Numerical study of temperature effects on jet turbulence ...gdr-turbulence.ec-lyon.fr/Oct2012_Poitiers/Daviller-Gdr-turbulence-2012.pdfNumerical study of temperature effects on jet

Motivation & objectives Numerical Tools : code NIGLO Temperature effects Conclusion

Numerical study of temperature effects on jet turbulence andradiated acoustics

G. Daviller, P. Jordan & P. Comte

Institut PprimeENSMA / Université de Poitiers / CNRS

16 octobre 2012

G. Daviller, P. Jordan & P. Comte LEA

Numerical study of temperature effects on jet turbulence and radiated acoustics Poitiers, 16/10/2012. 1 / 23

Contexte : calcul haute fidélité

Interac(on choc/couche limite (Shahab, Lehnasch, Comte,Gatski)

Bruit de jet subsonique (Daviller, Comte, Jordan)

Interac(on choc / couche de mélange (Daviller, Lehnasch, Jordan)

Décollement en tuyère (Shams, Lehnasch, Comte)

Jets fortement sous-‐détendus (BuHay, Lehnasch, Mura)

Couche de mélange réac(ve (Mar(nez, Lehnasch, Mura)


1 Motivation & objectives

2 Numerical Tools : code NIGLO

3 Temperature effects

4 Conclusion




Background

Lighthill’s theory in 1952

Understanding of jet noise inherently tied to the understanding of turbulence in jetflows

Real complexity of the developing turbulent flow

Bradshaw, Ferriss & Johnson (JFM1964), from Van Dyke (1982).

Role of coherent structures inturbulent mixing (Brown &Roshko, 1974)

Organized structures remainpresent at high-Reynolds Number

Contribution of coherent structureto the acoustic field(Mollo-Christensen et al., 1960)




Background : Noise source identification

y

x

cône potentiel

couche de mélange

tuyère

zone de mélange zone de transition zone développée

Flow regions in a subsonic jet

3 different regions in a turbulent jetMost powerful generation of sound occurs near the end of the potential coreCoherent structures observed in the initial mixing-layer regionFirst source : advection of coherent structures (Crow, 1972)Second source : “fine scale turbulence” (Mollo-Christensen et al. 1960,Tam 1998)




Background : temperature effects

Noise from heated subsonic jet studied since the early 1970s

Additional dipole term associated with temperature fluctuations (Fisher, 1973)

Acoustic Mach number dependance of the temperature effect (Tanna 1977)

Heating a jet at Ma = Uj/c∞ < 0.7 increased the sound level

Heating a jet at Ma = Uj/c∞ > 0.7 decreased the radiated sound=> SPL decrease in the high frequencies

Mean flow results when heating jet at constant velocity (Lau, 1979) :=> decreased the potential core length=> increased rate of centerline velocity decay=> increased the turbulence intensity

=> Mechanisms by which these changes is affected not yet understood.




Background : temperature effects

Bodony & Lele (2008) => “on the quieting of high-speed jets with heating”

LES database of unheated jets (Mj = 2) & heated jets (Mj = 1) at Ma = 1.5

Analysis of the sound radiated using Lighthill’s analogy (1952)

∂2ρ′

∂t2− c2∞

∂2ρ′

∂xi∂xjδij =

∂2Tij

∂xi∂xj

Lighthill’s tensor :

Tij = ρui uj + (p′ − c2∞ρ′)δij − τij

(p′ − c2∞ρ′)δij : entropy source term

τij : viscous shear stress tensor (found negligible)

=> Strong anti-correlation between the the far-field contribution of the momentum andentropy terms




Temperature effects investigation

Source terms structure differences in the turbulence of heated and isothermal round jet :

Momentum decomposition Bodony & Lele (2008) :

ρui uj = ρui uj + ρ(ui u′j + u′i uj )| z L1

+ ρ′ui uj| z L2

+ ρ′(ui u′j + u′i uj )| z Q1

+ ρu′i u′j| z

Q2

+ ρ′u′i u′j| z

C

ρui uj : only a mean component, does not radiate sound => not considered.L1 and L2 linear in the fluctuationsQ1 and Q2 quadratic in the fluctuationsC is cubic

Entropy term : p′ − c2∞ρ′

Analysis based on Fourier modes decomposition in the azimuthal direction

q′(x , r , θ, t) =a0(x , r , t)

2+

NXn=1

[an(x , r , t)cos(nθ) + bn(x , r , t)sin(nθ)]

=> Comparing low-order azimuthal modes of the turbulence get some insight regardingthe effect of temperature on the most acoustically efficient flow scales.




Compressible LES approach : “Le code, c’est le nerf de la guerre” P. Comte 2007

Present work (NIGLO 7.0) :

Macro-pressure $ & Macro-temperature ϑ (Lesieur & Comte, 2001)Turbulent eddy viscosity νsgs : Filtered Structure Function model (Ducros 1996)

Super-scalar parallelisation & optimisation (up to 4096 proc. on Babel at IDRIS)4th-order explicit differencing scheme (McCormack-type)3D-NSCBC non-reflective open boundary conditions (Lodato & al., 2008)MPI parallelisation, Domain decompositionInput/Output optimisation using MPI-IO library

Current version (NIGLO 9.0) :

Scalability optimisation (up to 32768 proc. on Curie at CEA)High-order low dissipative scheme (4, 6, 8, DRP & Compact) & RK4Skew symmetric formulationHybrid scheme (with WENO 3, 5 & 7 order) & Shock sensorsAdd SGS model : MSM, DSM, Vortex-streched model




Exemple : LES of single jets

Isothermal jet : Positive Q = 0.5(Uj/Dj )2

isosurfaces coloured by the streamwisevorticity 0.8 ≤ Ωx ≤ 0.8, fluctuating

pressure field −150Pa ≤ P ≤ 150Pa

Jet 1 Jet 2Mj = Uj/cj 0.9 0.54

Ma = Uj/c∞ 0.9 0.9Rej = Uj Dj/νj 4× 105 4× 105

Dj (m) 0.02 0.1Tj/T∞ 1 2.7

Momentum thickness δθ = 0.05ro

∆o = ro/32

[30Dj × 20Dj × 20Dj ]

∼ 200× 106 points

Typicall run time : ' 10 daysusing 512 processor IBM Power6(IDRIS).




Temperature effects on initial shear layer developpment

Q = 0.5(Uj/Dj )2 > 0 isosurfaces coloured by the streamwise vorticity 0.8 ≤ Ωx ≤ 0.8

Tj/T∞ = 1 Tj/T∞ = 2.7

Hypothesis :

=> Baroclinic torque :1ρ3~∇ρ× ~∇p

=> Should be a source of vorticity? Origin of secondary Kelvin-Helmholtz instability ?




Temperature effects in round jets : Turbulence kinetic energy & Pressure fluctuation levels

Tj/T∞ = 1 Tj/T∞ = 2.7

1

2

〈ρu′i u′i 〉

ρj U2j

〈p′p′〉

ρ2j U4

j

0 0.5 1 1.5 2 2.5x/xc

0

1

2

3

4

5

6

7

r/r o

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.5 1 1.5 2 2.5x/xc

0

1

2

3

4

5

6

7

r/r o

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.5 1 1.5 2 2.5x/xc

0

1

2

3

4

5

6

7

r/r o

0

0.005

0.01

0.015

0.02

0.025

0 0.5 1 1.5 2 2.5x/xc

0

1

2

3

4

5

6

7

r/r o

0

0.005

0.01

0.015

0.02

0.025

Higher levels in the heated jet : effect of the time-averaged local density=> generation of locally high levels of momentum fluctuation=> Higher levels of local acceleration and fluctuating pressure

tke : peak at x/xc = 1, < p′p′ > : peak at x/xc ' 0.7

Trend reversed with respect to the ambient conditions (acoustic analogy)




Temperature effects on tke budget

Radialy integrated turbulence kinetic energy budget normalized by ρj U3j /Dj

(Axial distance normalized by jet’s potential core length)

Tj/T∞ = 1

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

0 0.5 1 1.5 2 2.5x/xc

Production

DissipationAdvection

Turbulent diffusion

Pressure diffusion

Tj/T∞ = 2.7

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

0 0.5 1 1.5 2 2.5x/xc

Production

DissipationAdvection

Turbulent diffusion

Pressure diffusion

Plotted terms close TKE budget by less than 10%

Production initially balanced by mean transport upstream of the potential coreViscous & SGS dissipation act downstream of the potential coreAt x/xc > 1.25 viscous dissipation is the only sinkHigher TKE production, mechanism : baroclinic torque?




Temperature effects in round jets : Acoustic field

Far-field third-octave sound spectra at θ = 45 for a point at 72Dj from the jet exit.Tj/T∞ = 1

60

70

80

90

100

110

120

0.01 0.1 1 10

SP

L (d

B)

St=fD/Uj

SGE Tj/T∞=1Bodony sp7Tanna sp7

Tj/T∞ = 2.7

60

70

80

90

100

110

120

0.01 0.1 1 10

SP

L (d

B)

St=fD/Uj

SGE Tj/T∞=2.7Bodony sp46Tanna sp46

SPL overestimated for lower frequency St ≤ 0.07

SPL decrease in the higher frequency St > 1 due to the low-pass nature of theLES, and the limited grid resolution

SPL peak overestimated by ∼ 2dB in the isothermal case and by ∼ 5dB in theheated case.




Temperature effects in round jets : Acoustic field

Far-field sound spectra at θ = 35 for a point at 7.5Dj from the jet exit.

Decrease of SPL in highfrequency with heating

SPL level in low frequency similar

Results in agreement withexperimental observations (seeTanna 1977)

60

70

80

90

100

110

0 0.5 1 1.5 2

SP

L (d

B/S

t)

St=fDj/Uj

SGE Tj/T∞=1SGE Tj/T∞=2.7




Temperature effects on Lighthill’s tensor source terms on the jet lipline

ρui uj = ρui uj + ρ(ui u′j + u′i uj )| z L1

+ ρ′ui uj| z L2

+ ρ′(ui u′j + u′i uj )| z Q1

+ ρu′i u′j| z

Q2

+ ρ′u′i u′j| z

CTj/T∞ = 1

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2 2.5

<(ρ

ui u

j),2 >

/(ρ j

2 U

j4 )

x/xc

<L1xx,2>

<L2xx,2>

<Q1xx,2>

<Q2xx,2>

<Q2rr,2>

<Q2θθ,2>

<(ρ ui uj),2>

Tj/T∞ = 2.7

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2 2.5

<(ρ

ui u

j),2 >

/(ρ j

2 U

j4 )

x/xc

<L1xx,2>

<L2xx,2>

<Q1xx,2>

<Q2xx,2>

<Q2rr,2>

<Q2θθ,2>

<(ρ ui uj),2>

Heated jet present higher level of momentum fluctuation

L1xx dominates near the potential core x/xc = 1 (shear noise)

Q2xx dominates downstream of the potential core x/xc = 1.25 (self-noise)

Heated jet : L2xx dominate upstream of the potential core x/xc = 0.7




Temperature effects on Lighthill’s tensor source terms : azimuthal structure of L1xx

〈L′21xx〉 = 〈(2ρux u′x )′2〉 taken on cylindrical surface with radius r = ro .

Tj/T∞ = 1

0

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5

<L 1

xx,2

> (

%)

x/xc

<L1xx,2>

mode 0mode 1mode 2mode 3mode 4mode 5

Tj/T∞ = 2.7

0

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5

<L 1

xx,2

> (

%)

x/xc

<L1xx,2>


Far-field Tj/T∞ = 1 : L1xx dominates for St < 0.5 at 30 (Bodony & Lele , 2008)Axisymmetric mode m = 0 dominates upstream the potential coreHelical mode m = 1 dominates downstream the potential coreRelative energy of mode m = 2 similar to those of mode m = 1 in the heated caseIsothermal case : Non-linear interaction between Fourier mode m = 0, 1(Cavalieri et al. 2010)




Temperature effects on Lighthill’s tensor source terms : azimuthal structure of L2xx and (p′− c∞ρ′)

〈L′22xx〉 = 〈(ρ′ux ux )′2〉 (p′ − c∞ρ′)

Tj/T∞ = 1 Tj/T∞ = 2.7 Tj/T∞ = 2.7

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5

<L 2

xx,2

> (

%)

x/xc

<L2xx,2>


0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5

<L 2

xx,2

> (

%)

x/xc

<L2xx,2>


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.5 1 1.5 2 2.5

<(p

, -c ∞

2 ρ,

),2>

/P∞

x/xc

<(p, -c∞2 ρ,),2>/P∞mode 0

mode 1mode 2mode 3mode 4mode 5

Far-field Tj/T∞ = 1 : L2xx dominates for St ≥ 0.5 at 30 (Bodony & Lele , 2008)

Far-field Tj/T∞ = 2.7 : L2xx dominates SPL at 30 (Bodony & Lele , 2008)

Peak location and mode ordering is similar for L2xx and (p′ − c∞ρ′)

Contributions of these two terms closely correlated to the far-field at low angles(Bodony & Lele , 2008)

Correlation between momentum and entropy terms in the far-field causescancellation




Temperature effects on Lighthill’s tensor source terms : azimuthal structure of Q2rr

〈Q′22rr〉 = 〈(ρu′r u

′r )′2〉 taken on cylindrical surface with radius r = ro .

Tj/T∞ = 1

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5

<Q

2rr,2

> (

%)

x/xc

<Q2rr,2>


Tj/T∞ = 2.7

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5

<Q

2rr,2

> (

%)

x/xc

<Q2rr,2>


Q2rr dominates far-field SPL at 90 (Bodony & Lele , 2008)

Relative energy and modal distribution similar for both jets




Temperature effects on Lighthill’s tensor source terms : summary (jet’s lipline r = ro)

Tj/T∞ = 1 : L2xx contribution due to weak compressibility effect (velocityfluctuations)

Tj/T∞ = 2.7 : L2xx contribution due to temperature (entropy) effect

Needs far-field prediction using acoustic analogy to complete study




Conclusion

Temperature effect on subsonic round jet :

Performed a detailled description of the change in the near field

Heating a jet at constant velocity increases the energy of higher Fourier mode

Relation between linear momentum and entropy terms in the initial development ofheated jet

Increase of turbulent activity when heating a jet at constant velocity




Conclusion

Temperature effects on subsonic round jets :

Differences in azimuthal organisation of the lowest order azimuthal modesm = 0, 1, 2

Relative energy contained in modes 3,4 and 5 remains similar in the heated andisothermal flows

Level of energy contained in mode m = 2

Contribution of the highest order azimuthal mode is coherent with the increase ofthe turbulent activity in the heated case

Increase of Production

L2xx = ρ′uu contribution

Entropy contribution




Perspectives

Numerical issues :=> Curvilinear algorithm to include part of nozzle=> other SGS model implementation ?

Apply Lighthill’s tensor decomposition to full domain

Use acoustic analogy to obtain far-field prediction

Investigate baroclinic effect in heated jet=> Baroclinic torque should be a source of vorticity

Apply analysis on coaxial jets databases




Thanks for your attention

Thanks to :

P. Comte & P. Jordan



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Numerical study of temperature effects on jet turbulence ...gdr-turbulence.ec-lyon.fr/Oct2012_Poitiers/Daviller-Gdr-turbulence-2012.pdfNumerical study of temperature effects on jet