Abstract

We investigated the joint influences exerted by the nonuniform aerodynamic flow field surrounding the optical dome and the aerodynamic heating of the dome on imaging quality degradation of an airborne optical system. The Spalart–Allmaras model provided by FLUENT was used for flow computations. The fourth-order Runge–Kutta algorithm based ray tracing program was used to simulate optical transmission through the aerodynamic flow field and the dome. Four kinds of imaging quality evaluation parameters were presented: wave aberration of the exit pupil, point spread function, encircled energy, and modulation transfer function. The results show that the aero-optical disturbance of the aerodynamic flow field and the aerodynamic heating of the dome significantly affect the imaging quality of an airborne optical system.

© 2012 Optical Society of America

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References

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  1. H. S. Xiao and Z. G. Fan, “Imaging quality evaluation of aerodynamically heated optical dome using ray tracing,” Appl. Opt. 49, 5049–5058 (2010).
    [CrossRef]
  2. Q. Gao, Z. F. Jiang, S. H. Yi, and Y. X. Zhao, “Optical path difference of the supersonic mixing layer,” Appl. Opt. 49, 3786–3792 (2010).
    [CrossRef]
  3. L. Xu and Y. L. Cai, “Influence of altitude on aero-optic imaging deviation,” Appl. Opt. 50, 2949–2957 (2011).
    [CrossRef]
  4. L. Sjoqvist, O. Gustafsson, and M. Henriksson, “Laser beam propagation in close vicinity to a downscaled jet engine exhaust,” Proc. SPIE 5615, 137–148 (2004).
    [CrossRef]
  5. M. Henriksson, L. Sjoqvist, D. Seiffer, N. Wendelstein, and E. Sucher, “Laser beam propagation experiments along and across a jet engine plume,” Proc. SPIE 7115, 71150E (2008).
    [CrossRef]
  6. M. Henriksson, O. Gustafsson, L. Sjoqvist, D. Seiffer, and N. Wendelstein, “Laser beam propagation through a full scale aircraft turboprop engine exhaust,” Proc. SPIE 7836, 78360L (2010).
    [CrossRef]
  7. E. Frumker and O. Pade, “Generic method for aero-optic evaluations,” Appl. Opt. 43, 3224–3228 (2004).
    [CrossRef]
  8. T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46, 5545–5551 (2007).
    [CrossRef]
  9. FLUENT 6.3 User’s Guide (2004), http://www.ansys.com .
  10. W. Merzkirch, Flow Visulization, 2nd ed. (Academic, 1987).
  11. X. L. Yin, Principle of Aero-Optics (China Astronautics, 2003).
  12. L. Lees, “Laminar heat transfer over blunted-nosed bodies at hypersonic flight speeds,” Jet Propul. 26, 259–269 (1956).
    [CrossRef]
  13. R. Vaglio-Laurin, “Turbulent heat transfer on blunt-nosed bodies in two-dimensional and general three-dimensional hypersonic flow,” J. Aerosp. Sci. 27, 27–36 (1960).
  14. F. R. Dejarnette and T. C. Tai, “A method for calculating laminar and turbulent convective heat transfer over bodies at an angle of attack,” Tech. Rep. (Virginia Polytechnic Institute, 1969).
  15. J. F. Nye, Physical Properties of Crystals (Oxford University, 1985).
  16. D. C. Harris, Materials for Infrared Windows and Domes (SPIE, 1999).
  17. W. H. Yu and W. Y. Liu, Crystal Physics (University of Science and Technology of China, 1998).
  18. T. Zarutski, E. Arad, and R. Arieli, “Experimental and computational study on the effects of bumps on the aerodynamics of missile’s noses,” presented at the 42nd Israeli Conference on Aerospace Sciences, Haifa, Israel, 1–18 January 2002.
  19. E. Arad, M. Berger, M. Israeli, and M. Wolfshtein, “Numerical calculation of transitional boundary layers,” Int. J. Numer. Methods Fluids 2, 1–23 (1982).
  20. D. C. Reda, M. C. Wilder, and D. K. Prabhu, “Transition experiments on blunt bodies with isolated roughness elements in hypersonic free flight,” presented at the 48th AIAA Aerospace Science Meeting, Orlando, Florida, 1–13 January 2010.
    [CrossRef]
  21. M. R. Whiteley and D. J. Goorskey, “Influence of aero-optical disturbances on acquisition, tracking, and pointing performance characteristics in laser systems,” Proc. SPIE 8052, 805206 (2011).
    [CrossRef]

2011 (2)

L. Xu and Y. L. Cai, “Influence of altitude on aero-optic imaging deviation,” Appl. Opt. 50, 2949–2957 (2011).
[CrossRef]

M. R. Whiteley and D. J. Goorskey, “Influence of aero-optical disturbances on acquisition, tracking, and pointing performance characteristics in laser systems,” Proc. SPIE 8052, 805206 (2011).
[CrossRef]

2010 (3)

2008 (1)

M. Henriksson, L. Sjoqvist, D. Seiffer, N. Wendelstein, and E. Sucher, “Laser beam propagation experiments along and across a jet engine plume,” Proc. SPIE 7115, 71150E (2008).
[CrossRef]

2007 (1)

2004 (2)

E. Frumker and O. Pade, “Generic method for aero-optic evaluations,” Appl. Opt. 43, 3224–3228 (2004).
[CrossRef]

L. Sjoqvist, O. Gustafsson, and M. Henriksson, “Laser beam propagation in close vicinity to a downscaled jet engine exhaust,” Proc. SPIE 5615, 137–148 (2004).
[CrossRef]

1982 (1)

E. Arad, M. Berger, M. Israeli, and M. Wolfshtein, “Numerical calculation of transitional boundary layers,” Int. J. Numer. Methods Fluids 2, 1–23 (1982).

1960 (1)

R. Vaglio-Laurin, “Turbulent heat transfer on blunt-nosed bodies in two-dimensional and general three-dimensional hypersonic flow,” J. Aerosp. Sci. 27, 27–36 (1960).

1956 (1)

L. Lees, “Laminar heat transfer over blunted-nosed bodies at hypersonic flight speeds,” Jet Propul. 26, 259–269 (1956).
[CrossRef]

Arad, E.

E. Arad, M. Berger, M. Israeli, and M. Wolfshtein, “Numerical calculation of transitional boundary layers,” Int. J. Numer. Methods Fluids 2, 1–23 (1982).

T. Zarutski, E. Arad, and R. Arieli, “Experimental and computational study on the effects of bumps on the aerodynamics of missile’s noses,” presented at the 42nd Israeli Conference on Aerospace Sciences, Haifa, Israel, 1–18 January 2002.

Arieli, R.

T. Zarutski, E. Arad, and R. Arieli, “Experimental and computational study on the effects of bumps on the aerodynamics of missile’s noses,” presented at the 42nd Israeli Conference on Aerospace Sciences, Haifa, Israel, 1–18 January 2002.

Berger, M.

E. Arad, M. Berger, M. Israeli, and M. Wolfshtein, “Numerical calculation of transitional boundary layers,” Int. J. Numer. Methods Fluids 2, 1–23 (1982).

Cai, Y. L.

Dejarnette, F. R.

F. R. Dejarnette and T. C. Tai, “A method for calculating laminar and turbulent convective heat transfer over bodies at an angle of attack,” Tech. Rep. (Virginia Polytechnic Institute, 1969).

Fan, Z. G.

Frumker, E.

Gao, Q.

Goorskey, D. J.

M. R. Whiteley and D. J. Goorskey, “Influence of aero-optical disturbances on acquisition, tracking, and pointing performance characteristics in laser systems,” Proc. SPIE 8052, 805206 (2011).
[CrossRef]

Gustafsson, O.

M. Henriksson, O. Gustafsson, L. Sjoqvist, D. Seiffer, and N. Wendelstein, “Laser beam propagation through a full scale aircraft turboprop engine exhaust,” Proc. SPIE 7836, 78360L (2010).
[CrossRef]

L. Sjoqvist, O. Gustafsson, and M. Henriksson, “Laser beam propagation in close vicinity to a downscaled jet engine exhaust,” Proc. SPIE 5615, 137–148 (2004).
[CrossRef]

Harris, D. C.

D. C. Harris, Materials for Infrared Windows and Domes (SPIE, 1999).

Henriksson, M.

M. Henriksson, O. Gustafsson, L. Sjoqvist, D. Seiffer, and N. Wendelstein, “Laser beam propagation through a full scale aircraft turboprop engine exhaust,” Proc. SPIE 7836, 78360L (2010).
[CrossRef]

M. Henriksson, L. Sjoqvist, D. Seiffer, N. Wendelstein, and E. Sucher, “Laser beam propagation experiments along and across a jet engine plume,” Proc. SPIE 7115, 71150E (2008).
[CrossRef]

L. Sjoqvist, O. Gustafsson, and M. Henriksson, “Laser beam propagation in close vicinity to a downscaled jet engine exhaust,” Proc. SPIE 5615, 137–148 (2004).
[CrossRef]

Israeli, M.

E. Arad, M. Berger, M. Israeli, and M. Wolfshtein, “Numerical calculation of transitional boundary layers,” Int. J. Numer. Methods Fluids 2, 1–23 (1982).

Jiang, Z. F.

Lees, L.

L. Lees, “Laminar heat transfer over blunted-nosed bodies at hypersonic flight speeds,” Jet Propul. 26, 259–269 (1956).
[CrossRef]

Liu, W. Y.

W. H. Yu and W. Y. Liu, Crystal Physics (University of Science and Technology of China, 1998).

Merzkirch, W.

W. Merzkirch, Flow Visulization, 2nd ed. (Academic, 1987).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford University, 1985).

Pade, O.

Prabhu, D. K.

D. C. Reda, M. C. Wilder, and D. K. Prabhu, “Transition experiments on blunt bodies with isolated roughness elements in hypersonic free flight,” presented at the 48th AIAA Aerospace Science Meeting, Orlando, Florida, 1–13 January 2010.
[CrossRef]

Reda, D. C.

D. C. Reda, M. C. Wilder, and D. K. Prabhu, “Transition experiments on blunt bodies with isolated roughness elements in hypersonic free flight,” presented at the 48th AIAA Aerospace Science Meeting, Orlando, Florida, 1–13 January 2010.
[CrossRef]

Seiffer, D.

M. Henriksson, O. Gustafsson, L. Sjoqvist, D. Seiffer, and N. Wendelstein, “Laser beam propagation through a full scale aircraft turboprop engine exhaust,” Proc. SPIE 7836, 78360L (2010).
[CrossRef]

M. Henriksson, L. Sjoqvist, D. Seiffer, N. Wendelstein, and E. Sucher, “Laser beam propagation experiments along and across a jet engine plume,” Proc. SPIE 7115, 71150E (2008).
[CrossRef]

Sjoqvist, L.

M. Henriksson, O. Gustafsson, L. Sjoqvist, D. Seiffer, and N. Wendelstein, “Laser beam propagation through a full scale aircraft turboprop engine exhaust,” Proc. SPIE 7836, 78360L (2010).
[CrossRef]

M. Henriksson, L. Sjoqvist, D. Seiffer, N. Wendelstein, and E. Sucher, “Laser beam propagation experiments along and across a jet engine plume,” Proc. SPIE 7115, 71150E (2008).
[CrossRef]

L. Sjoqvist, O. Gustafsson, and M. Henriksson, “Laser beam propagation in close vicinity to a downscaled jet engine exhaust,” Proc. SPIE 5615, 137–148 (2004).
[CrossRef]

Sucher, E.

M. Henriksson, L. Sjoqvist, D. Seiffer, N. Wendelstein, and E. Sucher, “Laser beam propagation experiments along and across a jet engine plume,” Proc. SPIE 7115, 71150E (2008).
[CrossRef]

Tai, T. C.

F. R. Dejarnette and T. C. Tai, “A method for calculating laminar and turbulent convective heat transfer over bodies at an angle of attack,” Tech. Rep. (Virginia Polytechnic Institute, 1969).

Vaglio-Laurin, R.

R. Vaglio-Laurin, “Turbulent heat transfer on blunt-nosed bodies in two-dimensional and general three-dimensional hypersonic flow,” J. Aerosp. Sci. 27, 27–36 (1960).

Wang, T.

Wendelstein, N.

M. Henriksson, O. Gustafsson, L. Sjoqvist, D. Seiffer, and N. Wendelstein, “Laser beam propagation through a full scale aircraft turboprop engine exhaust,” Proc. SPIE 7836, 78360L (2010).
[CrossRef]

M. Henriksson, L. Sjoqvist, D. Seiffer, N. Wendelstein, and E. Sucher, “Laser beam propagation experiments along and across a jet engine plume,” Proc. SPIE 7115, 71150E (2008).
[CrossRef]

Whiteley, M. R.

M. R. Whiteley and D. J. Goorskey, “Influence of aero-optical disturbances on acquisition, tracking, and pointing performance characteristics in laser systems,” Proc. SPIE 8052, 805206 (2011).
[CrossRef]

Wilder, M. C.

D. C. Reda, M. C. Wilder, and D. K. Prabhu, “Transition experiments on blunt bodies with isolated roughness elements in hypersonic free flight,” presented at the 48th AIAA Aerospace Science Meeting, Orlando, Florida, 1–13 January 2010.
[CrossRef]

Wolfshtein, M.

E. Arad, M. Berger, M. Israeli, and M. Wolfshtein, “Numerical calculation of transitional boundary layers,” Int. J. Numer. Methods Fluids 2, 1–23 (1982).

Xiao, H. S.

Xu, D.

Xu, L.

Yang, Q. Y.

Yi, S. H.

Yin, X. L.

X. L. Yin, Principle of Aero-Optics (China Astronautics, 2003).

Yu, W. H.

W. H. Yu and W. Y. Liu, Crystal Physics (University of Science and Technology of China, 1998).

Zarutski, T.

T. Zarutski, E. Arad, and R. Arieli, “Experimental and computational study on the effects of bumps on the aerodynamics of missile’s noses,” presented at the 42nd Israeli Conference on Aerospace Sciences, Haifa, Israel, 1–18 January 2002.

Zhao, Y.

Zhao, Y. X.

Appl. Opt. (5)

Int. J. Numer. Methods Fluids (1)

E. Arad, M. Berger, M. Israeli, and M. Wolfshtein, “Numerical calculation of transitional boundary layers,” Int. J. Numer. Methods Fluids 2, 1–23 (1982).

J. Aerosp. Sci. (1)

R. Vaglio-Laurin, “Turbulent heat transfer on blunt-nosed bodies in two-dimensional and general three-dimensional hypersonic flow,” J. Aerosp. Sci. 27, 27–36 (1960).

Jet Propul. (1)

L. Lees, “Laminar heat transfer over blunted-nosed bodies at hypersonic flight speeds,” Jet Propul. 26, 259–269 (1956).
[CrossRef]

Proc. SPIE (4)

M. R. Whiteley and D. J. Goorskey, “Influence of aero-optical disturbances on acquisition, tracking, and pointing performance characteristics in laser systems,” Proc. SPIE 8052, 805206 (2011).
[CrossRef]

L. Sjoqvist, O. Gustafsson, and M. Henriksson, “Laser beam propagation in close vicinity to a downscaled jet engine exhaust,” Proc. SPIE 5615, 137–148 (2004).
[CrossRef]

M. Henriksson, L. Sjoqvist, D. Seiffer, N. Wendelstein, and E. Sucher, “Laser beam propagation experiments along and across a jet engine plume,” Proc. SPIE 7115, 71150E (2008).
[CrossRef]

M. Henriksson, O. Gustafsson, L. Sjoqvist, D. Seiffer, and N. Wendelstein, “Laser beam propagation through a full scale aircraft turboprop engine exhaust,” Proc. SPIE 7836, 78360L (2010).
[CrossRef]

Other (9)

FLUENT 6.3 User’s Guide (2004), http://www.ansys.com .

W. Merzkirch, Flow Visulization, 2nd ed. (Academic, 1987).

X. L. Yin, Principle of Aero-Optics (China Astronautics, 2003).

D. C. Reda, M. C. Wilder, and D. K. Prabhu, “Transition experiments on blunt bodies with isolated roughness elements in hypersonic free flight,” presented at the 48th AIAA Aerospace Science Meeting, Orlando, Florida, 1–13 January 2010.
[CrossRef]

F. R. Dejarnette and T. C. Tai, “A method for calculating laminar and turbulent convective heat transfer over bodies at an angle of attack,” Tech. Rep. (Virginia Polytechnic Institute, 1969).

J. F. Nye, Physical Properties of Crystals (Oxford University, 1985).

D. C. Harris, Materials for Infrared Windows and Domes (SPIE, 1999).

W. H. Yu and W. Y. Liu, Crystal Physics (University of Science and Technology of China, 1998).

T. Zarutski, E. Arad, and R. Arieli, “Experimental and computational study on the effects of bumps on the aerodynamics of missile’s noses,” presented at the 42nd Israeli Conference on Aerospace Sciences, Haifa, Israel, 1–18 January 2002.

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Figures (17)

Fig. 1.
Fig. 1.

Round-head high-speed aircraft.

Fig. 2.
Fig. 2.

Computational grid model for CFD computation.

Fig. 3.
Fig. 3.

Irregular refractive index grid model of the optical dome: (a) normal view and (b) cut-away view.

Fig. 4.
Fig. 4.

Cross-sectional view of the grid model for optical transmission simulation of the aerodynamic flow field (red, square) and grid model for the aerodynamic computation (black, triangular).

Fig. 5.
Fig. 5.

Definitions for azimuth and elevation incident angles. Curved arrows indicate positive angles [1].

Fig. 6.
Fig. 6.

Dependence of the static temperature of the stagnation point on the different mesh sizes (mesh number 1 denotes 150,310 tetrahedral elements, mesh number 2 denotes 211,724 tetrahedral elements, mesh number 3 denotes 508,481 tetrahedral elements, and mesh number 4 denotes 843,940 tetrahedral elements).

Fig. 7.
Fig. 7.

Mean density contour of the aerodynamic flow field surrounding the dome.

Fig. 8.
Fig. 8.

Wall static temperature contour of the aerodynamic flow field surrounding the dome.

Fig. 9.
Fig. 9.

Wall static pressure contour of the aerodynamic flow field surrounding the dome.

Fig. 10.
Fig. 10.

Heat flux contour on the outside surface of the dome.

Fig. 11.
Fig. 11.

Temperature field of the optical dome at 15 s: (a) normal view, (b) cut-away view 1, and (c) cut-away view 2. Maximum temperature is 459.47 K and minimum temperature is 333.55 K.

Fig. 12.
Fig. 12.

Sum deformation field of the optical dome at 15 s: (a) normal view, (b) cut-away view 1, and (c) cut-away view 2. Maximum sum deformation is 4.77×105m and minimum sum deformation is 0 m.

Fig. 13.
Fig. 13.

Equivalent von Mises strain field of the optical dome at 15 s: (a) normal view, (b) cut-away view 1, and (c) cut-away view 2. Maximum equivalent von Mises strain is 4.85×104 and minimum equivalent von Mises strain is 3.54×106.

Fig. 14.
Fig. 14.

Wave aberration results of the airborne optical system at different incident angles: (a) 0°/90° (azimuth/elevation), (b) 0°/88.73°, and (c) 0°/88.2°.

Fig. 15.
Fig. 15.

PSF results of the airborne optical system: (a) diffraction-limited PSF, and (b)–(d) PSF results at the 0°/90° (azimuth/elevation), 0°/88.73°, and 0°/88.2° incident angles, respectively.

Fig. 16.
Fig. 16.

Encircled energy results of the airborne optical system.

Fig. 17.
Fig. 17.

MTF results of the airborne optical system at different incident angles: (a) 0°/90° (azimuth/elevation), (b) 0°/88.73°, and (c) 0°/88.2°.

Tables (3)

Tables Icon

Table 1. Boundary Conditions for Aerodynamic Computation

Tables Icon

Table 2. Main Physical Properties of the Sapphire Crystal Near 300 K

Tables Icon

Table 3. Refractive Index Variations of the Center on the Outside Surface of the Dome and the Center on the Inside Surface of the Dome at 15 sa

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

n=1+KGDρ,
KGD(λ)=2.23×104(1+7.52×103λ2).
qws=(hshw)2Pr2/3[ρsμs(duedx)s]0.5,
μs=2.49×107Ts0.63,
(duedx)s=1RN[2(PsP)ρs]0.5,
qw=0.5Pr2/3(hehw)(μeμr)ρeueCf*,
lnCf*+ln(2.62he0.5vrh20Sueρeμeh2he0.5ρrμrdS)=0.4(2Cf*)0.5,
qwqws=RN0.5ρeμeueCf*μrG(2ρsμsV)0.5,
G={(11γa)[1+2(γ1)M2](11γM2)}0.25,
nFlow=i=18niFlowdi2i=18di2,
OPL=iOPLiFlow+jOPLjDome,
OPLiFlow=(1+KGDρi)liFlow,
OPLjDome=T0T0+ΔT(njljDomeT+ljDomenjT)dT+ϵ0ϵ0+Δϵ(njljDomeϵ+ljDomenjϵ)dϵ,
Wk(x,y)=2πλ(OPLkOPL0),
OPL0=1NkOPLk,
W(x,y)=kWk(x,y)=k2πλ(OPLkOPL0).

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