Bernardini, M.

Chiarini, A.

Gattere, F.

Gatti, D.

Quadrio, M.

Zanolini, M.

English

Archivio istituzionale della ricerca - Politecnico di Milano

Turbulent drag reduction using spanwise forcing incompressible regimeF. Gattere1, A. Chiarini1, M. Zanolini1, D. Gatti2, M. Bernardini3 & M. Quadrio1September 2022, European Drag Reduction and Flow Control Meeting 20221Politecnico di Milano, 2Karlsruhe Institute of Technology, 3La Sapienza Università di Roma1Skin friction drag reduction by spanwise forcingTravelling waves of spanwise oscillation(Quadrio et al., JFM 2009)W(x, t) = A sin(κxx − ωt)• At Reτ = 200 and A+ = 12 Dragreduction up to ≈ 48%• Steady waves and oscillating wall areobtained for ω = 0 and κx = 02Towards real-world applications• Reynolds number dependenceGatti & Quadrio, JFM 2016• Effect on the other drag sources incomplex bodiesQuadrio et al., JFM 2022• Effect of the Mach number≈ Yao & Hussain, JFM 20193Towards real-world applications• Reynolds number dependenceGatti & Quadrio, JFM 2016• Effect on the other drag sources incomplex bodiesQuadrio et al., JFM 2022• Effect of the Mach number≈ Yao & Hussain, JFM 20193Towards real-world applications• Reynolds number dependenceGatti & Quadrio, JFM 2016• Effect on the other drag sources incomplex bodiesQuadrio et al., JFM 2022• Effect of the Mach number≈ Yao & Hussain, JFM 20193In this workWe extend the work by Yao & Hussain (JFM, 2019) and study streamwise travelling wavesfor drag reduction in the compressible regime at different Mach numbersControlledUncontrolled ControlledMb = 0.8Mb = 1.54Simulation details• Direct Numerical Simulations of a perfect heat-conducting gas• STREAmS solver (Bernardini et al, CPC 2021)• Mb = Ub/cw = 0.3, 0.8 and 1.5• Constant flow rate (CFR)• For the uncontrolled case: Reτ = 400• For each Mb: 1 uncontrolled and 42 controlled simulations• A+ = 12 for the controlled simulations• (Lx, Ly, Lz) = (6πh, 2h, 2πh) with Lx that is adjusted depending on λx• (Nx,Ny,Nz) = (1024, 258, 512)5The bulk temperature TbTwo possibilities for the time evolution ofTb =12hρbUb∫ h−h〈ρuT〉dy• Tb freely evolves in time • Tb/Tw is kept constant• The asymptotic value is reached whenthe heat produced within the flow isbalanced by the heat flux at theisothermal walls• As in Yao & Hussain (JFM 2019)• TbTw =11+s γ−12 rM2bto set the ratio of bulkflow kinetic energy converted into wallheat flux s• s = 0.75, meaning that 75% of thekinetic energy is transformed intothermal energy6The bulk temperature TbTwo possibilities for the time evolution ofTb =12hρbUb∫ h−h〈ρuT〉dy• Tb freely evolves in time • Tb/Tw is kept constant• The asymptotic value is reached whenthe heat produced within the flow isbalanced by the heat flux at theisothermal walls• As in Yao & Hussain (JFM 2019)• TbTw =11+s γ−12 rM2bto set the ratio of bulkflow kinetic energy converted into wallheat flux s• s = 0.75, meaning that 75% of thekinetic energy is transformed intothermal energy6The bulk temperature TbTwo possibilities for the time evolution ofTb =12hρbUb∫ h−h〈ρuT〉dy• Tb freely evolves in time • Tb/Tw is kept constant• The asymptotic value is reached whenthe heat produced within the flow isbalanced by the heat flux at theisothermal walls• As in Yao & Hussain (JFM 2019)• TbTw =11+s γ−12 rM2bto set the ratio of bulkflow kinetic energy converted into wallheat flux s• s = 0.75, meaning that 75% of thekinetic energy is transformed intothermal energy6Simulations• Line 1: Oscillating wall• Line 2: Steady wave• Line 3: Travelling wave withκ+x = 0.005• Line 4: Travelling wave withω+ = −0.21• Line 5: Optimum ridge fordrag reduction7Performance indicator• Drag reduction rate DRDR = P0 − PP0whereP = UbTaveLxLz∫ tfti∫ Lx0∫ Lz0τxdzdxdt• Power required to create the wall forcing PinPin =1TaveLxLz∫ tfti∫ Lx0∫ Lz0Wτzdzdzdt• Net energy saving rate PnetPnet = DR−PinP08Line 1: Oscillating wall0 100 200 30002040T+DR%Mb = 0.3 Mb = 0.8Mb = 1.5 GQ-2016• For Mb = 0.3: T+max ≈ 100, like in theincompressible regime• When Mb ↑, the DR− T trendqualitatively does not change• When Mb ↑• DR ↓ for small T• DR ↑ for large T9Line 2: steady wave0 0.005 0.01 0.015 0.02 0.02502040k+xDR%Mb = 0.3 Mb = 0.8Mb = 1.5 GQ-2016• For Mb = 0.3: κ+x,max ≈ 0.005, like in theincompressible regime• When Mb ↑• DR ↑ for small κx• DR ↓ for large κx10Line 3: Travelling waves with κ+x = 0.005−0.2 −0.1 0 0.1 0.2 0.3−200204060ω+DR%Mb = 0.3 Mb = 0.8Mb = 1.5 GQ-2016• For Mb = 0.3: results agree with theincompressible regime• When Mb ↑:• DR ↓ for ω+ < 0 and ω+ > 0.06• DR ↑ for 0 < ω+ < 0.06• When Mb ↑• the global DR peak moves towardslarger ω• the second local DR peak movestowards smaller ω• When Mb ↑ the DI region shrinks11Power budgets: Line 3−0.2 0 0.2−200−150−100−500ω+−P in%Mb = 0.3 Mb = 0.8Mb = 1.5−0.2 0 0.2−150−100−500ω+P net%Mb = 0.3 Mb = 0.8Mb = 1.5• |Pin|% ↓ when Mb ↓• Pnet% ↑ when Mb ↑.• Pnet = 10%, 20% and 30% forMb = 0.3, 0.8 and 1.5.12Power budgets: Line 3−0.2 0 0.2−200−150−100−500ω+−P in%Mb = 0.3 Mb = 0.8Mb = 1.5−0.2 0 0.2−150−100−500ω+P net%Mb = 0.3 Mb = 0.8Mb = 1.5• |Pin|% ↓ when Mb ↓• Pnet% ↑ when Mb ↑.• Pnet = 10%, 20% and 30% forMb = 0.3, 0.8 and 1.5. 12The bulk temperature Tb: Line 3 (κ+x = 0.005)Mb = 0.8 Mb = 1.5• Tb ↑ when Mb ↑• Tb ↑ when the control is active and ∆Tb = Tb − Tb,0 ↑ with MbIs the increase of ∆Tb the dominant effect? 13The bulk temperature TbTwo possibilities for the time evolution ofTb =12hρbUb∫ h−h〈ρuT〉dy• Tb freely evolves in time • Tb/Tw is kept constant• The asymptotic value isreached when the heatproduced within the flow isbalanced by the heat flux atthe isothermal walls• As in Yao & Hussain (JFM 2019)• TbTw=11+ sγ−12 rM2bto set the ratio of bulk flowkinetic energy converted into wall heat flux s• 75% of the kinetic energy is transformed intothermal energy (s = 0.75)• Same Tb/Tw for the reference and controlledcases14The bulk temperature TbTwo possibilities for the time evolution ofTb =12hρbUb∫ h−h〈ρuT〉dy• Tb freely evolves in time • Tb/Tw is kept constant• The asymptotic value isreached when the heatproduced within the flow isbalanced by the heat flux atthe isothermal walls• As in Yao & Hussain (JFM 2019)• TbTw=11+ sγ−12 rM2bto set the ratio of bulk flowkinetic energy converted into wall heat flux s• 75% of the kinetic energy is transformed intothermal energy (s = 0.75)• Same Tb/Tw for the reference and controlledcases14The bulk temperature TbTwo possibilities for the time evolution ofTb =12hρbUb∫ h−h〈ρuT〉dy• Tb freely evolves in time • Tb/Tw is kept constant• The asymptotic value isreached when the heatproduced within the flow isbalanced by the heat flux atthe isothermal walls• As in Yao & Hussain (JFM 2019)• TbTw=11+ sγ−12 rM2bto set the ratio of bulk flowkinetic energy converted into wall heat flux s• 75% of the kinetic energy is transformed intothermal energy (s = 0.75)• Same Tb/Tw for the reference and controlledcases14Line 3 (κ+x = 0.005): Effect of TbTb freely evolving Tb/Tw fixed−0.2 0 0.2−200204060ω+DR%Mb = 0.3Mb = 0.8Mb = 1.5GQ-2016−0.20 0.00 0.20−200204060ω+DR%Mb = 0.3Mb = 0.8Mb = 1.5GQ-2016• When Tb/Tw is fixed the DR curves almost collapse15Line 3 (κ+x = 0.005): Effect of TbTb freely evolving Tb/Tw fixed−0.2 0 0.2−200204060ω+DR%Mb = 0.3Mb = 0.8Mb = 1.5GQ-2016−0.20 0.00 0.20−200204060ω+DR%Mb = 0.3Mb = 0.8Mb = 1.5GQ-2016• When Tb/Tw is fixed the DR curves almost collapse15Conclusions• Influence of the compressibility on the performance of spanwise forcing• Mb = 0.3, 0.8 and 1.5 at Reτ = 400• The effect of the control depends on how Tb is set• If Tb is left free to evolve the maximum DR increases by 27%, when the Mach numberincreases from Mb = 0.3 to Mb = 1.5• If Tb/Tw is kept constant the DR curves almost collapse16Thanks for your attention!1718DR for lines 4 and 519Pin and Pnet for line 120Pin and Pnet for line 221Pin and Pnet for line 422Pin and Pnet for line 523Governing Equations∂ρ∂t+∂ρui∂xi= 0 (1)∂ρui∂t+∂ρuiuj∂xj= − ∂p∂xi+∂σij∂xj+ f δi1 (2)∂ρe∂t+∂ρ(e+ p/ρ)uj∂xj=∂σijui − ∂qj∂xj+ fu1 +Φ (3)where: e = cvT + uiui/2, σij = µ(∂ui∂xj+∂uj∂xi− 23∂uk∂xk δij)qj is the heat flux vector, modelled as qj = −k ∂T∂xj , and k = cpµ/Pr where Pr = 0.72.Φ is a uniformly distributed cooling term (heat sink) to control the value of Tb and toabsorb, when needed, the heat produced by viscous dissipation. It is zero when Tb is leftfreely to evolve in time. When Tb/Tw is constant Φ is evaluated at each time step.24

Turbulent Drag Reduction Using Spanwise Forcing in Compressible Regime

https://re.public.polimi.it/bitstream/11311/1220998/2/GATTF03-22.pdf

Turbulent Drag Reduction Using Spanwise Forcing in Compressible Regime

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