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TECHNICAL PAPERS

Analysis of the Sutton Model for Aero-Optical Properties of Compressible Boundary Layers

[+] Author and Article Information
Eric Tromeur

 ONERA, Applied Aerodynamic Department, BP 72, 29 av. de la division Leclerc, 92322 Châtillon Cedex, France

Eric Garnier

 ONERA, Applied Aerodynamic Department, BP 72, 29 av. de la division Leclerc, 92322 Châtillon Cedex, Francegarnier@onera.fr

Pierre Sagaut

LMM-UPMC/CNRS, Université Paris VI, Boite 162, 4 Place Jussieu 75252, Paris cedex 5, France

J. Fluids Eng 128(2), 239-246 (Sep 22, 2005) (8 pages) doi:10.1115/1.2170128 History: Received March 16, 2004; Revised September 22, 2005

In order to assess the capability of the Sutton model to evaluate aero-optical effects in a turbulent boundary layer, large-eddy simulation (LES) evolving spatially and Reynolds averaged Navier-Stokes (RANS) computations are carried out at Mach number equal to 0.9. First aerodynamic fields are proved to compare favorably with theoretical and experimental results. Once validated, the characteristics of the boundary layer allow us to obtain information concerning optical beam degradation. On the one hand, the density field is used to compute phase distortion directly and, on the other hand, by means of the Sutton model. Therefore, LES and RANS simulations allow us to study optical models and the validity of their assumptions. Finally, LES is proved to be considered as a reference tool to evaluate aero-optical effects.

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Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Generation of inflow turbulent conditions

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Figure 2

Mesh in the (x-z) plane

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Figure 3

Van Driest transformed mean velocity profile. LES: —; u+=1∕0.41lnz++5.5: ----; u+=z+: ∙-∙-∙-; HW from Ref. 12: ◻

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Figure 4

Correlation of the streamwise velocity fluctuations Ruu(y): z+=20

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Figure 5

Correlation of the streamwise velocity fluctuations Ruu(y): z=0.5δ

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Figure 6

Density mean profiles. LES: —; RANS (Chien): -∙∙-∙∙-; HW (Ma=0,8883) from Ref. 12: ◻; HW (Ma=0,8865) from Ref. 12: ▵

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Figure 7

Autocorrelation of streamwise velocity and temperature fluctuations Ru′T′

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Figure 8

Density fluctuations ρrms. LES: —; RANS (Chien): -∙∙-∙∙-; HW (Ma=0,8883) from Ref. 12: ◻; HW (Ma=0,8865) from Ref. 12: ▵

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Figure 9

Normal turbulent scale size Lz∕δ. Lzρ∕δ: —; Lzu∕δ: ---; Lz(k−ϵ)∕δ: ---

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Figure 10

Spatial evolution of instantaneous index-of-refraction fluctuations n′ (top) and phase distortion Δϕ′ at z=3δ (bottom). Isovalue n′=0: ----.

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Figure 11

Variance of phase distortion fluctuations: α=2. LES (direct computation): —; Eq. 10 with RANS: ---; Eq. 10 with Lzρ LES: -∙∙-∙∙-; Eq. 10 with Lzu LES: ---; The analytical model Eq. 11 (for A=0,1): -∙-∙-∙-; The analytical model Eq. 11 (for A=0,2: ⋯ ⋯ ⋯; Experience: ▵

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Figure 12

Variance of phase distortion fluctuations: α=π. LES (direct computation): —; Eq. 10 with RANS: -----; Eq. 10 with Lzρ LES: -∙∙-∙∙-; Eq. 10 with Lzu LES: ---; The analytical model Eq. 11 (for A=0,1): -∙-∙-∙-; The analytical model Eq. 11 (for A=0,2): ⋯ ⋯ ⋯; Experience: ▵

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