global instability of (turbulent) separated flow · school of aeronautics 14/05/2010. efecto de las...

SCHOOL OF AERONAUTICS

14/05/2010 Efecto de las Características de Calidad de los Aerorreactores en ... 1

GLOBAL INSTABILITY OF (TURBULENT) SEPARATED FLOW

AFOSR Grant: FA8655-06-1-3066 (2006-2009) PM: Douglas Smith

Graduate Student: Daniel RodríguezPI: Vassilis Theofilis


OUTLINE

• Introduction: • Laminar & turbulent separation bubbles & BiGlobal instability analysis

• Parallel solution of the BiGlobal eigenvalue problem

• Identification of instability mechanisms in the eigenspectrum

• Separation bubbles on a flat-plate• Amplifier behavior vs Global modes• Structural changes induced: Origin of U-separation

• Massively separated NACA airfoil• Numerical developments and BiGlobal analysis• Origin of stall cells


OUTLINE

• Introduction: • Laminar & turbulent separation bubbles & BiGlobal instability analysis



• Separation bubbles on a flat-plate• Amplifier behaviour vs Global modes• Structural changes induced: Origin of U-separation



• Separation determines the performance of lifting surfaces• 2- and 3-dimensional direct numerical simulation results are essentially different

• The behavior of the 3D flow is determined by a “global” feedback mechanism (in turbulent flow)

(Jones, Sandberg & Sandham 2008, 2010)

OBSERVATIONS OF GLOBAL INSTABILITY


• Separation under adverse pressure gradient• Reversed flow region enclosed Shear layer • Kelvin-Helmholtz instability transition to turbulence • Turbulent strong mixing forces re-attachment

(Horton 1968)

COMMON WISDOM ON LSB


Th, Hein & Dallmann Phil. Trans. R. Soc. Lond. A (2000) 358: 3229-3246

• Two different classes of eigenmodes:Shear-layer/KH Global mode

A MORE RECENT VIEW


Configuration Authors MethodologyAirfoils Gaster (1964) -

APG flat plate BL Hammond & Redekopp (1998)Absolute/Convective

instability analysis

-//-Theofilis (1998, 1999)

Theofilis, Hein & Dallmann (2000)BiGlobal

instability analysis

Backward- and forward-facing steps

Barkley, Gomes, Henderson (2001)Marquet et al. (2006)

Marino & Luchini (2009)

BiGlobal instability analysis,

DNS

Low Pressure Turbine bladesAbdessemed, Sherwin & Theofilis

(2004; 2006; 2009)BiGlobal analysis, DNS

Shock / Boundary-Layer Interaction Boin, Robinet (2004; 2007) BiGlobal instability analysis, DNS

NACA Airfoils at AoATheofilis, Barkley & Sherwin (2002)

Crouch et al. (2007; 2009)BiGlobal instability analysis,

DNS

Rounded open cavity, S-shaped duct

Hoepffner et al. (2007), Akervik et al. (2007), Marquet et al. (2008) BiGlobal instability analysis, DNS

Bump-induced separation Ehrenstein et al. (2007) BiGlobal instability analysis, DNS

Low Pressure Turbine Cascade Brear & Hodson (2004) Experiment

Iced Airfoil Jacobs & Bragg (2006) Experiment

GLOBAL INSTABILITY OF LSB


FLAT-PLATE BOUDARY LAYER

Rodríguez & Theofilis AIAA 2008-4148

Parallel basic flow: (Artificially parallel Blasius BL)

Quasi-parallel basic flow: (True Blasius BL)

Non-parallel basic flow: (Separation bubble in BL)




Parallel basic flow: (Artificial parallel Blasius BL)

Local problem: Orr-Sommerfeld / Squire•1D basic flow•3D perturbations (Fourier in 2 directions)•Spatial or temporal problem





Quasi-parallel basic flow: (Real Blasius BL)

Local problem OS/Squire: approximationParabolized Stability Equations (PSE)





Local problem OS/Squire: approximation ?Parabolized Stability Equations (PSE) ?






Global instability analysis through the solution of two-dimensional partial-derivative-based eigenvalue problems, or






Global instability analysis through the solution of two-dimensional partial-derivative-based eigenvalue problems, or

BiGlobal Instability Analysis


Decomposition of the flowfield into• 2D Steady basic flow +• 3D unsteady linear disturbances (eigenmodes)

= +

Abdessemed, Sherwin, Theofilis, JFM (2009) 628: 57-83

BIGLOBAL INSTABILITY ANALYSIS



• Incompressible linearized NS equations

• Modal decomposition



Is a generalized EVP for the temporal evolution of perturbations

• Incompressible linearized NS equations

• Modal decomposition


CHALLENGES (I)• Storage and operation on large (O(1Tb)) dense matrices required !

Incompressible – Cartesian Compressible - Cartesian


CHALLENGES (II)• The solution of the EVPs delivers O(100-2000) eigenvalues• How to identify instability mechanisms in the eigenspectrum ?


OUTLINE

• Introduction: • Laminar separation bubbles & BiGlobal instability analysis






• Software developed

- Distributed-memory global eigenvalue problem solver

- Generic 2nd-order PDE-based EVP

- Generic # of PDE-based EVP solved(Aeroacoustic and hydrodynamic instabilities)

- Spectral-multidomain and High-order FD spatialdiscretization

- Arnoldi algorithm for the computation of Ritz values

- Good scalability on all machines used

MASSIVELY PARALLEL SOLUTION OF THE EVP

Rodríguez & Theofilis AIAA J 47 (10) 2009


• Implementation and scalability studies on(o) Own cluster “Aeolos”

64 of 128 Xeon procs usedOwn-compiled ScaLAPACK/BLACS

(o) UPM cluster “Magerit”512 of 2400 Power PC procs usedPESSL available

(o) EU-Spain facility “BSC - Mare Nostrum”World # 5 (2006) TOP-500 machine (now at # 60)1024 of 10240 IBM JS21 procs usedPESSL available

(o) EU-Germany facility “FZJ - JUGENE”World # 3 (currently) TOP-500 machine4096 of 294912 procs on Blue Gene/P






• Scalings:• Matrix generation and distribution

• LU decomposition

• Arnoldi iterarion

• Distributed eigensystem computation




FZJ - JUGENE


OUTLINE










Quasi-parallel basic flow: (Real Blasius BL)



COMPARISON WITH TEMPORAL OSEBasic Flow: Artificial parallel BlasiusMack’s Case: Re = 580, α = 0.179 (Mack JFM 1976)Streamwise extension of the domain: Lx = 4 π / α

O OSE α = 0.179

O OSE α = 2 x 0.179

O OSE α = 1/2 x 0.179

O OSE α = 3/2 x 0.179

+ BiGlobal

Rodríguez & Theofilis, AIAA-2008-4148


TOWARDS NON-PARALLELISM

Case: Reδ*=450 at inflow, Reδ*=700 at outflow

Analysis 1:- Basic Flow: Artificial parallel Blasius- Boundary conditions: Robin* at inflow & outflow

Analysis 2:- Basic Flow: Artificial parallel Blasius- Boundary conditions: Robin* at inflow & extrapolation at outflow

Analysis 3:- Basic Flow: Real Blasius boundary layer- Boundary conditions: Robin* at inflow & extrapolation at outflow

* Imposes the dispersion relation of TS (Ehrenstein & Gallaire JFM 2005)



EIGENSPECTRA MODIFICATIONSCase: Reδ*=450 at inflow, Reδ*=700 at outflowRobin boundary condition evaluated at: ω0 = 0.13

Analysis:

3 O Real Blasius, Robin + Extrapolation

2 + Parallel Blasius, Robin + Extrapolation

1 X Parallel Blasius, Robin + Robin



Case: Reδ*=450 at inflow, Reδ*=700 at outflow, Separation BubbleBoundary conditions: Dirichlet at inflow & Extrapolation at outflow

β = 1

GLOBAL MODES IN LSB FLOW ON A FLAT PLATE



OUTLINE







Amplifier behavior vs Global modes


Th, Hein & Dallmann Phil. Trans. R. Soc. Lond. A (2000) 358: 3229-3246

• Two different classes of eigenmodes:Shear-layer/KH Global mode

SEPARATION BUBBLES ON A FLAT PLATE


AMPLIFICATION OF TRAVELING MODES BY LSB

• TS-like waves are strongly amplified by the LSB

(the known result of classic LST has been recovered by global instability analysis)

• Very good agreement with LST results in the bubble region

Theofilis & Rodríguez, CEAS/KATnet II, 2009.


u - Direct (2008)

w - Direct (2008)

STATIONARY GLOBAL MODES OF LSB BL FLOW• Amplitude functions

u - Direct (1998)

w - Direct (1998)



Topological changes exerted:Origin of U-separation


Dallmann 1982, Hornung & Perry 1984, Perry & Chong 1987, Chong Perry & Cantwell 1990

CRITICAL POINTS THEORY

Critical point:

Taylor expansion of field around the critical pointRetain only linear terms

Trajectory solutions given as eigensolutions: Characteristic polynomial X

Incompressible flow



Trajectory solutions

•Swirling / No swirling

•Attractor / repeller

Borderline cases are

“structurally unstable”

Dallmann 1982, Hornung & Perry 1984, Perry & Chong 1987, Chong Perry & Cantwell 1990

X Xλ = 0, direction without flow



2D flow is always structurally unstable.

Example: Recirculation center + small perturbation

= A Focus !


U-SEPARATION


THE PRESENT TOPOLOGICAL ANALYSES

Reconstruct composite flowfields, using the Ansatz

for the 2D (structurally unstable) basic flow monitored

superimposing the respective 3D leading global eigenmode,

Keep ε small, for the linearization to hold


Rodríguez & Theofilis J. Fluid Mechanics – to appear

• Critical point analysis of composite flowEigenvalue spectrum BF + ε (Global Mode)

Critical Points of ( BF + ε S )


• Separation on Flat Plate

• Separation on Airfoil

WALL STREAMLINES – “MUSHROOMS”

Bippes 1982 Present Theory

Schewe 2001

U


Thick airfoils – trailing edge stall

AIRFOILS AT HIGH ANGLE OF ATTACK

Gault (1949), McCulllough & Gault (1951)

•Separation line at trailing edge moving up-chord with α

•Smooth lift reduction and drag increase

•Mean flow field predominantly 2D

•Except for α = (17º-19º)

1

2 3




Yon & Katz (1998) - Schewe (2001)

2 3

2

3

Appearance of stall cells α = (17º-19º)




Yon & Katz (1998) - Schewe (2001)

2 3

2

3

C

C

Appearance of stall cells α = (17º-19º)• Independent separated regions

• Spanwise periodic Lz ~ 3 chord

• Not a tip effect


OUTLINE







• Use the incompressible version of the unstructured code Stanford (CTR) CDP code

• Basic 2D laminar steady state at Rec= 200, α = 18ºChosen so as to isolate distinct instability mechanisms:Unsteady at Rec = 300

• Massive separation on the lee-side (over ~70 % chord)

STALLED NACA0015 AIRFOIL

Kitsios, Rodríguez, Theofilis, Ooi and Soria. – 2009 J. Comp. Phys 228 (19)


BIGLOBAL ANALYSIS

• Linearized incompressible NS equations in curvilinear coordinates

• Where the orthogonal basis and the metric functions are

• Decomposition of flow field in 2D steady basic flow + 3D modal disturbances -periodic in the spanwise direction



RESULTS OF THE ANALYSIS

β = 1

Branch of wave modes - unstable ?



RESULTS OF THE ANALYSIS

β = 1

Maximum amplification for β ~ 2, Lz ~ 3.14

Stationary unstable global mode



ORIGIN OF STALL CELLS

Rodríguez & Theofilis Theor. Comp. Fluid Dyn. (to appear 2010)


Journals

• [J-4] Rodríguez, D., Theofilis, V. 2009 Massively Parallel Numerical Solution of the Bi-Global Linear Instability Eigenvalue Problem Using Dense Linear Algebra AIAA Journal, 46(10), DOI: 10.2514/1.42714• [J-3] Kitsios, V., Rodríguez, D., Theofilis, V., Ooi, A., Soria, J. 2009 BiGlobal stability analysis in curvilinear coordinates of massively separated lifting bodies. Journal of Computational Physics, 228 (19) , DOI: 10.1016/j.jcp.2009.06.011• [J-2] Rodríguez, D., Theofilis, V. 2009 On the birth of stall cells on airfoils. Theoretical and Computational Fluid Dynamics (accepted for publication).• [J-1] Rodríguez, D., Theofilis, V. 2009 Structural changes of laminar separation bubbles induced by global linear instability . Journal of Fluid Mechanics(accepted for publication).

Book Chapters

• [B-1] de Vicente, J., Rodríguez, D., González, L. Theofilis, V. 2008. High-order numerical methods for BiGlobal flow instability analysis and control. In Associação Brasileira de Ciências Mecânicas, Volume 6 tomo 2: Turbulência. 6ª Escola de Primavera em Transição e Turbulência, Univ. São Paulo, Sao Carlos, 22- 26 Sept. 2008, (M. Teixeira Mendonça, M. Faraco de Medeiros, eds.), pp. 1-123.

Conferences

• [C-7] Rodríguez, D., Ekaterinaris, J., Valero, E., Theofilis, V. 2009 On receptivity and modal linear instability of laminar separation bubbles at all speeds. Seventh IUTAM Symposium on Laminar-Turbulent Transition, Stockholm, Sweden, June 23-26, 2009. Springer. • [C-6] Theofilis, V. Rodríguez, D. 2009 Global Linear Instability on Laminar Separation Bubbles – revisited: U-separation and the Birth of Stall Cells on Airfoils. CEAS/KATnet II Conference on Key Aerodynamic Technologies, Bremen, Germany, May 12-14, 2009. 12pp. ISBN 978-3-00-027782-5.• [C-5] González, L., Rodríguez, D., Theofilis, V., 2008. On instability analysis of realistic intake flows. AIAA 38th Fluid Dynamics Conference And Exhibit, Seattle, June 23-26, 2008. AIAA Paper 2008-4380.• [C-4] Kitsios, V., Rodríguez, D., Theofilis, V., Ooi, A., Soria, J. 2008. BiGlobal instability analysis of turbulent flow over an airfoil at an angle of attack layer. AIAA 38th Fluid Dynamics Conference And Exhibit, Seattle, June 23-26, 2008. AIAA Paper 2008-4384.• [C-3] Rodríguez, D., Theofilis, V. 2008 On instability and structural sensitivity of incompressible laminar separation bubbles in a flat-plate boundary layer. AIAA 38th Fluid Dynamics Conference And Exhibit, Seattle, June 23-26, 2008 AIAA Paper 2008-4148• [C-2] Rodríguez, D., 2008 On instability and active flow control of laminar separation bubbles. 4th PEGASUS-AIAA Student Conference, Prague, Czech Rep. April 23-26. • [C-1] Rodríguez, D., Theofilis, V. 2008 Massively Parallel Numerical Solution of the BiGlobal Linear Instability Eigenvalue Problem. AIAA 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 7-10, 2008. AIAA Paper 2008-0594.

PUBLICATIONS


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global instability of (turbulent) separated flow · school of aeronautics 14/05/2010. efecto de las...

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