Impulse Response in Turbulent Channel Flow A. Codrignani 1 , D. Gatti - PowerPoint PPT Presentation

Impulse Response in Turbulent Channel Flow A. Codrignani 1 , D. Gatti 1 , M. Quadrio 2 | April 4, 2017 EUROPEAN DRAG REDUCTION AND FLOW CONTROL MEETING, 3 - 6 APRIL 2017, MONTE PORZIO CATONE (ROMA), ITALY 1 Institute for Fluid Mechanics Karlsruhe Institute of Technology and 2 Dipartimento di Scienze e Tecnologie Aerospaziali Politecnico di Milano www.kit.edu KIT – The Research University in the Helmholtz Association

Motivation Impulse Response Features It describes the Input-Output relationship of a dynamic system. Perturbation propagation Flow control application (plasma actuators) Insights for development and testing of turbulent models 1 Background M. Jovanovi´ c and B. Bamieh, Componentwise energy amplification in channel flows - J. Fluid Mech., 2004 Impulse response for linearized laminar channel flow Goal Extend Jovanovi´ c’s work and provide the impulse response in the turbulent case 1) S. Russo, P . Luchini - J. Fluid Mech., 2016 Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 1/16

Jovanovi´ c 2004 Description Impulse response to volume force H ij ( k x , y , k z , ω ) linearized laminar base flow results averaged in the wall-normal direction forcing uniformly applied among the channel height Current work Impulse response to volume force H ij ( x , y , z , t ; y f ) turbulent base flow (DNS) physical space and time evolution influence of the wall-normal distance of the forcing y f Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 2/16

Plasma Actuators F v electrode y ′ induced flow plasma embedded electrode dielectric DBD configuration Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 3/16

Impulse Response H ij f j u i 1D definition: � H ( t − t ′ ) f ( t ) dt ′ u ( t ) = Impulse response H (fluid dynamics) Relationship between the body forcing input f ( x , t ) and the velocity output u ( x , t ) : � H ij ( x − x ′ , t − t ′ ) f j ( x ′ , t ) d x ′ dt ′ u i ( x , t ) = Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 4/16

Impulse Response Measurement Three possible techniques: Impulse Response ✓ easy implementation ✗ linear response ⇒ small perturbation ⇒ small S/N ratio Frequency Response 1 ✓ distributed force ✗ only one space-time frequency at once Input-Output correlation 2 ✓ tested for the wall blowing/suction input ✓ more homogeneous force distribution, all time-space frequency at once 1) A.K.M.F. Hussain, W.C. Reynolds - J. Fluid Mech., 1970 2) P . Luchini, M. Quadrio, S. Zuccher - Phys. Fluids, 2006 Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 5/16

Impulse Response Measurement Input-Output correlation 1 R in , out R in , in R in , out H � R in , out ( t ) = H ( t − τ ) R in , in ( τ ) d τ White noise input: R in , in ( τ ) = δ ( τ ) ⇒ R in , out ( τ ) = H ( τ ) 1) P . Luchini, M. Quadrio, S. Zuccher - Phys. Fluids, 2006 Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 6/16

3D Mean Impulse Response DNS of Turbulent channel flow at Re = 150 Volume force applied at a certain wall normal distance y f f j ( α, y , β, t ) = ǫ f j ( α, β, t ) δ ( y − y f ) Measurement formulation � u i ( α, y , β, t ) f ∗ j ( α, β, t − T ) � H ij ( α, y , β, T ; y f ) = ǫ 2 4+1 variables describe the impulse response H ij is a 3x3 tensor phase-locked averaged (mean) impulse response update DNS H forcing time step measurement Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 7/16

Results from Jovanovi´ c’s work H 2 norm: ensemble average energy density �H� 2 ∀ y f 2 ≡ � H � ∞ �H ( α, y , β, t ) � 2 HS dtdy 0 0 uniform forcing across the height M. Jovanovic, B. Bamieh - J. Fluid Mech., 2004 Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 8/16

Validation Response component H ux with laminar flow at Re P = 2000. Jovanovi´ c & Bamieh Direct Impulse 16 16 α 1 1 1 32 1 32 β β Input-Output correlation Channel resolution: 16 L x = 4 π H , L z = 2 π H , 128x100x128 Response resolution: α 64x100x64 with 100 time step from ˜ t = 0 to ˜ t = 100 1 1 32 β Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 9/16

Validation Linearity test f j ( α, y , β, t ) = ǫ f j ( α, β, t ) δ ( y − y f ) 4 . 2 5 ǫ = 2 e − 3 max ( H uz ) 4 4 ǫ = 1 e − 3 ǫ = 0 . 5 e − 3 3 . 8 3 3 . 6 2 3 . 4 0 2 4 6 8 1 1 . 5 2 2 . 5 3 τ τ Forcing distance: y f = 0 . 1 H Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 10/16

H 2 Norm, Laminar case H ux H uy H uz 16 α 1 1 32 1 32 1 32 H vx H vy H vz 16 α 1 1 32 1 32 1 32 H wx H wy H wz 16 α 1 1 32 1 32 1 32 β β β Re P = 2000 − 12 . 3 − 9 . 14 − 5 . 97 Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 11/16

Influence of the forcing distance y f Response component H uz y f = 0 . 01 h y f = 0 . 1 h y f = 0 . 2 h 16 α 8 1 1 16 32 1 16 32 1 16 32 y f = 0 . 3 h y f = 0 . 4 h y f = 0 . 5 h 16 α 8 1 1 16 32 1 16 32 1 16 32 β β β Re P = 2000 − 12 . 7 − 8 . 6 − 4 . 4 Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 12/16

H 2 Norm, Turbulent case H ux H uy H uz 16 α 1 1 32 1 32 1 32 H vx H vy H vz 16 α 1 1 32 1 32 1 32 H wx H wy H wz 16 α 1 1 32 1 32 1 32 β β β Re τ = 150 − 7 . 11 − 4 . 88 − 2 . 65 Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 13/16

Maxima of H ij vs. forcing distance y f 70 6 8 max ( H ux ) max ( H uy ) max ( H uz ) 60 4 6 50 4 2 0 0 . 5 1 0 0 . 5 1 0 . 5 1 6 10 20 max ( H vx ) max ( H vy ) max ( H vz ) 8 4 10 6 4 2 0 0 . 5 1 0 0 . 5 1 0 . 5 1 8 10 55 max ( H wx ) max ( H wy ) max ( H wz ) 8 6 50 6 45 4 4 40 2 2 0 0 . 5 1 0 0 . 5 1 0 . 5 1 y f y f y f ( ) Laminar, ( ) Turbulent Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 14/16

Conclusion & Outlook Conclusion Successful validation of new response measurement technique. First turbulent characterization almost done (just averaging). Analysis of the �H� 2 show that H uy and H uz are the most influent components. Influence of the forcing wall-normal distance. Outlook Further averaging turbulent simulations. Response measurements at higher Reynolds numbers. Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 15/16

Thank you for your attention! Special thanks to Mihailo Jovanovi´ c. andrea.codrignani@kit.edu Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 16/16

Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 17/16