Direct Numerical Simulation of Drag Reduction with Numerical Simulation of Drag Reduction with Uniform Blowing ... European Drag Reduction and Flow Control Meeting Rome, Apr. 3-6,

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  • Direct Numerical Simulation of

    Drag Reduction with Uniform Blowing

    over a Two-dimensional Roughness

    Eisuke Mori1, Maurizio Quadrio2 and Koji Fukagata1

    1 Keio University, Japan

    2 Politecnico di Milano, Italy

    European Drag Reduction and Flow Control Meeting

    Rome, Apr. 3-6, 2017

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 2/18

    Uniform blowing (UB)

    Drag contribution in a channel flow with UB(/US)

    Excellent performance (about 45% by = . %)

    Unknown over a rough wall

    =

    +

    (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

    : Blowing velocity

    (Kametani & Fukagata, J. Fluid Mech., 2011)

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 3/18

    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 4/18

    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 5/18

    Numerical procedure

    Based on FD code (for wall deformation)(Nakanishi et al., Int. J. Heat Fluid Fl., 2012)

    Constant flow rate, = / =

    - so that in a plane channel (K.M.M.)

    + = . , . < + < , + = .

    UB magnitude: = , . %, . %, %

    SMOOTH CASEROUGH CASE

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 6/18

    =

    Model of rough wall

    Roughness displacement

    : channel half height: Channel length, : Amplitude of each sinusoid

    = , = , ,

    with rescaling so that

    = .

    =

    =

    = .

    (Defined randomly)

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

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 7/18

    The result of the base flow

    +~6.5

    Transitionally-rough regime

    + =

    = 2ave ( + ,)ave: Overall drag coefficient: of the rough wall side

    ,: of the smooth wall side

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 8/18

    The result of UB

    ROUGH CASESMOOTH CASE

    Total, % % % % % %

    = 1 ,ctr,nc

    ,ctr: controlled

    ,nc: no control

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 9/18

    The result of UB

    ROUGH CASESMOOTH CASE

    Total, % % % % % %

    Friction, % % % % % %Pressure, - - % % %

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 10/18

    Bulk mean streamwise velocity

    Friction drag reduction mechanism

    Black: = 0Green: = 0.1%Red: = 0.5%Blue: = 1%

    +nc: normalization

    with no control case

    SMOOTH CASE

    ROUGH CASE

    +

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 11/18

    How does pressure drag decrease?

    Pressure contours averaged in the spanwise and timedashed lines: zero contour

    +nc

    = %

    =

    +

    +

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 12/18

    Smoothing effect

    Wall-normal velocity contours averaged in the spanwise and timedashed lines: zero contour

    +nc

    +

    +

    = %

    =

    + = 38

    + = 20

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 13/18

    Velocity defect

    Outer layer similarity with UB

    Base flow (No controlled) of

    one-side rough wall1% UB case of

    one-side rough wall

    Smooth side

    Rough side

    : distance from a wall to the minimum RMS location

    (K. Bhaganagar et al.,

    Flow, Turbul. Combust., 2004)

  • 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

    both-side smooth wall

    1% UB case of

    one-side rough wall

    Smooth

    side

    Rough

    side

    Suction

    side

    Blowing

    side

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 15/18

    Comparison with smooth case

    Velocity defect

    1% UB case of

    both-side smooth wall

    1% UB case of

    one-side rough wall

    Same tendency, but quantitatively weakened

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 16/18

    Stevensons law of the wall

    Plots using Stevensons law of the wall (Stevenson, 1963)2

    + 1 +

    ++ 1 =1

    ln + +

    +

    Modified law is suggested:

    2

    + 1 +

    ++ 1 =1

    ln + + +

    Roughness function

    +

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 17/18

    Normalization by +

    Drag reduction,

    = , ,

    Drag reduction rate,

    nc: no control

    ctr: controlled becomes similar when plotted with

    +

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 18/18

    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

    reduction amount (when normalized by +nc)

    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 Stevensons law of the wall is suggested

  • Thank you for your kind attention

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 21/18

    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 22/18

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

    Flow control

    strategies

    Passive

    Feedback Feedforward

    Active

    - Uniform blowing

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 23/18

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

    Incompressible Continuity and Navier-Stokes in coordinate

    =

    =

    +

    +

    = 2

    2

    2 +

    1

    2

    22

    + 2

    22 +

    1

    2

    2

    2

    =

    1

    1 + 2

    +0

    , for j = 1,3

    1

    1 + , for j = 2

    = 2 = 2

    where

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 24/18

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

    Calculation grids: (Cartesian with extra force)

    Actual grid points allocation

    wall

    = = + +

    = (, , : physical coordinate)

    =

    = , =

    , : displacement of lower/upper wall

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 25/18

    Post processing

    Drag coefficient decomposition for rough case

    Drag reduction rate

    =

    ,=0 100 [%]

    =8

    Re

    2=2

    =8

    Re

    2=0

    +

    2=0

    = 16

    1 +

    Only focusing on lower side,

    subscript omitted hereafter

    (Friction component)

    (Pressure component)

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 26/18

    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, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 27/18

    Validation & Verification

    Bulk mean streamwise velocity Time trace of instantaneous

    Less than 2% of difference

    from the most resolved case

  • E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 28/18

    Stevensons law of the wall

    Plots using Stevensons law of the wall (Stevenson, 1963)2

    + 1 +

    ++ 1 =1

    ln + +

    +

    Normalized by local Normalized by Stevensons law