Abstract

The exact time dependent solution for hole boring through fog is obtained for pulsed high energy lasers, which includes scattering, absorption, and the effect of realistic particle distributions. The results are applied to both haze burnout and fog hole boring. For the latter, at 10.6 μm, the calculated result is that 50% more laser pulse energy is required than that calculated from thermodynamic considerations alone. An absolute upper bound of 100% is also established. The results are compared to shorter wavelengths, e.g., 3.8 μm for which much larger fluences are required to evaporate fog or haze, and are also compared to other recent approximate results, which overestimate the required energy by a larger factor.

© 1978 Optical Society of America

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References

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  1. G. W. Sutton, AIAA J. 8, 1907 (1970).
    [CrossRef]
  2. S. L. Glicker, Appl. Opt. 10, 644 (1971).
    [CrossRef]
  3. R. C. Harney, Appl. Opt. 16, 2974 (1977).
    [CrossRef] [PubMed]
  4. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass., 1960).
  5. J. P. Reilly, P. I. Singh, S. L. Glicker, presented at AIAA 10th Fluid and Plasmadynamics Conference, Albuquerque (June 1977), AIAA paper 77–659.
  6. E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976), p. 43.
  7. Ref. 6, p. 168.
  8. A. D. Wood, M. Camac, E. T. Gerry, Appl. Opt. 10, 1877 (1971).
    [CrossRef] [PubMed]
  9. E. P. Shettle, R. W. Fenn, in Proceedings of the AGARD Conference on Optical Propagation in the Atmosphere, North Atlantic Treaty Organization, Denmark (October1975), paper 183.
  10. P. I. Singh, C. Knight, “Impulse Laser Induced Shattering of Water Drops,” AIAA Fluid and Plasma Dynamics Conference, Seattle (July1978), paper 78–1218.

1977

1971

1970

G. W. Sutton, AIAA J. 8, 1907 (1970).
[CrossRef]

Camac, M.

Fenn, R. W.

E. P. Shettle, R. W. Fenn, in Proceedings of the AGARD Conference on Optical Propagation in the Atmosphere, North Atlantic Treaty Organization, Denmark (October1975), paper 183.

Gerry, E. T.

Glicker, S. L.

S. L. Glicker, Appl. Opt. 10, 644 (1971).
[CrossRef]

J. P. Reilly, P. I. Singh, S. L. Glicker, presented at AIAA 10th Fluid and Plasmadynamics Conference, Albuquerque (June 1977), AIAA paper 77–659.

Harney, R. C.

Knight, C.

P. I. Singh, C. Knight, “Impulse Laser Induced Shattering of Water Drops,” AIAA Fluid and Plasma Dynamics Conference, Seattle (July1978), paper 78–1218.

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass., 1960).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass., 1960).

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976), p. 43.

Reilly, J. P.

J. P. Reilly, P. I. Singh, S. L. Glicker, presented at AIAA 10th Fluid and Plasmadynamics Conference, Albuquerque (June 1977), AIAA paper 77–659.

Shettle, E. P.

E. P. Shettle, R. W. Fenn, in Proceedings of the AGARD Conference on Optical Propagation in the Atmosphere, North Atlantic Treaty Organization, Denmark (October1975), paper 183.

Singh, P. I.

J. P. Reilly, P. I. Singh, S. L. Glicker, presented at AIAA 10th Fluid and Plasmadynamics Conference, Albuquerque (June 1977), AIAA paper 77–659.

P. I. Singh, C. Knight, “Impulse Laser Induced Shattering of Water Drops,” AIAA Fluid and Plasma Dynamics Conference, Seattle (July1978), paper 78–1218.

Sutton, G. W.

G. W. Sutton, AIAA J. 8, 1907 (1970).
[CrossRef]

Wood, A. D.

AIAA J.

G. W. Sutton, AIAA J. 8, 1907 (1970).
[CrossRef]

Appl. Opt.

Other

E. P. Shettle, R. W. Fenn, in Proceedings of the AGARD Conference on Optical Propagation in the Atmosphere, North Atlantic Treaty Organization, Denmark (October1975), paper 183.

P. I. Singh, C. Knight, “Impulse Laser Induced Shattering of Water Drops,” AIAA Fluid and Plasma Dynamics Conference, Seattle (July1978), paper 78–1218.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass., 1960).

J. P. Reilly, P. I. Singh, S. L. Glicker, presented at AIAA 10th Fluid and Plasmadynamics Conference, Albuquerque (June 1977), AIAA paper 77–659.

E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976), p. 43.

Ref. 6, p. 168.

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Figures (8)

Fig. 1
Fig. 1

Absorption and scattering coefficients for fog, haze, and clouds.

Fig. 2
Fig. 2

Time history of receding fog extinction profile for αso = αao.

Fig. 3
Fig. 3

Time history of fog extinction for αso = αao.

Fig. 4
Fig. 4

Length of fog cleared by a pulsed laser for 10.6-μm wavelength and equal initial scattering and absorption coefficients.

Fig. 5
Fig. 5

Effect of fluence on aerosol extinction.

Fig. 6
Fig. 6

Effect of vaporized liquid droplet on molecular absorption.

Fig. 7
Fig. 7

Absorption coefficient of vaporized droplets, km−1.

Fig. 8
Fig. 8

Measured water aerosol distribution functions.

Tables (1)

Tables Icon

Table I Liquid Water Content of Fogs6

Equations (44)

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ϕ x = ( α m + α a + α s ) ϕ .
h υ ρ [ ( V ) / ( t ) ] = α a ϕ ,
x > 0 t = 0 } V ( x , 0 ) = V 0 ,
x 0 { ϕ ( x , t ) = ϕ 0 V ( x , t ) = 0.
x ( 1 α a V t ) = α m + α a + α s α a V t .
t ( x d V α a ) = t α m + α a + α s α a d V .
/ x α a 1 d V = 0 ,
x V 0 V d V α a = V 0 V α m + α a + α s α a d V .
V ( 0 , t ) V ( x , t ) d V α a ( V ) V 0 V α m + α a + α s α a d V = x .
h υ ρ ϕ 0 V 0 V ( 0 , t ) d V α a = t .
ϕ ( x , t ) = h υ ρ α a ( x , t ) V t ( x , t ) .
( / t ) V ( x , t ) α a ( x , t ) V 0 V ( x , t ) α m + α a + α s α a d V = ( / t ) V ( 0 , t ) α a ( 0 , t ) V 0 V ( 0 , t ) α m + α a + α s α a d V .
ϕ 0 ϕ ( 0 , t ) = h υ ρ α a ( 0 , t ) V ( 0 , t ) t .
ϕ ( x , t ) ϕ 0 = V 0 V ( x , t ) α m + α a + α s α a d V V 0 V ( 0 , t ) α m + α a + α s α a d V ,
α a = K V ,
α s = β K V 2 ,
V ( 0 , t ) V 0 = exp ( ϕ 0 K t / h υ ρ ) ,
V 0 exp ( ϕ 0 K t / h υ ρ ) V ( x , t ) × d V K V [ α m K ln ( V V 0 ) + V V 0 + β 2 ( V 2 V 0 2 ) ] = x ,
ϕ ( x , t ) ϕ 0 α m V 0 K ln [ V ( x , t ) V 0 ] V ( x , t ) V 0 + 1 β V 0 2 [ V 2 ( x , t ) V 0 2 + 1 ] α m ϕ 0 t V 0 h υ ρ mol abs exp ( ϕ 0 K t / h υ ρ ) droplet vaporization + 1 β V 0 2 [ exp ( 2 ϕ 0 K t / h υ ρ ) droplet scattering + 1 ] .
f [ V ( x , t ) V 0 ] = f [ V ( 0 , t ) V 0 ] exp [ ( 1 + β V o ) ( 1 + β V 0 2 ) K V 0 x ] ,
f ( Z ) = Z 1 Z [ Z 2 1 Z + [ ( β V 0 ) / 2 ] ( 1 Z 2 ) ] β V 0 / 2 .
ϕ 0 t h υ ρ = ( 1 + β V 0 2 ) V 0 x + constant ,
υ f = ϕ 0 h υ ρ V 0 { 1 + [ ( β V 0 ) / 2 ] } .
Δ x = 1 / [ K ( V + β V 2 ) ] , Δ t = ( h υ ρ ) / ( K ϕ ) ,
υ f = K ϕ 0 ln ( r 0 / r f ) 3 h υ ρ α = K ϕ 0 h υ ρ ( α 1 2 α s ) . ( Ref . 3 ) ( present )
υ f = ϕ 0 exp ( α m x ) h υ ρ V 0 ( 2 α m K + 1 + β V 0 2 ) .
α = α a + α s = K V 0 [ exp ( K ϕ 0 t / h υ ρ ) + β V 0 exp ( 2 K ϕ 0 t / h υ ρ ) ] .
α ¯ = V 0 K y { 1 exp ( y ) + β V 0 2 [ 1 exp ( 2 y ) ] } .
α ¯ α 0 = y 1 { 1 [ 1 + exp ( y ) 2 ] 2 } .
J υ ϕ 0 t υ V 0 h υ ρ
α ¯ α 0 t υ / τ .
α ¯ / ( α 0 ) ( h υ ρ ) / ( K J 0 )
α = 10 3 V 0 α H 2 O ,
d n / d r = A r 4 , r s < r < r L .
r / r 0 = exp ( K ϕ d t / 3 h υ ρ )
[ ( n ) / ( r 0 ) ] = A r 0 4 .
N = r S r L n r 0 d r 0 = A 0 r S r L r 0 4 = A 0 3 ( r S 0 3 r L 0 3 ) ,
A 0 = 3 N r S 0 3 / ( 1 r S 0 3 / r L 0 3 ) .
n r = n r 0 · d r 0 d r = 3 r S 0 3 r 0 4 N 1 r S 0 3 / r L 0 3 exp ( K ϕ d t / 3 h υ ρ ) .
n r = 3 r S 3 N r 4 ( 1 r S 0 3 / r L 0 3 ) 1 ,
α a = K 4 π 3 r S r L r 3 n r d r K V ( x , t ) ,
α s r 6 n r d r .
α s N r s 6 ( r L r S ) 3 1 ( r S / r L ) 3 1 ( r S 0 / r L 0 ) 3 = N r S 6 ( r L r S ) 3 ,
V = 4 π N r S 3 ( 1 r S 3 r L 3 ) ln ( r L r S ) .

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