Abstract

The opacity of a black smoke (an aerosol of carbon spheres) is calculated from the Mie theory for several log-normal particle distributions. Calculations are presented at a wavelength of 0.55 μm for particle geometric mean diameters in the 10−3–1-μm range and geometric mean standard deviations in the 0 (monodisperse) to 0.4 range. For-a given mass concentration the extinction coefficient and, therefore, the opacity can vary by a factor of 2 or more as the size distribution is varied. For absorptive indexes (m2) near 0.7, typical of carbon, the smoke opacity is only weakly dependent on the real part of the particle refractive index.

© 1979 Optical Society of America

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Corrections

David M. Roessler and Fred R. Faxvog, "Opacity of black smoke: calculated variation with particle size and refractive index: erratum," Appl. Opt. 18, 2099_1-2099 (1979)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-18-13-2099_1

References

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  1. “Engine Smoke Exhaust Emission Regulations for New Diesel Heavy-Duty Engines,” Fed. Regist. 40, 27576 (1975).
  2. F. Pinolini, J. Spiers, “Diesel Smoke—A Comparison of Test Methods and Smoke-Meters on Engine Test Bed and Vehicle,” SAE Tech. Pap. 690491 (May1969) .
  3. A. W. Carey, “Steady-State Correlation of Diesel Smoke-Meters—an SAE Task Force Report,” SAE Tech. Pap. 690492 (May1969).
  4. F. J. Hills, T. O. Wagner, D. K. Lawrence, “CRC Correlation of Diesel Smoke-Meter Measurements,” SAE Tech. Pap. 690493 (May1969).
  5. “Diesel Engine Smoke Measurement (Steady State),” SAE J255, SAE Information Report, SAE Handbook (Society of Automotive Engineers, Warrendale, Pa., 1977).
  6. R. C. Bascom, W. S. Chiu, R. J. Padd, “Measurement and Evaluation of Diesel Smoke,” SAE Tech. Pap. 730212 (1973), see comment on p. 819.
  7. T. L. Rosebrock, GM Engineering Staff; private communication.
  8. R. J. Charlson, Environ. Sci. Technol. 3, 913 (1969).
    [CrossRef]
  9. D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
    [CrossRef] [PubMed]
  10. C. T. Vuk, M. A. Jones, J. H. Johnson, “The Measurement and Analysis of the Physical Character of Diesel Particulate Emissions,” SAE Tech. Pap. 760131 (February1976).
  11. J. E. McDonald, J. Appl. Meteorol. 1, 391 (1962).
    [CrossRef]
  12. G. Mie, Ann. Phys. 25, 337 (1908).
  13. F. R. Faxvog, D. M. Roessler, Appl. Opt. 17, 2612 (1978).
    [PubMed]
  14. P. J. Groblicki, GM Research Laboratories; private communication.

1978 (1)

1975 (1)

“Engine Smoke Exhaust Emission Regulations for New Diesel Heavy-Duty Engines,” Fed. Regist. 40, 27576 (1975).

1971 (1)

D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
[CrossRef] [PubMed]

1969 (1)

R. J. Charlson, Environ. Sci. Technol. 3, 913 (1969).
[CrossRef]

1962 (1)

J. E. McDonald, J. Appl. Meteorol. 1, 391 (1962).
[CrossRef]

1908 (1)

G. Mie, Ann. Phys. 25, 337 (1908).

Bascom, R. C.

R. C. Bascom, W. S. Chiu, R. J. Padd, “Measurement and Evaluation of Diesel Smoke,” SAE Tech. Pap. 730212 (1973), see comment on p. 819.

Carey, A. W.

A. W. Carey, “Steady-State Correlation of Diesel Smoke-Meters—an SAE Task Force Report,” SAE Tech. Pap. 690492 (May1969).

Charlson, R. J.

R. J. Charlson, Environ. Sci. Technol. 3, 913 (1969).
[CrossRef]

Chiu, W. S.

R. C. Bascom, W. S. Chiu, R. J. Padd, “Measurement and Evaluation of Diesel Smoke,” SAE Tech. Pap. 730212 (1973), see comment on p. 819.

Ensor, D. S.

D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
[CrossRef] [PubMed]

Faxvog, F. R.

Groblicki, P. J.

P. J. Groblicki, GM Research Laboratories; private communication.

Hills, F. J.

F. J. Hills, T. O. Wagner, D. K. Lawrence, “CRC Correlation of Diesel Smoke-Meter Measurements,” SAE Tech. Pap. 690493 (May1969).

Johnson, J. H.

C. T. Vuk, M. A. Jones, J. H. Johnson, “The Measurement and Analysis of the Physical Character of Diesel Particulate Emissions,” SAE Tech. Pap. 760131 (February1976).

Jones, M. A.

C. T. Vuk, M. A. Jones, J. H. Johnson, “The Measurement and Analysis of the Physical Character of Diesel Particulate Emissions,” SAE Tech. Pap. 760131 (February1976).

Lawrence, D. K.

F. J. Hills, T. O. Wagner, D. K. Lawrence, “CRC Correlation of Diesel Smoke-Meter Measurements,” SAE Tech. Pap. 690493 (May1969).

McDonald, J. E.

J. E. McDonald, J. Appl. Meteorol. 1, 391 (1962).
[CrossRef]

Mie, G.

G. Mie, Ann. Phys. 25, 337 (1908).

Padd, R. J.

R. C. Bascom, W. S. Chiu, R. J. Padd, “Measurement and Evaluation of Diesel Smoke,” SAE Tech. Pap. 730212 (1973), see comment on p. 819.

Pilat, M. J.

D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
[CrossRef] [PubMed]

Pinolini, F.

F. Pinolini, J. Spiers, “Diesel Smoke—A Comparison of Test Methods and Smoke-Meters on Engine Test Bed and Vehicle,” SAE Tech. Pap. 690491 (May1969) .

Roessler, D. M.

Rosebrock, T. L.

T. L. Rosebrock, GM Engineering Staff; private communication.

Spiers, J.

F. Pinolini, J. Spiers, “Diesel Smoke—A Comparison of Test Methods and Smoke-Meters on Engine Test Bed and Vehicle,” SAE Tech. Pap. 690491 (May1969) .

Vuk, C. T.

C. T. Vuk, M. A. Jones, J. H. Johnson, “The Measurement and Analysis of the Physical Character of Diesel Particulate Emissions,” SAE Tech. Pap. 760131 (February1976).

Wagner, T. O.

F. J. Hills, T. O. Wagner, D. K. Lawrence, “CRC Correlation of Diesel Smoke-Meter Measurements,” SAE Tech. Pap. 690493 (May1969).

Ann. Phys. (1)

G. Mie, Ann. Phys. 25, 337 (1908).

Appl. Opt. (1)

Environ. Sci. Technol. (1)

R. J. Charlson, Environ. Sci. Technol. 3, 913 (1969).
[CrossRef]

Fed. Regist. (1)

“Engine Smoke Exhaust Emission Regulations for New Diesel Heavy-Duty Engines,” Fed. Regist. 40, 27576 (1975).

J. Air Pollut. Control Assoc. (1)

D. S. Ensor, M. J. Pilat, J. Air Pollut. Control Assoc. 21, 496 (1971).
[CrossRef] [PubMed]

J. Appl. Meteorol. (1)

J. E. McDonald, J. Appl. Meteorol. 1, 391 (1962).
[CrossRef]

Other (8)

C. T. Vuk, M. A. Jones, J. H. Johnson, “The Measurement and Analysis of the Physical Character of Diesel Particulate Emissions,” SAE Tech. Pap. 760131 (February1976).

P. J. Groblicki, GM Research Laboratories; private communication.

F. Pinolini, J. Spiers, “Diesel Smoke—A Comparison of Test Methods and Smoke-Meters on Engine Test Bed and Vehicle,” SAE Tech. Pap. 690491 (May1969) .

A. W. Carey, “Steady-State Correlation of Diesel Smoke-Meters—an SAE Task Force Report,” SAE Tech. Pap. 690492 (May1969).

F. J. Hills, T. O. Wagner, D. K. Lawrence, “CRC Correlation of Diesel Smoke-Meter Measurements,” SAE Tech. Pap. 690493 (May1969).

“Diesel Engine Smoke Measurement (Steady State),” SAE J255, SAE Information Report, SAE Handbook (Society of Automotive Engineers, Warrendale, Pa., 1977).

R. C. Bascom, W. S. Chiu, R. J. Padd, “Measurement and Evaluation of Diesel Smoke,” SAE Tech. Pap. 730212 (1973), see comment on p. 819.

T. L. Rosebrock, GM Engineering Staff; private communication.

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Figures (5)

Fig. 1
Fig. 1

Opacity of typical heavy-duty diesel engine black smoke as a function of mass concentration. The curve is a best-fit to SAE Handbook data (Ref. 3) for 10.2-cm and 15.2-cm wide plumes but may be unreliable for mass concentrations below 50 mg/m3.

Fig. 2
Fig. 2

Theoretical extinction coefficient per unit mass concentration A as a function of the geometric mean diameter D1 for an aerosol of carbon spheres with single-sized (σ = 0) and polydisperse (σ = 0.2,0.3, and 0.4) distributions. The complex refractive index is taken as 1.95–0.66i at the illumination wavelength of 0.55 μm (green light). The error ordinate is explained in the text.

Fig. 3
Fig. 3

Opacity of a 10.2-cm column of carbon spheres as a function of their mass loading for a polydisperse system (σ = 0.2) with different geometric mean diameters D1. The SAE curve for black smoke is also shown.

Fig. 4
Fig. 4

Specific extinction of small spheres of given size distribution (D1 = 0.04 μm and σ = 0.25) as a function of refractive index m1.

Fig. 5
Fig. 5

Specific extinction of small spheres of given size distribution (D1 = 0.04 μm and σ = 0.25) as a function of absorptive index m2.

Equations (3)

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opacity = 1 - exp ( - b e L ) ,
b e = A M c ,
A = 1 M c 0 C ( D ) N ( D ) d D ,

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