validation of a low-cost transitional turbulence model for low-reynolds-number external...
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Validation of a Low-Cost Transitional
Turbulence Model for
Low-Reynolds-Number External
Aerodynamics
Joshua Counsil and K. Goni Boulama
Royal Military College of Canada
20th AIAA CFD Conference
June 29, 2011
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Outline
54Introduction
Validation of
Model
Results and
Discussion
Conclusion
Questions
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UAVs, Low-Re flow, and CFD
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Introduction
Low-Reynolds Number Flow
Laminar separation without reattachment
Courtesy of Yarusevych et al., 2010
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Introduction
Low-Reynolds Number Flow
Laminar Separation Bubble (LSB)
Courtesy of Yarusevych et al., 2010
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Introduction
URANSUnsteady Reynolds-Averaged Navier-Stokes Equations
• Turbulence models
• Approximate envelope (eN) method
• Specified transition point
• γ and Reθ
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Introduction
• γ and Reθ
• Empirical Correlations
• e.g., ( γ )( μt )
SST γ-Reθ
• e.g., Reθ = ƒ( Tu , dP/dx )
• Transport Equations
• e.g.,
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Turbulence Model and Numerical Setup
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Validation of Model
Parameters
• NACA 0012
• Re = 100k
• AoA = 4°
• Tu = 0.1%
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Validation of Model
Turbulence Model
• Shear Stress Transport Model (SST)
• Shear Stress Transport Transitional Model (SST γ-Reθ)
• XFLR5 eN Method
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Validation of ModelTurbulence Model
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Validation of Model
Sensitivity Studies
• 2 domain sizes
• 5 grid resolutions
• 2 grid “qualities”
• 2 timestepping schemes
• 6 turbulence intensities
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Validation of ModelDomain Inlet Radius
η = 10c η = 20c
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Validation of ModelAirfoil Grid Resolution
134 x 93 380 x 263
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Validation of ModelWake Grid Resolution
267 x 185 217 x 185
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Validation of ModelGrid Quality and Timestepping Scheme
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Validation of Model
NACA 0012
Re = 50k
AoA = 5
Test of Model against Published Results
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Validation of Model
NACA 0012
Re = 48k
AoA = 6
Test of Model against Published Results
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Validation of Model
NACA 0012
Re = 48k
AoA = 6
Test of Model against Published Results
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Validation of Model
SD7003
Re = 60k
AoA = 4
Test of Model against Published Results
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Flow-field Analysis, Parameterization
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Results and DiscussionInstantaneous Flow Features
• NACA 0012
• Re = 100k
• AoA = 4
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Results and DiscussionInstantaneous Flow Features
• NACA 0012
• Re = 100k
• AoA = 4
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Results and DiscussionInstantaneous Flow Features
• NACA 0012
• Re = 100k
• AoA = 4
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Results and DiscussionInstantaneous Flow Features
• NACA 0012
• Re = 100k
• AoA = 4
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Results and DiscussionTime-Averaged Flow Features
NACA 0012
Re = 50k
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Results and DiscussionTime-Averaged Flow Features
NACA 0012
Re = 100k
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Results and DiscussionTime-Averaged Flow Features
NACA 0012
Re = 250k
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Results and DiscussionTime-Averaged Flow Features
• NACA 0012
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Results and DiscussionTime-Averaged Flow Features
NACA 0012
Re = 50k
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Results and DiscussionTime-Averaged Flow Features
NACA 0012
Re = 100k
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Results and DiscussionTime-Averaged Flow Features
NACA 0012
Re = 250k
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Results and DiscussionTime-Averaged Flow Features
NACA 0012
Re = 50k Re = 100k
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Conclusions• Many CFD methods for low-Re flow
• Numerical validation verified accuracy of method
• Performance of models• XFLR5 typically underestimates separation/LSB
• SST γ-Reθ model typically overestimates separation/LSB• Very good aerodynamic performance estimation
• NACA 0012 at various Re and AoA• Laminar separation without reattachment
• All AoA = 0 and Re = 50k, AoA = 4
• Laminar separation bubble• All AoA = 8 and Re = 100k, AoA = 4
• With increase in Re or AoA, LSB shrinks and recedes
• Low-Re causes nonlinear aerodynamic characteristics