Mécanique des ﬂuides, transferts et rayonnement …acoustique.ec-lyon.fr/cours/AcadSciParis_slides_def.pdf · Mécanique des ﬂuides, transferts et ... – Role of coherent structures

Turbulence and AeroacousticsResearch team of the Centre AcoustiqueÉcole Centrale de Lyon & LMFA UMR CNRS 5509

SMI - Turbulence en mécanique des fluides, Académie des Sciences, 14 juin 2011

Mécanique des fluides, transferts et

rayonnement sonore

Christophe Bailly‡ & Christophe BogeyUniversité de Lyon, Ecole Centrale de Lyon & LMFA - UMR CNRS 5509

Institut universitaire de France‡

http://acoustique.ec-lyon.fr

1

http://acoustique.ec-lyon.fr

x Acknowledgments q

Olivier Marsden (ECL, Assitant Prof.)Thomas Castelain (ECL, Assitant Prof.)Sébastien Barré (Dassault-Aviation)Julien Berland (EDF)Vincent Fleury (ONERA)Benoît André (ECL, Ph.D. Student)

2 Académie des Sciences, 14 juin 2011 – Christophe Bailly & Christophe Bogey

x Outline of the talk q

Motivations

– Example of aeronautics, commercial air transport & military applications

Predicting jet mixing noise

– Scales and control parameters– Large-eddy simulation (LES) and direct noise computation (DNC)– Role of coherent structures– Mixing and noise of turbulent subsonic jets– Introduction to underexpanded supersonic screeching jets

Concluding remarks


x Motivations q

Physics-based predictions for real jets, i.e. dual, hot, with co-flow, shock-cellsand noise reduction devices : shape optimization, variable geometry chevrons orfluidic actuators

High-bypass-ratio nozzle (cfm56 type)chevrons on the fan and core nozzles

(Loheac et al., SNECMA, 2004)

QTD2 - Boeing - NASAAIAA Paper 2006-2720

Castelain et al.

AIAA Journal, 2008, 45(5)

understanding of noise generationmechanismsproviding reliable predictionsgiving insight for noise reduction

Lobed exhaust ejector/mixer systemCFM56-5C engine powering Airbus A340


x Motivations q

Supersonic jets

Ariane V ECA - CNESflight 185 - 41st launch V - 2008

acoustic environment of space launchers at lift-off and protection of payloadsmilitary aircrafts (e.g. hearing protection of navalcrew on aircraft carrier deck)broadband shock-associated noise in cruiseconditions : cabin noise

Pratt & Whitney FX631jet engine (F-35 JointStrike Fighter)http://www.jsf.mil

Kleine & Settles,Shock Waves (2008)

Take off from aircraft carrier(noise levels exceed 140 dB)


http://www.jsf.mil

x Motivations q

Economic and societal impacts

Noise levels (EPNdb, sideline), no normalization

1960 1970 1980 1990 2000 201085

90

95

100

105

110

115

120

A300

A300−600

A319 A320−200 A321−200

A330−300 A340−300

A340−600

B707

B720

B727−100

B737−200

B747−100

B747−400

B767−200 B777−200

Falcon 900

F28

F100

G−IV G−V

DC−8 DC−10

MD−80

Comet 4

BAe 146

Trident 1

Caravelle 10

ERJ 145

ATR42

ATR72

L−1011

VC−10

year of entry into service

EP

Nd

B (

sid

elin

e) 3rd generation

turbofan

turbojet

2nd generationturbofan

1st generationturbofan

A380

Advisory Council for Aero-nautics Research in Europe(ACARE 2000 → 2020) ; Traf-fic growth must be compensa-ted for by quieter aircrafts

Jet noise during take-off re-mains the major component oftotal aircraft community noise(between a third and half ofthe energy)

Sound insulation tax, France(TNSA) ∼ 50 M€/year


x Subsonic turbulent jets q

Aeroacoustic scaling

Acoustic Mach number Ma

Ma = ujc∞

noise ∝ Mna

Strouhal number St

St = fDuj

= fuj/D

non-dimension frequency

Reynolds number ReD

ReD = ujDν = D2/ν

D/uj∼ viscous time

convective time

Duj

nozzle



Reynolds number ReD = ujD/ν

Prasad & Sreenivasan (1989)ReD ≃ 4000

Dimotakis et al. (1983)ReD ≃ 104

Kurima, Kasagi & Hirata (1983)ReD ≃ 5.6 × 103

Ayrault, Balint & Schon (1981)ReD ≃ 1.1 × 104

Mollo-Christensen (1963)ReD = 4.6 × 105



Initial conditions at the nozzle exit

Kolpin, J. Fluid Mech. (1964)Mollo-Christensen, Kolpin & Martucelli, J. Fluid Mech. (1964)

ReD = 0.85 × 105 ReD = 1.82 × 105 ReD = 5.24 × 105 ReD = 6.85 × 105

Transition region moves from the mixing layer to thenozzle boundary layer as ReD ր



Disparity of scales

Isothermal jet, λa/δθ ≃√

ReD/(Ma × St) (ReD = 106, Ma = 0.9, r/D ∼ 10)

Mollo-Christensen (1963), ReD = 4.6 × 105

δθ

D

uj xc

laminar potentialcore length xc

u′ p′

λa

u′a p′

a

λa/δθ ≃ 103

u′/uj ≃ 0.16

u′a/u′ ∼ 10−4

p′a/p′ ∼ 10−3

p′2a

∣∣∣θ=90o

∼ M7.5a


x Direct computation of aerodynamic noise q

High fidelity flow/noise simulation in a physically and numerically

controlled environment

artificial turbulentstate at nozzle exit

to mimic turbulent BLReD, Reδθ , u′

e/uj

non-reflectingboundary conditions

& WEM

an error of 1% onthe aerodynamic

pressure fieldyields an errorof 100% on theacoustic field !

Barré et al., Int. J. AeroAcous. (2006)Bogey & Bailly, J. Fluid Mech. (2007)

fluctuating pressure fieldp′ outside of the flow

vorticity ω in the flow



First Direct Noise Computation (DNC) of a subsonic round jet

Freund, J. Fluid Mech. (2001), ReD = 3600 & M = 0.9

see also Colonius, J. Fluid Mech. (1997)

Kurima, Kasagi & Hirata (1983)ReD ≃ 5.6 × 103

nx × nr × nθ = 640 × 250 × 160 ≃ 29 × 106 ptsδθ/r0 ≃ 0.02small random perturbation to seedthe instabilities and turbulence



Direct Numerical Simulation M = 0.9 & ReD = 11000

×4

×16

vorticity norm in the plane z = 0full jet in top view 0 ≤ x ≤ 27.5r0

(116 pts bottom figure)

NEC SX-8 cluster at HLRS center in Stuttgart, Germany212 GFlops, 250 GB of memory, 30,000 CPU hours

nx × ny × nz = 2010 × 613 × 613 ≃ 755 × 106 ptskcη ≃ 1.5 kc grid cut-off wavenumber∆x = ∆y = ∆z = r0/68simulation time T = 3000r0/uj , 295,000 iterationsδθ = 0.01 × r0

Bogey & Marsden in Advances in Parallel Computing, 19, 2009see also Bogey & Bailly, J. Fluid Mech., 629, 2009


x Large Eddy Simulation of turbulent jets q

Energy budget across a self-preserving jet M = 0.9 & ReD = 11000

– nx × ny × nz = 651 × 261 × 261 = 44 × 106 pts2.8 × 106 time steps Nec SX-5/8 104 h CPU

– Expts of Panchapakesan & Lumley (1993)– Self-similarity region for 120r0 ≤ x ≤ 150r0

– All the terms are explicitly calculated including thefiltering dissipation, to check the sum.

vorticity norm in the plane z = 0 0 0.5 1 1.5 2

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

y/δ0.5

(normalized by ρcu3cδ0.5)

mean flow convection

production

dissipation

turbulence diffusion

pressure diffusion

◦ expt. data of P. & L. (1993)


x Large Eddy Simulation of turbulent jets q

Energy budget across a self-preserving jet M = 0.9 & ReD = 11000

Interpretation of Panchapakesan & Lumley (J. Fluid Mech., 1993) versusHussein, Capp & George (J. Fluid Mech., 1994)

P. & L. H.C. & G.

0 0.5 1 1.5 2

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

y/δ0.5

0 0.5 1 1.5 2

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

y/δ0.5

in agreement with P. & L. who neglected presssure diffusion and not with H.C.& G. who used turbulence modelling for dissipation

Bogey & Bailly, J. Fluid Mech. (2009)


x Large eddy simulation q

Closure : subgrid-scale model e.g. Sagaut (2006), Lesieur (2007)

Projection modeling by a spacial convolution filtering u = G ∗ u

∂tu + ∇ · (uu) + ∇(p/ρ) + ν∇2u = ∇ · σ sgs

structural approach, find a model for the sgs stress tensorfunctional approach, surrogate the mean action– turbulent kinetic energy balance is more important– turbulent kinetic energy cascade is dominant → dissipation

Two main classes of methods in physical space

turbulent eddy viscosity modelshyperviscosity (∇ · σ sgs → νh∇2n) or high-order explicit filtering

Pruett et al. – Domaradzki, Adams et al. – Visbal, Gaitonde, Rizzetta – ADM – ...

LES - Relaxation filtering ∇ · σ sgs = −χG ∗ u

Berland et al., J. Comput. Phys. (2008) & JOT (2008)


x Large eddy simulation q

Status of large eddy simulation

full-scale for laboratory jets (typically D = 2 cm, M = 0.9, ReD = 4 × 105)and nearly mature numerical tool (basic statistics, turbulent kinetic energy

budget, two-point space-time correlations, Reynolds effects)

advances in « alternative subgrid-scale models »e.g. removing energy at the smallest resolved scale by explicit filtering

with N ∼ 108 points, DNS at ReD ∼ 104 and LES at ReD ∼ 105, St ∼ 10.


x Subsonic turbulent jet flow q

Space-time velocity correlations by dual-PIV (Fleury et al., AIAA Journal, 2008)

ReD = 7.5 × 105, M = 0.9, D = 3.8 cm, δθ/D|init ≃ 3 × 10−3

At x = 5D, L(1)11 ≃ 0.27D, Kolmogorov scale lη ≃ 10−4D

Space-time second-order correlation functions R11(x, ξ, τ) andR22(x, ξ, τ) measured at x = (6.5D, 0.5D)

L(1)11 ≃ 2δθ L

(1)22 ≃ δθ

τ = 0 µs τ = 50 µs τ = 150 µs τ = 250 µs

replacements

ξ1/D

ξ2D

-2 -1 0 1 2-1.0-0.5

00.51.0

ξ1/D

ξ2D

-2 -1 0 1 2-1.0-0.5

00.51.0

ξ1/D

ξ2D

-2 -1 0 1 2-1.0-0.5

00.51.0

ξ1/D

ξ2D

-2 -1 0 1 2-1.0-0.5

00.51.0

ξ1/D

ξ2D

-2 -1 0 1 2-1.0-0.5

00.51.0

ξ1/D

ξ2D

-2 -1 0 1 2-1.0-0.5

00.51.0

ξ1/D

ξ2D

-2 -1 0 1 2-1.0-0.5

00.51.0

ξ1/D

ξ2D

-2 -1 0 1 2-1.0-0.5

00.51.0



Initial conditions at the nozzle exit

(visualizations by T. Castelain, ECL)

ReD ∼ 3.3 × 104 ReD ∼ 1.2 × 105 ReD ∼ 3 × 107

fully laminaru′

e/uj < 1%fully

turbulenttransitional jetsReD

ReD ∼ 105

(Reδθ ≃ 300)ReD ∼ 3 × 105

nominally laminaru′

e/uj ∼ 1%nominally turbulent

u′e/uj ∼ 10%

ReD = ujD/ν Reδθ = ujδθ/ν σue = u′e/uj


x Transition from initially laminar jets q

Influence of exit boundary-layer thickness

δθ = 0.024r0

δθ = 0.012r0

δθ = 0.006r0

δθ = 0.003r0

M = 0.9 ReD = 105

σue ≤ 1%

Smaller shear-layer thick-ness results in delayed jetdevelopment and longer po-tential core

All transitions are characte-rized by shear-layer rolling-up and a first stage ofstrong vortex pairings

Bogey & Bailly,J. Fluid Mech., 2010, 663



Influence of exit boundary-layer thickness M = 0.9 ReD = 105 σue ≤ 1%

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

z/r0

<u′

zu′z>

1/2 /u

j

u′z/uj along r = r0

δθ = 0.024r0δθ = 0.012r0δθ = 0.006r0δθ = 0.003r0

⋄ Fleury et al., AIAA Journal (2008), M = 0.9 & ReD = 7.7 × 105

rms velocity profiles (dual-peak shape, high values) typicalof a first stage of vortex pairings



Influence of exit boundary-layer thickness M = 0.9 ReD = 105 σue ≤ 1%

θ = 40 deg

10−1

100

101

97.5

102.5

107.5

112.5

117.5

122.5

127.5

132.5

St

SP

L (d

B/S

t)

θ = 90 deg

10−1

100

101

97.5

102.5

107.5

112.5

117.5

122.5

127.5

132.5

St

SP

L (d

B/S

t)

⊳ ⊲ Experimental data at ReD ≥ 5 × 105

Additional noise induced by vortex pairing at frequency f0/2,with Stδθ = f0δθ/uj ≃ 0.012, see Zaman, AIAA Journal (1985)



Consequences on noise prediction from turbulent jets

Need for considering initially turbulent jets, i.e. u′e/uj ∼ 10%, to prevent any form

of pairing noise like in jets at high Reynolds number : less noisy jets are indeedobserved for a natural smooth development of their turbulent boundary layer.

This is of course not a denial of the existence of coherent structures !

ExptsZaman, 1985, AIAA Journal & J. Fluid Mech.

Bridges & Hussain, 1987, J. Sound Vib.

Raman, Zaman & Rice, 1989, Phys. Fluids A

ReD = 1.3 × 105

laminar jet (u′e/uj ≃ 0.03%, δθ/D ≃ 2.8 × 10−3)

tripped jet (u′e/uj ≃ 0.09%, δθ/D ≃ 9 × 10−2)

far field pressure spectraat θ = 90o

10−1

100

101

St

4 dB



Tripped subsonic round jets

fully laminaru′

e/uj < 1%fully

turbulenttransitional jetsReD

ReD ∼ 105 ReD ∼ 3 × 105

nominally laminaru′

e/uj ∼ 1%nominally turbulent

u′e/uj ∼ 10%

nominally laminar → nominally turbulentby tripping with a laminar mean velocity

profile, u′e/uj ∼ 10% and δθ ր

Computing initially fully turbulent jets is still a challenge :only jets at ReD ≃ 105 can usually be considered using LESi.e. jets whose initial state should naturally be laminar


x Tripped subsonic round jets q

Influence of the initial turbulence levels M = 0.9 ReD = 105 δθ/r0 = 1.8%

σue = 0%, 3%, 6%, 9%, 12%

nr × nθ = nz = 256 × 1024 × 962= 252 million pts

as the exit turbulence level in-creases, coherent structures (andconsequently vortex rolling-ups andpairings) gradually disappear

higher initial turbulence levels leadto longer potential coresfrom Lc = 9.3r0 for σue = 0%to 17r0 for σue = 12%



Influence of the initial turbulence levels M = 0.9 ReD = 105 δθ/r0 = 1.8%

0 2 4 6 8 100

0.05

0.1

0.15

0.2

0.25

z/r0

<u′

zu′z>

1/2 /u

j

u′z/uj along r = r0

σue = 0%σue = 3%σue = 6%σue = 9%σue = 12%

as the initial turbulence level increases, the shear layers developmore slowly with lower rms velocity peaks (from 22.6% to 14.5% of uj)... in particular for σue = 12%, flat profile of rms velocities



Computing initially fully turbulent jets is still a challenge

M = 0.9 ReD = 105 δθ/r0 = 1.8% Reδθ= 900 σue = 9%

snapshots of vorticity norm ω and ωz component at x = r0

Large scales, i.e. integral length scales L(θ)uiui, must be well discretized

❀ mesh grid should be nearly isotropic near the nozzle exit∆r, r0∆θ and ∆z < δθ/2 seems recommendednr × nθ × nz = 256 × 1024 × 962

Bogey et al., Phys. Fluids (2010)


x Underexpanded supersonic screeching jets q

Schlieren pictures NPR = 3.68 Mj = 1.50

free jetboundary incident

shocktriple point

Mach disk reflectedshock

slip line

e c

Mach diamond

pe > p∞

André et al., AIAA Journal (2011)



Acoustic spectra NPR = 3.68 Mj = 1.50 r = 53.2Dp

10−1

100

90

θ = 15090

θ = 130

90

θ = 110

90

θ = 90

90

θ = 70

90

θ = 50

90

θ = 30

10 dB

St

DS

P (

dB

/St)

↑ harmonics of screech tone

Tam’s model for BBSAN

Ste = uc(De/ue)Ls(1 − Mc cos θ)



Frequency of screech tones

1 1.1 1.2 1.3 1.4 1.5 1.60.2

0.4

0.6

0.8

Mj

St s

mode A2(symmetric)mode A1

(symmetric)

mode B(sinuous)

mode b(sinuous)

mode C(helical)

André et al., AIAA Paper 2011-2794



Flight effects : spark Schlieren pictures of the jet plume

Mj = 1.5 Mf = 0.

Mj = 1.5 Mf = 0.39



DNC of a screeching plane jet

pR/p∞ = 2.48, D = 5.76 cmpe/p∞ = 2.48, Mj = 1.67

Westley & Wooley, Prog. Astro. Aero., 43, 1976

Computation of the generation of screechtones in a underexpanded plane jet

Mj = 1.55 & Reh = 6 × 104

pe/p∞ = 2.09Berland, Bogey & Bailly, Phys. Fluids, 19, 2007


x Concluding remarks q

Turbulent shear flows at high Reynolds number

LES should display the same initial conditions as experiments

Slower development in the laminar case but stronger turbulent transition ;jets with initially laminar BL are noisier : not the same physics

To evaluate control efficiency, it seems interesting to find the quietest configu-ration by changing exit flow conditions in laboratory for instance, even by usingunrealistic devices for an aircraft, but by considering relevant noise generationmechanisms.

... Zaman (1985) « Turbulence and noise are suppressed at the most to theasymptotic levels which occur for the high-speed jets »

Further efforts to understand the mixing in initially turbulent shear flows athigh Reynolds number and consequences on acoustics are still required, evenif the subject is undoubtedly difficult and requires high-fidelity large eddysimulations.


x Concluding remarks q

Some open questions

Research tools should not always induce research topics, but research topicsshould drive to the development and/or selection of suitable tools.

Challenge : how to transpose high-order numerical algorithms in industrialcontexts ?

LES is not so often. Evolution from RANS to LES is usually done for highReynolds number flows - currently difficult.Complexity in the considered physics, and not only in ‘pratical geometries’

Interaction of turbulence with shock-waves (BBSAN), time dependent inflowconditions, impedance in time domain with TBL, TBL noise, ...


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Mécanique des ﬂuides, transferts et rayonnement …acoustique.ec-lyon.fr/cours/AcadSciParis_slides_def.pdf · Mécanique des ﬂuides, transferts et ... – Role of coherent structures