large eddy simulation of trailing edge acoustic emissions
TRANSCRIPT
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Large Eddy simulation of Trailing Edge Acoustic Emissions of an Airfoil
Jinlong Wu!William Devenport!Eric Paterson!Rui Sun!Heng Xiao!
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Main Topics
❖ Computational Aeroacoustics (CAA)!
!
❖ The role of Large Eddy Simulation (LES) in CAA!
!
❖ Results and Discussion
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General Acoustic Problem
Source Receiver
∂2 p∂t 2
− c02∇2p = 0
Acoustic Wave Equation
Assumptions
medium at rest
irrotational flow
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wave propagation
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Aeroacoustic Problem
http://www.cascadetechnologies.com/wp-content/uploads/crackle.pnghttp://www.totalsimulation.co.uk/wp/aeroacoustic-modelling-openfoam
http://flowgallery.stanford.edu/research.html
http://www.engineering.com/
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Computational Aeroacoustic(CAA)
❖ Methods with high fidelity:!
❖ Direct simulation (DNS/LES)!
❖ LES + Integral methods
airfoil
fully nonlinear domain
linear domain
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Acoustic Analogy
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∂2ρ∂t 2
− c02∇2ρ = ∂2
∂xi ∂x jTij
∂2 p∂t 2
− c02∇2p = 0
Acoustic Wave EquationLighthill’s Equation
Tij = ρuiu j + (p − c02ρ)δ ij −τ ij
momentum flux entropy production viscous stress
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Acoustic Analogy
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p(x!,t) ≅
xix j4π x! 3
c02
∂2
∂t 2Tij⎡⎣ ⎤⎦te dV (y
!)
V∫ space integration
surface integration
Simplifications can be made if Mach number is
small (Acoustic Compactness)
−x j
4π x! 2
c0
∂∂t
pni[ ]te dSS∫
p(x!,t) ≅ −
x j4π x! 2
c0
∂∂t
pni dSS∫
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Problem Description
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U = 40m / s
NACA0012
0.1524m
Re ≈ 400,000
Ma ≈ 0.115
❖ The Mach number is around 0.1, which indicates that the space integral can be neglected.!
❖ The unsteady pressure around the airfoil needs to be obtained before acoustic calculation.
trip wires is mounted at x/c=0.127
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Large Eddy Simulation (LES)
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❖ The role of LES is to provide unsteady pressure information around the airfoil.!
❖ Two main prerequisites of LES are required:!
❖ The design of a high-quality and affordable mesh, especially in the near wall region;!
❖ The generation of turbulent boundary layer in numerical simulation.
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Wall Resolved Cost
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W.Wolf & S.Lele, 2012
wall resolved54,000,000 grid points!
Re=408,000Δx+ ≈ 50Δz+ ≈ 20y+ ≈ 0.5
❖ This state-of-the-art simulation focuses on the influence of space integral in acoustic prediction.!
❖ For the engineering application, such cost is too high to be feasible currently.!
❖ What if we only put high resolution mesh in the near wall region and use relatively coarse mesh out of the region of interest?
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Aspect Ratio
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❖ It turns out that if the aspect ratio is too high, the information communication is unbalanced along different directions and leads to the pressure convergence problem.
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Pressure Convergence
❖ It is shown that the convergence problem can be solved if the highest aspect ratio of mesh is reduced.!
❖ It also indicates that the mesh design will influence not only the quality of LES result, but also the time cost.
original mesh new mesh
mesh 5.5 M 6 M
aspect ratio ~150 ~75
pressure iterations for each time step ~1000 ~10
total time cost estimation ~180 days ~5 days
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Mean Flow Information
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❖ It seems that the mean flow information around the airfoil is captured in the present simulation.
-Cp
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Boundary Layer Development
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❖ It is shown that an obvious offset of boundary layer development between our result and benchmark.
Cf
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Boundary Layer Development
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❖ The offset of boundary layer development is even more obvious near the trailing edge, which is the exact region of interest in our work.!
❖ It indicates that the numerical tripping needs to be adjusted.
Displacement thickness Momentum thickness
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Friction Coefficient
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Old tripping New tripping
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Reynolds Stress
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Rxy Rxy
Ryy Ryy
Old tripping New tripping
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Conclusions❖ Unsteady flow information can be obtained by LES, which
can be used for the further acoustic calculation.!
❖ Mesh design will influence not only the quality of LES result, but also the convergence and time cost consequently.!
❖ Numerical tripping will directly influence the development of boundary layer, which is the region of interest for CAA. !
❖ Since that the turbulent boundary layer exits for many engineering applications, finding a suitable numerical tripping is important for obtaining a reliable acoustic result.
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Thank you!
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