Abstract

A vortex gas lens concept is presented. Such a lens has a potential power density capability of 109–1010 w/cm2. An experimental prototype was constructed and the divergence half angle of the exiting beam was measured as a function of the lens operating parameters. Reasonably good agreement is found between the experimental results and theoretical calculations. The expanded beam was observed to be steady, and no strong, potentially beam-degrading jets were found to issue from the ends of the lens. Estimates of random beam deflection angles to be expected due to boundary layer noise are presented; these angles are very small.

© 1989 Optical Society of America

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References

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  1. Newport Catalog, No: 100, (Newport Corporation, P.O. Box 8020, Fountain Valley, CA 92728-8020) pp. M-78, M-81.
  2. Data Sheet No. 710, (Spawr Optical Research, Inc., P.O. Box 1899, Corona, CA 91718-1899, Apr.1984).
  3. J. F. Ready, Effects of High-Power Laser Radiation (Academic, New York, 1971), pp. 213–275.
  4. M. Autric, J. P. Caressa, D. Dufresne, P. Bournet “Propagation of High Energy Pulsed Laser Beam in the Atmosphere: Experimental Study of Air Breakdown over Long Distances for 10.6 μ Radiation” in Gas-Flow and Chemical Lasers, J. F. Wendt, Ed. (Hemisphere, Washington DC, 1979), pp. 481–490.
  5. V. E. Zuev, Laser Beams in the Atmosphere (translation by Consultants Bureau, New York, 1982), pp. 243–250.
    [CrossRef]
  6. J. P. Reilly, “High Flux Propagation Through the Atmosphere,” in Proceedings of SPIE—The International Society for Optical Engineering, J. C. Leader, ed., 410, 2–12 (1983).
  7. D. W. Bogdanoff, “Gasdynamic Light Guide: High Power Density Transmission Measurements,” App. Opt. 19, 3326–3334 (1980).
    [CrossRef]
  8. D. W. Berreman, “A Lens or Light Guide Using Connectively Distorted Thermal Gradients in Gases,” Bell Sys. Tech. J. 43, 1469–1475 (1964).
  9. D. W. Berreman, “A Gas Lens Using Unlike, Counter-Flowing Gases,” Bell Sys. Tech. J. 43, 1476–1479 (1964).
  10. D. Marcuse, S. E. Miller, “Analysis of a Tubular Gas Lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).
  11. W. H. Steier, “Measurements on a Thermal Gradient Gas Lens,” IEEE Trans. Microwave Theory Tech. MTT-13, 740–748 (1965).
    [CrossRef]
  12. A. J. Westphal, Master's Thesis, University of Washington, Department of Aeronautics & Astronautics (1986).
  13. M. Kurosaka, “Acoustic Streaming in Swirling Flow and the Ranque-Hilsch (Vortex-Tube) Effect,” J. Fluid Mech. 124, 139–172 (1982).
    [CrossRef]
  14. M. Kurosaka, J. R. Goodman, H. Kuroda, J. Q. Chu, “An Interplay Between Acoustic Waves and Steady Vortical Flow,” presented at the AIAA 8th Aeroacoustics Conference (Atlanta, April 1983), paper AIAA-83-0740.
  15. M. Kurosaka, J. Q. Chu, J. R. Goodman, presented at the AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference (St. Louis, Missouri, June 1982). Paper AIAA-82-0952.
  16. A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow (Ronald, New York, 1953), pp. 99–100.
  17. Ref. 16, chap. 4.
  18. H. Schlichting, Boundary-Layer Theory (McGraw-Hill, New York, 1979), pp. 638.
  19. H. W. Liepmann, A. Roshko, Elements of Gasdynamics (Wiley, New York, 1957), pp. 154–155.
  20. G. W. Sutton, “Effect of Turbulent Fluctuations in an Optically Active Medium,” AIAA J. 7, 1737–1743 (1969).
    [CrossRef]
  21. M. K. Bull, “Boundary Layer Pressure Fluctuations,” in Noise and Acoustic Fatigue in Aeronautics, E. J. Richards, D. J. Mead, Eds. (Wiley, New York, 1968), pp. 171–173.
  22. C. F. Coe, “Surface-Pressure Fluctuations Associated with Aerodynamic Noise,” in NASA SP-207, I. R. Schwartz, Ed. (U.S. Government Printing Office, Washington, 1969), pp. 411–413.

1982

M. Kurosaka, “Acoustic Streaming in Swirling Flow and the Ranque-Hilsch (Vortex-Tube) Effect,” J. Fluid Mech. 124, 139–172 (1982).
[CrossRef]

1980

D. W. Bogdanoff, “Gasdynamic Light Guide: High Power Density Transmission Measurements,” App. Opt. 19, 3326–3334 (1980).
[CrossRef]

1969

G. W. Sutton, “Effect of Turbulent Fluctuations in an Optically Active Medium,” AIAA J. 7, 1737–1743 (1969).
[CrossRef]

1965

W. H. Steier, “Measurements on a Thermal Gradient Gas Lens,” IEEE Trans. Microwave Theory Tech. MTT-13, 740–748 (1965).
[CrossRef]

1964

D. W. Berreman, “A Lens or Light Guide Using Connectively Distorted Thermal Gradients in Gases,” Bell Sys. Tech. J. 43, 1469–1475 (1964).

D. W. Berreman, “A Gas Lens Using Unlike, Counter-Flowing Gases,” Bell Sys. Tech. J. 43, 1476–1479 (1964).

D. Marcuse, S. E. Miller, “Analysis of a Tubular Gas Lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).

Autric, M.

M. Autric, J. P. Caressa, D. Dufresne, P. Bournet “Propagation of High Energy Pulsed Laser Beam in the Atmosphere: Experimental Study of Air Breakdown over Long Distances for 10.6 μ Radiation” in Gas-Flow and Chemical Lasers, J. F. Wendt, Ed. (Hemisphere, Washington DC, 1979), pp. 481–490.

Berreman, D. W.

D. W. Berreman, “A Lens or Light Guide Using Connectively Distorted Thermal Gradients in Gases,” Bell Sys. Tech. J. 43, 1469–1475 (1964).

D. W. Berreman, “A Gas Lens Using Unlike, Counter-Flowing Gases,” Bell Sys. Tech. J. 43, 1476–1479 (1964).

Bogdanoff, D. W.

D. W. Bogdanoff, “Gasdynamic Light Guide: High Power Density Transmission Measurements,” App. Opt. 19, 3326–3334 (1980).
[CrossRef]

Bournet, P.

M. Autric, J. P. Caressa, D. Dufresne, P. Bournet “Propagation of High Energy Pulsed Laser Beam in the Atmosphere: Experimental Study of Air Breakdown over Long Distances for 10.6 μ Radiation” in Gas-Flow and Chemical Lasers, J. F. Wendt, Ed. (Hemisphere, Washington DC, 1979), pp. 481–490.

Bull, M. K.

M. K. Bull, “Boundary Layer Pressure Fluctuations,” in Noise and Acoustic Fatigue in Aeronautics, E. J. Richards, D. J. Mead, Eds. (Wiley, New York, 1968), pp. 171–173.

Caressa, J. P.

M. Autric, J. P. Caressa, D. Dufresne, P. Bournet “Propagation of High Energy Pulsed Laser Beam in the Atmosphere: Experimental Study of Air Breakdown over Long Distances for 10.6 μ Radiation” in Gas-Flow and Chemical Lasers, J. F. Wendt, Ed. (Hemisphere, Washington DC, 1979), pp. 481–490.

Chu, J. Q.

M. Kurosaka, J. Q. Chu, J. R. Goodman, presented at the AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference (St. Louis, Missouri, June 1982). Paper AIAA-82-0952.

M. Kurosaka, J. R. Goodman, H. Kuroda, J. Q. Chu, “An Interplay Between Acoustic Waves and Steady Vortical Flow,” presented at the AIAA 8th Aeroacoustics Conference (Atlanta, April 1983), paper AIAA-83-0740.

Coe, C. F.

C. F. Coe, “Surface-Pressure Fluctuations Associated with Aerodynamic Noise,” in NASA SP-207, I. R. Schwartz, Ed. (U.S. Government Printing Office, Washington, 1969), pp. 411–413.

Dufresne, D.

M. Autric, J. P. Caressa, D. Dufresne, P. Bournet “Propagation of High Energy Pulsed Laser Beam in the Atmosphere: Experimental Study of Air Breakdown over Long Distances for 10.6 μ Radiation” in Gas-Flow and Chemical Lasers, J. F. Wendt, Ed. (Hemisphere, Washington DC, 1979), pp. 481–490.

Goodman, J. R.

M. Kurosaka, J. Q. Chu, J. R. Goodman, presented at the AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference (St. Louis, Missouri, June 1982). Paper AIAA-82-0952.

M. Kurosaka, J. R. Goodman, H. Kuroda, J. Q. Chu, “An Interplay Between Acoustic Waves and Steady Vortical Flow,” presented at the AIAA 8th Aeroacoustics Conference (Atlanta, April 1983), paper AIAA-83-0740.

Kuroda, H.

M. Kurosaka, J. R. Goodman, H. Kuroda, J. Q. Chu, “An Interplay Between Acoustic Waves and Steady Vortical Flow,” presented at the AIAA 8th Aeroacoustics Conference (Atlanta, April 1983), paper AIAA-83-0740.

Kurosaka, M.

M. Kurosaka, “Acoustic Streaming in Swirling Flow and the Ranque-Hilsch (Vortex-Tube) Effect,” J. Fluid Mech. 124, 139–172 (1982).
[CrossRef]

M. Kurosaka, J. Q. Chu, J. R. Goodman, presented at the AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference (St. Louis, Missouri, June 1982). Paper AIAA-82-0952.

M. Kurosaka, J. R. Goodman, H. Kuroda, J. Q. Chu, “An Interplay Between Acoustic Waves and Steady Vortical Flow,” presented at the AIAA 8th Aeroacoustics Conference (Atlanta, April 1983), paper AIAA-83-0740.

Liepmann, H. W.

H. W. Liepmann, A. Roshko, Elements of Gasdynamics (Wiley, New York, 1957), pp. 154–155.

Marcuse, D.

D. Marcuse, S. E. Miller, “Analysis of a Tubular Gas Lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).

Miller, S. E.

D. Marcuse, S. E. Miller, “Analysis of a Tubular Gas Lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).

Ready, J. F.

J. F. Ready, Effects of High-Power Laser Radiation (Academic, New York, 1971), pp. 213–275.

Reilly, J. P.

J. P. Reilly, “High Flux Propagation Through the Atmosphere,” in Proceedings of SPIE—The International Society for Optical Engineering, J. C. Leader, ed., 410, 2–12 (1983).

Roshko, A.

H. W. Liepmann, A. Roshko, Elements of Gasdynamics (Wiley, New York, 1957), pp. 154–155.

Schlichting, H.

H. Schlichting, Boundary-Layer Theory (McGraw-Hill, New York, 1979), pp. 638.

Shapiro, A. H.

A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow (Ronald, New York, 1953), pp. 99–100.

Steier, W. H.

W. H. Steier, “Measurements on a Thermal Gradient Gas Lens,” IEEE Trans. Microwave Theory Tech. MTT-13, 740–748 (1965).
[CrossRef]

Sutton, G. W.

G. W. Sutton, “Effect of Turbulent Fluctuations in an Optically Active Medium,” AIAA J. 7, 1737–1743 (1969).
[CrossRef]

Westphal, A. J.

A. J. Westphal, Master's Thesis, University of Washington, Department of Aeronautics & Astronautics (1986).

Zuev, V. E.

V. E. Zuev, Laser Beams in the Atmosphere (translation by Consultants Bureau, New York, 1982), pp. 243–250.
[CrossRef]

AIAA J.

G. W. Sutton, “Effect of Turbulent Fluctuations in an Optically Active Medium,” AIAA J. 7, 1737–1743 (1969).
[CrossRef]

App. Opt.

D. W. Bogdanoff, “Gasdynamic Light Guide: High Power Density Transmission Measurements,” App. Opt. 19, 3326–3334 (1980).
[CrossRef]

Bell Sys. Tech. J.

D. W. Berreman, “A Lens or Light Guide Using Connectively Distorted Thermal Gradients in Gases,” Bell Sys. Tech. J. 43, 1469–1475 (1964).

D. W. Berreman, “A Gas Lens Using Unlike, Counter-Flowing Gases,” Bell Sys. Tech. J. 43, 1476–1479 (1964).

D. Marcuse, S. E. Miller, “Analysis of a Tubular Gas Lens,” Bell Sys. Tech. J. 43, 1759–1782 (1964).

IEEE Trans. Microwave Theory Tech.

W. H. Steier, “Measurements on a Thermal Gradient Gas Lens,” IEEE Trans. Microwave Theory Tech. MTT-13, 740–748 (1965).
[CrossRef]

J. Fluid Mech.

M. Kurosaka, “Acoustic Streaming in Swirling Flow and the Ranque-Hilsch (Vortex-Tube) Effect,” J. Fluid Mech. 124, 139–172 (1982).
[CrossRef]

Other

M. Kurosaka, J. R. Goodman, H. Kuroda, J. Q. Chu, “An Interplay Between Acoustic Waves and Steady Vortical Flow,” presented at the AIAA 8th Aeroacoustics Conference (Atlanta, April 1983), paper AIAA-83-0740.

M. Kurosaka, J. Q. Chu, J. R. Goodman, presented at the AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference (St. Louis, Missouri, June 1982). Paper AIAA-82-0952.

A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow (Ronald, New York, 1953), pp. 99–100.

Ref. 16, chap. 4.

H. Schlichting, Boundary-Layer Theory (McGraw-Hill, New York, 1979), pp. 638.

H. W. Liepmann, A. Roshko, Elements of Gasdynamics (Wiley, New York, 1957), pp. 154–155.

M. K. Bull, “Boundary Layer Pressure Fluctuations,” in Noise and Acoustic Fatigue in Aeronautics, E. J. Richards, D. J. Mead, Eds. (Wiley, New York, 1968), pp. 171–173.

C. F. Coe, “Surface-Pressure Fluctuations Associated with Aerodynamic Noise,” in NASA SP-207, I. R. Schwartz, Ed. (U.S. Government Printing Office, Washington, 1969), pp. 411–413.

A. J. Westphal, Master's Thesis, University of Washington, Department of Aeronautics & Astronautics (1986).

Newport Catalog, No: 100, (Newport Corporation, P.O. Box 8020, Fountain Valley, CA 92728-8020) pp. M-78, M-81.

Data Sheet No. 710, (Spawr Optical Research, Inc., P.O. Box 1899, Corona, CA 91718-1899, Apr.1984).

J. F. Ready, Effects of High-Power Laser Radiation (Academic, New York, 1971), pp. 213–275.

M. Autric, J. P. Caressa, D. Dufresne, P. Bournet “Propagation of High Energy Pulsed Laser Beam in the Atmosphere: Experimental Study of Air Breakdown over Long Distances for 10.6 μ Radiation” in Gas-Flow and Chemical Lasers, J. F. Wendt, Ed. (Hemisphere, Washington DC, 1979), pp. 481–490.

V. E. Zuev, Laser Beams in the Atmosphere (translation by Consultants Bureau, New York, 1982), pp. 243–250.
[CrossRef]

J. P. Reilly, “High Flux Propagation Through the Atmosphere,” in Proceedings of SPIE—The International Society for Optical Engineering, J. C. Leader, ed., 410, 2–12 (1983).

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Figures (7)

Fig. 1
Fig. 1

Sketch of vortex gas lens. Ps are plenums and VT is the vortex tube.

Fig 2
Fig 2

Section through vortex gas lens showing key dimensions and gas state variables at key locations. See text for detailed discussion of variables.

Fig 3
Fig 3

Experimental setup. Ms are mirrors and CL is the center-line of the gas lens. Dimensions are in cm.

Fig 4
Fig 4

Beam divergence half angle, θ, vs plenum pressure, po, for a lens length of 14.61 cm. Experimental data and results from both the basic and the adjusted theoretical calculations are shown.

Fig 5
Fig 5

Beam divergence half angle, θ, vs plenum pressure, po, for all four lens lengths. The lens lengths, in cm, are indicated next to the curves. Experimental results are denoted by dashed lines, (adjusted) theoretical results are denoted by solid lines.

Fig 6
Fig 6

Profiles of density vs radius across the vortex tube. Solid line is for simple wheel vortex with no total temperature separation. Dashed line is a possible profile for a vortex with Ranque–Hilsch tube total temperature separation (see text). A denotes maximum of dashed curve.

Fig 7
Fig 7

Use of suction at both ends of a vortex gas lens to avoid disturbance of light rays due to axial turbulent jets issuing from the ends of the lens. Injection plenums are denoted by pi; suction plenums are denoted by ps.

Equations (27)

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( p t + ρ t u t 2 p w ) n C d π d t 2 4 d 2 1 2 ρ w u w 2 ƒ π d L d 2 ρ t u t n C d π d t 2 4 u w 2 d 2 = 0 ,
τ w = ƒ 1 2 ρ w u w 2 ,
p t + ρ t u t 2 p w 1 2 ρ w u w 2 ƒ R A ρ t u t u w 2 = 0.
u a e = C d n ρ t ρ w u t ( d t d ) 2 .
u a = u a e x L .
d s = u w u a d x .
Δ s = s 2 s 1 = u w L u a e ln ( x 2 x 1 ) ,
Re = ( ρ w u w Δ s ) / μ ,
ƒ = 0.0576 Re 0.2 ,
δ = 0.37 Re 0.2 Δ s ,
d p d r = ρ u 2 r ,
u = 2 u w r d .
p = ρ R T ,
d ρ d r = ρ ω 2 r R T ,
d θ d x = d d x ( d r d x ) = d n d r ,
n = 1 + β ρ ρ s ,
d 2 r d x 2 K 2 r = 0 ,
K 2 = β ρ o ω 2 ρ s R T .
θ = d r d x = K r o 2 ( e K x e K x ) .
θ L = K r o 2 ( e 2 K L e 2 K L ) .
θ L , c = θ L + θ o ,
θ π n
N 2 L λ .
θ N θ = π 2 n L λ .
θ = π n L Λ ,
θ = π 2 β γ L λ ρ ¯ ρ s p p ¯ ,
p p ¯ 1.6 x 10 5 M 2 .

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