Wall Turbulence Control by spanwise-traveling waves Wenxuan Xie, - - PowerPoint PPT Presentation

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 Fz = Af sin(κzz − ωt)e−y/∆ Acts directly on the bulk fluid Oriented in the spanwise direction Varies sinusoidally The wave travels along the spanwise direction Decays exponentially with the wall normal distance spanwise wall velocity (EFMC 2012) w = Avelsin(κzz − ωt) In-plane wall deformation Oriented in the spanwise direction Varies sinusoidally The wave travels along the spanwise direction One parameter less! How is the performance of the traveling wave of body forcing? (Drag and Energetic) Key conclusion: spanwise wall

• scillation (κz = 0) outperforms all
• ther 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 − κz − Af − ∆) parametric space more exhausitively Find the best drag reduction and energetic performance

Approach

Near 800 turbulent channel flow DNS simulations at Reτ = 200 ω ∈ [0.5, 10], κz ∈ [0, 9.8], Af ∈ [0.1, 2], ∆ ∈ [0.01, 1] Constant Flow Rate Definition: R(%) ≡ P0 − P P0 × 100 S(%) ≡ P0 − (P + Pin) P0 × 100 in which Pin = 1 tf − ti tf

ti

Lx Lz 2h ρfzw dydzdxdt

W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 4 / 12

Modification of Near Wall Turbulence

1 2 3 4 0.5 1 1.5 2 2.5 3 0.3 0.276 0.252 0.228 0.204 0.18 0.156 0.132 0.108 0.084 0.06

x z

1 2 5 10 20 50 200 5 10 15 20 Ref DR

U+ y+

1 2 3 4 0.5 1 1.5 2 2.5 3 0.15 0.14 0.13 0.12 0.11 0.1 0.09 0.08 0.07 0.06

x z

1 2 5 10 20 50 200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Ref DR

u+ rms y+ W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 5 / 12

Results: R

2 4 6 8 10 2 4 6 8 10 1 2

R: -70 -60 -50 -40 -30 -20 -10 0 10 20 30

κz ω Af ∆ = 0.01

2 4 6 8 10 2 4 6 8 10 1 2

κz ω Af ∆ = 0.02

2 4 6 8 10 2 4 6 8 10 1 2

κz ω Af ∆ = 0.04

2 4 6 8 10 2 4 6 8 10 1 2

κz ω Af ∆ = 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

2 4 6 8 10 2 4 6 8 10 1 2

S: -60 -50 -40 -30 -20 -10 0 10

κz ω Af ∆ = 0.01

2 4 6 8 10 2 4 6 8 10 1 2

κz ω Af ∆ = 0.02

2 4 6 8 10 2 4 6 8 10 1 2

κz ω Af ∆ = 0.04

2 4 6 8 10 2 4 6 8 10 1 2

κz ω Af ∆ = 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 Rmax 47 (ω = 1, κz = 0, Af = 2, ∆ = 0.04) 38 (ω = 0.5, κz = 0, Avel = 0.5) Smax 12 (ω = 0.75, κz = 0, Af = 0.5, ∆ = 0.04) 10 (ω = 0.5, κz = 0, Avel = 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 (Pin) Both Rmax and Smax are always found to be at κz = 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 κz = 0 The spanwise traveling wave concept is outperformed by the spanwise

• scillatory 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 (Smax > 25)

W.Xie, M.Quadrio (Polimi) Wall Turbulence Control by spanwise-traveling waves Sep 2013 11 / 12