Cimarelli, Andrea

Frohnapfel, Bettina

Gatti, Davide

Hasegawa, Yosuke

Quadrio, Maurizio

Remigi, Alberto

English

KITopen

www.kit.eduKIT – The Research University in the Helmholtz Association16th EUROPEAN TURBULENCE CONFERENCE, Stockholm, Sweden𝒀𝒄𝒖(𝒀𝒄 − Τ𝒓 2)𝒖(𝒀𝒄 + Τ𝒓 2)𝑟𝑧𝑟𝑦𝑟𝑥Scale energy fluxes in turbulent channelswith drag reductionat constant power inputDavide Gatti, A. Remigi, A. Cimarelli, Y. Hasegawa, B. Frohnapfel, M. Quadrio2 23.08.2017The question in drag reduction“how do turbulent flows with and without drag reduction differ?”Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power inputComparison between different flows requiredVery different outcomes depending upon how flow is driven13 23.08.2017Our question in drag reduction“how do turbulent flows with and without drag reduction differ energetically?”Comparison between different flows requiredVery different outcomes depending upon how flow is drivenAn example: enstrophy in drag reduced flows:Ricco et al., JFM12: at CPG increasesAgostini, et al., JFM14: at CFR decreasesGatti et al., submitted: …it depends!Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input24 23.08.2017Today’s goalDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input3controlinputXPcPpviscous dissipation ratepumping powertransporttransform“how do turbulent flows with and without drag reduction differ energetically?”Assess changes of scale energy fluxes in turbulent channels driven at Constant Power Input (Hasegawa et al., JFM14)5 23.08.2017A model control strategy𝑥𝑦𝑧𝑧𝑦𝑠𝑣𝑤 = −𝑣(𝑥, 𝑦𝑠, 𝑧, 𝑡)𝑦𝑠−𝑣𝑤Opposition Control (Choi, Moin & Kim, JFM94)𝑅𝑒𝜏 =𝑢𝜏ℎ𝜈= 200 𝑅𝑒𝜏 = 190.5𝑅𝑒𝑏 =𝑈𝑏ℎ𝜈= 3177 𝑅𝑒𝑏 = 3474𝑅 = 1 − ൘𝐶𝑓𝐶𝑓,0= 23.9%drag reductioncontrol power fraction𝑈𝑏𝑈𝑏,𝑟𝑒𝑓= 1.094𝛾 = ൗP𝑐P𝑡= 0.0035reference controlledDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input46 23.08.2017Second-order structure function (1)𝛿𝑢2 𝒓, 𝑿𝑐 = 𝑢 𝑿𝒄 − Τ𝒓 2 − 𝑢 𝑿𝒄 + Τ𝒓 2 𝑖2𝛿𝒖𝒖′ = 𝒖 𝒙 + 𝒓, 𝑡𝒖 = 𝒖 𝒙, 𝑡𝒙𝑿𝒄𝒓loosely speaking, amount of fluctuation energy at scale 𝒓𝒙′Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input57 23.08.2017Second-order structure function (2)𝛿𝑢2 𝒓, 𝑌𝑐 = 𝑢 𝑿𝒄 − Τ𝒓 2 − 𝑢 𝑿𝒄 + Τ𝒓 2 𝑖2in channels function of wall-normal coordinate 𝑌𝑐 and vector 𝒓𝑌𝑐𝑟𝑥𝑟𝑧𝑟𝑦Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input68 23.08.2017Kinetic energy budget𝑃dΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budgetDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑌𝑐+79 23.08.2017Kinetic energy budget𝑠dΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budgetDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑌𝑐+710 23.08.2017Kinetic energy budget𝑠ΦdΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budgetDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑌𝑐+711 23.08.2017Scale energy budgetdΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budget𝛁𝒓 ⋅ 𝚽𝒓 +𝜕Φc𝜕𝑌𝑐= 𝑠(𝒓, 𝑌𝑐)𝛿𝑢2 budget𝑠ΦDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑌𝑐+812 23.08.2017Scale energy budget: 𝒓𝒛, 𝒀𝒄 spacedΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budget𝛁𝒓 ⋅ 𝚽𝒓 +𝜕Φc𝜕𝑌𝑐= 𝑠(𝒓, 𝑌𝑐)𝛿𝑢2 budget𝑠Φ𝑠𝑌𝑐𝑟𝑧Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑟𝑧+𝑌𝑐+𝑌𝑐+913 23.08.2017Scale energy budget: 𝒓𝒛, 𝒀𝒄 spacedΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budget𝛁𝒓 ⋅ 𝚽𝒓 +𝜕Φc𝜕𝑌𝑐= 𝑠(𝒓, 𝑌𝑐)𝛿𝑢2 budget𝑠Φ𝑠Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑟𝑧+𝑌𝑐+𝑌𝑐+914 23.08.2017Scale energy budget: 𝒓𝒛, 𝒀𝒄 spacedΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budget𝛁𝒓 ⋅ 𝚽𝒓 +𝜕Φc𝜕𝑌𝑐= 𝑠(𝒓, 𝑌𝑐)𝛿𝑢2 budget𝑠Φ𝑠Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑟𝑧+𝑌𝑐+𝑌𝑐+915 23.08.2017𝒓𝒛, 𝒀𝒄 space with drag reduction𝑠𝑠Opposition Control ReferenceDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑟𝑧+ 𝑟𝑧+𝑌𝑐+ 𝑌𝑐+1016 23.08.2017𝒓𝒛, 𝒀𝒄 space with drag reduction𝑠𝑠Opposition Control ReferenceDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑟𝑧+ 𝑟𝑧+𝑌𝑐+ 𝑌𝑐+1017 23.08.2017𝒓𝒙, 𝒓𝒛, 𝒀𝒄 space𝑟𝑧𝑟𝑥𝑌𝑐𝑌𝑐𝑟𝑧𝑟𝑥referenceopposition controlDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input118 23.08.2017ConclusionConstant Power Input (CPI) approach is essential to assess energy transfer rates in drag-reduced flowsScale energy budget is modified by the control in the near-wall regionhighlights some mechanisms of drag reductionPaths of energyonly small differences in drag reduced flow…… when the comparison is fair! (CPI)small differences are important!!Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input1219 23.08.2017OutlookQuantitatively assess small control-induced changesConsider the whole 4D 𝑟𝑥, 𝑟𝑦, 𝑟𝑧, 𝑌𝑐 -space Consider the budget equation for 𝛿𝑢𝛿𝑣Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input1320 23.08.2017THANKSfor your kind attention!for questions, suggestions, complaints:davide.gatti@kit.edu14 Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input21 23.08.2017Comparing energy transfer rates correctlyHasegawa et al., JFM (2014) propose Constant Power Input:CPI =CFR = ?𝑈𝑏 −d𝑝d𝑥𝐏𝐩 = −d𝑝d𝑥ℎ𝑈𝑏 𝐏𝐭 = 𝐏𝐩 + 𝐏𝐜 𝑪𝒇CPG =successful control 𝑹 = 1 −𝐶𝑓𝐶𝑓,0> 0 in turbulent channelsDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input3𝑃𝑝 and 𝑃𝑡 change between controlled and natural flow!!22 23.08.2017OutlookQuantitatively assess small control-induced changesConsider the whole 4D 𝑟𝑥, 𝑟𝑦, 𝑟𝑧, 𝑌𝑐 -space Consider the budget equation for 𝛿𝑢𝛿𝑣Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑌𝑐𝑟𝑦𝑟𝑧23 23.08.2017Results - vcProf. Max Mustermann - Title𝑃Φ24 23.08.2017Results - owProf. Max Mustermann - Title𝑃Φ25 23.08.2017Results - refProf. Max Mustermann - Title26 23.08.2017Results - refProf. Max Mustermann - Title27 23.08.2017Results - refProf. Max Mustermann - Title28 23.08.2017CFR = ?𝑈𝑏 −d𝑝d𝑥𝐏𝐩 = −d𝑝d𝑥ℎ𝑈𝑏 𝐏𝐭 = 𝐏𝐩 + 𝐏𝐜 𝑪𝒇CPG =successful control 𝑹 = 1 −𝐶𝑓𝐶𝑓,0> 0How to drive the flow?Dr.-Ing. Davide Gatti – Energy transfer rates in turbulent channels with drag reduction29 23.08.2017Control strategiesSpanwise wall oscillations𝑅 = 1 − ൘𝐶𝑓𝐶𝑓,0= 17.1%drag reductioncontrol power fraction𝑈𝑏𝑈𝑏,𝑟𝑒𝑓= 1.028𝛿𝑤𝑤 = 𝐴sin(𝜔𝑡)𝑥𝑦𝑧𝛾 = ൗP𝑐P𝑡= 0.098Dr.-Ing. Davide Gatti – Energy transfer rates in turbulent channels with drag reductionOpposition control𝑥𝑦𝑧𝑦𝑧𝑦𝑠𝑣𝑤 = −𝑣(𝑥, 𝑦𝑠, 𝑧, 𝑡)𝑦𝑠−𝑣𝑤𝑅 = 23.9%𝛾 = 0.0035𝑈𝑏𝑈𝑏,𝑟𝑒𝑓= 1.09430 23.08.2017Scale energy budgetdΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budget𝛁𝒓 ⋅ 𝚽𝒓 +𝜕Φc𝜕𝑌𝑐= 𝑠(𝒓, 𝑌𝑐)𝛿𝑢2 budget𝑠Φdivergence of fluxesDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑌𝑐+931 23.08.2017Scale energy budgetdΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budget𝛁𝒓 ⋅ 𝚽𝒓 +𝜕Φc𝜕𝑌𝑐= 𝑠(𝒓, 𝑌𝑐)𝛿𝑢2 budget𝑠Φsource term𝑠 𝒓, 𝑌𝑐budget between 𝑃 and dissipation 𝜖Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑌𝑐+932 23.08.2017Scale energy budgetdΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budget𝛁𝒓 ⋅ 𝚽𝒓 +𝜕Φc𝜕𝑌𝑐= 𝑠(𝒓, 𝑌𝑐)𝛿𝑢2 budget𝑠Φspace fluxΦ𝑐 𝒓, 𝑌𝑐transport of 𝛿𝑢2 in geometric spacein a channel flow, transfer of energyat scale 𝒓 in 𝑌𝑐-directionDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑌𝑐+933 23.08.2017Scale energy budgetdΦd𝑌𝑐= 𝑃 − 𝜖 = 𝑠(𝑌𝑐)𝑘 = 12𝑢𝑖2 budget𝛁𝒓 ⋅ 𝚽𝒓 +𝜕Φc𝜕𝑌𝑐= 𝑠(𝒓, 𝑌𝑐)𝛿𝑢2 budget𝑠Φscale flux𝚽𝐫 𝒓, 𝑌𝑐transport of 𝛿𝑢2 across scales 𝒓not visible in the TKE budget!Davide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input𝑌𝑐+934 23.08.2017A model control strategy𝑥𝑦𝑧𝑧𝑦𝑠𝑣𝑤 = −𝑣(𝑥, 𝑦𝑠, 𝑧, 𝑡)𝑦𝑠−𝑣𝑤Opposition Control (Choi, Moin, Kim, JFM94)𝑅𝑒𝜏 =𝑢𝜏ℎ𝜈= 200 𝑅𝑒𝜏 = 190.5𝑅𝑒Π =𝑈𝜋ℎ𝜈= 6500 𝑅𝑒Π = 6500𝑅𝑒𝑏 =𝑈𝑏ℎ𝜈= 3177 𝑅𝑒𝑏 = 3474𝑅 = 1 − ൘𝐶𝑓𝐶𝑓,0= 23.9%drag reductioncontrol power fraction𝑈𝑏𝑈𝑏,𝑟𝑒𝑓= 1.094𝛾 = ൗP𝑐P𝑡= 0.0035reference controlledDavide Gatti - Scale energy fluxes in turbulent channels with drag reduction at constant power input4

Scale energy fluxes in turbulent channels with drag reduction at constant power input

https://publikationen.bibliothek.kit.edu/1000091449/23313143

Scale energy fluxes in turbulent channels with drag reduction at constant power input

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