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

11 th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurement Palermo, Sept. 21-23, 2016 Direct Numerical Simulation of Drag Reduction with Uniform Blowing over a Rough Wall Eisuke Mori 1,2 , Maurizio Quadrio 2 and Koji Fukagata 1 1 Keio University, Japan 2 Politecnico di Milano, Italy

Background Turbulence - Huge drag - Environmental problems - High operation cost - How to control ? E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 2/15

Flow control classification (M. Gad-el-Hak, J. Aircraft , 2001) Flow control strategies Active Passive Feedback Feedforward - Uniform blowing E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 3/15

Uniform blowing (UB) (Sumitani & Kasagi, AIAA J. , 1995 Kametani & Fukagata, J. Fluid Mech. , 2011) • 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 On a boundary layer, White: vortex core, Colors: wall shear stress E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 4/15

Goal Investigate the interaction between roughness and UB for drag reduction - DNS of turbulent channel flow - Focus on drag reduction performance and mechanism E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 5/15

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: 𝑁 = 0, 𝟏. 𝟏𝟏𝟐, 𝟏. 𝟏𝟏𝟔 ROUGH CASE SMOOTH CASE E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 6/15

Model of rough wall (E. Napoli et al., J. Fluid Mech. , 2008) Roughness displacement 𝟓 𝑩 𝒋 𝐭𝐣𝐨 𝟑 𝒋 𝝆𝒚 𝒆 𝒚 = 𝜺 ෍ Τ 𝑴 𝒚 𝟑 𝒋=𝟐 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, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 7/15

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, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 8/15

Post processing • Drag coefficient decomposition for rough case 8 𝑒ത 𝑣 𝐷 𝐸𝑣𝑔 = ቤ Re 𝑐 𝑒𝑧 𝜊 2 =2 𝐷 𝐸𝑚𝑔 = 8 𝑒𝑣 𝑒𝑤 ቤ + ቤ (Friction component) Re 𝑐 𝑒𝑧 𝜊 2 =0 𝑒𝑦 𝜊 2 =0 𝐷 𝐸𝑚𝑞 = −16 𝑒𝑄 − 𝐷 𝐸𝑚𝑔 + 𝐷 𝐸𝑣𝑔 (Pressure component) 𝑒𝜊 1 • Drag reduction rate ∆𝐷 𝐸 𝑆 𝐸𝑚 = × 100 [%] 𝐷 𝐸,𝑁=0 Only focusing on lower side , subscript “ 𝑚 ” omitted hereafter E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 9/15

Drag reduction rate, 𝑺 𝑬 SMOOTH CASE ROUGH CASE ↓ 𝟐𝟐% ↓ 𝟒𝟖% ↓ 𝟖% ↓ 𝟑𝟕% Total 𝑆 𝐸 ↓ 𝟐𝟐% ↓ 𝟒𝟖% ↓ 𝟘% ↓ 𝟒𝟓% Friction 𝑆 𝐸,𝐺 ↓ 𝟔% ↓ 𝟐𝟘% Pressure 𝑆 𝐸,𝑄 - - E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 10/15

How does friction drag decrease? Bulk mean streamwise velocity Smooth Rough Black: 𝑁 = 0 Green: 𝑁 = 0.001 Red: 𝑁 = 0.005 Normalization based on 𝑁 = 0 E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 11/15

How does pressure drag decrease? averaged in the spanwise and time Pressure contours dashed lines: zero contour 𝑵 = 𝟏 𝑵 = 𝟏. 𝟏𝟏𝟔 𝑞 + 𝒆 𝒚 𝐧𝐛𝐲 𝒆 𝒚 𝐧𝐣𝐨 E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 12/15

Stream function Solid lines: 𝑁 = 0 Dashed lines: 𝑁 = 0.005 Uniform Blowing E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 13/15

In practical applications Drag reduction amount, ∆𝑫 𝑬 = 𝑫 𝑬,𝑵=𝟏 − 𝑫 𝑬,𝑵=𝟏.𝟐,𝟏.𝟔 [%] E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 14/15

Concluding remarks DNS of turbulent channel flow over a rough wall with UB • UB is effective over rough walls - Lower drag reduction rate ( 7%, 𝟑𝟕% / 11%, 𝟒𝟖% in rough / smooth case, with 𝑁 = 0.001, 0.005 ) • Drag reduction mechanism - Friction drag by wall-normal convection (=conventional) - Pressure drag by prevention of stagnant flow • Outlook toward practical applications - More saving opportunity over rough walls E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 15/15

Future plans • Another drag reduction technique on rough surface - Spanwise oscillation (ongoing) • Assessment of net energy? (should be external flow) • Calculation at higher Reynolds number? • Other types of rough surfaces (e.g., 3D structure)? E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 17/15

Uniform blowing (UB) (Sumitani & Kasagi, AIAA J. , 1995 Kametani & Fukagata, J. Fluid Mech. , 2011) • Drag contribution in a channel flow with UB(/US) 𝟑 𝟑 𝑾 𝒙 : Blowing velocity 𝑫 𝒈 = 𝟐𝟑 −𝒗 ′ 𝒘 ′ 𝒆𝒛 − 𝟐𝟑𝑾 𝒙 න 𝟐 − 𝒛 ഥ + 𝟐𝟑 න 𝟐 − 𝒛 𝒗𝒆𝒛 𝑺𝒇 𝒄 Blowing 𝟏 𝟏 Viscous Turbulent Convective (=UB/US) side 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 White: vortex core, Colors: wall shear stress E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 18/15

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 2 𝜖𝜊 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, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 19/15

Discretization methods • Energy-conservative second-order finite difference schemes (In space) • Low-storage third-order Runge-Kutta / Crank- Nicolson scheme (In time) + SMAC method for pressure correction Discretized in the staggered grid system E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 20/15

Validation & Verification (B. Milici et al., J. Fluid Mech. , 2014) Time trace of instantaneous C D,r Bulk mean streamwise velocity Less than 2% of difference with most resolved one E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 21/15

How does friction drag decreases? *averaged in the spanwise and time Reynolds shear stress contour dashed lines: zero contour 𝑵 = 𝟏 𝑵 = 𝟏. 𝟏𝟏𝟔 𝑣 ′+ 𝑤 ′+ 𝒆 𝒚 𝐧𝐛𝐲 E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 22/15

𝒘 distribution (2D contour) ഥ Based on 𝑣 𝜐 in w/o control case UB 0.5% case No control case E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 23/15

𝒗 distribution (2D contour) ഥ Based on 𝑣 𝜐 in w/o control case UB 0.5% case No control case E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 24/15

Stream function (detailed) E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 25/15

𝒗 𝐬𝐧𝐭 distribution Black: w/o control Green: UB 0.1% Red: UB 0.5% Normalized by 𝑣 𝜐 in w/o control case E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 26/15