✬ ✩ Modification of Turbulent Flow using Distributed Suction Maurizio Quadrio a , J. Maciej Floryan b & Paolo Luchini c a Dip. Ingegneria Aerospaziale Politecnico di Milano, maurizio.quadrio@polimi.it b Dept. Mechanical and Materials Eng. University of Western Ontario, c Dip. Ingegneria Meccanica Universit` a di Salerno ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 1
✬ ✩ Introduction I NTRODUCTION Use of wall-normal blowing/suction is very effective for turbulence control. Sumitani & Kasagi, AIAA J. 1995: constant blowing (suction) is known to affect significantly the friction drag and the heat transfer. Choi et al. JFM 1994: use of time- and space-dependent blowing/suction (difficult to implement in practice!) is known to allow 25% turbulence drag reduction. Jim´ enez et al JFM 2001: active/passive porous walls, increase in drag. ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 2
✬ ✩ Introduction M OTIVATION I Study the effect of a steady, longitudinal distribution of suction at the wall, with low amplitude and zero net mass flux. A λ s = 2 π/α s Tool: DNS of the turbulent plane channel flow. v ( x, y = ± h, z, t ) = A sin ( α s x ) ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 3
✬ ✩ Introduction M OTIVATION II Schoppa & Hussain, PoF 1998: large-scale streamwise vortices are known to produce a signifcant drag reduction. In laminar regime, Floryan JFM 2003 has shown that sinusoidal suction creates such vortices. Result from stability analysis with mean turbulent profile as base flow: ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 4
✬ ✩ Introduction 5 4.5 4 3.5 3 � 2.5 2 1.5 1 0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 � Re = 3300 , A = 0 . 004 U c ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 5
✬ ✩ Introduction M OTIVATION III Floryan JFM 2003: the laminar case is qualitatively analogous to the flow over a wavy wall. Many papers exist on turbulent flow over wavy walls. It is currently believed that the wavelength of the wavyness by itself does not play any role, von R¨ ohr, JFM 2003. The same is assumed by Jim´ enez et al (suction). Does the wavelength matter? ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 6
✬ ✩ Numerical issues T HE NUMERICAL METHOD Our solver of the incompressible Navier–Stokes equations has: ➜ II-order equation for the normal vorticity and IV-order equation for the normal velocity, without pressure Fourier discretization in the homogeneous directions ➜ Fourth-order compact finite-differences over a 5-point unevenly ➜ spaced computational molecule in the wall-normal direction ➜ Three-substeps Runge–Kutta partially implicit time advancement Parallel execution on both shared-memory and distributed-memory ➜ computers ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 7
✬ ✩ Numerical issues P ARAMETERS OF THE SIMULATIONS Computational parameters: the same as Kim, Moin & Moser in JFM , 1987 (longer integration time). 8 · 10 6 d.o.f. Plane turbulent channel flow at Re τ = 180 . • Periodic-box dimensions: L y = 2 h L x = 4 πh L z = 2 πh • Spatial discretization: N x = 193 N z = 129 N y = 161 • Spatial resolution: ∆ x + = 11 . 7 ∆ y + = 0 . 8 to 4 . 5 ∆ z + = 7 . 0 • Temporal resolution: ∆ t + ≈ 0 . 15 • Total integration time: T ≈ 600 h/U c Calculations run on Itanium II machines of the SHARCNET Computing Center at the University of Western Ontario. Approx. 40 ✫ cases plus some accuracy checks. ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 8
✬ ✩ Results F RICTION VS . SUCTION AMPLITUDE C f = 2 τ/ρU 2 b . Reference: C f = 8 . 15 · 10 − 3 , within 0.3 % from KMM 25 α s =1/h 20 3 C f 15 10 10 0.01 0.02 0.03 0.04 ✫ ✪ A/U P M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 9
✬ ✩ Results F RICTION VS . SUCTION WAVELENGTH 25 20 A=0.03 U P 3 C f 15 10 10 0 5 10 α s h ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 10
✬ ✩ Results D ISCUSSION ➀ The effect is proportional to A at fixed α s . The threshold of minimum A depends on α s . ➁ A better parameter could be the product Aλ s (flow rate) ➂ Suction wavelength does matter! ➃ When λ s → ∞ the limit of uniform blowing + uniform suction is recovered. Agreement with λ + s ≈ 4000 from Jim` enez, and with results from Sumitani & Kasagi. Is the flow over a wavy wall really independent on the wavelength of the corrugation? Probably not... ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 11
✬ ✩ Results U NEXPECTED RESULT : SMALL DRAG REDUCTION 4 3 A=0.03 U P 2 1 % C f 0 -1 -2 -3 -4 4 6 8 10 α s h ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 12
✬ ✩ Turbulence statistics M EAN PROFILE 0.8 0.7 0.6 0.5 U/U P 0.4 ref 0.3 α h=5 0.2 α h=1 0.1 0 0 0.25 0.5 0.75 1 y/h ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 13
✬ ✩ Turbulence statistics M EAN PROFILE IN WALL UNITS 18 ref 16 α h=5 14 α h=1 12 10 + U 8 6 4 2 0 0 1 2 10 10 10 + y ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 14
✬ ✩ Turbulence statistics V ELOCITY FLUCTUATIONS 3 2.5 2 ’+ ’+ , w 1.5 ’+ , v u 1 0.5 0 0 25 50 75 100 + y ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 15
✬ ✩ Turbulence statistics 1 D STREAMWISE SPECTRA -2 10 -3 10 -4 10 S u -5 10 -6 10 ref α h=1 -7 10 α h=5 -8 10 10 20 30 40 α ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 16
✬ ✩ Turbulence statistics S TREAMWISE DIRECTION IS NOT - HOMOGENOUS ! 0.7 0.6 0.5 0.4 U/U P α h=1 0.3 λ =0 λ =1/4 0.2 λ =1/2 λ =3/4 0.1 mean 0 0 0.1 0.2 0.3 0.4 y/h ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 17
✬ ✩ Turbulence statistics V ERTICAL MEAN VELOCITY AND STREAMLINES 0.4 α h=5 0.3 y/h 0.2 0.1 0 0 0.5 1 x/h 0.4 α h=1 0.3 y/h 0.2 0.1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 ✫ ✪ x/h M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 18
✬ ✩ Turbulence statistics T RANSVERSAL CORRELATIONS , u AT y + ≈ 10 2 α h=5 1.5 ∆ z 1 0.5 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 x/h 2 α h=1 1.5 ∆ z 1 0.5 0 ✫ ✪ 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 x/h M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 19
✬ ✩ Turbulence statistics S TREAMWISE FRICTION α h=5 2 z/h 0 -2 -5 0 5 x/h α h=2 2 z/h 0 -2 -5 0 5 ✫ ✪ x/h M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 20
✬ ✩ C ONCLUSIONS Suction wavelength λ s plays a fundamental role. Dramatic drag increase at wavelenghts λ + s > 350 , towards the asymptotic value of uniform blowing and uniform suction. Usual turbulence structure (elongated low-speed streaks) disappear. Small drag reduction below the threshold λ + s = 350 . Critical wavelength is related to the typical size of near-wall turbulent structures. No evidence of large-scale vortices. Basic flow structure is a pair of large-scale spanwise rolls. ✫ ✪ M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 21
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