Abstract

A procedure has been developed for deconvoluting line-of-sight average measurements of droplet-size distribution and optical extinction into the actual radial variations of droplet-size distribution and droplet number density in axisymmetric sprays. Preconditioning the line-of-sight average data via spline smoothing was shown to be necessary to prevent a complete loss of accuracy in the central region of the spray. After preconditioning, uncertainties in the average data propagated about 1:1 into the deconvoluted results. Cumulative truncation errors for a worst-case analysis approached 15% in the central region of the spray. A sample analysis for a typical hollow-cone spray is presented.

© 1981 Optical Society of America

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References

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  1. J. Swithenbank et al., “A Laser Diagnostic Technique for the Measurement of Droplet and Particle Size Distribution,” in Experimental Diagnostics in Gas Phase Combustion Systems, Progress in Astronautics and Aeronautics (AIAA, New York, 1976), Vol. 53, pp. 421–447.
  2. R. A. Dobbins, G. S. Jizmagian, J. Opt. Soc. Am. 56, 1345 (1966).
    [CrossRef]
  3. “Data Criteria and Processing for Liquid Drop Size Analysis,” proposed ASTM Standard (Jan.1980).
  4. R. S. Anderssen, F. R. deHoog, “Application and Numerical Solution of Abel-Type Integral Equations,” Division of Mathematics and Statistics, Commonwealth Scientific and Industrial Research Organization, Australia, unpublished manuscript.
  5. C. H. Reinsch, Numer. Math. 10, 177 (1967).
    [CrossRef]

1980 (1)

“Data Criteria and Processing for Liquid Drop Size Analysis,” proposed ASTM Standard (Jan.1980).

1967 (1)

C. H. Reinsch, Numer. Math. 10, 177 (1967).
[CrossRef]

1966 (1)

Anderssen, R. S.

R. S. Anderssen, F. R. deHoog, “Application and Numerical Solution of Abel-Type Integral Equations,” Division of Mathematics and Statistics, Commonwealth Scientific and Industrial Research Organization, Australia, unpublished manuscript.

deHoog, F. R.

R. S. Anderssen, F. R. deHoog, “Application and Numerical Solution of Abel-Type Integral Equations,” Division of Mathematics and Statistics, Commonwealth Scientific and Industrial Research Organization, Australia, unpublished manuscript.

Dobbins, R. A.

Jizmagian, G. S.

Reinsch, C. H.

C. H. Reinsch, Numer. Math. 10, 177 (1967).
[CrossRef]

Swithenbank, J.

J. Swithenbank et al., “A Laser Diagnostic Technique for the Measurement of Droplet and Particle Size Distribution,” in Experimental Diagnostics in Gas Phase Combustion Systems, Progress in Astronautics and Aeronautics (AIAA, New York, 1976), Vol. 53, pp. 421–447.

J. Opt. Soc. Am. (1)

Numer. Math. (1)

C. H. Reinsch, Numer. Math. 10, 177 (1967).
[CrossRef]

proposed ASTM Standard (1)

“Data Criteria and Processing for Liquid Drop Size Analysis,” proposed ASTM Standard (Jan.1980).

Other (2)

R. S. Anderssen, F. R. deHoog, “Application and Numerical Solution of Abel-Type Integral Equations,” Division of Mathematics and Statistics, Commonwealth Scientific and Industrial Research Organization, Australia, unpublished manuscript.

J. Swithenbank et al., “A Laser Diagnostic Technique for the Measurement of Droplet and Particle Size Distribution,” in Experimental Diagnostics in Gas Phase Combustion Systems, Progress in Astronautics and Aeronautics (AIAA, New York, 1976), Vol. 53, pp. 421–447.

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Figures (12)

Fig. 1
Fig. 1

Measurement volume geometry.

Fig. 2
Fig. 2

Deconvolution ring and line-of-sight geometry.

Fig. 3
Fig. 3

Base case droplet-size distribution.

Fig. 4
Fig. 4

Line-of-sight average droplet-size distributions for sample analysis 1.

Fig. 5
Fig. 5

Line-of-sight average extinction for sample analysis 1.

Fig. 6
Fig. 6

Comparison of deconvoluted and actual droplet number densities for sample analysis 1.

Fig. 7
Fig. 7

Distribution and number density errors for sample analysis 1.

Fig. 8
Fig. 8

Deconvoluted droplet-size distributions for sample analysis 1.

Fig. 9
Fig. 9

Extinction error for sample analysis 1.

Fig. 10
Fig. 10

Droplet-size distribution for sample analysis 2.

Fig. 11
Fig. 11

Line-of-sight average extinction for sample analysis 2.

Fig. 12
Fig. 12

Deconvoluted number density for sample analysis 2.

Tables (3)

Tables Icon

Table I Experimental Geometry

Tables Icon

Table II Droplet-Size Distribution Category Bounds

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Table III Variation of Droplet-Size Distribution with Radius for the First Sample Analysis

Equations (13)

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E = 1 - exp ( - η L 0 π 4 Q D 2 d n d D d D )
E i = 1 - exp ( - 0 L i η 0 π 4 Q D 2 d n d D d D d L )             i = 1 , 2 , , N R .
n k = D l b , k D u b , k d n d D d D             k = 1 , 2 , , N c .
Ω k = π 4 D u b , k 3 - D l b , k 3 3 ( D u b , k - D l b , k ) 2 D l b , k D u b , k Q ( m , D ) d D             k = 1 , 2 , , N c .
E i = 1 - exp [ - j = 1 i ( L i j η j k = 1 N c n k , j Ω k ) ]             i = 1 , 2 , , N R .
E i = 1 - exp [ - ( j = 1 i L i j η j ) ( k = 1 N c n k , i Ω k ) ]             i = 1 , 2 , , N R ,
j = 1 i L i j η j             i = 1 , 2 , , N R .
n k , i j = 1 i L i j η j = j = 1 i L i j η j n k , j             i = 1 , 2 , , N R             k = 1 , 2 , , N c .
j = 1 i L i j η j             i = 1 , 2 , , N r
k = 1 N c n k , i = 1             i = 1 , 2 , , N R .
k = 1 N c η i n k , i = η i k = 1 N c n k , i = η i             i = 1 , 2 , , N R .
η i = k = 1 N c η i n k , i             i = 1 , 2 , , N R ,
n k , i = ( η i n k , i ) η i i = 1 , 2 , , N R , k = 1 , 2 , , N c , η i 0 ,

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