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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

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Direct Numerical Simulation of Drag Reduction with Uniform Blowing

  • ver a Rough Wall

Eisuke Mori1,2, Maurizio Quadrio2 and Koji Fukagata1

1 Keio University, Japan 2 Politecnico di Milano, Italy

11th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurement Palermo, Sept. 21-23, 2016

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Background

Turbulence

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

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Flow control classification

(M. Gad-el-Hak, J. Aircraft, 2001)

Flow control strategies Passive Feedback Feedforward Active

  • Uniform blowing
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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Uniform blowing (UB)

(Sumitani & Kasagi, AIAA J., 1995 Kametani & Fukagata, J. Fluid Mech., 2011)

  • Drag contribution in a channel flow with UB(/US)
  • Excellent performance (about 45% by 𝑾𝒙 = 𝟏. πŸ”%π‘½βˆž)
  • Unknown over a rough wall

π‘«π’ˆ = πŸπŸ‘ π’πŸπ’„ + πŸπŸ‘ ΰΆ±

𝟏 πŸ‘

𝟐 βˆ’ 𝒛 βˆ’π’—β€²π’˜β€² 𝒆𝒛

(Fukagata et al., Phys. Fluids, 2002)

Viscous Contribution (= laminar drag, const.) Turbulent contribution Convective (=UB/US) contribution On a boundary layer, White: vortex core, Colors: wall shear stress

𝑾𝒙: Blowing velocity

βˆ’πŸπŸ‘π‘Ύπ’™ ΰΆ±

𝟏 πŸ‘

𝟐 βˆ’ 𝒛 ΰ΄₯ 𝒗𝒆𝒛

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Goal

Investigate the interaction between roughness and UB for drag reduction

  • DNS of turbulent channel flow
  • Focus on drag reduction performance and

mechanism

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Numerical procedure

  • Based on FD code (for wall deformation)

(Nakanishi et al., Int. J. Heat Fluid Fl., 2012)

  • Constant flow rate, π’πŸπ’„ = πŸ‘π‘½π’„πœΊ/𝝃 = πŸ”πŸ•πŸπŸ
  • so that π’πŸπŠ β‰ˆ πŸπŸ—πŸ in a plane channel (K.M.M.)
  • βˆ†π’š+ = πŸ“. πŸ“, 𝟏. πŸ˜πŸ’ < βˆ†π’›+ < πŸ•, βˆ†π’œ+ = πŸ”. 𝟘
  • UB magnitude: 𝑁 = 0, 𝟏. 𝟏𝟏𝟐, 𝟏. πŸπŸπŸ”

SMOOTH CASE ROUGH CASE

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

7/15 𝒛 = 𝟏

Model of rough wall

(E. Napoli et al., J. Fluid Mech., 2008)

Roughness displacement

𝜺: channel half height π‘΄π’š: Channel length, πŸ“π†πœΊ 𝑩𝒋: Amplitude of each sinusoid 𝑩𝒋 = α‰Š 𝟐, 𝐠𝐩𝐬 𝒋 = 𝟐 𝟏, 𝟐 , 𝐠𝐩𝐬 𝒋 β‰  𝟐 with rescaling so that 𝒆 π’š = 𝟏. πŸπŸ”πœΊ

𝒆 π’š = 𝜺 ෍

𝒋=𝟐 πŸ“

𝑩𝒋 𝐭𝐣𝐨 πŸ‘π’‹π†π’š Ξ€ π‘΄π’š πŸ‘

𝒆 π’š

𝐧𝐛𝐲 = 𝟏. 𝟐𝟐𝜺

(Defined randomly)

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Coordinate transformation

(S. Kang & H. Choi, Phys. Fluids, 2000)

Calculation grids: 𝝄𝒋 (Cartesian with extra force)

Actual grid points allocation

wall

ቐ π’š = π„πŸ 𝒛 = π›πŸ‘ 𝟐 + 𝛉 + π›‰πž π’œ = π›πŸ’

(𝑦, 𝑧, 𝑨: physical coordinate) 𝛉 ≑ Ξ€ 𝛉𝐯 βˆ’ 𝛉𝒆 πŸ‘ = βˆ’ Ξ€ 𝒆 𝐲 πŸ‘ π›‰πž = 𝐬 𝐲 , 𝛉𝒗 = 𝟏 π›‰πž, 𝛉𝐯: displacement of lower/upper wall

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Post processing

  • Drag coefficient decomposition for rough case
  • Drag reduction rate

π‘†πΈπ‘š = βˆ†π·πΈ 𝐷𝐸,𝑁=0 Γ— 100 [%] 𝐷𝐸𝑣𝑔 = 8 Re𝑐 ቀ 𝑒ഀ 𝑣 𝑒𝑧 𝜊2=2 π·πΈπ‘šπ‘” = 8 Re𝑐 ቀ 𝑒𝑣 𝑒𝑧 𝜊2=0 + ቀ 𝑒𝑀 𝑒𝑦 𝜊2=0 π·πΈπ‘šπ‘ž = βˆ’16 𝑒𝑄 π‘’πœŠ1 βˆ’ π·πΈπ‘šπ‘” + 𝐷𝐸𝑣𝑔

Only focusing on lower side, subscript β€œπ‘šβ€ omitted hereafter

(Friction component) (Pressure component)

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Drag reduction rate, 𝑺𝑬

ROUGH CASE SMOOTH CASE

Total 𝑆𝐸 β†“πŸπŸ% β†“πŸ’πŸ–% β†“πŸ–% β†“πŸ‘πŸ•% Friction 𝑆𝐸,𝐺 β†“πŸπŸ% β†“πŸ’πŸ–% β†“πŸ˜% β†“πŸ’πŸ“% Pressure 𝑆𝐸,𝑄

  • β†“πŸ”%

β†“πŸπŸ˜%

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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How does friction drag decrease?

Bulk mean streamwise velocity

Black: 𝑁 = 0 Green: 𝑁 = 0.001 Red: 𝑁 = 0.005 Normalization based on 𝑁 = 0

Smooth Rough

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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How does pressure drag decrease?

Pressure contours 𝑡 = 𝟏 𝑡 = 𝟏. πŸπŸπŸ”

𝒆 π’š 𝐧𝐛𝐲

averaged in the spanwise and time dashed lines: zero contour

π‘ž+

𝒆 π’š 𝐧𝐣𝐨

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Stream function

Uniform Blowing Solid lines: 𝑁 = 0 Dashed lines: 𝑁 = 0.005

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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In practical applications

Drag reduction amount, βˆ†π‘«π‘¬ = 𝑫𝑬,𝑡=𝟏 βˆ’ 𝑫𝑬,𝑡=𝟏.𝟐,𝟏.πŸ” [%]

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Concluding remarks

DNS of turbulent channel flow over a rough wall with UB

  • UB is effective over rough walls
  • Lower drag reduction rate (7%, πŸ‘πŸ•% / 11%, πŸ’πŸ–% 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
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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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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)?
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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Uniform blowing (UB)

(Sumitani & Kasagi, AIAA J., 1995 Kametani & Fukagata, J. Fluid Mech., 2011)

  • Drag contribution in a channel flow with UB(/US)
  • Excellent performance (about 45% by 𝑾𝒙 = 𝟏. πŸ”%π‘½βˆž)
  • Unknown over a rough wall

π‘«π’ˆ = πŸπŸ‘ 𝑺𝒇𝒄 + πŸπŸ‘ ΰΆ±

𝟏 πŸ‘

𝟐 βˆ’ 𝒛 βˆ’π’—β€²π’˜β€² 𝒆𝒛 βˆ’ πŸπŸ‘π‘Ύπ’™ ΰΆ±

𝟏 πŸ‘

𝟐 βˆ’ 𝒛 ΰ΄₯ 𝒗𝒆𝒛

(Fukagata et al., Phys. Fluids, 2002) Viscous Contribution (= laminar drag, const.) Turbulent contribution Convective (=UB/US) contribution White: vortex core, Colors: wall shear stress

𝑾𝒙: Blowing velocity

Blowing side

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Governing equations

(S. Kang & H. Choi, Phys. Fluids, 2000)

Incompressible Continuity and Navier-Stokes in 𝝄𝒋 coordinate π›œπ’—π’‹ π›œπ„π’‹ = βˆ’π‘» π›œπ’—π’‹ 𝝐𝒖 = βˆ’ π›œ π’—π’‹π’—π’Œ π›œπ„π’Œ βˆ’ 𝝐𝒒 π›œπ„π’‹ + 𝟐 π’πŸπ’„ ππŸ‘π’—π’‹ π›œπ„π’Œπ„π’Œ βˆ’ 𝒆𝑸 πžπ„πŸ πœΊπ’‹πŸ + 𝑻𝒋

𝑇𝑗 = βˆ’πœ’π‘’ πœ–π‘£π‘— πœ–πœŠ2 βˆ’ πœšπ‘˜ πœ– π‘£π‘—π‘£π‘˜ πœ–πœŠ2 βˆ’ πœšπ‘˜ π‘’π‘ž π‘’πœŠ2 πœ€π‘—π‘˜ + 1 𝑆𝑓 2πœšπ‘˜ πœ–2𝑣𝑗 πœ–πœŠπ‘˜πœŠ2 + πœšπ‘˜πœšπ‘˜ πœ–2𝑣𝑗 πœ–πœŠ2

2 + 1

2 πœ– πœšπ‘˜πœšπ‘˜ πœ–πœŠ2 πœ–π‘£π‘— πœ–πœŠ2 πœ’π‘˜ = βˆ’ 1 1 + πœƒ 𝜊2 πœ–πœƒ πœ–πœŠπ‘— + πœ–πœƒ0 πœ–πœŠπ‘— , for j = 1,3 1 1 + πœƒ , for j = 2 πœšπ‘˜ = πœ’π‘˜ βˆ’ πœ€

π‘˜2

𝑇 = πœšπ‘˜ πœ–π‘£π‘— πœ–πœŠ2

where

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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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

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Validation & Verification

(B. Milici et al., J. Fluid Mech., 2014)

Bulk mean streamwise velocity Time trace of instantaneous CD,r Less than 2% of difference with most resolved one

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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How does friction drag decreases?

Reynolds shear stress contour

𝒆 π’š 𝐧𝐛𝐲

𝑣′+𝑀′+ *averaged in the spanwise and time dashed lines: zero contour

𝑡 = 𝟏 𝑡 = 𝟏. πŸπŸπŸ”

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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ΰ΄₯ π’˜ distribution (2D contour)

No control case UB 0.5% case Based on π‘£πœ in w/o control case

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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ΰ΄₯ 𝒗 distribution (2D contour)

No control case UB 0.5% case Based on π‘£πœ in w/o control case

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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Stream function (detailed)

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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𝒗𝐬𝐧𝐭 distribution

Black: w/o control Green: UB 0.1% Red: UB 0.5% Normalized by π‘£πœ in w/o control case

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π’˜π¬π§π­ distribution

Black: w/o control Green: UB 0.1% Red: UB 0.5% Normalized by π‘£πœ in w/o control case

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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𝒙𝐬𝐧𝐭 distribution

Black: w/o control Green: UB 0.1% Red: UB 0.5% Normalized by π‘£πœ in w/o control case

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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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𝒗′+π’˜β€²+ distribution

Black: w/o control Green: UB 0.1% Red: UB 0.5% Normalized by π‘£πœ in w/o control case

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SLIDE 30
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E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall

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  • Effective slope = about 0.2
  • k_rms
  • Sand grain roughness
  • 3D?
  • How to calculate skin-friction drag
  • The history of UB
  • Pressure component legend (purple) of smooth case

should be removed

  • More time for drag reduction rate slide