Direct Numerical Simulation of Drag Reduction with Uniform Blowing - PowerPoint PPT Presentation

European Drag Reduction and Flow Control Meeting Rome, Apr. 3-6, 2017 Direct Numerical Simulation of Drag Reduction with Uniform Blowing over a Two-dimensional Roughness Eisuke Mori 1 , Maurizio Quadrio 2 and Koji Fukagata 1 1 Keio University, Japan 2 Politecnico di Milano, Italy

Uniform blowing (UB) • Drag contribution in a channel flow with UB(/US) 𝟑 𝟑 𝑾 𝒙 : Blowing velocity 𝑫 𝒈 = 𝟐𝟑 −𝒗 ′ 𝒘 ′ 𝒆𝒛 + 𝟐𝟑 න 𝟐 − 𝒛 𝟐 − 𝒛 ഥ −𝟐𝟑𝑾 𝒙 න 𝒗𝒆𝒛 𝐒𝐟 𝒄 𝟏 𝟏 Viscous Turbulent Convective (=UB/US) Contribution contribution contribution (= laminar drag, const. ) (Fukagata et al., Phys. Fluids , 2002) • Excellent performance (about 45% by 𝑾 𝒙 = 𝟏. 𝟔%𝑽 ∞ ) • Unknown over a rough wall (Kametani & Fukagata, J. Fluid Mech. , 2011) On a boundary layer, White: vortex core, Colors: wall shear stress E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 2/18

UB over a rough wall Experimental results so far • Similar to the smooth-wall cases - Schetz and Nerney, AIAA J. , 1977 - Voisinet, 1979 • Opposite behavior (drag increased, turbulent intensity suppressed) - Miller et al., Exp. Fluids , 2014 Contradicting remarks exist E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 3/18

Goal Investigate the interaction between roughness and UB for drag reduction using numerical simulation - DNS of turbulent channel flow - Drag reduction performance and mechanism - Combined effect of UB and roughness E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 4/18

Numerical procedure • Based on FD code (for wall deformation) (Nakanishi et al., Int. J. Heat Fluid Fl. , 2012) • Constant flow rate, 𝐒𝐟 𝒄 = 𝟑𝑽 𝒄 𝜺/𝝃 = 𝟔𝟕𝟏𝟏 - so that 𝐒𝐟 𝝊 ≈ 𝟐𝟗𝟏 in a plane channel (K.M.M.) • ∆𝒚 + = 𝟓. 𝟓, 𝟏. 𝟘𝟒 < ∆𝒛 + < 𝟕, ∆𝒜 + = 𝟔. 𝟘 • UB magnitude: Τ 𝑾 𝒙 𝑽 𝒄 = 𝟏, 𝟏. 𝟐%, 𝟏. 𝟔%, 𝟐% ROUGH CASE SMOOTH CASE E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 5/18

Model of rough wall Roughness displacement 𝟗 𝑩 𝒋 𝐭𝐣𝐨 𝟑𝒋𝝆𝒚 𝒆 𝒚 = 𝜺 ෍ Τ 𝑴 𝒚 𝟑 𝒋=𝟐 (E. Napoli et al., J. Fluid Mech. , 2008) 𝜺 : channel half height 𝑴 𝒚 : Channel length, 𝟓𝝆𝜺 𝒆 𝒚 𝐧𝐛𝐲 = 𝟏. 𝟐𝟐𝜺 𝑩 𝒋 : Amplitude of each sinusoid 𝑩 𝒋 = ቊ 𝟐, 𝐠𝐩𝐬 𝒋 = 𝟐 𝒛 = 𝟏 𝟏, 𝟐 , 𝐠𝐩𝐬 𝒋 ≠ 𝟐 (Defined randomly) with rescaling so that 𝒆 𝒚 = 𝟏. 𝟏𝟔𝜺 E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 6/18

The result of the base flow ∆𝑉 + ~6.5 + = 𝟒𝟗 𝒍 𝒕 𝐷 𝐸𝑞 = 2𝐷 𝐸ave − (𝐷 𝐸𝑔 + 𝐷 𝐸𝑔,𝑣 ) 𝐷 𝐸ave : Overall drag coefficient 𝐷 𝐸𝑔 : 𝐷 𝑔 of the rough wall side 𝐷 𝐸𝑔,𝑣 : 𝐷 𝑔 of the smooth wall side “Transitionally - rough regime” E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 7/18

The result of UB SMOOTH CASE ROUGH CASE Total, 𝑆 𝟐𝟐% 𝟒𝟖% 𝟔𝟘% 𝟖% 𝟑𝟕% 𝟓𝟒% 𝑆 = 1 − 𝐷 𝐸,ctr 𝐷 𝐸,ctr : controlled 𝐷 𝐸,nc 𝐷 𝐸,nc : no control E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 8/18

The result of UB SMOOTH CASE ROUGH CASE Total, 𝑆 𝟐𝟐% 𝟒𝟖% 𝟔𝟘% 𝟖% 𝟑𝟕% 𝟓𝟒% Friction, 𝑆 𝐺 𝟐𝟐% 𝟒𝟖% 𝟔𝟘% 𝟘% 𝟒𝟓% 𝟔𝟖% Pressure, 𝑆 𝑄 𝟔% 𝟐𝟘% 𝟒𝟑% - - E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 9/18

Friction drag reduction mechanism Bulk mean streamwise velocity SMOOTH CASE ROUGH CASE Τ 𝑽 𝒄 𝑾 𝒙 = 0 Black: Τ 𝑽 𝒄 𝑾 𝒙 = 0.1% Green: Τ 𝑽 𝒄 𝑾 𝒙 = 0.5% Red: Τ 𝑽 𝒄 𝑾 𝒙 = 1% Blue: + 𝒆 𝒚 𝐧𝐛𝐲 +nc: normalization with no control case 𝒗 𝝊 E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 10/18

How does pressure drag decrease? averaged in the spanwise and time Pressure contours dashed lines: zero contour 𝑞 +nc Τ 𝑽 𝒄 𝑾 𝒙 = 𝟏 Τ 𝑽 𝒄 𝑾 𝒙 = 𝟐% + 𝒆 𝒚 𝐧𝐛𝐲 + 𝒆 𝒚 𝐧𝐣𝐨 E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 11/18

“Smoothing effect” averaged in the spanwise and time Wall-normal velocity contours dashed lines: zero contour 𝑤 +nc + = 38 𝑙 𝑡 Τ 𝑽 𝒄 𝑾 𝒙 = 𝟏 + = 20 𝑙 𝑡 Τ 𝑽 𝒄 𝑾 𝒙 = 𝟐% + 𝒆 𝒚 𝐧𝐛𝐲 + 𝒆 𝒚 𝐧𝐣𝐨 E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 12/18

Outer layer similarity with UB Velocity defect Base flow (No controlled) of 1% UB case of one-side rough wall one-side rough wall 𝜺 𝒖 : distance from a wall to the Smooth side minimum RMS location (K. Bhaganagar et al., Rough side Flow, Turbul. Combust. , 2004) E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 13/18

Comparison with smooth case Velocity defect 1% UB case of 1% UB case of both-side smooth wall one-side rough wall Suction Smooth side side Blowing Rough side side E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 14/18

Comparison with smooth case Velocity defect 1% UB case of 1% UB case of both-side smooth wall one-side rough wall Same tendency, but quantitatively weakened E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 15/18

Stevenson’s law of the wall Plots using Stevenson’s law of the wall (Stevenson, 1963) 2 = 1 𝜆 ln 𝑧 + + 𝐶 + 𝑉 + − 1 1 + 𝑊 𝑥 + 𝑊 𝑥 𝑉 +𝑇 Roughness function ∆𝑉 + Modified law is suggested: 2 = 1 𝜆 ln 𝑧 + + 𝐶 − ∆𝑉 + + 𝑉 + − 1 1 + 𝑊 𝑥 + 𝑊 𝑥 E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 16/18

𝐨𝐝+ Normalization by 𝒗 𝝊 Drag reduction rate, Drag reduction, ∆𝑫 𝑬 = 𝑫 𝑬,𝐨𝐝 − 𝑫 𝑬,𝐝𝐮𝐬 𝑆 + 𝑆 becomes similar when plotted with 𝑊 nc: no control 𝑥 ctr: controlled E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 17/18

Concluding remarks DNS of turbulent channel flow is performed over a rough wall with UB • UB is effective over a rough wall - Almost same in drag reduction rate, but larger in drag +nc ) reduction amount (when normalized by 𝑣 𝜐 • Drag reduction mechanisms are considered - Friction drag is reduced by wall-normal convection - Pressure drag is reduced by “smoothing effect” • Combined effect (UB + roughness) slightly exists • Modified Stevenson’s law of the wall is suggested E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 18/18

Thank you for your kind attention

Background Turbulence - Huge drag - Environmental problems - High operation cost - How to control ? E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 21/18

Flow control classification (M. Gad-el-Hak, J. Aircraft , 2001) Flow control strategies Active Passive Feedback Feedforward - Uniform blowing E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 22/18

Governing equations (S. Kang & H. Choi, Phys. Fluids , 2000) Incompressible Continuity and Navier-Stokes in 𝝄 𝒋 coordinate 𝛜𝒗 𝒋 = −𝑻 𝛜𝝄 𝒋 𝝐 𝟑 𝒗 𝒋 𝛜 𝒗 𝒋 𝒗 𝒌 𝛜𝒗 𝒋 − 𝝐𝒒 + 𝟐 − 𝒆𝑸 𝝐𝒖 = − 𝜺 𝒋𝟐 + 𝑻 𝒋 𝛜𝝄 𝒌 𝛜𝝄 𝒋 𝐒𝐟 𝒄 𝛜𝝄 𝒌 𝝄 𝒌 𝐞𝝄 𝟐 where 𝜖 2 𝑣 𝑗 𝜖 2 𝑣 𝑗 𝜖 𝑣 𝑗 𝑣 𝑘 𝜖 𝜚 𝑘 𝜚 𝑘 𝜖𝑣 𝑗 𝑒𝑞 𝜀 𝑗𝑘 + 1 2 + 1 𝜖𝑣 𝑗 𝑇 𝑗 = −𝜒 𝑢 − 𝜚 𝑘 − 𝜚 𝑘 𝑆𝑓 2𝜚 𝑘 + 𝜚 𝑘 𝜚 𝑘 𝜖𝜊 2 𝜖𝜊 2 𝑒𝜊 2 𝜖𝜊 𝑘 𝜊 2 𝜖𝜊 2 2 𝜖𝜊 2 𝜖𝜊 2 𝜖𝑣 𝑗 1 𝜖𝜃 + 𝜖𝜃 0 𝑇 = 𝜚 𝑘 − 1 + 𝜃 𝜊 2 , for j = 1,3 𝜚 𝑘 = 𝜒 𝑘 − 𝜀 𝑘2 𝜖𝜊 2 𝜖𝜊 𝑗 𝜖𝜊 𝑗 𝜒 𝑘 = 1 1 + 𝜃 , for j = 2 E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 23/18

Coordinate transformation (S. Kang & H. Choi, Phys. Fluids , 2000) Calculation grids: 𝝄 𝒋 (Cartesian with extra force) 𝒚 = 𝝄 𝟐 𝒛 = 𝛐 𝟑 𝟐 + 𝛉 + 𝛉 𝐞 ቐ Actual grid points allocation 𝒜 = 𝛐 𝟒 ( 𝑦, 𝑧, 𝑨 : physical coordinate) 𝛉 ≡ 𝛉 𝐯 − 𝛉 𝒆 Τ 𝟑 = − 𝒆 𝐲 Τ 𝟑 𝛉 𝐞 = 𝐬 𝐲 , 𝛉 𝒗 = 𝟏 𝛉 𝐞 , 𝛉 𝐯 : displacement of wall lower/upper wall E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 24/18