32 36 37 38 37 36 26 1 -8 -1 19 29 29 24 16 34 36 35 33 22 5 -9 4 27 32 0 16 18 22 27 32 34 33 34 33 33 33 32 31 27 21 5 3 5 0 0 -6 -3 -7 -7 -9 -7 -9 -7 -6 -3 5 0 0 3 5 21 27 31 32 33 34 33 34 32 27 22 18 16 -3 -2 -1 0 1 2 3 ω

Turbulent drag reduction Laminar GSL Putting things together Laboratory experiment (cylindrical pipe) Auteri et al, Phys. Fluids (2010), in press Flow traveling wave wall velocity�

Turbulent drag reduction Laminar GSL Putting things together Drag variation

Turbulent drag reduction Laminar GSL Putting things together Outline Turbulent drag reduction with streamwise-travelling waves Laminar Generalized Stokes Layer (GSL) Putting things together

Turbulent drag reduction Laminar GSL Putting things together Laminar flow: the GSL equation Quadrio & Ricco JFM 2010, in press � ∂ 2 w ∂ x 2 + ∂ 2 w � ∂ w ∂ t + u ∂ w ∂ x = ν ∂ y 2 • TSL (Stokes) • SSL • All together: GSL • one-way coupling with streamwise flow

Turbulent drag reduction Laminar GSL Putting things together The analytical solution 1. δ ≪ h (translates into λ/ h ≪ Re b ) 2. Linear u profile w ( x , y , t ) = � � ��� � 1 / 3 � � 2 π u y , w c Ce 2 π i ( x − ct ) /λ Ai e π i / 6 A ℜ y − λν u y , w

Turbulent drag reduction Laminar GSL Putting things together Outline Turbulent drag reduction with streamwise-travelling waves Laminar Generalized Stokes Layer (GSL) Putting things together

Turbulent drag reduction Laminar GSL Putting things together Turbulent spanwise flow agrees with laminar GSL!

Turbulent drag reduction Laminar GSL Putting things together Using the GSL solution R vs analytical δ GSL Black points are “good” waves 50 40 30 20 100 * R 10 0 -10 -20 -30 0 2 4 6 8 10 12 14 16 18 20 δ lam +

Turbulent drag reduction Laminar GSL Putting things together How the waves increase drag Key parameter: phase speed • Waves lock with the convecting structures • Steady forcing in the convective reference frame: c + ≈ U + c

Turbulent drag reduction Laminar GSL Putting things together How the waves decrease drag Key parameter: unsteadiness • Drag reduction is proportional to δ GSL (WHY?) • Large δ GSL ⇒ large T • Quasi-steady forcing when T ≫ T ℓ

Turbulent drag reduction Laminar GSL Putting things together Limit to drag reduction Forcing must be ’unsteady’ Forcing on a timescale ≫ T ℓ does not yield DR Oscillating wall • Forcing timescale: oscillation period T Travelling waves • Forcing timescale: oscillation period T as seen by the convecting structures λ T = U c − c

Turbulent drag reduction Laminar GSL Putting things together Waves and turbulent friction Waves in (1) and (2) are ”good” waves

Turbulent drag reduction Laminar GSL Putting things together Conclusions • Waves reduce drag and are energy-efficient • Waves useful for understanding drag-reduction mechanism • Still incomplete understanding of the physics • Analytical solution for the GSL • Relation between laminar GSL and turbulent drag reduction

Turbulent drag reduction Laminar GSL Putting things together Issues • Further understanding (why is δ GSL ∼ R ?) • Actuators • Higher efficiency? • Re effects

Turbulent drag reduction Laminar GSL Putting things together THANK YOU