Wall Turbulence Control by spanwise-traveling waves Wenxuan Xie, Maurizio Quadrio Department of Aerospace Science and Technology Politecnico di Milano European Turbulence Conference, ENS Lyon, Sep 2013 W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 1 / 12
Turbulence Skin Friction Drag Reduction Various flow control techniques have been proposed The spanwise-traveling wave concept was first studied by Du and Karniadakis ( JFM 2002, Science 2003) Large drag reduction (up to more than 30%) Modified near wall turbulence structure XXX A Picuture Here XXX Some interesting part in the parametric space is not covered by the existing simulation cases The energetic performance is not presented W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 2 / 12
Two types of spanwise-traveling wave spanwise body forcing spanwise wall velocity (EFMC 2012) F z = A f sin( κ z z − ω t ) e − y / ∆ w = A vel sin( κ z z − ω t ) � Acts directly on the bulk fluid � In-plane wall deformation � Oriented in the spanwise � Oriented in the spanwise direction direction � Varies sinusoidally � Varies sinusoidally � The wave travels along the � The wave travels along the spanwise direction spanwise direction � Decays exponentially with the � One parameter less! wall normal distance How is the performance of the Key conclusion: spanwise wall traveling wave of body forcing? oscillation ( κ z = 0) outperforms all (Drag and Energetic) other waves in the parametric space W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 3 / 12
Purpose and Method Aim Explore the 4-D ( ω − κ z − A f − ∆) parametric space more exhausitively Find the best drag reduction and energetic performance Approach Near 800 turbulent channel flow DNS simulations at Re τ = 200 ω ∈ [0 . 5 , 10] , κ z ∈ [0 , 9 . 8] , A f ∈ [0 . 1 , 2] , ∆ ∈ [0 . 01 , 1] Constant Flow Rate Definition: S (%) ≡ P 0 − ( P + P in ) R (%) ≡ P 0 − P × 100 × 100 P 0 P 0 � t f � L x � L z � 2 h 1 in which P in = ρ f z w d y d z d x d t t f − t i 0 0 0 t i W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 4 / 12
Modification of Near Wall Turbulence 20 3 0.3 2.5 15 0.276 0.252 2 U + 0.228 10 z 0.204 1.5 0.18 0.156 1 0.132 5 0.108 0.5 0.084 Ref 0.06 DR 0 0 1 2 3 4 x 0 1 2 5 10 20 50 200 y + 3.0 3 0.15 2.5 0.14 2.5 0.13 2.0 0.12 rms 2 0.11 u + 1.5 z 0.1 1.5 0.09 0.08 1.0 1 0.07 0.06 0.5 0.5 Ref DR 0 0.0 0 1 2 3 4 x 1 2 5 10 20 50 200 y + W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 5 / 12
Results: R R: -70 -60 -50 -40 -30 -20 -10 0 10 20 30 10 10 8 8 6 6 κ z κ z 2 2 4 4 A f A f 1 1 2 2 0 0 2 4 6 8 10 2 4 6 8 10 ω ω ∆ = 0 . 01 ∆ = 0 . 02 10 10 8 8 6 6 κ z κ z 2 2 4 4 A f A f 1 1 2 2 0 0 2 4 6 8 10 2 4 6 8 10 ω ω ∆ = 0 . 04 ∆ = 0 . 1 W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 6 / 12
The iso-surfaces of R (%) W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 7 / 12
Results: S S: -60 -50 -40 -30 -20 -10 0 10 10 10 8 8 6 6 κ z κ z 2 2 4 4 A f A f 1 1 2 2 0 0 2 4 6 8 10 2 4 6 8 10 ω ω ∆ = 0 . 01 ∆ = 0 . 02 10 10 8 8 6 6 κ z κ z 2 2 4 4 A f A f 1 1 2 2 0 0 2 4 6 8 10 2 4 6 8 10 ω ω ∆ = 0 . 04 ∆ = 0 . 1 W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 8 / 12
The iso-surfaces of S (%) W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 9 / 12
Comparison with wall based forcing Body Forcing Wall Motion R max 47 ( ω = 1, κ z = 0, A f = 2, 38 ( ω = 0 . 5, κ z = 0, A vel = ∆ = 0 . 04) 0 . 5) S max 12 ( ω = 0 . 75, κ z = 0, A f = 10 ( ω = 0 . 5, κ z = 0, A vel = 0 . 5, ∆ = 0 . 04) 0 . 2) 1 more parameter (∆) enables the Body forcing to be better tuned The gain in R is largely cancelled out by the power required to manipulate the flow ( P in ) Both R max and S max are always found to be at κ z = 0 in both cases W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 10 / 12
Conclusion Body forcing and wall motion behave similarly Both R and S reach the optimal at κ z = 0 The spanwise traveling wave concept is outperformed by the spanwise oscillatory body forcing Even the Spanwise oscillatory body forcing/wall oscillation isn’t particularly appealing in the sense of S compare to other techniques. e.g. Streamwise traveling wave of transverse wall velocity ( S max > 25) W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 11 / 12
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