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Research Papers: Flows in Complex Systems

Delayed Detached Eddy Simulation of Airfoil Stall Flows Using High-Order Schemes

[+] Author and Article Information
Hong-Sik Im

Mem. ASME
Department of Mechanical and
Aerospace Engineering,
University of Miami,
Coral Gables, FL 33124

Ge-Cheng Zha

Professor
Fellow ASME
Department of Mechanical and
Aerospace Engineering,
University of Miami,
Coral Gables, FL 33124
e-mail: gzha@miami.edu

1Present address: Honeywell, Torrance, CA 90505.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 27, 2013; final manuscript received June 3, 2014; published online September 4, 2014. Assoc. Editor: Zvi Rusak.

J. Fluids Eng 136(11), 111104 (Sep 04, 2014) (12 pages) Paper No: FE-13-1122; doi: 10.1115/1.4027813 History: Received February 27, 2013; Revised June 03, 2014

An advanced hybrid Reynolds-Averaged Navier–Stokes/large eddy simulation (RANS/LES) turbulence model delayed detached eddy simulation (DDES) is conducted in thispaper to investigate the dynamic stall flows over 3D NACA0012 airfoil at 17 deg, 26 deg, 45 deg, and 60 deg angle of attack (AOA). The spatially filtered unsteady 3D Navier–Stokes equations are solved using a fifth-order weighted essentially nonoscillatory (WENO) reconstruction with a low diffusion E-CUSP (LDE) scheme for the inviscid fluxes and a conservative fourth-order central differencing for the viscous terms. An implicit second-order time marching scheme with dual time stepping is employed to achieve high stability and convergency rate. A 3D flat plate is validated for the DDES model. For quantitative prediction of lift and drag of the stalled NACA0012 airfoil flows, the detached eddy simulation (DES) and DDES achieve much more accurate results than the Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulation. In addition to the quantitative difference, the DES/DDES and URANS also obtain qualitatively very different unsteady stalled flows of NACA0012 airfoil with different vortical structures and frequencies. This may bring a significantly different prediction if those methods are used for fluid–structural interaction. For comparison purpose, a third-order WENO scheme with a second-order central differencing is also employed for the DDES stalled NACA0012 airfoil flows. Both the third- and fifth-order WENO schemes predict the stalled flow similarly for lift and drag at AOA less than 45 deg, while at AOA of 60 deg, the fifth-order WENO scheme shows better agreement with the experiment than the third-order WENO scheme. The high-order scheme of WENO 5 also resolves more small scales of flow structures than the second-order scheme. The prediction of the stalled airfoil flow using DDES with both the high-order scheme and second-order scheme is overall significantly more accurate than the URANS simulation.

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References

Figures

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Fig. 3

Predicted turbulent boundary layer using the coarse grid: Δx = 0.033L, Re = 6.5 × 106, M = 0.1

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Fig. 4

Predicted turbulent boundary layer using the fine grid: Δx = 0.00417 L, Re = 6.5 × 106, M = 0.1

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Fig. 2

Fine mesh for the flat plate: Δx≈Δz≈0.00417L, where L is the flat plate height

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Fig. 1

Coarse mesh for the flat plate: Δx≈Δz≈0.033L, where L is the flat plate height

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Fig. 16

Predicted frequencies of drag coefficients from URANS, DES, and DDES

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Fig. 5

Distributions of u/U∞,0.002(νt/ν) in the flat plate boundary layer

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Fig. 10

Measured the boundary layer thickness (δ) on the pressure surface near half chord for the DES

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Fig. 11

Instantaneous drag coefficients predicted by URANS

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Fig. 12

Instantaneous drag coefficients predicted by DES

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Fig. 13

Instantaneous drag coefficients predicted by DDES

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Fig. 6

Distributions of u/U∞,0.002(νt/ν) and fd in the flat plate boundary layer

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Fig. 14

Vorticity at T = 200 predicted by URANS (top), DES (middle), and DDES (bottom)

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Fig. 15

Instantaneous drag coefficients predicted by DDES with Δt = 0.01 and Δt = 0.02

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Fig. 7

3D mesh for NACA0012 airfoil at 45 deg AOA: 193 × 101 × 31, dn = 1.0 × 10−5c, ΔZ∕C = 0.033

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Fig. 8

Unsteady pseudo step residual at AOA 45 deg from DDES, DES, and URANS

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Fig. 9

Computational Mesh near NACA0012 airfoil leading edge

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Fig. 17

Pseudo step convergence behavior at AOA 17 deg and AOA 60 deg obtained by WENO scheme with DDES

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Fig. 18

Instantaneous DDES vorticity contours of cross sections at z/c = 0.25 (top), 0.50 (middle), and 0.75 (bottom) predicted by WENO 3 (left) and WENO 5 (right); AOA = 60 deg

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Fig. 19

Instantaneous DDES vorticity contours of cross sections at z/c = 0.25 (top), 0.50 (middle), and 0.75 (bottom) predicted by WENO 3 (left) and WENO 5 (right); AOA = 17 deg

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Fig. 20

Instantaneous lift and drag coefficients for AOA 17 deg, 26 deg, 45 deg, and 60 deg predicted by WENO scheme with DDES

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Fig. 21

Comparison of time averaged lift coefficient, CL (top) and drag coefficient, CD (bottom) predicted by WENO schemes with the experiment at Re = 2 × 106 [18,23,24]

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