Radiation properties of soot from diffusion flames

J. Quam. Spectrosc. Radiat. Transfer VoL 23. No. 4, pp. 387-396, 1982 Prinled in Great Britain,

0022J,073/82/040387-10503.00/0 © 1982 Pergamon Press Ltd.

RADIATION PROPERTIES OF SOOT FROM DIFFUSION FLAMES S. C. LEE, Q. Z. Yut, and C. L. TEIN Department of Mechanical Engineering, Universityof California, Berkeley, CA 94720,U.S.A. (Received 16 September 1981)

Abstract--The spectral extinction coefficients kx of soot from flame transmission data are obtained for small pool diffusionflamesof various fuels includingsolid polystyreneand plexiglas; foam polystyreneand polyurethane; and liquid isooctane and toluene. Good agreement between experimental and predicted kA from Mie theory and soot optical properties throughout the visible and infrared ranges substantiates the general applicability of these optical properties. On the other hand, the determination of soot sizes and volume fractions from visible range data and optical properties requires the form of the size distribution be known. The effect of using different size distributions on these soot results is evaluated by using the three-parameter distribution for the particle number density N(r) = ar b exp (- bdr~), with b varied to create different functional dependence on radius r. The most probable radius rm is found to increase by about 80% as b is changed from 2 to 6, while the volume fraction changes by less than 10%. Hence, the most probable radius is rather sensitive to this functional dependance, while the volumefraction is only slightly affected.

a, b, c /~ k m Nt n Q r F

NOTATION coefficientsin the particle size distribution, N(r) volumefraction extinctioncoefficientor imaginarypart of m complexindex of refraction (n - ik) particlenumber density real part of m extinctionefficiencyof spherical particles radius Gammafunction

Subscripts

a absorptionlimit of small particles m mostprobable A spectral

INTRODUCTION Radiation from flames is mainly contributed by the combustion products consisting of gases and particulates. The various aspects of gas radiation have been explored in detail and well summarized/-3 On the other hand, the problem of soot radiation is commonly treated by assuming that the particles are homogeneous and spherical and that Mie theory 4 can be employed. Accurate prediction of soot radiation also requires detailed information on soot optical properties and particle size distribution. The optical properties of soot have received considerable attention in the past. The Fresnel reflectivity analysis was usually employed to determine the refractive index of various forms of carbon outside the flame. 5-~3 The results so obtained do not necessarily correspond to that of soot in flames. Janzen ~3 pointed out that the presence of surface inhomogeneities such as voids and asperities in the microscopic scale, particularly in the compressed soot samples, usually invalidates the Fresnel assumption, thus rendering the Fresnel analysis inappropriate to determine the optical constants. Recently, Lee and Tien Z4 established a dispersion model and deduced soot optical properties from in s i t u flame transmission data of diffusion flames. In particular, agreement was sought between experimental and predicted spectral extinction coefficients of soot from polystyrene and plexiglas, It is necessary, however, to determine if these optical properties are also representative of that of soot from other fuels. tVisiting scholar from the Harbin PolytechnicUniversity. China. QSRT Vol. 27, No. 4--A

38'7

S.C. LEE et al.

388

Another factor affecting the calculation of soot radiation is the size distribution of soot. Soot particles are generally regarded as spherical and polydisperse, and the size distribution can be determined, for example, by the method of Pagni and Bard, ~5if the functional form of the size distribution is known. For diffusion flames, there is no experimental evidence to support the use of a particular form of distribution. The estimated soot size may vary, depending on the form of particle size distribution used in the analysis. It is then important to evaluate the effect of size distribution on the determined soot size and volume fraction. The objective of the present study is two-fold: first, to evaluate the general applicability of the soot optical properties due to Lee and Tien and, secondly, to investigate the effect of using different size distributions on the determination of soot particle size and volume fraction. In the following section, the formulation to calculate the soot extinction coefficient, particle size, and volume fraction, is first presented. ANALYTICAL BASIS In flame radiation calculations, soot particles are commonly assumed to be spherical and polydisperse and their radiation properties can be obtained from Mie theory.4 Of particular interest to radiation calculations is the spectral extinction coefficient of soot, defined as ka =

Irr2N(r) Q(m, a) dr,

(1)

where r is the radius, N the particle number density, Q the extinction efficiency, m ( - n - ik) the complex index of refraction, and a( -= 2zrdA) the size parameter. A general, three-parameter skewed distribution often employed for soot polydispersion is ~6 N(r) = ar ~ e -or, c > 0,

(2)

where a = Ntcb+JlF(b + 1), r~ = b/c, or/r,. = C ( b + 1)lb. The soot volume fraction is then obtained as F(b + 4) [o= f : ~ ~rr3N(r)dr= ~ ~ra ~ cb+4

(3)

The spectral extinction coefficient can be rewritten in terms of the most probable radius rm and volume fraction f~ as

3:° ka = 4F(b + 4) \ rm /

Jo

r ~+2e-b'~" Q dr.

(4)

In order to calculate k~, it is necessary to know b, rm, and fv, which are the characteristics of the system being studied. Light scattering methods are extensively employed in the determination of particle sizes in colloidal systems. In general, they all involve spectral extinction measurements or measurements of the angular scattered intensity distribution.t7-21 The method of Pagni and Bard 15 is used here to determine r~ and Iv from visible range flame transmission data. These authors suggested the normalized extinction factor XI2 = [(kJk2)- 1]][(kJk2)- 1]a,

(5)

where the subscripts 1 and 2 denote two different wavelengths in the visible range and the subscript a refers to the absorption limit. This parameter is calculated as a function of rm for any pair of k~ in the visible range. Then, r,, is obtained by matching the experimental and calculated X~2.

Radiationpropertiesof soot fromdiffusionflames

389

Another quantity essential to the calculation of soot radiation is the soot volume fraction. It can be shown from Eq. (3) that f~ = ~n (b + 3)(b + 2)(b + 1) ka b3 kA' rm,

(6)

where kA' is the non-dimensional extinction coefficient defined as

(7)

kA' = kA/Ntrm2 = [1r/ rmZF(b + I)] ( b/ r,n) b+4 f : r b+2 e -b'¢'- Q dr

Consequently, the volume fraction is determined by using this theoretical k~' along with experimental values of k~ and r,~ in Eq. (6). The general applicability of the soot optical properties is assessed by observing the agreement between the experimental and predicted k~ of soot from various fuels in the visible and infrared ranges. This is achieved by first determining r,, and .f~,then extrapolating ka to the infrared using Eq. (4) and comparing with experiment. It should be noted that the value of b in the size distribution is not a priori known because it depends on the system being studied and characterizes the width, as well as the radius dependence, of the distribution. The effect of using different values of b in the analysis is subsequently evaluated. The experimental system for the flame transmission measurements is next described. FLAME TRANSMISSION

EXPERIMENT

The schematic diagram of the experimental apparatus is shown in Fig. 1. This system is designed mainly for transmission and emission measurements and allows data in the visible and infrared to be taken simultaneously. Major components of the apparatus include a test chamber, two light sources, and detection units. Fuels are placed inside the test chamber where the exhaust rate is minimal to simulate a natural diffusion condition.

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Fig. 1.

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,1/34)

390

S.C. LEz et

al.

Two light sources are used in this experiment. The infrared source is produced by a giobar made of carboradium with approximately gray characteristics. It is heated electrically to about 1200°K, and the radiant beam is focussed, collimated, and chopped for identification. The exiting beam, first passing through a heat transmitting mirror (HTM), traverses the test chamber and is focussed into a monochromator (Perkin-Elmer Model 99) which resolves the beam spectrally with a sodium chloride prism. The beam is then focused onto a thermocouple detector and is converted to an electrical signal which is input into a lock-in voltmeter (Brower Laboratory Model 131). The visible source is a continuous argon-krypton laser (Coherent CRMG) that is tunable from 0.4762 to 0.6764/z. The laser beam is first chopped for identification and then directed by the HTM to coincide with the infrared beam in traversing the test chamber. The beam is then deflected to a laser power detector (Newport Research Corporation Model 820), and the signal is input into an Ithaco lock-in amplifier (Model 395). The outputs resulting from both visible and i.r. sources are either recorded on charts or stored in the PDP 11/34 computer for subsequent analysis. Primary data are the intensities of the source beams before and after traversing the flame; extinction coefficient is obtained by dividing the logarithm of their ratio by the flame pathlength. The fuels used in the present experiment include the solids: polystyrene and plexiglas (polymethylmethacrylate), the foams: polystyrene and polyurethane, and the liquids: isooctane and toluene. A schematic diagram of the burning configuration is shown in Fig. 2. The solid fuels were contained in disks I cm high and 7.6 cm in diameter. The fuel surface receded less than 2 mm during each run of about 3 min. In burning liquid fuels, asbestos coils were soaked thoroughly with the fuel and were placed in pyrex disks 1 cm high 9.7 cm in diameter. The use of asbestos coils resolved the problem of a rapidly receding surface and the source beams were maintained at a constant height above the fuel surface. For the foam plastics, each piece of 20 x 7.5 (width)× 5 cm was set on an aluminum foil tray. Upon ignition, the foam plastics melted quickly and burned as pool fires. Data were taken during the pool burning period. RESULTS AND DISCUSSION The spectral extinction coefficients of soot from various fuels have been obtained from flame transmission experiments. Pertinent soot results, such as the most probable radius r,, and volume fraction/v, were determined from visible range data and optical constants. Without loss of generality, the size distribution with b = 3 was used, and the effect of using other values of b, corresponding to different size distributions, on these soot properties were later assessed. Table 1 shows a summary of the soot results based on the optical properties of Lee and

Light

Light

begin

begin

~ cm

L

I

~-

I

Disk 76 Cm diom.

Disk 9.7cm diom.

Polys~/rene ond Plexiqlos (solid)

L,:h:I

~' 3cm

Toluene ond T.so-Octone (liquid)

,~h, [

1

5 cm

20 cm

Po!ystyrene (foam)

Polyuret hone foom

Fig. 2.

I/I

I10,63

111

110.62

I/0.44

110.88

'lexiglas solid)

Polystyrene (foam)

Polyurethane (foam)

Iso-Octane (liquid)

Toluene (liquid)

Fuel atomic H/C ratio

'olyst~rene solid)

Fuel

X2 & ~3 >'2 & 7"4 %3 & S4

~2 & ~3

~I & ~2 ~I & ~3

>'I & )'2 ~I & )'4 >'2 & ~4

~I & ~2 ~I & ~4 X2 & ~4

X1 & X4

)'I & X2 Xl & X4

X1 & ~2 ~I & X4 7'2 & X4

Wavelength pair

0.22 0.22 0.22 3.8 4.2 4.2 0.19 0.18 0.18 0.50 0.50 0.55 4.6

0.036 O.038 O.039 0.053 0.067 0.070 0.031 0.035 0.035 0.047 0.038 0,032 0,046 0.041 0,035

4.7 5.1

3.3 3.3 3.3

0.049 0,045 0.044

v

Present studies Volume Most probable fraction radius rm(~) f x 106

0.027

0.035

'A"

"k"

0.044 0.056 0.059

0.083

0.039

v

5.5

O. 56

4.2 4.6 4.6

0.35

3.8

From Dalzell and Sarofim I0 Most probable Volume fraction radius rm(U) f x 106

A3 = 0.5682~, ~4 = 0.6471~, *indicates that experiments and predictions are incompatible).

Table I. Soot results from the present experiment and reported soot optical properties (~.~ = 0,488tz, A2 0.5145~t,

8"

-c~

392

S.C. LEE, et aL

Tien '4 and the widely accepted values of Dalzell and Sarofim. ~° A set of r,, and f~ is determined from matching of the experimental and theoretical X~ for each pair of k~ in the visible range. It is expected that the different sets of rm and 1",, obtained by using different pairs of k~ should also agree with each other, thus providing a check for the consistency of the soot results. It is observed that the experimental Xii is always incompatible with the prediction based on the optical properties of Dalzeli and Sarofim. Such agreement, on the other hand, exists when the optical properties of Lee and Tien were used, thus allowing the r,, and/',. of the fuels to be determined. The extinction coefficients were then extrapolated to the infrared and compared with experiments using the average r,, and f,,. As shown in Figs. 3-5, the agreement is quite good. The consistency of the soot properties determined from different pairs of k~, as well as the agreement between the experimental and theoretical k~ for the various fuels, indicate that the optical properties of Lee and Tien are indeed representative of that of soot from flames of different fuels. Moreover, althot;gh chemical analysis of the soot was not performed, it is reasonable to expect that the hydrogen/carbon (H/C) ratios of the soot are different for different fuels. Therefore, the present results indicate that the optical constants are relatively independent of the soot H/C ratio. The effect of size distribution on the soot properties of Table 1 is next investigated. Previous studies 15 indicate that the case of b = 3 is almost indistinguishable from the zeroth order logarithmic distribution. Although there exist many representations of a general size distribution, most of them exhibit the same general nature. Hence, a good estimate of the effect of size distribution can be obtained by considering the 3-parameter skewed distribution of Eq. (2), with the radius dependence varied from the first power to the sixth power, i.e., b = 1 to 6, corresponding to 1.41 > tr/r,, > 0.44. Using the optical properties of Lee and Tien, 14 r,, and [o are determined for each size distribution and the result of a typical fuel, say isooctane, is shown in Table 2. For each value of b, the soot results (r,, and [~) of all the fuels based on pairs of visible range data agree very well with each other. The case b = 1 (o,[r,, = 1.41) indicates too large a distribution width which may not be physically realistic. The maximum variation for a given fuel between the rm from different wavelength pairs is about _+20%, while the variation in .fv is usually around _ 6%. These discrepancies are, of course, due to uncertainties in the visible range data based on which the soot results were determined. On the other hand, r,~ increases by about 80% as b is changed from

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Radiation properties of soot from diffusion flames

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2 to 6 (dr,, from 0.87 to 0.44). The correspoding change in Iv is only about __.7%. The variations of r,, and .fv of various fuels with the size distribution parameter are summarized in Table 3. The increase in rm, while [~ remains almost constant, means that the total number of particles decreases as r,~ becomes larger. This is evident from the total area under the size distribution curves shown in Fig. 6, where the total area under the curve decreases with increasing r,~. The ka for the fuels are then extrapolated to the infrared (using the average soot properties of Table 3) and compared with experiment. The worst agreement is exhibited by

S. C. LEE et al.

394

Table 2. Effect of size distribution on soot results of iso-octane diquid) flames IN(r) = arbe -b"'-, Xt = 0.488tz, A2 = 0.5145#, A3 = 0.5682t~1.

b

Most probable radius

Wavelength pair

rm(~)

Volume fraction f x 106 V

0.022 0.014

0.52 0.53 0.60

0.037 0.029 0.024

0.5l 0.51 0.56

}`I & x2 }`I & A3 }`2 & >'3

0.047 0.038 0.032

0.50 0.50 0.55

}`I & >`2 >`I & >`3 }`2 & >`3

0.055 0.050 0.039

0.50 0.55 0.54

0.065 0.054 0.048

0.48 0.48 0.52

}`1

& >`2 }`I & }`3 >`2 & }`3

0.017

>`I }`I & x3 }'2 & ~3

>`I & >`2 ~I & X3 X2 & >`3

Table3. Averagesootresultsof variousflamesbasedon differentsizedistributions[N(r)= a~e-~,,~r=];x, yrepresents rm(#), f~,x l&. l

2

(x,y)

(x,y)

3 (x,y)

(x,y)

(x,y)

Polystyrene

0.021,3,4

0.036,3.4

0.046,3.3

0.054,3.3

0.065,312

Plexiglas (solid)

0.017,0.23

0.029,0.23

0.038,0.22

0.044,0.22

0.054,0.21

Polystyrene (foam)

0.031,4.2

0.051,4.2

0.063,4.1

0.072,3.9

0.085,3.9

Polyurethane (foam)

0.014,0.20

0.025,0.19

0.033,0.19

0.040,0.18

0.051,0.17

Iso-Octane (liquid)

0.018,0.55

0.030,0.53

0.039,0.52

0.048,0.53

0.056,0.49

Toluene (liquid)

0.018,5.2

0.031,4.8

0.041,4.8

0.048,4.7

0.059,4.3

(solid)

4

6

l

polystyrene foam, which indicates a discrepancy of about 5% from the reference value corresponding to the case with b = 3. Hence, agreement between the experimental and theoretical kA is always observed regardless of which size distribution was used. Although only 5 size distributions have been employed, it is reasonable to expect that similar conclusions can be drawn if other size distributions were used. It is apparent that the most probable radius is quite sensitive to the functional dependence of the size distribution. The volume fraction, being an integrated property, is only slightly affected.

Radiation properties of soot from diffusion flames

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I 0.12

Fig. 6.

Table 4. Soot results based on the monodisperse assumption [A~ = 0.488 p., ,~2 = 0.5145 p,, ,~3 = 0.5682/~, A4 = 0.6471 p]

Fuel

Wavelength pair

Most probably

radius rm(~)

Polystyrene (solid)

Xl & ;~2 ~I & ~4 ~2 &l~4

Plexiglas (solid)

~I & ~2 ~I & ~4 ~2 & ~4

Polystyrene (foam)

~I & ~2 ~I & L4 ;~2 & ;k4

Polyurethane (foam)

kl & ~3 ~I & X4 ~3 & ~4

Iso-Octane (liquid)

Toluene (liquid)

'~I & ~'2 ~I & )~3 ~2 & ~'3

~2 & ~3 ~2 & )'4 ~3 & >'4

Volume fraction

f

V

x 106

0.I02 0.108 0.109

2.8 2.9 2.8

0.092 O.lOl 0.105

0.19 0.19 O.IB

0,105 0,126 O.131

3,1 3.5 3.5

O.092 0.097 0.0118

0.15 0.15 0.13

0.101 0.097 0.094

0.42 0.40 0.43

0.107 0.107 0.107

4.0 4.0 4.0

396

S. C. LEE et aL

A logical extension would be to consider also the monodisperse assumption of soot particles. As shown in Table 4, agreement is also observed between the soot results determined from pairs of visible data. The soot volume fraction is always lower than that based on the polydisperse assumption by as much as 15%. The most probable radius is considerably larger (rm -0.1 tz) and is almost independent of fuel. This excessively large size shows that all of the particles are outside the Rayleigh limit in the visible and near infrared ranges. The predicted ka based on the monodisperse assumption are also about 30% lower than the experimental values, indicating that the monodisperse assumption is not appropriate for the soot particles. CONCLUSION

Flame radiation is usually recognized as a critical factor in many combustion phenomena. In particular, soot particles contribute significantly to the infrared radiation from flames as well as the flame luminosity. Pertinent parameters required for calculating soot radiation include the soot optical properties and the size distribution. The optical properties of soot were usually inferred from reflectance analysis on various forms of carbon outside the flame. However, Lee and Tien recently obtained the soot optical properties based on in situ flame data. The values so obtained truely reflect those of soot in flames. In the present study, extensive experiments have been performed on various fuels, including solid, liquid, and foam fuels, to evaluate the general applicability of these optical properties. The good agreement between the experimental and predicted spectral extinction coefficients establishes the usefulness of these optical properties. The effect of size distribution on the soot properties (rm and f~) was assessed by employing size distributions with different radius dependence. It is shown that the most probable radius is rather sensitive to this functional dependence, while the soot volume fraction is only slightly affected. The consistency of rm and [~ determined from each pair of visible range data regardless of the form of size distribution corroborates the general applicability of the soot optica[~ ~perties. ':

REFERENCES

1. S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities. Addison-Wesley, Reading, Mass. (1959). 2. C. L. Tien, Advances in Heat Transfer 5, 253 (1968). 3. D. K. Edwards, Advances in Heat Trans[er 12, 115 (1976). 4. M. Kerker, The Scattering o[ Light and Other Electromagnetic Radiation. Academic Press, New York (1969). 5. H. Senftleben and E. Benedict, Annalen der Physik 54, 65 0918). 6. J. T. McCartney and S. Ergun, Proc. 3rd Conf. on Carbon 223 (1958). 7. V. R. Stull and G. N. Plass, J. Opt. Soc. o[Am. 50, 121 (1960). 8. C. R. Howarth, P. J. Foster and M. W. Thring. Proc. 3rd Int. Heat Trans. Conf. 5, 122 (1966). 9. P. J. Foster and C. R. Howarth, Carbon 6, 719 (1968). I0. W. H. Dalzell and A. F. Sarofim, J. Heat Trans[er 91, 100 (1969). I1. S. C. Graham, Comb. ScL and Teclt 9, 159 (1974). 12. S. Chippett and W. A. Gray, Comb. and Flame 31, 149 (1978), 13. J. Janzen, J. Colloid. Interface ScL 69, 436 (1979). 14. S. C. Lee and C. L. Tien, 18th Symp. (Int.) on Combustion, The Combustion Institute, pp. 1159--1166 (1981). 15. P. J. Pagni and S. Bard, 17th Symp. (Int.) on Combustion, The Combustion Institute, pp. 1017-1028 (1979). 16. C. L. Tien, B. G. Doornink, and D. A. Rafferty, Comb. ScL and Teclt 6, 55 (1972). 17. W. D. Erickson, G. C. Williams and H. C. Hottel, Comb. and Flame 8, 127 (1964). 18. R. A. Dobbins and G. S. Jizmagan, J. Opt. Soc. of Am. 56, 1351 (1%6). 19. W. H. Dalzell, G. C. Williams and H. C. Hottel, Comb. and Flame 14, 161 (1970). 20. J. N. Desai and D. B. Vaidya, J. Colloid. Interface ScL 51, 527 (1975). 21. P. A. Bronczyk, Comb. and Flame 35, 191 (1979).