Abstract

Fly ash, a fine gray powder, is filtered out of the flue gas in coal-fired power stations. It consists of silicon oxide, metal oxides, and unburned carbon. An optical sensor system for measurement of the carbon content of fly ash is described. Based on a mathematical model, an algorithm is deduced that allows the carbon content to be calculated from two measurements of the diffuse reflectivity of a fly ash sample before and after a surface-grinding process. In this model the fly ash sample is assumed to be composed of three types of cube: light-scattering cubes, soft absorbing cubes (carbon), and hard absorbing cubes (iron oxide).

© 1999 Optical Society of America

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References

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  1. L. Mortensen, G. Sotter, “Instrumentation helps optimize pulverized coal combustion,” Power Eng.33–36, (March1989).
  2. E. Peltonen, A. Somerikko, T. Viitanen, “Verfahren und Einrichtung zum Messen des Kohlegehalts in Flugasche,” German patent (Deutsche Offenlegungsschrift)DE3303177A1 (31January1983).
  3. D. A. Abernethy, N. G. Cutmore, S. I. Doumit, T. G. Evans, M. J. Millen, B. D. Sowerby, “Development of techniques for the on-line determination of unburnt carbon in fly-ash,” in Proceedings of the IAEA International Symposium on Nuclear Techniques in Exploration and Exploitation of Energy and Mineral Resources (Commonwealth Scientific and Industrial Research Organisation, Menai, Australia, 1990), pp. 71–84.
  4. N. G. Cutmore, “Determination of carbon in fly-ash from microwave attenuation and phase-shift,” U.S. patent5,177,444 (5January1993).
  5. R. C. Brown, “Method and apparatus of measuring unburned carbon in fly-ash,” U.S. patent5,069,551 (3December1991).
  6. R. D. Kempster, P. A. E. Crosse, “Apparatus for monitoring the carbon content of boiler flue ash,” European patent application86,307,677.4 (3October1986), publication number EP0217677A2 (8April1987).
  7. D. N. Trerice, C. R. Buffler, “Method and associated apparatus for determining carbon content in fly-ash,” U.S. patent5,109,201 (28April1992).
  8. A. Schneider, R. Chabicovsky, A. Aumüller, “Sensor for monitoring carbon in fly-ash,” in Proceedings of the Joint Meeting of the Portuguese, British, Spanish and Swedish Sections of the Combustion Institute (Combustion Institute, Lisbon, 1996), pp. 3.6.1.–3.6.4.
  9. A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche,” Austrian patentAT 402571 B, Int. Cl. G01N, 21/47 (6June1997).
  10. A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche, Strahlungsablenkelement hiefür sowie ein Verfahren zu dessen Herstellung,” European patent application95,890,211.6, publication number EP 0714023 A2, Int. Cl. G01N21/47, G01N1/28 (29May1996).
  11. A. Schneider, R. Chabicovsky, A. Aumüller, “Optical sensor system for the on-line measurement of carbon in fly-ash,” Sens. Actuators A 67, 24–31 (1998).
    [CrossRef]
  12. A. Schneider, “Optisches Sensorsystem zur on-line-Bestimmung des Kohlenstoffgehalts von Flugasche in einem Kohlekraftwerk,” Ph.D. dissertation (Vienna University of Technology, Vienna, 1997).
  13. W. Theiss, “Optische Eigenschaften inhomogener Materialien,” Ph.D. dissertation (Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1989).
  14. P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).
  15. G. Kortüm, Reflexionsspektroskopie (Springer-Verlag, Berlin, 1969), pp. 109–114.
  16. E. L. Simmons, “Diffuse reflectance spectroscopy: a comparison of the theories,” Appl. Opt. 14, 1380–1386 (1975).
    [CrossRef] [PubMed]
  17. N. T. Melamed, “Optical properties of powders. Part I. Optical absorption coefficients and the absolute value of the diffuse reflectance. Part II. Properties of luminescent powders,” J. Appl. Phys. 34, 560–570 (1963).
    [CrossRef]
  18. H. A. Van Der Sloot, E. G. Weijers, “Physikalische und chemische Kenndaten von 50 Kohlenstaubaschen mit Blick auf die Verwendung als Betonzusatzstoff,” VGB Kraftwerkstechnik 67, 527–534 (1987).
  19. B. Prause, K. Kautz, “Die granulometrische Aufnahme von Elektrofilterstäuben aus Kohlekraftwerken mit dem Retsch-Präzisions-Kaskadenimpaktor PI1,” VGB Kraftwerkstechnik 68, 958–962 (1988).
  20. R. J. Lauf, “Application of materials characterization techniques to coal and coal wastes,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1981).
  21. H.-J. Hagemann, W. Gudat, C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu,Ag, Au, Bi, C and Al2O3,” J. Opt. Soc. Am. 65, 742–744 (1975).
    [CrossRef]
  22. D. R. Lide, ed., Handbook of Chemistry and Physics, 75th ed. (CRC Press, Boca Raton, Fla., 1994–1995).

1998

A. Schneider, R. Chabicovsky, A. Aumüller, “Optical sensor system for the on-line measurement of carbon in fly-ash,” Sens. Actuators A 67, 24–31 (1998).
[CrossRef]

1989

L. Mortensen, G. Sotter, “Instrumentation helps optimize pulverized coal combustion,” Power Eng.33–36, (March1989).

1988

B. Prause, K. Kautz, “Die granulometrische Aufnahme von Elektrofilterstäuben aus Kohlekraftwerken mit dem Retsch-Präzisions-Kaskadenimpaktor PI1,” VGB Kraftwerkstechnik 68, 958–962 (1988).

1987

H. A. Van Der Sloot, E. G. Weijers, “Physikalische und chemische Kenndaten von 50 Kohlenstaubaschen mit Blick auf die Verwendung als Betonzusatzstoff,” VGB Kraftwerkstechnik 67, 527–534 (1987).

1975

1963

N. T. Melamed, “Optical properties of powders. Part I. Optical absorption coefficients and the absolute value of the diffuse reflectance. Part II. Properties of luminescent powders,” J. Appl. Phys. 34, 560–570 (1963).
[CrossRef]

1931

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Abernethy, D. A.

D. A. Abernethy, N. G. Cutmore, S. I. Doumit, T. G. Evans, M. J. Millen, B. D. Sowerby, “Development of techniques for the on-line determination of unburnt carbon in fly-ash,” in Proceedings of the IAEA International Symposium on Nuclear Techniques in Exploration and Exploitation of Energy and Mineral Resources (Commonwealth Scientific and Industrial Research Organisation, Menai, Australia, 1990), pp. 71–84.

Aumüller, A.

A. Schneider, R. Chabicovsky, A. Aumüller, “Optical sensor system for the on-line measurement of carbon in fly-ash,” Sens. Actuators A 67, 24–31 (1998).
[CrossRef]

A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche,” Austrian patentAT 402571 B, Int. Cl. G01N, 21/47 (6June1997).

A. Schneider, R. Chabicovsky, A. Aumüller, “Sensor for monitoring carbon in fly-ash,” in Proceedings of the Joint Meeting of the Portuguese, British, Spanish and Swedish Sections of the Combustion Institute (Combustion Institute, Lisbon, 1996), pp. 3.6.1.–3.6.4.

A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche, Strahlungsablenkelement hiefür sowie ein Verfahren zu dessen Herstellung,” European patent application95,890,211.6, publication number EP 0714023 A2, Int. Cl. G01N21/47, G01N1/28 (29May1996).

Brown, R. C.

R. C. Brown, “Method and apparatus of measuring unburned carbon in fly-ash,” U.S. patent5,069,551 (3December1991).

Buffler, C. R.

D. N. Trerice, C. R. Buffler, “Method and associated apparatus for determining carbon content in fly-ash,” U.S. patent5,109,201 (28April1992).

Chabicovsky, R.

A. Schneider, R. Chabicovsky, A. Aumüller, “Optical sensor system for the on-line measurement of carbon in fly-ash,” Sens. Actuators A 67, 24–31 (1998).
[CrossRef]

A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche,” Austrian patentAT 402571 B, Int. Cl. G01N, 21/47 (6June1997).

A. Schneider, R. Chabicovsky, A. Aumüller, “Sensor for monitoring carbon in fly-ash,” in Proceedings of the Joint Meeting of the Portuguese, British, Spanish and Swedish Sections of the Combustion Institute (Combustion Institute, Lisbon, 1996), pp. 3.6.1.–3.6.4.

A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche, Strahlungsablenkelement hiefür sowie ein Verfahren zu dessen Herstellung,” European patent application95,890,211.6, publication number EP 0714023 A2, Int. Cl. G01N21/47, G01N1/28 (29May1996).

Crosse, P. A. E.

R. D. Kempster, P. A. E. Crosse, “Apparatus for monitoring the carbon content of boiler flue ash,” European patent application86,307,677.4 (3October1986), publication number EP0217677A2 (8April1987).

Cutmore, N. G.

D. A. Abernethy, N. G. Cutmore, S. I. Doumit, T. G. Evans, M. J. Millen, B. D. Sowerby, “Development of techniques for the on-line determination of unburnt carbon in fly-ash,” in Proceedings of the IAEA International Symposium on Nuclear Techniques in Exploration and Exploitation of Energy and Mineral Resources (Commonwealth Scientific and Industrial Research Organisation, Menai, Australia, 1990), pp. 71–84.

N. G. Cutmore, “Determination of carbon in fly-ash from microwave attenuation and phase-shift,” U.S. patent5,177,444 (5January1993).

Doumit, S. I.

D. A. Abernethy, N. G. Cutmore, S. I. Doumit, T. G. Evans, M. J. Millen, B. D. Sowerby, “Development of techniques for the on-line determination of unburnt carbon in fly-ash,” in Proceedings of the IAEA International Symposium on Nuclear Techniques in Exploration and Exploitation of Energy and Mineral Resources (Commonwealth Scientific and Industrial Research Organisation, Menai, Australia, 1990), pp. 71–84.

Evans, T. G.

D. A. Abernethy, N. G. Cutmore, S. I. Doumit, T. G. Evans, M. J. Millen, B. D. Sowerby, “Development of techniques for the on-line determination of unburnt carbon in fly-ash,” in Proceedings of the IAEA International Symposium on Nuclear Techniques in Exploration and Exploitation of Energy and Mineral Resources (Commonwealth Scientific and Industrial Research Organisation, Menai, Australia, 1990), pp. 71–84.

Gudat, W.

Hagemann, H.-J.

Kautz, K.

B. Prause, K. Kautz, “Die granulometrische Aufnahme von Elektrofilterstäuben aus Kohlekraftwerken mit dem Retsch-Präzisions-Kaskadenimpaktor PI1,” VGB Kraftwerkstechnik 68, 958–962 (1988).

Kempster, R. D.

R. D. Kempster, P. A. E. Crosse, “Apparatus for monitoring the carbon content of boiler flue ash,” European patent application86,307,677.4 (3October1986), publication number EP0217677A2 (8April1987).

Kortüm, G.

G. Kortüm, Reflexionsspektroskopie (Springer-Verlag, Berlin, 1969), pp. 109–114.

Kubelka, P.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Kunz, C.

Lauf, R. J.

R. J. Lauf, “Application of materials characterization techniques to coal and coal wastes,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1981).

Melamed, N. T.

N. T. Melamed, “Optical properties of powders. Part I. Optical absorption coefficients and the absolute value of the diffuse reflectance. Part II. Properties of luminescent powders,” J. Appl. Phys. 34, 560–570 (1963).
[CrossRef]

Millen, M. J.

D. A. Abernethy, N. G. Cutmore, S. I. Doumit, T. G. Evans, M. J. Millen, B. D. Sowerby, “Development of techniques for the on-line determination of unburnt carbon in fly-ash,” in Proceedings of the IAEA International Symposium on Nuclear Techniques in Exploration and Exploitation of Energy and Mineral Resources (Commonwealth Scientific and Industrial Research Organisation, Menai, Australia, 1990), pp. 71–84.

Mortensen, L.

L. Mortensen, G. Sotter, “Instrumentation helps optimize pulverized coal combustion,” Power Eng.33–36, (March1989).

Munk, F.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Peltonen, E.

E. Peltonen, A. Somerikko, T. Viitanen, “Verfahren und Einrichtung zum Messen des Kohlegehalts in Flugasche,” German patent (Deutsche Offenlegungsschrift)DE3303177A1 (31January1983).

Prause, B.

B. Prause, K. Kautz, “Die granulometrische Aufnahme von Elektrofilterstäuben aus Kohlekraftwerken mit dem Retsch-Präzisions-Kaskadenimpaktor PI1,” VGB Kraftwerkstechnik 68, 958–962 (1988).

Schneider, A.

A. Schneider, R. Chabicovsky, A. Aumüller, “Optical sensor system for the on-line measurement of carbon in fly-ash,” Sens. Actuators A 67, 24–31 (1998).
[CrossRef]

A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche,” Austrian patentAT 402571 B, Int. Cl. G01N, 21/47 (6June1997).

A. Schneider, R. Chabicovsky, A. Aumüller, “Sensor for monitoring carbon in fly-ash,” in Proceedings of the Joint Meeting of the Portuguese, British, Spanish and Swedish Sections of the Combustion Institute (Combustion Institute, Lisbon, 1996), pp. 3.6.1.–3.6.4.

A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche, Strahlungsablenkelement hiefür sowie ein Verfahren zu dessen Herstellung,” European patent application95,890,211.6, publication number EP 0714023 A2, Int. Cl. G01N21/47, G01N1/28 (29May1996).

A. Schneider, “Optisches Sensorsystem zur on-line-Bestimmung des Kohlenstoffgehalts von Flugasche in einem Kohlekraftwerk,” Ph.D. dissertation (Vienna University of Technology, Vienna, 1997).

Simmons, E. L.

Somerikko, A.

E. Peltonen, A. Somerikko, T. Viitanen, “Verfahren und Einrichtung zum Messen des Kohlegehalts in Flugasche,” German patent (Deutsche Offenlegungsschrift)DE3303177A1 (31January1983).

Sotter, G.

L. Mortensen, G. Sotter, “Instrumentation helps optimize pulverized coal combustion,” Power Eng.33–36, (March1989).

Sowerby, B. D.

D. A. Abernethy, N. G. Cutmore, S. I. Doumit, T. G. Evans, M. J. Millen, B. D. Sowerby, “Development of techniques for the on-line determination of unburnt carbon in fly-ash,” in Proceedings of the IAEA International Symposium on Nuclear Techniques in Exploration and Exploitation of Energy and Mineral Resources (Commonwealth Scientific and Industrial Research Organisation, Menai, Australia, 1990), pp. 71–84.

Theiss, W.

W. Theiss, “Optische Eigenschaften inhomogener Materialien,” Ph.D. dissertation (Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1989).

Trerice, D. N.

D. N. Trerice, C. R. Buffler, “Method and associated apparatus for determining carbon content in fly-ash,” U.S. patent5,109,201 (28April1992).

Van Der Sloot, H. A.

H. A. Van Der Sloot, E. G. Weijers, “Physikalische und chemische Kenndaten von 50 Kohlenstaubaschen mit Blick auf die Verwendung als Betonzusatzstoff,” VGB Kraftwerkstechnik 67, 527–534 (1987).

Viitanen, T.

E. Peltonen, A. Somerikko, T. Viitanen, “Verfahren und Einrichtung zum Messen des Kohlegehalts in Flugasche,” German patent (Deutsche Offenlegungsschrift)DE3303177A1 (31January1983).

Weijers, E. G.

H. A. Van Der Sloot, E. G. Weijers, “Physikalische und chemische Kenndaten von 50 Kohlenstaubaschen mit Blick auf die Verwendung als Betonzusatzstoff,” VGB Kraftwerkstechnik 67, 527–534 (1987).

Appl. Opt.

J. Appl. Phys.

N. T. Melamed, “Optical properties of powders. Part I. Optical absorption coefficients and the absolute value of the diffuse reflectance. Part II. Properties of luminescent powders,” J. Appl. Phys. 34, 560–570 (1963).
[CrossRef]

J. Opt. Soc. Am.

Power Eng.

L. Mortensen, G. Sotter, “Instrumentation helps optimize pulverized coal combustion,” Power Eng.33–36, (March1989).

Sens. Actuators A

A. Schneider, R. Chabicovsky, A. Aumüller, “Optical sensor system for the on-line measurement of carbon in fly-ash,” Sens. Actuators A 67, 24–31 (1998).
[CrossRef]

VGB Kraftwerkstechnik

H. A. Van Der Sloot, E. G. Weijers, “Physikalische und chemische Kenndaten von 50 Kohlenstaubaschen mit Blick auf die Verwendung als Betonzusatzstoff,” VGB Kraftwerkstechnik 67, 527–534 (1987).

B. Prause, K. Kautz, “Die granulometrische Aufnahme von Elektrofilterstäuben aus Kohlekraftwerken mit dem Retsch-Präzisions-Kaskadenimpaktor PI1,” VGB Kraftwerkstechnik 68, 958–962 (1988).

Z. Tech. Phys.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Other

G. Kortüm, Reflexionsspektroskopie (Springer-Verlag, Berlin, 1969), pp. 109–114.

A. Schneider, “Optisches Sensorsystem zur on-line-Bestimmung des Kohlenstoffgehalts von Flugasche in einem Kohlekraftwerk,” Ph.D. dissertation (Vienna University of Technology, Vienna, 1997).

W. Theiss, “Optische Eigenschaften inhomogener Materialien,” Ph.D. dissertation (Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1989).

R. J. Lauf, “Application of materials characterization techniques to coal and coal wastes,” (Oak Ridge National Laboratory, Oak Ridge, Tenn., 1981).

E. Peltonen, A. Somerikko, T. Viitanen, “Verfahren und Einrichtung zum Messen des Kohlegehalts in Flugasche,” German patent (Deutsche Offenlegungsschrift)DE3303177A1 (31January1983).

D. A. Abernethy, N. G. Cutmore, S. I. Doumit, T. G. Evans, M. J. Millen, B. D. Sowerby, “Development of techniques for the on-line determination of unburnt carbon in fly-ash,” in Proceedings of the IAEA International Symposium on Nuclear Techniques in Exploration and Exploitation of Energy and Mineral Resources (Commonwealth Scientific and Industrial Research Organisation, Menai, Australia, 1990), pp. 71–84.

N. G. Cutmore, “Determination of carbon in fly-ash from microwave attenuation and phase-shift,” U.S. patent5,177,444 (5January1993).

R. C. Brown, “Method and apparatus of measuring unburned carbon in fly-ash,” U.S. patent5,069,551 (3December1991).

R. D. Kempster, P. A. E. Crosse, “Apparatus for monitoring the carbon content of boiler flue ash,” European patent application86,307,677.4 (3October1986), publication number EP0217677A2 (8April1987).

D. N. Trerice, C. R. Buffler, “Method and associated apparatus for determining carbon content in fly-ash,” U.S. patent5,109,201 (28April1992).

A. Schneider, R. Chabicovsky, A. Aumüller, “Sensor for monitoring carbon in fly-ash,” in Proceedings of the Joint Meeting of the Portuguese, British, Spanish and Swedish Sections of the Combustion Institute (Combustion Institute, Lisbon, 1996), pp. 3.6.1.–3.6.4.

A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche,” Austrian patentAT 402571 B, Int. Cl. G01N, 21/47 (6June1997).

A. Aumüller, R. Chabicovsky, A. Schneider, “Verfahren und Vorrichtung zur Bestimmung des Kohlegehalts in Asche, Strahlungsablenkelement hiefür sowie ein Verfahren zu dessen Herstellung,” European patent application95,890,211.6, publication number EP 0714023 A2, Int. Cl. G01N21/47, G01N1/28 (29May1996).

D. R. Lide, ed., Handbook of Chemistry and Physics, 75th ed. (CRC Press, Boca Raton, Fla., 1994–1995).

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Figures (18)

Fig. 1
Fig. 1

Schematic illustration of the carbon-in-fly-ash sensor system: LED, high-efficiency light-emitting diode; PD, measuring photodiode; RD, reference photodiode; POL, polarization foil; G, glass disk; ST, sensor tube (measuring cylinder); WG’s, waveguides; FA, fly ash sample; SH, sample holder. Diameter of the cavity, 40 mm; depth of the cavity, 12 mm.

Fig. 2
Fig. 2

Diffuse reflectivity (represented by the photodiode current I) of three different fly ash samples as a function of the number of twists of the measuring cylinder. Reflection measurements are carried out before and after a defined number of twists (points 1 and 2). The difference D depends on the carbon content.

Fig. 3
Fig. 3

Principle of the cube model: The fly ash sample is assumed to be composed of bright light-scattering cubes and of dark totally absorbing cubes, representing carbon and iron oxide. FA, fly ash; LED, light source (high-efficiency LED); PD, photodiode; POL, polarization foil; G, glass window.

Fig. 4
Fig. 4

Scattering element of the fly ash sample. Its edge length amounts to many wavelengths. It contains a great number of optical inhomogenities with dimensions in the range of the wavelength. It is assumed that interference patterns of the single-scattering processes are uncorrelated as seen from outside. So the cube is assumed to scatter the light in all directions, and each surface of the cube scatters one sixth of the incoming light power isotropically into the half-space. The incoming light entering the cube in all directions through one side is symbolized by an ingoing arrow, and the scattered part of the light leaving the cube through one side in all directions is indicated by outgoing arrows.

Fig. 5
Fig. 5

Dissipationless single layer. (a) Oblique view, (b) cross-sectional view. For reasons of symmetry the reflectivity of the whole layer is equal to the reflectivity of a single cube within the layer.

Fig. 6
Fig. 6

Contribution of zero order: one sixth of the light coming into the cube is directly backscattered.

Fig. 7
Fig. 7

Contributions of first order originate from irradiation of the four closest-neighbor cubes. (a) Cross-sectional view, (b) top view.

Fig. 8
Fig. 8

Contributions of second order are caused by the irradiation of those cubes that lie within a distance of two steps. The cube under consideration belongs to them as well. (a) Cross-sectional view, (b) top view.

Fig. 9
Fig. 9

Reflectivity of the dissipationless single-layer. (a) Reflectivity of one cube within the layer. (b) Symbolic representation of the reflectivity of the whole layer. For reasons of symmetry the distinction of single cubes is no longer necessary. The diagonal representation of the arrows has no physical meaning but it is used for easier illustration of multiple layers.

Fig. 10
Fig. 10

One glass cube replaced by a black cube.

Fig. 11
Fig. 11

Reflectivity of the dissipative single layer. The diagonal representation of the arrows at the right is made not for physical reasons but for a better illustration of multiple layers.

Fig. 12
Fig. 12

To calculate the reflectivity of the infinitely thick sample it is sufficient to consider the first layer and lift off the other layers (which again form a semi-infinite stack of layers). The diagonal representation of the arrows is made not for physical reasons but for a better illustration of multiple reflections.

Fig. 13
Fig. 13

Reflectivity as a function of the relative number a of black cubes. R 1, upper curve before the grinding procedure; R 2, lower curve after the grinding procedure. Ω = 1.443.

Fig. 14
Fig. 14

Difference D = R 1 - R 2 as a function of the relative number a of black cubes. Ω = 1.443.

Fig. 15
Fig. 15

Difference D = R 1 - R 2 as a function of carbon content C with fictitious iron oxide content F as a parameter.

Fig. 16
Fig. 16

Difference D of reflectivities R 1 and R 2 as a function of carbon content C for numerical value F = 20% (see also Fig. 17) according to the cube model and the experiment. The offset is explained by the polishing effect.

Fig. 17
Fig. 17

Functional connection among reflectivity R 2 (second reflectivity after a defined number of twists), measured difference D REAL (difference in the levels of reflectivity before and after a defined number of twists of the measuring cylinder), mass-related carbon content C MAS, and fictitious iron oxide content F according to the cube model. The line C MAS = 0 is given by the straight line D REAL = 0.014R 2.

Fig. 18
Fig. 18

Experimental results achieved with the present prototype sensor. The sensor output (carbon concentration C SEN) is compared with results of laboratory measurements (carbon concentration C LAB obtained by chemical analysis of the fly ash with the carbon–hydrogen–nitrogen determinator CHN 600 from Leco Corp., St. Joseph, Mich.). Number of samples, 110.

Tables (2)

Tables Icon

Table 1 Chemical Composition of Fly Ash Produced at the Dürnrohr Power Stationa

Tables Icon

Table 2 Comparison of Values of C MAS Calculated with the Evaluating Algorithm (a) and with the Linear Approximation (b)a

Equations (52)

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

KS=1-R22R.
R=1-2A-A21-A,
R=exp-2nkd/3,
Rs=1/2.
RS=16+4162+42163+43164+=161+46+462+463+=1611-4/6=12.
2462+4263+4364+.
2463+4264+4365+.
24264+4365+4466+,
2462+4263+1+16+462+4263+=2 1332=1.
A=2a if a1.
A=fa=2a2a+b=2a1+a.
X=1-A=1-2a1+a=1-a1+a.
RS=12 X=121-a1+a.
R=X2+RX22+R2X23+=X21+R X2+R X22+=X211-RX/2.
R2X2-R+X2=0.
R=1-1-X2X.
R=SS+K+KK+2S,
R1=1-1-X12X1.
R2=1-1-X22X2,
X2=1-a1+Ωa.
a=C+F,  0C+F1.
X1=1-C+F1+C+F.
C=C1-FC-F2,
X1=XFXC=1-F1+F1-C1+C,
R1=1-1-XF2XC2XFXC.
XC=1-C1+ΩC.
R1=1-1-1-C1+C21-F1+F21/21-C1+C1-F1+F
R2=1-1-1-C1+ΩC21-F1+F21/21-C1+ΩC1-F1+F,
X=2R1+R2.
2R11+R12=X1=1-C1+C1-F1+F,
2R21+R22=X2=1-C1+ΩC1-F1+F.
R11+R22R21+R12=1+ΩC1+C.
C=R21+R12-R11+R22R11+R22-ΩR21+R12.
2R11+C1+R121-C=1-F1+F=Z.
F=1-Z1+Z
C=C 1-F21+CF.
DREAL-DMODEL=0.014R 0<DMODEL<1, 0<R<1.
CMAS=CVOL1.3+F-0.3CVOL.
Input: R2, DREAL    0R21, 0DREAL1. D=DMODEL=DREAL-0.014R2, R1=R2+D, C=R21+R12-R11+R22R11+R22-1.443R21+R12, Z=2R11+C1+R121-C, F=1-Z1+Z, C=C 1-F21+CF=CVOL, CMAS=CVOL1.3+F-0.3CVOL0F1-CVOL. Output: F, CMAS.
dCMAS=CMASR2dR2+CMASDREALdDREAL.
ΔCMAS=CMASR2 ΔR2+CMASDREAL ΔDREAL.
CC˜=CMASR2R2=R˜2DREAL=D˜REALR2R˜2+CMASDREALR2=R˜2DREAL=D˜REALDREALD˜REAL.
CMAS=CMASR2R2=R˜2DREAL=D˜REALk1R2+CMASDREALR2=R˜2DREAL=D˜REALk2DREALCMASR2R2=R˜2DREAL=D˜REALR˜2CMASDREALR2=R˜2DREAL=D˜REALD˜REAL+C˜k3=k1R2+k2DREAL+k3
CMASR2=CMASCVOLCVOLCCR2,
CMASDREAL=CMASCVOLCVOLCCDREAL,
CMAS=3.4DREAL-0.15R2+0.035,  0CMAS1.
nmin=10.960.6×1.46+0.31×1.65+0.05×1.84=1.54.
nmax=10.960.48×1.46+0.32×1.65+0.2×1.84=1.66.
C=R21+R12-R11+R22R11+R22-1.443R21+R12,
R1=1.02R2.
C=-0.02+0.02R22-0.441-0.48R22.
ΔCC=3.82-3.763.76=1.6%.

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