Abstract

A numerical method based on the uniform and hexahedral grids generated from computational fluid dynamics is presented for the analysis of aero-optical performance. A single grid is taken as a cell with isotropy and homogeneity inside, and it is assumed that the light rays transmit grid by grid. Ray tracing is employed to track the transmission through the flow of supersonic fluids, and a recursive algorithm is derived. The line-of-sight errors and optical path differences produced by the mean density fields were calculated, the phase variances brought from the density fluctuations were computed, and the Strehl ratios were figured out. This method potentially provides a solution for the prediction of aero-optical effects.

© 2007 Optical Society of America

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References

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  1. E. J. Jumper and E. J. Fitzgerald, "Recent advances in aero-optics," Prog. Aerosp. Sci. 37, 299-339 (2001).
    [CrossRef]
  2. G. W. Sutton, "Aero-optical foundations and applications," AIAA J. 23, 1525-1537 (1985).
    [CrossRef]
  3. G. W. Sutton, J. E. Pond, R. Snow, and Y. Hwang, "Hypersonic interceptor performance evaluation center: aero-optics performance predictions," presented at the Proceedings of the second Annual AIAA SDIO interceptor Technology Conference, AIAA-93-2675, American Institute of Aeronautics and Astronautics, Washington, D.C., 1993.
  4. E. J. Jumper, "Recent advance in the measurement and analysis of dynamic aero-optic interactions," AIAA-97-2350 (1997).
  5. B. Thurow, M. Samimy, W. Lempert, S. R. Harris, J. Widiker, and B. Duncan, "Simultaneous MHz rate flow visualization and wavefront sensing for aero-optics," in Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2003-0684. (American Institute of Aeronautics and Astronautics, Washington, D.C., 2003).
  6. C. M. Wyckham, S. H. Zaidi, R. B. Miles, and A. J. Smits, "Characterization of optical wavefront distortions due to a boundary layer at hypersonic speeds," In Proceedings of the 34th AIAA Plasmadynamics and Lasers Conference, AIAA-2003-4308. (American Institute of Aeronautics and Astronautics, Washington, D.C., 2003).
  7. G. W. Sutton, J. E. Pond, R. Snow, and Y. Hwang, "Hypersonic interceptor aero-optics performance predictions [J]," J. Spacecr. Rockets 31, 592-599 (1994).
    [CrossRef]
  8. G. W. Sutton, "Effect of inhomogeneous turbulence on imaging through turbulent layers," Appl. Opt. 33, 3972-3976 (1994).
    [CrossRef] [PubMed]
  9. M. M. Malley, G. W. Sutton, and N. Kincheloe, "Beam-jitter measurements of turbulent aero-optical path differences," Appl. Opt. 31, 4440-4443 (1992).
    [CrossRef] [PubMed]
  10. R. L Clark and R. C. Farris, "A numerical method to predict aero-optical performance in hypersonic flight," in Proceedings of the 19th Fluid Dynamics, Plasma Dynamics and Lasers Conference, AIAA-87-1396. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1987).
  11. J. J. Gierloff, S. J. Robertson, and D. H. Bouska, "Computer analysis of aero-optic effects," in Proceedings of AIAA SDIO Annual Interceptor Technology Conference, AIAA-92-2794. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).
  12. M. I. Jones and E. E. Bender, "CFD-based computer simulation of optical turbulence through aircraft flowfields and wakes," in Proceedings of the 32nd Plasmadynamics and Lasers Conference, AIAA.2001-2798. (American Institute of Aeronautics and Astronautics, Washington, D.C., 2001).
  13. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press,1999), pp. 92-93.
  14. G. Havener, "Optical wavefront variance: A study on analytic modes in use today," in Proceedings of the 30th Aerospace Sciences Meeting & Exhibit, AIAA Paper 92-0654. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).
  15. M. R. Baxter and C. R. Truman, "Predicting the optical quality of supersonic shear layer," in Proceedings of AIAA Thermo physics, Plasma dynamics and Lasers Conference, AIAA-88-2771. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1988).
  16. L. C. Sheng, "Recent researches on the optical transmission distortions throughout the average flow field," Syst. Eng. Electron. 25, 940-944 (2003).
  17. H. H. Klein, M. M. Malley, O. Sapp, D. Shough, G. W. Sutton, and J. H.-Y. Yu, "Experimental measurements of the optical path difference of a four-meter dual aerocurtain," in Proceeding of Propagation of High-Energy Laser Beams through the Earth's Atomsphere, Proc. SPIE 1221, 404-410 (1990).

2003

L. C. Sheng, "Recent researches on the optical transmission distortions throughout the average flow field," Syst. Eng. Electron. 25, 940-944 (2003).

2001

E. J. Jumper and E. J. Fitzgerald, "Recent advances in aero-optics," Prog. Aerosp. Sci. 37, 299-339 (2001).
[CrossRef]

1994

G. W. Sutton, J. E. Pond, R. Snow, and Y. Hwang, "Hypersonic interceptor aero-optics performance predictions [J]," J. Spacecr. Rockets 31, 592-599 (1994).
[CrossRef]

G. W. Sutton, "Effect of inhomogeneous turbulence on imaging through turbulent layers," Appl. Opt. 33, 3972-3976 (1994).
[CrossRef] [PubMed]

1992

1985

G. W. Sutton, "Aero-optical foundations and applications," AIAA J. 23, 1525-1537 (1985).
[CrossRef]

AIAA J.

G. W. Sutton, "Aero-optical foundations and applications," AIAA J. 23, 1525-1537 (1985).
[CrossRef]

Appl. Opt.

J. Spacecr. Rockets

G. W. Sutton, J. E. Pond, R. Snow, and Y. Hwang, "Hypersonic interceptor aero-optics performance predictions [J]," J. Spacecr. Rockets 31, 592-599 (1994).
[CrossRef]

Prog. Aerosp. Sci.

E. J. Jumper and E. J. Fitzgerald, "Recent advances in aero-optics," Prog. Aerosp. Sci. 37, 299-339 (2001).
[CrossRef]

Syst. Eng. Electron.

L. C. Sheng, "Recent researches on the optical transmission distortions throughout the average flow field," Syst. Eng. Electron. 25, 940-944 (2003).

Other

H. H. Klein, M. M. Malley, O. Sapp, D. Shough, G. W. Sutton, and J. H.-Y. Yu, "Experimental measurements of the optical path difference of a four-meter dual aerocurtain," in Proceeding of Propagation of High-Energy Laser Beams through the Earth's Atomsphere, Proc. SPIE 1221, 404-410 (1990).

G. W. Sutton, J. E. Pond, R. Snow, and Y. Hwang, "Hypersonic interceptor performance evaluation center: aero-optics performance predictions," presented at the Proceedings of the second Annual AIAA SDIO interceptor Technology Conference, AIAA-93-2675, American Institute of Aeronautics and Astronautics, Washington, D.C., 1993.

E. J. Jumper, "Recent advance in the measurement and analysis of dynamic aero-optic interactions," AIAA-97-2350 (1997).

B. Thurow, M. Samimy, W. Lempert, S. R. Harris, J. Widiker, and B. Duncan, "Simultaneous MHz rate flow visualization and wavefront sensing for aero-optics," in Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2003-0684. (American Institute of Aeronautics and Astronautics, Washington, D.C., 2003).

C. M. Wyckham, S. H. Zaidi, R. B. Miles, and A. J. Smits, "Characterization of optical wavefront distortions due to a boundary layer at hypersonic speeds," In Proceedings of the 34th AIAA Plasmadynamics and Lasers Conference, AIAA-2003-4308. (American Institute of Aeronautics and Astronautics, Washington, D.C., 2003).

R. L Clark and R. C. Farris, "A numerical method to predict aero-optical performance in hypersonic flight," in Proceedings of the 19th Fluid Dynamics, Plasma Dynamics and Lasers Conference, AIAA-87-1396. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1987).

J. J. Gierloff, S. J. Robertson, and D. H. Bouska, "Computer analysis of aero-optic effects," in Proceedings of AIAA SDIO Annual Interceptor Technology Conference, AIAA-92-2794. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).

M. I. Jones and E. E. Bender, "CFD-based computer simulation of optical turbulence through aircraft flowfields and wakes," in Proceedings of the 32nd Plasmadynamics and Lasers Conference, AIAA.2001-2798. (American Institute of Aeronautics and Astronautics, Washington, D.C., 2001).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press,1999), pp. 92-93.

G. Havener, "Optical wavefront variance: A study on analytic modes in use today," in Proceedings of the 30th Aerospace Sciences Meeting & Exhibit, AIAA Paper 92-0654. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).

M. R. Baxter and C. R. Truman, "Predicting the optical quality of supersonic shear layer," in Proceedings of AIAA Thermo physics, Plasma dynamics and Lasers Conference, AIAA-88-2771. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1988).

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Figures (15)

Fig. 1
Fig. 1

Relationship between the CFD calculation mesh and the optical transmission.

Fig. 2
Fig. 2

Reference frame between the flow and the incident light rays.

Fig. 3
Fig. 3

Geometry of the optical transmission in two dimensions.

Fig. 4
Fig. 4

Interpolated mesh cell.

Fig. 5
Fig. 5

(a) Initial refractive index distributions and (b) interpolated refractive index distributions.

Fig. 6
Fig. 6

LOS deviation angle.

Fig. 7
Fig. 7

Density fluctuation distributions along the flow direction ( H = 35 k m and Ma = 7 ).

Fig. 8
Fig. 8

Density fluctuation distributions in the Y direction ( H = 35 k m , Ma = 7 ).

Fig. 9
Fig. 9

RMS wavefront errors in the flow direction ( H = 35   km , Ma = 7 ).

Fig. 10
Fig. 10

RMS wavefront errors in the Y positive direction ( H = 35   km , Ma = 7 ).

Fig. 11
Fig. 11

Strehl ratio in the flow direction ( H = 35   km and Ma = 7 ).

Fig. 12
Fig. 12

Strehl ratio in the Y positive direction ( H = 35   km and Ma = 7 ).

Fig. 13
Fig. 13

Comparison of OPD at different angles of incidence ( H = 40   km and Ma = 7 ).

Fig. 14
Fig. 14

Comparison of OPD at different altitudes ( Ma = 7 and θ 0 = 5 ° ).

Fig. 15
Fig. 15

Comparison of OPD at different Mach Numbers ( H = 30   km and θ 0 = 5 ° ).

Tables (1)

Tables Icon

Table 1 Maximum Deviation Angles

Equations (24)

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( n 2 1 n 2 + 2 ) 1 ρ = 2 3 K GD .
n = 1 + K GD ρ ,
K GD = 0.113 + 0.0009 / λ 2 ,
| n j n i | s < λ / 4 ,
Δ x 1 = d tan θ 1 ,
n 21 sin θ 1 = n 11 sin θ 0 .
Δ x k = d tan θ k ,
n k + 1 , l sin θ k = n k , l sin θ k 1 ( l , k = 1 , 2 ,   … ) ,
OPL k = n k + 1 , l d / cos θ k .
M = ( Δ x k l × d ) cot θ k .
Δ x k = M cot θ k + ( d M ) tan θ k ,
OPL k = n k + 1 , l ( d M ) / cos θ k + n k + 1 , l + 1 M / sin θ k .
n k + 1 , l cos θ k = n k + 1 , l + 1 sin θ ,
θ k + 1 = 90 ° θ k .
θ k = θ k .
OPL = ray n d l .
OPD = 0 L ( n 1 ) d l = K GD 0 L ρ d l ,
OPD = OPL OPL ref .
Δ ϕ ( r , t ) = k OPD ,
σ 2 = 2 K GD 2 0 L ( ρ ) 2 l d l ,
SR = exp [ δ ϕ 2 ] .
δ ϕ 2 = k 2 σ 2 .
τ = q / R .
q = h tan θ Δ X i .

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