Cimarelli, Andrea

Frohnapfel, Bettina

Gatti, Davide

Hasegawa, Yosuke

Quadrio, Maurizio

English

KITopen

www.kit.eduKIT – The Research University in the Helmholtz AssociationGAMM Meeting 2018, March 19—23, Munich, GermanyIntegral energy budgets in turbulent channels with and without drag reductionDavide Gatti, M. Quadrio, Y. HasegawaB. Frohnapfel and A. Cimarelli2 16.10.2018Today’s goal“how do dissipation and production of turbulent kinetic energy relate to turbulent friction drag?”1 Davide Gatti – Energy transfer rates in turbulent channels with drag reduction3 16.10.2018Today’s goalXpumping powerturbulentproduction“how do dissipation and production of turbulent kinetic energy relate to turbulent friction drag?” turbulent 𝜖 + mean 𝜙dissipation rateΠp𝑃𝑢 = 𝑢 + 𝑢′Reynolds decomposition1 Davide Gatti – Energy transfer rates in turbulent channels with drag reduction4 16.10.2018Today’s goalcontrolinputXΠcpumping powerturbulentproduction“how do dissipation and production of turbulent kinetic energy relate to turbulent friction dragin drag-reduced flows?”turbulent 𝜖 + mean 𝜙dissipation rateΠp𝑃Seemingly trivial, nontrivial problem! Example turbulent dissipation in drag-reduced flow:Ricco et al., JFM (2012): it increasesAgostini, et al., JFM14: it decreases𝑢 = 𝑢 + 𝑢′Reynolds decomposition1 Davide Gatti – Energy transfer rates in turbulent channels with drag reductionConstant Power Input (CPI)6 16.10.2018Constant Power Input (CPI)Total power Π𝑡 is kept constant  Davide Gatti – Energy transfer rates in turbulent channels with drag reductionDefinitions and characteristic quantitiesΠ𝑡 = Π𝑝 + Π𝑐Π𝑝 = 1 − 𝛾 Π𝑡Π𝑐 = 𝛾Π𝑡pumping power control power A power-based velocity scale 𝑈Π =Π𝑡ℎ3𝜇Bewley (JFM, 2009), Fukagata et al. (Physica D, 2009)A power-based Reynolds number 𝑅𝑒Π =𝑈Πℎ𝜈Hasegawa, Frohnapfel, Quadrio (JFM, 2009)“The Stokes flow minimizes the power consumption for given flow rate”2„Drag reduction“ increases flow rate 𝑈𝑏/𝑈𝑏,0> 1The wind of turbulence8 16.10.2018The “wind decomposition” of turbulenceDavide Gatti – Energy transfer rates in turbulent channels with drag reductionA triple decomposition with analytical advantages𝑢 = 𝑢 + 𝑢′3Eckhardt et al, JFM 20079 16.10.2018The “wind decomposition” of turbulenceDavide Gatti – Energy transfer rates in turbulent channels with drag reductionA triple decomposition with analytical advantages𝑢 = 𝑈ℓ + 𝑈Δ + 𝑢′𝑢3Eckhardt et al, JFM 200710 16.10.2018Production and mean dissipationDavide Gatti – Energy transfer rates in turbulent channels with drag reductionMean dissipation decouples!𝜙 = 𝜙ℓ + 𝜙Δ + 𝜙ℓ,Δ𝑃 = 𝑃ℓ + 𝑃Δ 0411 16.10.2018Analytical derivationsDavide Gatti – Energy transfer rates in turbulent channels with drag reductionA fair amount of cumbersome algebra[This page intentionally left blank.]D. Gatti et al., J. Fluid Mech. (submitted)512 16.10.2018The new descriptionDavide Gatti – Energy transfer rates in turbulent channels with drag reduction613 16.10.2018The new descriptionDavide Gatti – Energy transfer rates in turbulent channels with drag reduction614 16.10.2018The new descriptionDavide Gatti – Energy transfer rates in turbulent channels with drag reduction615 16.10.2018The new descriptionDavide Gatti – Energy transfer rates in turbulent channels with drag reduction616 16.10.2018The new descriptionDavide Gatti – Energy transfer rates in turbulent channels with drag reduction617 16.10.2018Two integrals of the turbulent shear stressVia FIK-like derivations, it is discovered that 𝛼 and 𝛽 parametrize all the fluxesE.g. Davide Gatti – Energy transfer rates in turbulent channels with drag reduction𝛼 = න011− 𝑦 𝑟 𝑦 d𝑦𝛽 = න01𝑟2 𝑦 d𝑦 ≥ 3𝛼2𝑃Δ = −𝜙Δ = 𝑅𝑒Π 3𝛼2 − 𝛽2 ≤ 0718 16.10.2018Key results𝜙ℓ is the best way to dissipate pumping power𝑃ℓ is the fraction of pumping power wasted to produce turbulenceit decreases when control is successfulit can be negative as 𝑃ℓ ~ 𝛼𝜙Δ is the penalty for not being laminar𝜙Δ + 𝜖 is the fraction of total power wasted by turbulenceit cannot be negativeDavide Gatti – Energy transfer rates in turbulent channels with drag reductionEvery flux has a physical meaning819 16.10.2018A drag reduction modelControl effect parametrized through Δ𝐵Davide Gatti – Energy transfer rates in turbulent channels with drag reductionapplicable to:riblets and roughnesssuperhydrophobic surfacesspanwise wall forcingsome feedback controls920 16.10.2018A drag reduction modelControl effect parametrized through Δ𝐵Empirical description of velocity profile (Luchini, Phys. Rev. Letters, 2017)CPI contraint 3𝑅𝑒Π2 1− 𝛾 = 𝑅𝑒𝜏2𝑅𝑒𝐵Davide Gatti – Energy transfer rates in turbulent channels with drag reduction921 16.10.2018How do dissipations change with control?Davide Gatti – Energy transfer rates in turbulent channels with drag reduction10Back to our initial question22 16.10.2018How do dissipations change with control?Davide Gatti – Energy transfer rates in turbulent channels with drag reductionspanwise wall oscillations𝛿𝑊𝑤 = 𝐴sin(𝜔𝑡)𝑥𝑦𝑧11Back to our initial question23 16.10.2018How do dissipations change with control?Davide Gatti – Energy transfer rates in turbulent channels with drag reductionopposition control𝑦𝑠𝑣𝑤 = −𝑣(𝑥, 𝑦𝑠, 𝑧, 𝑡)𝑥𝑦𝑧12Back to our initial question24 16.10.2018How do dissipations change with control?Davide Gatti – Energy transfer rates in turbulent channels with drag reduction13Back to our initial question25 16.10.2018Conclusion and outlookDavide Gatti – Energy transfer rates in turbulent channels with drag reduction“Wind” decomposition and CPI introducedTheoretical framework for the flow control problem from energy perspective……relevant also for uncontrolled flows: FIK-like identity for 𝜖Optimal control theory: better choice of cost functionDevelopment of drag-reduction-aware RANS turbulence modelsCPI-enabled scale-energy analysis of drag reduced flows1426 16.10.2018Bad Herrenalb (near Karlsruhe, Germany)26—29 March 2019Davide Gatti – Energy transfer rates in turbulent channels with drag reductionEuropean Drag Reduction and Flow Control Meeting1527 16.10.2018European Drag Reduction and Flow Control Meeting Topics:all laminar and turbulent drag reduction flow & noise control studiesAttended by all major scientists in the fieldYoung contributors are invited to submit abstractsConference fee ~ 400€ including accommodation!  More info: www.edrfcm.scienceDavide Gatti – Energy transfer rates in turbulent channels with drag reduction28 16.10.2018THANKSfor your kind attention!for questions, complaints, ideas:davide.gatti@kit.edu16 Davide Gatti – Energy transfer rates in turbulent channels with drag reduction

Integral energy budgets in turbulent channels with and without drag reduction

https://publikationen.bibliothek.kit.edu/1000091445/23291438

Integral energy budgets in turbulent channels with and without drag reduction

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