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

EUROPEAN DRAG REDUCTION AND FLOW CONTROL MEETING, 3 - 6 APRIL 2017, MONTE PORZIO CATONE (ROMA), ITALY

Impulse Response in Turbulent Channel Flow

• A. Codrignani1, D. Gatti1, M. Quadrio2 | April 4, 2017

KIT – The Research University in the Helmholtz Association

www.kit.edu

1Institute for Fluid Mechanics

Karlsruhe Institute of Technology and

2Dipartimento di Scienze e Tecnologie Aerospaziali

Politecnico di Milano

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 models1

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 Hij(kx, y, kz, 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 Hij(x, y, z, t; yf) turbulent base flow (DNS) physical space and time evolution influence of the wall-normal distance of the forcing yf

Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 2/16

Plasma Actuators

embedded electrode dielectric electrode plasma induced flow

Fv y′

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

Hij

fj ui 1D definition: u(t) =

• H(t − t′)f(t)dt′

Impulse response H (fluid dynamics)

Relationship between the body forcing input f(x, t) and the velocity output u(x, t): ui(x, t) =

• Hij(x − x′, t − t′)fj(x′, t)dx′dt′

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 correlation2 ✓ tested for the wall blowing/suction input ✓ more homogeneous force distribution, all time-space frequency at

• nce

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 correlation1 Rin,out

H Rin,in Rin,out Rin,out(t) =

• H(t − τ)Rin,in(τ)dτ

White noise input: Rin,in(τ) = δ(τ) ⇒ Rin,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 yf fj(α, y, β, t) = ǫfj(α, β, t)δ(y − yf)

Measurement formulation Hij(α, y, β, T ; yf) = ui(α, y, β, t)f∗

j (α, β, t − T )

ǫ2

4+1 variables describe the impulse response

Hij is a 3x3 tensor

phase-locked averaged (mean) impulse response

update forcing DNS time step

H

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

H2 norm: ensemble average energy density ∀yf H2

2 ≡

H ∞ H(α, y, β, t)2

HSdtdy

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 Hux with laminar flow at ReP = 2000.

1 32 1 16 α

Jovanovi´ c & Bamieh

β 1 32 1 16

Direct Impulse

β 1 32 1 16

Input-Output correlation

β α

Channel resolution: Lx = 4πH, Lz = 2πH, 128x100x128 Response resolution: 64x100x64 with 100 time step from ˜ t = 0 to ˜ t = 100

Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 9/16

Validation

Linearity test fj(α, y, β, t) = ǫfj(α, β, t)δ(y − yf) 2 4 6 8 2 3 4 5

τ

ǫ = 2e−3 ǫ = 1e−3 ǫ = 0.5e−3

max(Huz) 1 1.5 2 2.5 3 3.4 3.6 3.8 4 4.2

τ

Forcing distance: yf = 0.1H

Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 10/16

H2 Norm, Laminar case

1 32 1 16

α Hux

1 32

Huy

1 32

Huz

1 32 1 16

α Hvx

1 32

Hvy

1 32

Hvz

1 32 1 16

α Hwx β

1 32

Hwy β

1 32

Hwz β ReP = 2000

−5.97 −9.14 −12.3 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 yf

Response component Huz

1 16 32 1 8 16 α

yf = 0.01h

1 16 32

yf = 0.1h

1 16 32

yf = 0.2h

1 16 32 1 8 16 α

yf = 0.3h

β 1 16 32

yf = 0.4h

β 1 16 32

yf = 0.5h

β

ReP = 2000

−4.4 −8.6 −12.7 Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 12/16

H2 Norm, Turbulent case

1 32 1 16

α Hux

1 32

Huy

1 32

Huz

1 32 1 16

α Hvx

1 32

Hvy

1 32

Hvz

1 32 1 16

α Hwx β

1 32

Hwy β

1 32

Hwz β Reτ = 150

−2.65 −4.88 −7.11 Introduction Measurement technique Validation Impulse Response Conclusion Codrignani et al. – Impulse Response in Turbulent Channel Flow April 4, 2017 13/16

Maxima of Hij vs. forcing distance yf

0.5 1 50 60 70 max(Hux ) 0.5 1 2 4 6 max(Huy ) 0.5 1 4 6 8 max(Huz) 0.5 1 2 4 6 max(Hvx ) 0.5 1 10 20 max(Hvy ) 0.5 1 4 6 8 10 max(Hvz) 0.5 1 2 4 6 8 max(Hwx ) yf 0.5 1 2 4 6 8 10 max(Hwy ) yf 0.5 1 40 45 50 55 max(Hwz) yf

( ) 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 H2 show that Huy and Huz 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