Impact of Drag Reduction Control on Energy Box of a Fully Developed - PowerPoint PPT Presentation

Nov. 20, 2017 APS DFD@Denver Impact of Drag Reduction Control on Energy Box of a Fully Developed T urbulent Channel Flow Yosuke Hasegawa Instjtute of Industrial Science, The University of Tokyo, Japan Davide Gattj , Bettjna Frohnapfel Karlsruhe Instjtute of Technology, Germany Andrea Cimarelli Universita Plitecnica delle Marche, Italy Maurizio Quadrio Politecnico di Milano, Italy

2 Back ckgr ground nd • A Fully Developed Channel Flow  Essentjal physics of near-wall turbulence  Flow control ( drag reductjon , mixing enhancement, etc.) • Global Energy Budget Total kinetjc energy = Mean Turbulent 1/24

Back ckgr ground nd • A Fully Developed Channel Flow  Essentjal physics of near-wall turbulence  Flow control ( drag reductjon , mixing enhancement, etc.) • Global Energy Budget Total kinetjc energy = Mean Turbulent Energy Box Direct dissipatjon (diss. of mean fjeld) Turbulent fjeld Mean fjeld 2 𝑒 ´ 𝑣 𝜚 = 1 𝑆𝑓 ( 𝑒𝑧 ) Turbulent Pumping Productjon Power Turbulent dissipatjon 2 ´ 𝑒𝑣 ′ 𝑗 𝑒𝑣 ′ 𝑗 𝜁 = 1 𝑆𝑓 ( 𝑒 𝑦 𝑘 ) 𝑒 𝑦 𝑘 Turbulent dissipatjon Direct dissipatjon 2/24

Dir irect ect and nd Tur urbu bulent lent Dis issipa ipatio ion in in Unco Uncont ntrolle le d Flow Turbulent dissipatjon 𝑺𝒇 𝝊 𝟔𝟏𝟏 Direct dissipatjon 3/24

Objec jectives ves • Drag reductjon control is somewhat similar to make the “efgec tjve” Re lower  Then, the direct dissipatjon increases, while the turbulent dissipatjo n decreases ? • Ultjmate control: complete relaminarizatjon  All input energy should be dissipated by the direct dissipatjon only. Questjons  Is there an unique relatjonship between the changes in direct/turbulent dissipatjon and a drag reductjon efgect ? 4/24

Flow ow Cond nditions ns Flow Rate: Pressure Gradient: Pump X Pumping Power: 5/24

Flow ow Cond nditions ns Flow Rate: Pressure Gradient: Pump X Pumping Power: Flow Rate: Pressure Gradient: Pumping Power: Constant Flow Rate Constant Flow Rate (CFR) (CFR) Constant Constant Constant Pressure Constant Pressure Constant Constant Gradient (CPG) Gradient (CPG) 6/24

Ener ergy Bo Box Under der CP CPG Ricco et al. JFM (2011) Direct Spanwise Wall Oscillatjon Control dissipatjon of U Pumping Mean U Power Turbulence Turbulent productjon Turbulent dissipatjon Control input Mean W Direct Pumping power input changes due to dissipatjon of W the applied control…. 7/24

Flow ow Cond nditions ns Flow Rate: Pressure Gradient: Pump X Pumping Power: Flow Rate: Pressure Gradient: Pumping Power: Constant Flow Rate Constant Flow Rate Constant Constant (CFR) (CFR) Constant Pressure Constant Pressure Constant Constant Gradient (CPG) Gradient (CPG) Constant Power Input Constant Power Input Constant Constant (CPI) (CPI) 8/24

Co Conce cept pt of of Con onst stan ant Pow ower er Inpu put (C (CPI PI) (Frohnapfel et al. JFM 2012, Hasegawa et al. JFM 2014) Flow Rate: Pumping Power : Control Pump Input : X Dissipatjon • Fractjon of Control Power Input • Total Power Input 𝛅 = Π 𝑑 / Π t 𝚸 𝐮 = 𝑑𝑝𝑜𝑡𝑢 . ∗ ∗ = Π 𝑞 ∗ + Π 𝑑 ∗ ∗ • Power-based Reynolds Number • Max. Achievable Flow Rate ∗ 𝜀 ∗ 𝑆𝑓 Π = 𝑽 𝜬 𝚸 𝐮 ∗ 𝜀 ∗ = √ ∗ 𝑉 Π 𝜉 ∗ 3 𝜈 ∗ 9/24

Exampl Exa ple Flow Rate: Pumping Power : - (CPG) Pump Control - (CFR) X Input : • Control Schemes - Oppositjon Control (Choi et al. JFM 1998) - Spanwise Wall Oscillatjon (Jung et al. PoF 1992) / Reference (NC) Reference (NC) 1.0 1.0 0.4887 0.4887 0 0 10/24

Exa Exampl ple Flow Rate: Pumping Power : - (CPG) Pump Control - (CFR) X Input : • Control Schemes - Oppositjon Control (Choi et al. JFM 1998) - Spanwise Wall Oscillatjon (Jung et al. PoF 1992) / Reference (NC) Reference (NC) 1.0 1.0 0.4887 0.4887 0 0 Wall Oscillatjon Wall Oscillatjon 1.028 1.028 0.5026 0.5026 0.0978 0.0978 Oppositjon Control Oppositjon Control 1.094 1.094 0.5345 0.5345 0.0035 0.0035 11/24

En Ener ergy gy Bo Box of Unco ncontr ntrolle lled Fl ow 12/24

En Ener ergy Box unde der Op Oppo posi siti tion Co Contr trol Direct dissipatjon increases Turbulent dissipatjon decreases 13/24

Ene nergy Box und nder er Wall all Os Osci cilla llatio tion Co Cont ntrol Direct dissipatjon decreases Turbulent dissipatjon increases 14/24

Ene nergy Box und nder er Wall all Os Osci cilla llatio tion Co Cont ntrol Direct dissipatjon decreases Opposite trends in the changes of direct/turbulent dissipatjon for drag-reduced fmows Turbulent dissipatjon increases Can we explain it ? 15/24

Fl Flow Rate te Und nder er CP CPI • FIK Identjty (Fukagata et al. PoF 2002) 𝑽 𝒄 = 𝜷 𝑺𝒇 𝚸 𝟑 { − 𝟐 + √ 𝟑 } 𝟐 + 𝟓 ( 𝟐 − 𝜹 ) ( 𝜷 𝑺𝒇 𝚸 ) (Hasegawa et al. JFM 2014) The fmow rate is determined by and only. • Fractjon of Control Power Input Two Limitjng Cases 𝛅 = Π 𝑑 / Π t ∗ ∗ 𝜷 → 𝟏 { 𝜹 → 𝟏 𝑽 𝒄 → 𝟐 • Weighted Reynolds Shear Stress 𝟐 ′ 𝒘 ′ ) 𝒆𝒛 ´ ( 𝟐 − 𝒛 ) ( 𝜷 = ∫ − 𝒗 𝜷 →∞ 𝑽 𝒄 → 𝟏 𝟏 16/24

Ener nergy Flu lux Unde der CP CPI • Triple Decompositjon 𝑣 = 𝑉 + 𝑣 ′ 17/24

Ener nergy Flu lux Unde der CP CPI : parabolic profjle with the same fmow rate : deviatjon from parabola • Triple Decompositjon 𝑣 = 𝑉 + 𝑣 ′ = 𝑉 𝑚𝑏𝑛 + Δ 𝑉 + 𝑣 ′ (Echhardt et al., JFM 2007) 𝑽 𝑉 𝑚𝑏𝑛 Δ 𝑉 18/24

Ener nergy Flu lux Unde der CP CPI • Productjon 1 1 ′ 𝑤 ′ 𝑒𝑉 𝑚𝑏𝑛 ′ 𝑤 ′ 𝑒 Δ 𝑉 ´ ´ 𝑄 = 𝑄 𝑚𝑏𝑛 + 𝑄 Δ = ∫ 𝑣 𝑒𝑧 + ∫ 𝑣 𝑒𝑧 − − 𝑒𝑧 𝑒𝑧 0 0 • Direct Dissipatjon 1 1 2 2 𝑒𝑉 𝑒 1 1 { 𝑒𝑧 ( 𝑉 𝑚𝑏𝑛 + Δ 𝑉 ) } ( 𝑒𝑧 ) 𝜚 = 𝑒𝑧 = 𝑒𝑧 𝑆𝑓 Π ∫ 𝑆𝑓 Π ∫ 0 0 1 2 𝑒𝑉 𝑚𝑏𝑛 𝑒𝑉 𝑚𝑏𝑛 2 { ( 𝑒𝑧 ) } 𝑒𝑧 𝑒 Δ 𝑉 𝑒 Δ 𝑉 1 𝑒𝑧 ) + ( 𝑒𝑧 ) ( + ( 𝑒𝑧 ) 𝑆𝑓 Π ∫ ¿ 0 ¿ 𝜚 𝑚𝑏𝑛 + 𝜚 Δ Only true in the present triple decompositjon In additjon, it can be shown that 19/24

Mod odifj ifjed ed En Energy Box 20/24

Mod Modifje fjed Energy Box • Direct Dissipatjon () 2 𝑆𝑓 Π { ( 𝜷 𝑆𝑓 Π ) 2 ) + ( 1 − 𝛿 ) } 1 + 4 ( 1 − 𝛿 ) 3 ( 1 − √ 𝜚 𝑚𝑏𝑛 = 2 𝜷 𝑆𝑓 Π 𝜚 Δ = 𝑆𝑓 Π ( 𝜸 − 3 𝜷 2 ) • Turbulent Dissipatjon 2 2 𝑆𝑓 Π { ( 𝜷 𝑆𝑓 Π ) + 𝛿 } 2 ) − 𝜸 𝑆𝑓 𝛲 1 + 4 ( 1 − 𝛿 ) 3 ( 1 + √ 𝜁 = 2 3 𝜷 𝑆𝑓 Π The following two quantjtjes dictates all the fmuxes in Energy Box !!! 𝟐 𝟐 𝟑 𝒆𝒛 ′ 𝒘 ′ ) 𝒆𝒛 ´ ´ − 𝒗 ′ 𝒘 ′ ) ( 𝟐 − 𝒛 ) ( ( 𝜷 = ∫ − 𝒗 𝜸 = ∫ 𝟏 𝟏 21/24

Con onclusions ns • Constant Power Input (CPI) is benefjcial to analyze global energy • budgets of turbulent fmows w/wo control • There exists no unique relatjonship between the changes in direc t/turbulent dissipatjon and DR efgect • DR efgect under CPI is determined only by : the integral of weight ed RSS • Triple decompositjon of the velocity fjeld reveals that global ener gy fmuxes are expressed by two quantjtjes: and . 𝟐 𝟐 𝟑 𝒆𝒛 ′ 𝒘 ′ ) 𝒆𝒛 ´ ´ − 𝒗 ′ 𝒘 ′ ) ( 𝟐 − 𝒛 ) ( ( 𝜷 = ∫ − 𝒗 𝜸 = ∫ 𝟏 𝟏 • Total dissipatjon: • “Wind” dissipatjon can be considered to be a loss from energetjc viewpoint.  A target quantjty to be minimized 23/24

Th Thank you for yo your kin ind atten tten tio tion Questions ?