Large-eddy Simulation of Separated Flows Using a …€¦ · 30/6/2016 · Large-eddy Simulation of...
Transcript of Large-eddy Simulation of Separated Flows Using a …€¦ · 30/6/2016 · Large-eddy Simulation of...
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Large-eddy Simulation of Separated Flows Using a New Integral Wall Model
Francois Cadieux, Xiang I.A. Yang, Jasim Sadique, Rajat Mittal, Charles Meneveau
AMS Seminar SeriesNASA Ames Research Center, June 30, 2016
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Motivation
• Separated flows and recirculation regions occur on airfoils and blades for a wide range of Reynolds numbers from 𝑂 104 to 𝑂 106
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Separation Bubbles
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Laminar: 10,000 < Re < 200,000Turbulent: Re > 200,000
Sketch based off Horton H (1968) “Laminar separation bubbles in two and three dimensional incompressible flow”, Ph.D. diss., University of London.
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Research Goals
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• Create predictive simulation tool for separated flows that is:
• High-fidelity• Tractable for high Reynolds number flows
• To enable:• Optimization of wing, blade, flap design• Rapid testing of active flow control strategies
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Why not RANS?
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RANS:
• length of recirculation strongly depends on turbulence model
• transition to turbulence is difficult to predict
Spalart, P. and Strelets, M. (2000), “Mechanisms of transition and heat transfer in a separation bubble”, J. Fluid Mech. 403, 329.
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Why LES?
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LES:• Can capture mean flow,
Cp, Cf, and Reynolds stress accurately at resolutions on the order of 1% of DNS
• Largely insensitive to choice of subgrid-scale model
Cadieux, F. and Domaradzki, J. (2015) “Performance of subgrid-scale models in coarse large eddy simulations of a laminar separation bubble”, Phys Fluids, 27, 045112
DNSLES DSMLES sigmaLES TNSNo model
Skin-friction coefficients
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Wall-resolved LES:
• # of points resolve viscous sublayer: (𝑁𝑥𝑁𝑦𝑁𝑧) ∝ 𝑅𝑒2−𝜖𝜖 < 0.2
• For Re>105, >90% of grid points are used in <10% of the simulation domain (near boundaries)
Why Wall-Modeled LES?
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Piomelli, U. (2008), “Wall-layer models for large-eddy simulations”, Progress in Aerospace Sciences 44, 437.
102
107 109103 105
108
106
104
1010
1000 days
10 days
1 days
Rex
CPU
Seco
nds
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Why Wall-Modeled LES?
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Rex=106 Rex=107
Wall Resolved LES 8.7x107 1.4x1010
Hybrid RANS-LES 1.4x107 2.0x107
Integral Wall Model LES* 3.0x106 3.0x106
Estimated # of grid points in the boundary layer regionfor different methods and Reynolds numbers.
*Yang, X.I.A., Sadique, J., Mittal, R. & Meneveau, C. (2015), “Integral Wall Model for Large Eddy Simulations of wall-bounded turbulent flows”. Phys. Fluids 27, 025112.
Estimates for Canonical Turbulent Boundary Layer
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What is wall-modeled LES?
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Immersed boundary
ULES
Wwall
Gi
integral Wall Model (iWMLES)
Highly unsteady 3D inflow
U∞(t)
𝜏𝑤𝑎𝑙𝑙 =?
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LES Wall-modeling approaches
Equilibrium Zonal/Hybrid Dynamic Slip Integral WMSolves Equilibrium
TBL (log law)Full RANS ODE for slip
velocityVertically Integrated Momentum
Strength Simple Wealth of experience
Simple Versatile
Weaknesses Needscorrection for laminar/transitional flow
Requiresembedded grid and RANS solver
Grid dependence, slip is not physical
Assumed profile may not be valid for all flows
CPU Cost Negligible High Low Very Low
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Integral Wall Model (iWMLES)
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Filter velocities in time to match near wall time scale
𝑢𝑖 = න−∞
𝑡
𝑢𝑖 𝑥, 𝑦, 𝑧, 𝑡′1
𝑇𝑤𝑎𝑙𝑙𝑒−
𝑡−𝑡′𝑇𝑤𝑎𝑙𝑙 𝑑𝑡′
𝑈𝐿𝐸𝑆 = ∞−𝑡 𝑢 𝑥, 𝑦 = Δ𝑦, 𝑧, 𝑡′
1𝑇𝑤𝑎𝑙𝑙
𝑒− 𝑡−𝑡′
𝑇𝑤𝑎𝑙𝑙 𝑑𝑡′
where 𝑇𝑤𝑎𝑙𝑙 =Δ𝑦𝜅𝑢𝜏
Æ Obtain RANS like equations for 𝑢𝑖 with 𝜈𝜏 = 𝑙𝑚𝜕 𝑈𝜕𝑦
Æ Vertically integrate equations from 0 to Δ𝑦Æ Solve for 𝜏𝑤 using a parametric velocity profile
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Integral Wall Model (iWMLES)
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Use von-Karman-Paulhausen’s integral method: Assume velocity profile & integrate BL eqn analytically
𝑢 = 𝑢𝜈𝑦𝛿𝜈
𝑢 = 𝑢𝜏𝐶 +
1𝜅log
𝑦Δ𝑦
+𝐴𝑦Δ𝑦
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Integral Wall Model (iWMLES)
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1, 2) Velocity Continuity: 𝑢 𝑦 = Δ𝑦 = 𝑈𝐿𝐸𝑆 → 𝑢𝜏 𝐶 + 𝐴 = 𝑈𝐿𝐸𝑆
𝑢 𝑦 = 𝛿𝑖+ = 𝑢 𝑦 = 𝛿𝑖− → 𝑢𝜈𝛿𝑖𝛿𝑣
= 𝑢𝜏 𝐶 +1𝜅log
𝛿𝑖Δ𝑦
+ 𝐴𝛿𝑖Δ𝑦
3) Inner Layer Height: 𝛿𝑖 = min max 𝑘, 11 𝜈𝑢𝜏
, Δ𝑦
4) Inner Length Scale: 𝛿𝜈 =1𝑢𝜈
𝜈 + 𝜈𝜏,𝑦=0
5) Wall shear stress: 𝜏𝑤 = 𝑢𝜏2 = 𝑢𝜈2 + 0𝑘 𝐶𝑑𝑎𝐿 𝑢 2𝑑𝑦
6) Vertically Integrated Momentum Equation:
Solve for 6 parameters to satisfy 6 constraints (for x):
Evaluated Analytically
𝜕𝜕𝑡න0
Δ𝑦
𝑢 dy +𝜕𝜕𝑥
න0
Δ𝑦
𝑢 2dy − 𝑈𝐿𝐸𝑆𝜕𝜕𝑥
න0
Δ𝑦
𝑢 dy +1𝜌𝜕𝑝𝜕𝑥
Δ𝑦 = 𝜈 + 𝜈𝜏𝜕 𝑢𝜕𝑦
ቚ𝑦=Δ𝑦
− 𝜏𝑤
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Numerical Methods
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ViCar3D
• Cartesian finite difference: 2nd order in space and time
• 𝜎-model for subgrid-scale stress term in LES equations
• Recycle-rescale method of Lund et al. for developing turbulent boundary layer
• Sharp immersed boundary method
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iWMLES Validation I
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Flat plate developing boundary layer
Developing boundary layer with unresolved surface roughness
• k=0.01, 0.005 for Re=2×105, 106 , y0 = 0.0016, 0.00075;
1st grid-point, 𝑅𝑒𝛿0 = 5000(“wall-resolving”)
1st grid-point, 𝑅𝑒𝛿0=5000
1st point𝑅𝑒𝛿0=105
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iWMLES Validation II
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• i-WMLES
• Equilibrium wall model 𝒙
𝒚
𝒛
𝒚 𝒙i-WM
No Stress
Periodic— E. Meinders and K. Hanjalic, “Vortex structure and heat transfer in turbulent flow over a wall-mounted matrix of cubes," International Journal of Heat and Fluid Flow 20, 255 (1999).
uW uW
• i-WMLES
ᴏ left: iWMLES; right: equilibrium wall model;
• Equilibrium wall model
𝑈 𝑈
3.6
32y
y
L HN
864
z
z
L HN
864
x
x
L HN
ReH = 3,800
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iWMLES: Influence of parameters
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• Effect of height of linear layer 𝛿𝑖
• Effect of non-equilibrium terms
i
y
G'
A𝑈
𝑈
ReH = 3,800𝑢 = 𝑢𝜏 𝐶 +
1𝜅log
𝑦Δ𝑦
+ 𝐴𝑦Δ𝑦
Yang, X.I.A., Sadique, J., Mittal, R. & Meneveau, C. (2015), “Integral Wall Model for Large Eddy Simulations of wall-bounded turbulent flows”. Phys. Fluids 27, 025112.
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Specific Objectives
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• Demonstrate that iWMLES can predict transition to turbulence and separation
• Laminar separation bubble application
• Validate integral Wall Model (iWMLES) for separated flows at high Re against wall-resolved LES
• Create benchmark wall-resolved LES• For the same grid except near wall, compare Cf, Cp
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Setup: Laminar Separation Bubble
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Flow over flat plate with suction boundary condition
Suction BC – Vm = 0.65U0L = 10δ, xc = 12δ
<U>
Blasius inlet - 256 x 64 x 3232δ x 4δ x 4δ
Reδ = 105
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Results: Laminar Separation Bubble
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Instantaneous streamwise velocity
Blasius inlet - 256 x 64 x 3232δ x 4δ x 4δ
Reδ = 105
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Results: Laminar Separation Bubble
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Instantaneous U with iso-surfaces of Q-criterion
Blasius inlet - 256 x 64 x 3232δ x 4δ x 4δ
Reδ = 105
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Results: Laminar Separation Bubble
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Turbulent Kinetic EnergyBlasius inlet - 256 x 64 x 32
32δ x 4δ x 4δReδ = 105
Wall (x-z plane at y/ δ = 0.02)
Side view
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Setup: Turbulent Recirculation Zone
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Turbulent flow over flat plate with suction BC
42𝛿
4𝛿
6𝛿
5.25𝛿
Recycle-rescale plane
26𝛿
𝑣 𝑥, 6𝛿 = 0.6 exp(−62 x − 27
26
8𝑅𝑒𝛿 = 16,000
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Setup: Turbulent Recirculation Zone
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Wall-resolved LES vs iWMLES ResolutionLES iWMLES
𝑁𝑥 × 𝑁𝑦 × 𝑁𝑧 256 × 128 × 33 256 × 96 × 33Δ𝑥/𝛿, Δ𝑥+ 0.164, 100 0.164, 100Δ𝑧/𝛿, Δ𝑧+ 0.125, 75 0.125, 75Δ𝑦/𝛿, Δ𝑦+ 0.00125, <1 0.05, 16
Δ𝑦, Δ𝑦+ -- 0.175, ~100
Δ𝑦 ~ 3 Δ𝑦 𝑦 = 0 to avoid feeding the WM the LES under-resolution error in near-wall and to eliminate log-layer mismatch*
*Larsson, J. et al (2016). “Large eddy simulation with modeled wall-stress:recent progress and future directions”, Mechanical Engineering Reviews, 3:1.
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Preliminary Results: Turbulent Recirculation Zone
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Wall-resolved LES (lines) vs iWMLES (dashes)
<U>
<V>
Δ𝑦+~ 1 Δ𝑦+~ 16, Δ𝑦+~100
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26
Wall-resolved LES (lines) vs iWMLES (dashes)
separated regioninflow after reattachment
<U>
Profiles are NOT normalized
Δ𝑦+~ 16, Δ𝑦+~100Δ𝑦+~ 1
Preliminary Results: Turbulent Recirculation Zone
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27
Wall-resolved LES (lines) vs iWMLES (dashes)
separated regioninflow after reattachment
u’ rms
Profiles are NOT normalized
Δ𝑦+~ 16, Δ𝑦+~100Δ𝑦+~ 1
Preliminary Results: Turbulent Recirculation Zone
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28
Wall-resolved LES (lines) vs iWMLES (dashes)
separated regioninflowafter reattachment separated regioninflow
after reattachment
v’ rms w’ rms
Δ𝑦+~ 1 Δ𝑦+~ 16, Δ𝑦+~100
Preliminary Results: Turbulent Recirculation Zone
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29
Wall-resolved LES (lines) vs iWMLES (dashes)
<𝑪𝒑> <𝑪𝒇>
Peak Cf overshoot: sign of LES under-resolution in spanwise, streamwise direction
Δ𝑦+~ 1 Δ𝑦+~ 16, Δ𝑦+~100
Peak Cp deficit: possibly due to higher w’ in iWMLES inflow, shielding near-wall
Preliminary Results: Turbulent Recirculation Zone
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Wall-resolved LES (lines) vs iWMLES (dashes)
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Δ𝑦+~ 1 Δ𝑦+~ 16, Δ𝑦+~100
Log Law
iWMLES disagreement with log-law at ‘inflow’ could be an indication of coupling of WM and recycle-rescale method
Preliminary Results: Turbulent Recirculation Zone
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iWMLES Influence of non-equilibrium terms
21 log
y y
yu u
y yu u C A
W
G
N
ª º « »
¬ ¼ª º§ ·
� �« »¨ ¸¨ ¸' '« »© ¹¬ ¼
<𝑨𝒙>
31
Currently analyzing strong fluctuations in A to refine numerical treatment of wall-model in ViCar3D
Preliminary Results: Turbulent Recirculation Zone
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Conclusions
32
• Proposed a low-cost non-equilibrium integral Wall Model for LES (iWMLES)
• Validated iWMLES for canonical turbulent BL and wall-mounted cubes in turbulent channel flow
• Demonstrated iWMLES capability to predict separation, transition and reattachment for a laminar separation bubble flow
• Showed preliminary, but promising comparison of iWMLES to wall-resolved LES for a turbulent separating and reattaching boundary layer
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Outlook
• Ongoing: validation of turbulent recirculation zone over flat plate
• Increase resolution in streamwise and spanwise• Address inflow recycling problem
• Next: perform validation for turbulent flow over airfoil against experimental data
• Future: use iWMLES to investigate active flow control to reattach flow over wing-flap or tail-rudder at operating Reynolds number
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Thank You
Questions?
AcknowledgmentsResearch supported by AFOSR under Grant FA9550-14-1-0289
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Preliminary Results: Turbulent Recirculation Zone
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