Introduction Talk Outline Ph.D Defense Large-Eddy ...levass/these/teza_pres.pdfPh.D Defense 1...

Ph.D Defense1

January 11, 2007

V. Levasseur

Introduction

Talk OutlineI : Development andanalysis of LES modeling

II : Application to thepassive control of cavityflows

Introduction Talk Outline

Large-Eddy Simulations in a stabilized finite elementframework:

A Variational MultiScale approach

Vincent Levasseur1,2

Supervisor : Pr. Pierre Sagaut1

Industrial correspondants : M. Mallet2, F. Chalot2

1Laboratoire de Modélisation en MécaniqueUniversité Pierre et Marie Curie

2Dassault AviationDGT/DTIAE/AERAV

PhD Defense - January 11, 2006

V. Levasseur Dassault-Aviation / Laboratoire de Modélisation en Mécanique

Ph.D Defense2

January 11, 2007

V. Levasseur

Introduction




IntroductionWhy Large-Eddy Simulations ?Currrent need for real unsteady simulations, required for a wide rangeof technical flows:

flows involving large scales unsteadiness, which dominates themean solutionaeroacoustic problems

Dassault-Aviation computation, using Aether code

RANS is enough


Ph.D Defense3

January 11, 2007

V. Levasseur

Introduction






Dassault-Aviation computation, using Aether code

Unsteady needs


Ph.D Defense4

January 11, 2007

V. Levasseur

Introduction






Unsteady needs

Remedies:

URANS : quickly limited (often unphysical since providingsolutions with one dominated mode)

LES : less expensive than DNS, but still often limitedbecause of computing resources, particularly forwall-bounded flows

Hybrid RANS/LES methods (among which DES, SAS, zonaldecomposition, . . . ).


Ph.D Defense5

January 11, 2007

V. Levasseur

Introduction






Unsteady needs

Remedies:





Ph.D Defense6

January 11, 2007

V. Levasseur

Introduction






Unsteady needs

Remedies:





Ph.D Defense7

January 11, 2007

V. Levasseur

Introduction




IntroductionRANS vs. LES: an example

Subsonic-Supersonic mixing layer with injection

k-ε computation LES computation

From Marquez and Ravachola

Experimented at CEAT, Poitiers

aChalot et al., AIAA Paper 99-3358, 1999


Ph.D Defense8

January 11, 2007

V. Levasseur

Introduction




IntroductionLarge-Eddy Simulation

Reminder

Turbulent complexity O(Re3)+ very high computational cost

Navier-Stokes nonlinearity:+ All scales are coupled

LES: the small scales are filtered and a subgrid scale model isintroduced in the large-scale equations

Main physical process: kinetic-energy cascade 7−→ turbulentviscosity concept


Ph.D Defense9

January 11, 2007

V. Levasseur

Introduction




IntroductionLarge-Eddy Simulation

Our goal: investigate LES as an industrial toolA “universal” model;

Low additional cost;

Robust when simulating complex geometries on distorded grids;

Natural implentation in a finite element framework: theDassault-Aviation N.-S. solver AETHER;

A model which accounts for the numerical dissipation Sketch ;

Suitable on unstructured meshes.


Ph.D Defense10

January 11, 2007

V. Levasseur

Introduction




Outline of talk

I : Development and analysis of LES modelingII : Application to the passive control of cavity flowsConclusions and Future works


Ph.D Defense11

January 11, 2007

V. Levasseur

Introduction




Outline of 1st part: Development and analysis of LESmodeling

1 Numerics and LESThe Finite Element methodTowards LES in entropy variablesHomogeneous Isotropic Turbulence

2 The Variational MultiScale ApproachMain featuresFreely decaying isotropic turbulence

3 Concluding remarks


Ph.D Defense12

January 11, 2007

V. Levasseur

Introduction




Outline of 2nd part: Application to the passive control ofcavity flows

4 Configurationsexperimentalnumerical

5 Cavity without control deviceLES computations and subgrid modelsMesh convergence

6 Assessment of the pressure-fluctuation control devices



Ph.D Defense13

January 11, 2007

V. Levasseur

Numerics and LESThe Finite Element method

Towards LES in entropyvariables

Homogeneous IsotropicTurbulence

The VariationalMultiScale ApproachMain features

Freely decaying isotropicturbulence

Concluding remarks

Numerics and LES The Variational MultiScale Approach Concluding remarks

Part I

Development of LES modeling


Ph.D Defense14

January 11, 2007

V. Levasseur






Concluding remarks


The numerical method

A Finite Element approachThe symmetric formulation of the compressible Navier-Stokesequations: the entropy variables.

In conservation form, the N.-S. equations write: U,t + Fi,i = Fdi,i ou

U,t + AiU,i = (KijU,j)Using entropy variables :

eA0V,t + eAiV,i =“eKijV,j

”,i

with :eA0 = U,VeAi = AieA0eKij = KijeA0

et V =1T

8<: µ− |u|2/2u1

9=; , µ = e + pv− Ts


Ph.D Defense15

January 11, 2007

V. Levasseur






Concluding remarks



A Finite Element approachA stabilization procedure: the Galerkin/Least-Squaresformulation.Z

Qn

“−Wh

,t · U“

Vh”−Wh

,i · Fi

“Vh

”+ Wh

,i · eKijVh,j

”dQ

+

ZΩ

“Wh(t−n+1) · U

“Vh(t−n+1)

”−Wh(t+n ) · U

“Vh(t−n )

””dΩ

+

ZPn

“Wh ·

“Fi(Vh)− eKijVh

,j

””ni dP = 0

+

nelXe=1

ZQe

n

L (Wh) τ“eA0V,t + L(Vh)

”dQ

L = eAi∂

∂xi− ∂

∂xi

“eKij∂

∂xj

”HH

HH

HHY

nthe characteristictime-scale matrix


Ph.D Defense16

January 11, 2007

V. Levasseur






Concluding remarks



A Finite Element approachA stabilization procedure: the Galerkin/Least-Squaresformulation.Z

Qn

“−Wh

,t · U“

Vh”−Wh

,i · Fi

“Vh

”+ Wh

,i · eKijVh,j

”dQ

+

ZΩ

“Wh(t−n+1) · U

“Vh(t−n+1)

”−Wh(t+n ) · U

“Vh(t−n )

””dΩ

+

ZPn

“Wh ·

“Fi(Vh)− eKijVh

,j

””ni dP = 0

+

nelXe=1

ZQe

n

L (Wh) τ“eA0V,t + L(Vh)

”dQ

L = eAi∂

∂xi− ∂

∂xi

“eKij∂

∂xj

”HHH

HHHY

nthe characteristictime-scale matrix


Ph.D Defense17

January 11, 2007

V. Levasseur






Concluding remarks



A Finite Element approachA spatial discretization using P1 elements.

∀x ∈ Ω, t ∈ In Vh(x, t) =

npnXa=1

Nava

Wh(x, t) =

npnXa=1

Nawa

A semi-discrete approach. A 2nd order backward difference scheme

v,t (tn+1) =32

vn+1 − 2vn +12

vn−1 +O“∆t2

”A dual time-stepping strategy is used to solve the non-linear system:

G“

vn+1 ; vn, vn−1”

= 0


Ph.D Defense18

January 11, 2007

V. Levasseur






Concluding remarks



A Finite Element approachA spatial discretization using P1 elements.

∀x ∈ Ω, t ∈ In Vh(x, t) =

npnXa=1

Nava

Wh(x, t) =

npnXa=1

Nawa

A semi-discrete approach. A 2nd order backward difference scheme

v,t (tn+1) =32

vn+1 − 2vn +12

vn−1 +O“∆t2

”A dual time-stepping strategy is used to solve the non-linear system:

G“

vn+1 ; vn, vn−1”

= 0


Ph.D Defense19

January 11, 2007

V. Levasseur






Concluding remarks


Towards LES

Application of the entropy change of variables to the filtered NSequations More details

bVT=

∂H`U

´∂UbA0 = U,bVbAi = AibA0bKij = KijbA0

bA0 bV,t + bAi bV,i =“bKij bV,j

”,i−

`AiU,i − AiU,i

´+

`KijU,j − KijU,j

´,i

=“bKij bV,j

”,i−

“eAiV,i − bAi bV,i

”+

“eKijV,j − bKij bV,j

”,i| z

Subgrid terms


Ph.D Defense20

January 11, 2007

V. Levasseur






Concluding remarks


Towards LES

Application of the entropy change of variables to the filtered NSequations More details

bVT=

∂H`U

´∂UbA0 = U,bVbAi = AibA0bKij = KijbA0

bA0 bV,t + bAi bV,i =““bKij + bKLES

ij

” bV,j

”,i

bKLESij = bKij

“µt, κt, bU”

when using and eddy-viscosity hypothesis


”,i−

`AiU,i − AiU,i

´+

`KijU,j − KijU,j

´,i

=“bKij bV,j

”,i−


”+


”,i| z

Subgrid terms


Ph.D Defense21

January 11, 2007

V. Levasseur






Concluding remarks


Towards LESSubgrid closures

Some subgrid closuresSmagorinsky modelνtsmag = (CS∆)2 |S(u)|, Sij = 1

2 (ui,j + uj,i)− 13 uk,kδij

Selective criterion νt = H(x, t)νtsmag

H(x, t) =

1 si α ≥ α0

0 with α(x, t) = arcsinh‖ω(x,t)∧ω(x,t)‖‖ω(x,t)‖·‖ω(x,t)‖

iα0 = π

9

Mixed scales model νt = Cm|S(u)|α`q2

c´ 1−α

α ∆1+α


Ph.D Defense22

January 11, 2007

V. Levasseur






Concluding remarks


First attempts simulating HITEuler computations

@@

213 GridNo subgrid model


Ph.D Defense23

January 11, 2007

V. Levasseur






Concluding remarks


First attempts simulating HITLarge-Eddy Simulations

213 GridRe ∼ ∞

Comparison ofsubgrid closures


Ph.D Defense24

January 11, 2007

V. Levasseur






Concluding remarks



513 GridRe ∼ ∞


Z=⇒ Overdissipation of the small scales !


Ph.D Defense25

January 11, 2007

V. Levasseur






Concluding remarks



513 GridRe ∼ ∞


+ Self-adaptive models: Multiscale / Multilevel approaches(Domaradzki, Terracol and Sagaut, Hughes, Adams and Stolz, . . . )


Ph.D Defense26

January 11, 2007

V. Levasseur






Concluding remarks


The Variational MultiScale Approach (VMS)The original formulation by Hughes et al. relies on:

An a priori variational projection is preferred with respect to thefiltering for the resolved scale separation.

A partial subgrid modes reconstruction

The resolved large scales and the subgrid scales are supposeddistant enough so that they do not directly interact.

τ dij = −2µt

„12

ù′′i,j + u′′j,i

´−

13

u′′k,k

«= −2µtSij

ù′′

´3 available Smagorinsky-like

closures:

µt = ρ (C1∆)2 |Sù′′

´| Small-Small

µt = ρ (C1∆)2 |S (u) | Large-Small

µt = ρ (C1∆)2 |SùR´

| All-Small


Ph.D Defense27

January 11, 2007

V. Levasseur






Concluding remarks


The filtered VMS approach

A hyperviscosity formulationHow to differentiate the large scales from the resolved small scales (hierarchicalbases(Jansen et al.), multigrid approaches, cell agglomeration(Farhat et al.),residual-based reconstruction (Scovazzi, Hughes et al.), . . . )?

Z=⇒ When computing at high Reynolds number, a Gaussian filter is advocatedin spectral space (Sagaut and Levasseur, Phys. Fluids, 2005) See spectral analysis

Taylor series expansion

u′′ = −∆′′

24∇2uR

with ∆′′

=π

kc

Following Kraichnan analysis, at vanishing viscosity, 75% of the triadicinteractions affecting a wavenumber k are included in a [0.5k;2k] range.


Ph.D Defense28

January 11, 2007

V. Levasseur






Concluding remarks


Filtered VMS models analysisHomogeneous isotropic turbulence

Turbulent kinetic energy spectra

GLS +subgridmodel513 Grid

Re ∼ ∞


Ph.D Defense29

January 11, 2007

V. Levasseur






Concluding remarks





Re ∼ ∞


Ph.D Defense30

January 11, 2007

V. Levasseur






Concluding remarks





Re ∼ ∞


Ph.D Defense31

January 11, 2007

V. Levasseur






Concluding remarks





Re ∼ ∞


Ph.D Defense32

January 11, 2007

V. Levasseur






Concluding remarks



Subgrid dissipation vs. Stabilization

Dissipationspectra

513 Grid

Re ∼ ∞


Ph.D Defense33

January 11, 2007

V. Levasseur






Concluding remarks




Origin ofdissipation (%)

Gray: numericalWhite: subgrid

513 GridRe ∼ ∞

Smagorinsky model


Ph.D Defense34

January 11, 2007

V. Levasseur






Concluding remarks






513 GridRe ∼ ∞

Dynamic model


Ph.D Defense35

January 11, 2007

V. Levasseur






Concluding remarks






513 GridRe ∼ ∞

VMS model (S.S)


Ph.D Defense36

January 11, 2007

V. Levasseur






Concluding remarks





Re ∼ ∞


Ph.D Defense37

January 11, 2007

V. Levasseur






Concluding remarks


Conclusions of part I

LES modelingIntroduction of a filtered VMS approach, using a Gaussiandecomposition of the resolved scales. Reduction of the supportof the turbulent viscosity. Adaptivity to the small-scale flowfeatures, including numerical effects.

The method has been tested on :

Application to more complexe mechanisms: the compressibleflow over an open cavity See Part II


Ph.D Defense38

January 11, 2007

V. Levasseur






Concluding remarks




The method has been tested on :1 Freely decaying isotropic turbulence:

Satisfactory prediction of the energy-transfer mechanisms(Kolmogorov law is recovered, despite the dominance of thenumerical dissipation).



Ph.D Defense39

January 11, 2007

V. Levasseur






Concluding remarks




The method has been tested on :2 Mixing layer:

Considering a mean-sheared flow, because it is based on asmall-scale information, near the cut-off, the VMS approachdetects the fully turbulent zones.



Ph.D Defense40

January 11, 2007

V. Levasseur






Concluding remarks




The method has been tested on :2 Mixing layer:

Considering a mean-sheared flow, because it is based on asmall-scale information, near the cut-off, the VMS approachdetects the fully turbulent zones.



Ph.D Defense41

January 11, 2007

V. Levasseur

Introduction

Configurationsexperimental

numerical

Cavity without controldeviceLES computations andsubgrid models

Mesh convergence

Assessment of thecontrol devices

Concluding remarks

Introduction Configurations Cavity without control device Assessment of the control devices Concluding remarks

Part II

Application to the passive control of cavity flows


Ph.D Defense42

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


IntroductionFramework

In AerodynamicsFlows over cavities are very common in both internal and externalAerodynamics. (Example: “pipe tone” occuring during take-off andlanding)

Noise (Automobile industry, train, airplane, . . . )

Potentially damageable for the integrity of the aircraft.

+ Major problem for aircraft manufacturers designing stealthvehicle.


Ph.D Defense43

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


IntroductionFramework

Motivations1 Dynamic mechanisms still poorly described.

Hydrodynamic and acoustic modes;Aeroacoustic non-linear coupling;

+ Rossiter modes (low frequency)2 Designing strong structure not feasible: weight penalty.

Depending on the flight altitude, the Rossiter modes can cover a0-150Hz range, leading to an overlap with structural modes.


Ph.D Defense44

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


IntroductionDynamics of the flows over cavities

The main mechanism: the feedback loop

Pressure spectra decomposed into low frequency tones (Rossitermodes) and broadband noise.

6

Rossiter modes

Broadband noise

Rossiter’s formula: fn =U∞

Ln− γ

M∞ + 1κ


Ph.D Defense45

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Introductionthe goals

Question :How to reduce the aerodynamic loads inside the bay?

Two pressure fluctuation suppression devices:the rod-in-crossflow

modification of the mean flowfield;turbulent wake and mixing layer non-linear coupling.

the flat-top spoilerdeflection of the mixing layer.


Ph.D Defense46

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Outline of 2nd part: the cavity flows

4 Configurationsexperimentalnumerical

5 Cavity without control deviceLES computations and subgrid modelsMesh convergence

6 Assessment of the pressure-fluctuation control devices



Ph.D Defense47

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Experimental configurationwithout control

Wind tunnel experiments (QinetiQ)

Kulite transducers

Figure: QinetiQ configuration,MJ de C Henshaw, RTO-TR-26,AC/323(AVT)TP/19

International benchmarkM219 Cavity

L/D = 5 W/D = 1

M∞ = 0.85 ReL = 7.106

Ti = 301K Pi = 99540Pa


Ph.D Defense48

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Experimental configurationwith control

Figure: Sketch of the control devices

flat-top spoiler rod-in-crossflowh (mm) 11.34mm φ (mm) 7.56mmd (mm) 3.78mm d (mm) 7.56mml (mm) 7.56mm h (mm) 3.78mm

Table: Geometric parameters


Ph.D Defense49

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Numerical configurationThe meshes

M1 mesh M2 mesh M3 meshNumber of nodes 0.5e6 1.e6 1.5.e6

Number of elements 3.e6 6.e6 9.e6Domain size(×D) (13,4,10) (13,4,10) (20,6,10)

Table: Features of the meshes


Ph.D Defense50

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Numerical configurationThe meshes

The pressure oscillation suppression devices:flat-top spoiler rod-in-crossflow


Ph.D Defense51

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow without controlCoarse mesh M1 - VMS closure

Instantaneous visualizations

Pressure Mach

Schlieren

Temperature Vorticity


Ph.D Defense52

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks



Acoustic pressure spectra (SPL) at the bottom of the bay - K29 Kulite


Ph.D Defense53

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks



Root-mean-square of thepressure at thebottom of the bay(dB).

AAU

Emax ' 2dB


Ph.D Defense54

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow without controlCoarse mesh M1 - Comparison of subgrid models

Selective Smagorinsky vs. VMS/Small-Small


Ph.D Defense55

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow without controlCoarse mesh M1 - Comparison of subgrid models

Selective Smagorinsky vs. VMS/Small-Small


Ph.D Defense56

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow without controlMesh convergence


Ph.D Defense57

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks



Mode 1 2 3 4Rossiter’s formula 148 Hz 357 Hz 566 Hz 775 Hz

Experiment 144 Hz 353 Hz 594 Hz 813 HzM1 mesh 136 Hz 462 Hz 625 Hz 873 HzM2 mesh 160 Hz 412 Hz 625 Hz 880 HzM3 mesh 108 Hz 362 Hz 594 Hz 838 Hz

Table: Rossiter mode frequency. Selective Smagorinsky closure.


Ph.D Defense58

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks







Ph.D Defense59

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks







Ph.D Defense60

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks



Pressure energy contained in band encompassing each Rossiter tone


Ph.D Defense61

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow without controlFine mesh M3 - Selective Smagorinsky


Ph.D Defense62

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow with passive controlThe mean fields

Streamwisevelocity

Turbulentkinetic energy

x = 0

Verticalvelocity

Reynoldsstress 〈u′w′〉


Ph.D Defense63

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks



Streamwisevelocity


x = L/10

Verticalvelocity



Ph.D Defense64

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks



Streamwisevelocity


x = L/2

Verticalvelocity



Ph.D Defense65

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks



Streamlines

No controlSpoiler Rod


Ph.D Defense66

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks



Streamlines

No control

Pressure coefficients at the bottom of the bay

Spoiler Rod

:

*

BB

BBBM


Ph.D Defense67

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow with passive controlComparison of devices

Root-mean-square of thepressure at thebottom of the bay(dB).


Ph.D Defense68

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow with passive control

The rod-in-crossflow The flat-top spoiler

Karman street


Ph.D Defense69

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow with passive controlComparison of devices

Effect of the Karman street and the Rossiter tones on the totalaerodynamic load


Ph.D Defense70

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Cavity flow with passive controlVortices structures

Flat-top spoiler: Rod-in-crossflow:


Ph.D Defense71

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks


Conclusions of part II

The numerical approach enables the prediction of the Rossitertones in both frequency and amplitude, as well as the broadbandnoise, on unstructured meshes, with a very good precision.Two fluctuation suppresion devices have been furtherinvestigated, with an overall 3-4 dB reduction.

1 The flat-top spoiler:- deflection effect of the mixing layer;- Lowering of the Rossiter tones amplitude;- but a high base-level pressure fluctuation.

Work in progress, in collaboration with L. Larchevêque, IUSTI,should determine whether a non-linear coupling of the mixinglayer and the rod wake really occurs, unveiling its reduction effect(hypothesis of Stanek et al., Air Force Research Lab.)


Ph.D Defense72

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks




2 The rod-in-crossflow:- deflection effect of the mixing layer;- mechanism of production of the Rossiter modes still active;- decrease of the base-level pressure fluctuation.



Ph.D Defense73

January 11, 2007

V. Levasseur

Introduction


numerical


Mesh convergence


Concluding remarks




2 The rod-in-crossflow:- deflection effect of the mixing layer;- mechanism of production of the Rossiter modes still active;- decrease of the base-level pressure fluctuation.



Ph.D Defense74

January 11, 2007

V. Levasseur

Part III

Conclusions and Future works


Ph.D Defense75

January 11, 2007

V. Levasseur

Conclusions and future worksLES has been proven to be a valuable tool for industrial design.

Prospect:

( About VMS approach:

A filtered formulation has been proposed with very satisfying results.Yet, this formulation doesn’t fully address the original link with the sta-bilization procedures. Future works should investigate a small-scalesreconstruction through higher order elements, approximate Green’sfunction, . . .The VMS approach still offers a huge potential.

Near-wall treatment and synthetic turbulence generation will also haveto be addressed.


Ph.D Defense76

January 11, 2007

V. Levasseur

Conclusions and future worksLES has been proven to be a valuable tool for industrial design.

( About the application fields:


Ph.D Defense77

January 11, 2007

V. Levasseur

Towards an industrial applicationA generic weapon bay simulation


Ph.D Defense78

January 11, 2007

V. Levasseur

Further slides


Ph.D Defense79

January 11, 2007

V. Levasseur

Subgrid dissipation and Stabilization ...

Back to presentation


Ph.D Defense80

January 11, 2007

V. Levasseur

About the boundary conditions

4 treatment of boundary conditions:( Fixed pressure

( Characteristic conditions

( Buffer layer PMLU,t + L (U) = −σ(x) (U − U0) σ(x) = σm

“|x−L|

δ

”n

( Ta’asan and Nark conditions:

∂

∂t−→ ∂

∂t+ U′ · ∇ with U′

0 = β (x− L)m , V ′0 = 0


Ph.D Defense81

January 11, 2007

V. Levasseur

About the boundary conditions



Ph.D Defense82

January 11, 2007

V. Levasseur

Towards LES

Two modeling strategies for the subgrid tensor:

The structural modeling: approximation of the subgrid tensor, constructedupon the resolved velocity field or series expansion (scale-similaritymodel, Approximate Deconvolution Model, . . . ).

The functional modeling: representation of the subgrid-scale effects onthe resolved large-scale field (Smagorinsky closure, structure functionmodel, mixed scales, . . . ).

We postulate a perfect correlation between the subgrid tensor and the

large-scale deformation rate tensor: τ dij = τij −

13τkkδij = −2ρνteSij

(eddy-viscosity hypothesis)

Modeling of the energy equation:The turbulent heat flux is modeled by analogy with the heat flux, by defining aturbulent heat conductivity, which is linked with the eddy-viscosity via aturbulent Prandtl number set equal to 0.9.


Ph.D Defense83

January 11, 2007

V. LevasseurThe Variational MultiScale Approach (VMS)

Large-scale motion:


”,i− bB1

“bV, VR”− bB2

`V, VR´

Small-scale motion:

A′′0 V′′

,t + A′′i V′′

,i =`K′′

ij V′′,j

´,i− B′′1

`V′′, VR´

− B′′2`V, VR´

After summation, the VMS system of equations reads:

AR0 VR

,t + ARi VR

,i =`KR

ijVR,j´

,i− B′′2

`V, VR´

KVMSij = Kij

`µt, κt, u′′, TR´ bVVMS

=1

TR

8<:TRVR

1u′′

2

−1

9=; bVR=

1TR

8<:µ− |uR|2/2

uR2

−1

9=;

?

@@

Z=⇒`KVMS

ij VVMS,j

´,i


Ph.D Defense84

January 11, 2007


Large-scale motion:


”,i− bB1

“bV, VR”− bB2

`V, VR´

Small-scale motion:

A′′0 V′′

,t + A′′i V′′

,i =`K′′

ij V′′,j

´,i− B′′1

`V′′, VR´

− B′′2`V, VR´


AR0 VR

,t + ARi VR

,i =`KR

ijVR,j´

,i− B′′2

`V, VR´

KVMSij = Kij


=1

TR

8<:TRVR

1u′′

2

−1

9=; bVR=

1TR

8<:µ− |uR|2/2

uR2

−1

9=;

?

@@

Z=⇒`KVMS

ij VVMS,j

´,i


Ph.D Defense85

January 11, 2007


Large-scale motion:


”,i− bB1

“bV, VR”− bB2

`V, VR´

Small-scale motion:

A′′0 V′′

,t + A′′i V′′

,i =`K′′

ij V′′,j

´,i− B′′1

`V′′, VR´

− B′′2`V, VR´


AR0 VR

,t + ARi VR

,i =`KR

ijVR,j´

,i− B′′2

`V, VR´

KVMSij = Kij


=1

TR

8<:TRVR

1u′′

2

−1

9=; bVR=

1TR

8<:µ− |uR|2/2

uR2

−1

9=;

?

@@

Z=⇒`KVMS

ij VVMS,j

´,i


Ph.D Defense86

January 11, 2007


Large-scale motion:


”,i− bB1

“bV, VR”− bB2

`V, VR´

Small-scale motion:

A′′0 V′′

,t + A′′i V′′

,i =`K′′

ij V′′,j

´,i− B′′1

`V′′, VR´

− B′′2`V, VR´


AR0 VR

,t + ARi VR

,i =`KR

ijVR,j´

,i− B′′2

`V, VR´

KVMSij = Kij


=1

TR

8<:TRVR

1u′′

2

−1

9=; bVR=

1TR

8<:µ− |uR|2/2

uR2

−1

9=;

?

@@

Z=⇒`KVMS

ij VVMS,j

´,i


Ph.D Defense87

January 11, 2007


Large-scale motion:


”,i− bB1

“bV, VR”− bB2

`V, VR´

Small-scale motion:

A′′0 V′′

,t + A′′i V′′

,i =`K′′

ij V′′,j

´,i− B′′1

`V′′, VR´

− B′′2`V, VR´


AR0 VR

,t + ARi VR

,i =`KR

ijVR,j´

,i− B′′2

`V, VR´

KVMSij = Kij


=1

TR

8<:TRVR

1u′′

2

−1

9=; bVR=

1TR

8<:µ− |uR|2/2

uR2

−1

9=;

?

@@

Z=⇒`KVMS

ij VVMS,j

´,i


Ph.D Defense88

January 11, 2007

V. Levasseur

Simulation des Grandes ÉchellesLes équations filtrées φ =

ρφ

ρ

∂ρ

∂t+

∂ρuj∂x j

= 0

∂ρui

∂t+

∂ρuiuj

∂xj+

∂p∂xi

=∂

∂xj[2µSij(u)]− ∂τij

∂xj

∂ρE∂t

+∂ρEuj

∂xj+

∂puj

∂xj=

∂

∂xj[2µSij(u)ui] +

∂

∂xi

ˆκ∂iT

˜+

∂Qi

∂xi+

∂τijui

∂xi

Qi = (ρEui − ρEui) + (pui − pui)− τijuj and τij = ρ fuiuj − ρuiuj

Sij(u) = 1/2 (∂jui + ∂iuj)− 1/3τkkδij.


Ph.D Defense90

January 11, 2007

V. Levasseur


The filtering is achieved with an integration-by-part:

u′′A =∆′′2

24MAA−1 X

B

„ZΩ

NA,i NB,i dΩ−Z

Γ

NANB,i ni dΓ

«uR

B

with MABL

e =

8>>>>><>>>>>:

ZΩe

N2A dΩe

nXC=1

ZΩe

N2C dΩe

· Ve if A = B

0 otherwise

Scale separation:The cut-off corresponds to the mesh size;

The resolved-scale separation ∆′′ is the size of the macro-elementattached to a given node.

Considering a 3D isotropic mesh, this leads to a kc/k′c = 0.35 ratio.


Ph.D Defense91

January 11, 2007

V. Levasseur

Filtered VMS models analysisIsotropic homogeneous turbulence

Time evolution of enstropy

Time evolutionof enstrophy

513 Grid

Re ∼ ∞


Ph.D Defense92

January 11, 2007

V. Levasseur

Spectral analysis of VMS closures

A straightforward orthogonal scale separation

„∂

∂t+ ν|k|2

« buk = −ıkbpk − ık · (uR ⊗ uR)k |k| ≤ kc„∂

∂t+ ν|k|2

« bu′′k = −ıkbp′′k − ık · [ (uR ⊗ uR)k + bR′′k ] kc < |k| ≤ k′c



Ph.D Defense93

January 11, 2007

V. Levasseur


Orthogonal scale separation

Figure: Kinetic energy spectrum - 643 grid



Ph.D Defense94

January 11, 2007

V. Levasseur


Orthogonal scale separation




Ph.D Defense95

January 11, 2007

V. Levasseur


Influence of scale partition




Ph.D Defense96

January 11, 2007

V. Levasseur


Gaussian scale separation




Ph.D Defense97

January 11, 2007

V. Levasseur

Some details, from Levasseur et al., Comp. Meth. Appl. Mech. Eng., 2006

Large-scale motion:


”,i−


”+


”,i

bB1

“bV, VR”

=“

ARi VR

,i − bAi bV,i

”−

“KR

ijVR,j − bKij bV,j

”,ibB2

`V, VR´

=“eAiV,i − AR

i VR,i

”−

“eKijV,j − KRijVR

,j

”,i

= bτ s

Small-scale motion:

A′′0 V′′

,t + A′′i V′′

,i =`K′′

ij V′′,j

´,i− B′′1

`V′′, VR´

− B′′2`V, VR´

B′′1`V′′, VR´

=“`

ARi VR

,i´′ − A′′

i V′′,i

”−

“`KR

ijVR,j´′ − K′′

ij V′′,j

”,i

B′′2`V, VR´

=““eAiV,i

”′′−

`AR

i VR,i´′”− ““eKijV,j

”′′−

`KR

ijVR,j´′”

,i= τ ′′

s



Ph.D Defense98

January 11, 2007

V. Levasseur

Subsonic-supersonic mixing layer with injectionConfiguration


Ph.D Defense99

January 11, 2007

V. Levasseur

Subsonic-supersonic mixing layer with injectionConfiguration

*

Experimented at CEAT, Poitiers


Ph.D Defense100

January 11, 2007

V. Levasseur

Subsonic-supersonic mixing layer with injectionWITHOUT CONTROL

Figure: Mean Mach number profilex = 23mm et y = 8.5mm



Ph.D Defense101

January 11, 2007

V. Levasseur

Subsonic-supersonic mixing layer with injectionWITH SUPERSONIC INJECTION




Ph.D Defense102

January 11, 2007

V. Levasseur

Subsonic-supersonic mixing layer

Instantaneous view of the vortices

Figure: Iso-surfaces of Q-criterium Figure: Iso-surfaces of vorticity


Introduction Talk Outline Ph.D Defense Large-Eddy ...levass/these/teza_pres.pdfPh.D Defense 1...

Documents

Transcript of Introduction Talk Outline Ph.D Defense Large-Eddy ...levass/these/teza_pres.pdfPh.D Defense 1...