* Engler-Bunte-Institut, Bereich Feuerungstechnik
** Institut für Thermische Strömungsmaschinen
Universität Karlsruhe (T.H.)
Karlsruhe (Germany)



Radiation heat transfer in flames depends strongly on the local quantities such as pressure, temperature and concentration of participating species. In the present study, detailed measurements of the concentration and temperature field of a model combustor are presented together with an experimental analysis of the spectral radiative heat transfer. The combustor was defined by the flame research group TECFLAM as a standardized flame for an extensive measurement campaign of the reacting fluid flow. The geometry of the combustion chamber (D=0.5m), the flame configuration (type-II swirling diffusion flame) and the highly turbulent flow conditions were selected to resemble the characteristics of industrial combustors. The combustor is fired by natural gas. The thermal power is about 150 kW at an air fuel ratio of 0.83 and a swirl number of 0.9. The walls of the combustion chamber are cooled by water.

Measurement Techniques

The concentration measurements of CO2 , H2O, CO, CH4 , NO, NOx , O2 and H2 were performed isokinetically by means of a thermostatisized multihole suction probe and a gas analysis system. The local mean temperatures and their fluctuations were measured by time-compensated thermocouples. Temperatures and concentrations were recorded at 300 locations at 14 axial planes. For the radiation measurements an IR-spectroscope has been employed. The radiation intensity incident on the walls was measured spectrally and time resolved (sampling rate of 1000) at 11 axial planes within the spectral range of 1.4 to 5.4 .

Flame Structure

Induced by the swirl, a ring vortex flow structure with an inner and outer recirculation zone is formed. The flame is located at the shear layer between the outer and the inner recirculation zone.

Temperature Measurements

As typical examples, the results for two axial planes are presented. The plane x/D=0.5 represents the beginning of the reaction zone. It is characterized by a highly complex flame structure, as it is revealed by the temperature plot. The temperature records show a maximum at the edge of the inner recirculation zone. This is the main reaction zone with near-stoichiometric conditions. Outside the reaction zone, the temperature decreases as consequence of the injected cold combustion air, and finally increases again in the outer recirculation zone. The plane x/D=5.0 represents the end of the visible flame. Due to intensive mixing, the temperature profiles are almost even over the radius.

Radiation Measurements

The radiation spectra and the corresponding fluctuations have also been recorded for both planes, x/D=0.5 and x/D=5.0. Due to lean combustion conditions no soot radiation was detected and the emission is restricted to the well known radiation bands of water vapour and carbon dioxide. In the reaction zone, the 3.4 band of unburned methane is visible. Highest mean intensities and fluctuations are found at x/D=5.0, at the end of the visible flame. This is due to the high temperatures and concentration of emitting species at this location. Moreover, the hot gas zone is extended over the whole cross-section of the combustor. Close to the nozzle at x/D=0.5, higher intensities as expected from the flame geometry can be found. The reason is the recirculation of hot reaction products within the outer recirculation zone.


Shinya Kamiyama, Junko Konno and Masakazu Yamazaki
Thermal Energy and Combustion Engineering Department
National Institute for Resources and Environment
16-3 Onogawa, Tsukuba, 305 Japan


For radiative heat transfer in a furnace filled with high temperature combustion gas medium it has been widely recognized that the spectral absorption/emission characteristics of CO2 and H2O should be considered instead of the former gray body approximation. For the purpose of engineering calculation of radiative heat transfer in a combustion furnace a number of band models have been proposed1. In the present paper spectral absorption coefficients and total emissivities of CO2 and H2O were numerically calculated by adopting the combination of Elsasser's narrow band model and Edwards' wide band model for the range of temperature and partial pressure expected in a combustion furnace. The availability of the relevant band models was discussed by comparing the calculation results with existing experimental measurements.


According to Elsasser's narrow band model2 the spectral absorption coefficient at a wave number is given by


where S is the line intensity, d is the line spacing, is the line half-width and designates the spectral location of each band. The parameters of S/d and in Eq.(1) are specified by Edwards' wide band model2-3.



where is the integrated band intensity, is the exponential decay width, is the mean-line-width- to-spacing parameter and Pe is the equivalent broadening pressure. Substituting Eqs.(2) and (3) into Eq.(1) gives


For large the lines become broad compared to their spacing and the line structure is lost as the lines strongly overlap and can be neglected. Under this condition Eq.(4) is simplified and becomes


Adopting this simplified form of the model makes the numerical calculations very convenient4. Using Eq.(4) or Eq.(5) the total emissivity of CO2 and H2O are calculated by the following equation.


where T is the gas temperature, Ib is the spectral intensity of blackbody and is the optical path length.


Fig.1 compares total emissivities calculated from Elsasser model ( Eq.(4)) and its simplified form ( Eq.(5)) with measured values by Hottel5 at several conditions of optical depth, in limit of zero partial pressure in a mixture having a total pressure of 1 atm. In both cases of CO2 and H2O the total emissivities calculated from Eq.(4) show good agreement with the experiments in the whole temperature range. Comparison of calculated emissivities from Eq.(4) with those from Eq.(5) shows discrepancy in relatively lower temperature range and at smaller optical depth conditions. This feature is more significant for the emissivities of H2O than those of CO2.

Fig.1 Comparison of the total emissivities calculated from the band models with experimental measurements.
: Elsasser model
: simplified form of Elsasser model
: measured values by Hottel

Fig.2 shows the effect of the partial pressure on the discrepancy of calculated emissivities caused by the simplification included in Eq.(5). At the temperature conditions in Fig.2 almost no difference between two cases is shown for CO2, however, for H2O, calculated emissivity from Eq.(5) gives about the half of that from Eq.(4) at some extreme conditions.

Fig.2 Effect of the partial pressure on the discrepancy between calculated emissivityies from Eq.(4) and Eq.(5)
: Elsasser model
: simplified form of Elsasser model

The discrepancy of calculated emissivities shown in Figs.1 and 2 suggests that the values of the parameter are not large enough and discrete line structure in each band can not be neglected at low temperature and small partial pressure conditions.


For engineering calculation of radiative heat transfer in a combustion furnace spectral absorption coefficients and total emissivities of CO2 and H2O calculated from the combination of Elsasser model and Edwards model proved to be well available. The simplified form of Elsasser model is very convenient for the numerical calculations, however its availability is limited and it should be noted that the simplified calculation may lead to very significant errors especially at low temperature and small partial pressure conditions for H2O.


  1. Modest, M.F., Radiative Heat Transfer, McGraw-Hill, 1993
  2. Irvine, T.F.Jr. and Hartnet, J.P., Advances in Heat Transfer, Volume 12, Academic Press, 1976
  3. Edwards, D.K. and Balakrishnan, A., Thermal Radiation by Combustion Gases, Int.J.Heat Mass Transfer, Vol.16, pp 25-40, 1973
  4. Kudo, K, Improvement of Analytical Method on Radiative Heat Transfer in Nongray Media by Monte Carlo Method, Trans.JSME (B), Vol.59, No.560, pp 1265-1270, 1993
  5. Hottel, H.C. and Sarofim, A.F., Radiative Transfer, McGraw-Hill, 1967


Cavaliere A.*, Ciajolo A. **, de Joannon M.*, Ragucci R.**
* Dip. Ingegneria Chimica, Università Federico II, Napoli Italia
** Istituto di Ricerche sulla Combustione, C.N.R., Napoli, Italia


The spectral characteristics of spontaneous emission of an igniting spray injected in high pressure, high temperature ambience are of interest not only for identification of species present during this part of combustion process, but also because they can help in the understanding of electromagnetic energy transfer from emitting regions to adjacent region where fuel mixture is not in the temperature range suitable for autoignition yet.

The results presented here evidence the presence of visible emission very early after ignition time before the soot formation to which this visible emission was erroneously related in the past.


A five-hole injector, in the class of light duty engines, injects 6 mg/stroke/hole of tetradecane into a high pressure (3.6 MPa), high temperature (873K) nearly quiescent air environment. The injection lasts 1.2 ms as it is shown in the "window" of Fig. l. Only one of the five spray plumes, tilted 53o on the horizontal plane has been studied during experimental tests.

The ignition delay, defined as the time from injection at which the first luminosity is detected, is measured by means a UV-enhanced photodiod with a sensitivity spectral range from 200 to 1150 nm.

Fig. 1 Optical set-up.

The core of the diagnostic apparatus is a Jobin-Yvon spectrograph. The objective lenses in front of the spectrograph collect the light from a linear objective field which is focused on the entrance slit of the spectrograph. The holographic plate of the spectrograph separates along one direction the different wavelengths components of the light, so that at the output section a 2-D field is formed in which one direction represents a spatial linear image of the objective feld at fixed wavelength whereas the perpendicular direction represents the spectral dispersion at a fixed spatial position1. The photocathode entrance section of a micro channel plate is placed in the image plane of the spectrograph outlet. This intensifies the incident light with adjustable gain up to fixed intensity of electron excited phosphorescent light. A CCD-camera collects this light from the phosphorescent screen generating a discretized analog image that is then converted to a digital one using an A/D converter.

Stray light rejection, filtering of supernumerary wavelength contribution, spectral range identification, intensity calibration have been obtained by means of light sealing, band pass filter, filament and gas lamps.


Some spatial-spectral patterns of light emitted from the whole spray, have been collected at several times after ignition ( is the algebraic difference between the measuring time and the ignition time). An example of the optical characterization is shown in Fig. 2 where two single images (relative to two single injection events) of light emitted spontaneously from the igniting spray taken at =0.17 ms and at =0.30 ms are reported For each image two profiles of light intensity have been reported (in the right part) versus the collection wavelength () for two spatial positions. Below the pictures, two profiles of light intensity versus the spatial position in the spray at wavelengths of 550 and 350 nm have been reported. The spectral profiles show as, just after the ignition has taken place, an ultraviolet contribution to the emitted light can be detected along with a visible emission one. This latter increases with time becoming the predominant one, but also an ultraviolet contribution can be detected over the whole investigated time domain. The analysis of pattern like those reported in the figure, or of average pattern, permits a thorough characterization of both spatial and spectral behaviour of light (due to spontaneous or stimulated emission) coming from the burning spray. The emission could be observed at all distances greater than 10 mm from the nozzle exit, but it seems to extend downward at higher times due to the flame propagation. It must be underlined as the patterns are not spatially uniform (for the single event images), testifying the intrinsic randomness of the process. An extensive illustration of the emission characteristics with time is shown in the results reported in the following part.

Fig.2 Examples of pattern analysis by means of spatial and spectral profiles determination.

Temporally averaged images have been reported in a false colour scale, on the left side of Fig. 3 for from 0.04 to 0.36 ms. On the right side spatially averaged intensity profiles of these patterns are reported.

Just few milliseconds after ignition an emission signal, ranging from ultraviolet to visible, could be detected, as it is shown by intensity profile at = 0.04 ms. At this time luminous signal extends in a limited part of the spray, as the blue zone in the visible range of corresponding spectral pattern evidences.

Fig 3 Average emission patterns and intensity profiles at different time after ignition (), at T=873K, P=3.6 MPa.

At = 0.08 ms the signal intensity increases and its visible part expands along the spray axis. The light intensity reaches a relative maximum at = 0.12 ms and slightly decreases at = 0.16 ms. After this time it grows continuously in the whole investigated temporal range.

In the full presentation the comparison of the temporal profile of the emission intensity with the temporal profile of scattering intensity is also presented. This shows that visible emission precedes the first formation of soot so that thermal emission from carbonaceous particles can be neglected.


  1. Ragucci R., de Joannon M., Cavaliere A.: 26th Symp. (Int) on Combustion (in press) The Combustion Institute, Pittsburgh ( 1996).


Timo Joutsenoja, Jari Stenberg, Rolf Hernberg
Tampere University of Technology, Department of Physics, Plasma Technology Laboratory
P.O.Box 692, FIN-33100 Tampere, Finland

ABSTRACT. A two-colour pyrometric method for simultaneous in situ measurement of temperature and size of individual fuel particles in a pressurised entrained flow reactor (PEFR) has been developed. The method includes a novel technique for particle discrimination based on a two-focus optical system. This technique can be used for the identification of measured particles through a single optical port. The particle sizing is based on the proportionality of the measured radiative flux and the cross sectional area of a particle at known temperature. Several series of measurements were made at a PEFR at different process conditions and some typical results are presented.


The combustion of coal is a complex phenomenon involving the effects on heterogeneous and homogenous reactions, heat and mass transfer and two-phase fluid flow. In recent years several research groups have been studying the combustion of coal and char in order to get better fundamental understanding of the combustion process and aiding in the development and evaluation of comprehensive combustion models. The temperature of burning fuel particles affects both the combustion rate and the characteristics of combustion products. The fuel particle temperature and size also have a significant role, in particular, when the radiative heat transfer is studied. In consequence, the accurate measurement of fuel particle temperature has an important contribution to this research.

Optical two-colour and three-colour pyrometry has been widely used for particle temperature measurements in flow reactors. Simultaneous non-intrusive in situ particle size measurements have been performed in combustion reactors using methods based on the coded aperture method and particle imaging. A common feature of these sizing techniques, as well as techniques based on light scattering, is that they require optical access from at least two non-collinear directions. This requirement cannot always be met, especially in pressurised installations. Therefore, there was an interest to develop a technique by which the particle size can be inferred from optical measurement through a single port.

The industrial scale pulverised coal boilers typically burn particles around 100 mm. However, there is scatter in particle size, and laboratory scale studies have included particles that are typically at the range from 30 to 300 . The gas temperature in commercial pulverised coal boilers is typically 1500- 1700 K, but the laboratory studies often have lower temperatures down to 1000 K. The observed fuel particle temperatures vary significantly due to strong dependence on the process conditions and properties of fuel. Measured temperatures have varied from the gas temperature up to 2500 K.


The optical setup of the pyrometric measurements in a flow reactor is shown in Fig. l. Only one optical port is necessary, in principle. Here the opposite port is forms the cold background for the optical field of view. The absence of radiation from the plug is of some advantage for the accuracy, particularly if particle temperatures are measured under pyrolysis conditions. In such a case, namely, the fuel particles may be of the same temperature as or even colder than the reactor wall. Under combustion conditions the particle temperatures are typically several hundred degrees above the wall temperature, and the temperature measurement against a hot wall does not cause problems.

Radiation from a particle is collected via a lens system and focused to the ends of two optical fibres. One of these fibres, called the primary fibre, is used for pyrometry. The other one, called the reference fibre, is used for particle discrimination. The radiation entering the primary fibre is measured in a radiometric unit on two wavelength bands. The lens system has been optimised so that the effective focal length is the same at centre wavelengths of both bands. The used wavelengths were chosen so that emission bands of combustion gases and absorption of media gas do not affect the temperature measurement.

When a fuel particle passes through the probe's field of view a pulse is detected in the pyrometric signals. The particle temperature is solved using the ratio of the pulse heights measured at the two wavelength bands. The pyrometric response signal is proportional to the particle cross sectional area in the FOV when the particle temperature is fixed. This proportionality can be used for particle sizing. The evaluation must be performed at a moment when all of the particle is visible to the detecting device. The crucial part of the method is to be able to determine when full visibility is at hand. This is done using the particle discrimination procedure, which is based on dual-focus optics.

Figure 1 shows the end-faces of the primary optical fibre, which is used for the transport of the pyrometric signals, and the thinner reference flbre, which is used for particle discrimination. The reference fibre is located next to the primary fibre in the flow direction. The discrimination procedure is based on the ratio of intensities measured on the same wavelength band from reference and primary fibres. The optical probe can be optimised so that the measuring volume and detection limit are the most practical for the fuel particle number density, size distribution and expected temperatures of the experiment. This is made by selecting the f-number of the optics, the magnification and the diameters of the fibres.

The uncertainty of the particle temperature measurement is ± 30 K, which include both the accuracy of calibration and uncertainty due to electronic noise. The uncertainty of particle size measurement is at most ± 10 % for temperatures above 1500 K. The sources of uncertainty in sizing are the uncertainty in temperature determination, emissivity of particle, solid angle and noise. At lower temperatures the uncertainty of particle sizing grows with decreasing temperature. The method has been described in greater detail in Ref. [ 1 ].

Figure 1. The optical setup of pyrometric measurements at a pressurised entrained flow reactor.

Figure 2. Typical results from the fuel particle temperature and size measurements at a pressurised entrained flow combustion reactor. Fuel particle temperature (a) and size (b) distribution, individual fuel particles in temperature-size plane (c). (Gardanne lignite, Tg =1153 K, c[O2] =15 vol%)


Several series of measurements have been made at the PEFR of VTT Energy in Jyväskylä, Finland, with various fuels and process conditions. Figure 1 shows the optical setup and instrumentation. The reactor consists of a heated ceramic tube of 60 mm diameter and about 2 m length. A typical reactor temperature is 1000-1300 K. The reactor is contained inside a pressure vessel designed for operation up to 2 MPa pressure. Observation ports with 20 mm diameter are located at five levels. The background of the measurement was either cold or at the reactor wall temperature, depending on whether the measurement was made through one of two paired collinear observation ports or through an unpaired port. Figure 1 shows the case of a paired port.

Figure 2 shows typical distributions of fuel particle temperature (a) and size (b). Dp and Tp of individual particles of the same experiment are plotted in Fig. 2c. The fuel in the experiment was Gardanne lignite that was sieved to a nominal particle size fraction of 140-180 mm. The location of the measurement downstream of the beginning of the reactor tube corresponds to a particle residence time in the reactor of 130 ms. The temperature distribution is relatively narrow (standard deviation 95 K) due to the relatively homogenous fuel sample, the uniform environment and dilute suspension. The correlation between temperature and size was usually weak. Detailed report of the experiments at VTT Energy is given in Ref. [2].


  1. Joutsenoja, T., Stenberg, J., Hernberg, R. and Aho, M., Pyrometric measurement of the temperature and size of individual combusting fuel particles, Applied Optics, Vol. 36, pp.1525-1535,1997.
  2. Joutsenoja, T., Stenberg, J., Hernberg, R., Aho, M., Richard, J.R., Mallet, C. and Bonn, B., Pyrometric fuel particle measurements in pressurised reactors, JOULE II Extension programme, Novel Approaches in Advanced Combustion Technologies, Contract JOU2-CT93-0331, Final Report,1996


D. Eklund, A. Haghighi, T. Badinand, T. Fransson
Department of Energy Technology,
The Royal Institute of Technology
S-100 44 Stockholm, Sweden


A long term effort has been started to investigate the role that radiation plays in the overall heat transfer to wall liners and in the rate of emissions of NOx and other pollutants within gas turbine combustion chambers. In the present paper radiation from combustion gases with cylindrical geometries is studied. The finite volume technique is used to solve the axisymmetric Radiative Transfer Equation (RTE). The first case considered is an absorbing, emitting but nonscattering gas at a constant temperature within a black-walled cylindrical enclosure at zero temperature. Two different discretization schemes are used to relate the intensities along a control volume face to the cell center values: the step scheme and the higher order scheme of Raithby and Chui (1990). The accuracy (relative to the exact solution) and efficiency (in terms of cpu time) of the two discretization schemes are compared. The finite volume technique for the RTE is then coupled to a three dimensional CFD code to examine the radiative heat transfer from three axisymmetric chemically reacting flow fields. The first two cases are a turbulent flame stabilized behind a cylindrical body and a furnace. These cases were presented by a 1994 ERCOFTAC Workshop on turbulent non premixed flames. The third case is an experiment performed at KTH in which a propane jet is injected into a concentric coflow of air within a cylindrical enclosure. The fuel and air are originally separated by a bluff body that is used to stabilize the flame. Measurements and calculations of the intensity are compared.


W M G Malalasekera and J C Jones
Department of Mechanical Engineering
Loughborough University, Loughborough
Leicestershire LE11 3TU, United Kingdom


In the area of combustion modelling, there are a number of issues which need further research and improvements. Among them, the accurate description of turbulence/radiation interaction and the effect of radiation fluctuations (up to 25-30% in certain practical instances of turbulent combustion) on combustion have received very little attention. Since radiation is not a local effect, evaluation of radiation on the basis of local mean properties in a highly turbulent situation can give rise to significant errors on mean radiation intensities. Moreover, the radiative fluctuations are dependent on the spectral radiative properties of the combustion gases (CO2, H2O, CxHy), which are affected by temperature. The presence of spectral dependence greatly increases the complexity of the problem. In addition, since all the different geometrical locations surrounding a point contribute to the fluctuations of the radiative intensity, local fluctuations are the result of integration over all possible radiation paths.

The present study attempts to provide quantitative evidence of the effects of fluctuations and develop a modelling approach that will account for turbulence/radiation interactions in combustion. The work seeks to develop a modelling approach for turbulence/radiation interaction effects requiring modest computing resources based on the discrete transfer method of radiative transfer. The discrete transfer method is based on a ray tracing technique and offers a way of incorporating local variations of temperature and species concentration as well as fluctuating effects along the path contributing to the local intensity. For a control volume of concern, the information regarding the radiative contributions from the surrounding points is available as part of the calculation procedure. This can be used as a basis to develop a technique to account for the effect of radiative fluctuations due to fluctuations of temperature and species concentrations.

In the work presented here simple one-dimensional parametric studies have been considered as an initial attempt to identify the most important parameters in radiation fluctuating situations. One-dimensional problems involving fluctuating temperatures and absorption coefficients have been solved to calculate resulting wall flux distributions and source distributions. A number of test cases have been considered with sinusoidal fluctuations at a local layer and the Discrete Transfer method has been used to solve for wall flux distributions and source term distributions. The results obtained using the discrete transfer method have been validated using the Monte Carlo method and steady state (non- fluctuating) solutions of both methods have been compared with analytical solutions. Further, one-dimensional simulations have been repeated using random fluctuations of temperature and absorption coefficients and resulting mean flux distributions have been calculated. These results will be used to identify the effects of fluctuations and their significance on mean flux and intensity distributions. One-dimensional results will also be used to identify suitable assumptions for averaging the transfer equations and authors intend to develop a technique of incorporating radiation fluctuations in multi-dimensional systems using the discrete transfer method.


S. Carlucci*, A. D'Alessio *, G. Gambi* , P. Minutolo**
* Dip. di Ingegneria Chimica, Università degli Studi di Napoli Federico II, Napoli, Italy
** Istituto di Ricerche sulla Combustione, C.N.R., Napoli, Italy


In the last few years it has been found that the formation of soot particles in flames, i.e. highly absorbing particles with a typical size around 20 nm, is accompanied and sometimes preceded by the formation of particles with a much smaller size around 2-3 nm, absorbing in the ultraviolet region but transparent to the visible light (1). Both classes of particles contribute to the presence of carbonaceous aerosols in the atmosphere and it is therefore of great interest to characterise them separately.

The object of this communication is the spectroscopic characterisation, in the UV-visible region, of ethylene/air premixed flames with C/O ratios ranging from the stoichiometric to the rich sooting conditions by employing absorption spectroscopy, laser induced fluorescence and elastic light- scattering. With regard to the presence of different aerosols different regimes are identified.


Flat premixed laminar ethylene/air flames, with C/O ratio ranging from the 0.33 to 0.77, and the material sampled in the flame were examined by employing a Nd:YAG laser (o=266 and 532 nm) and a high pressure Xenon lamp as light sources.

The condensable material produced in flame, sampled by employing a stainless steel water cooled probe, was stopped in a cold trap containing distilled water placed on the sample line. Soot particles were sampled on a quartz plate inserted into the fully-sooting zone of the flame.

In analogy to the aromatic molecules, in carbonaceous structures the energy gap between the highest occupied electronic level in the valence band and the lowest unoccupied level in the conduction band, namely the band gap, decreases with the increase of the degree of aromatization of the species. The band gap has been evaluated from the measured absorption spectra following the procedure described in (2).


The absorption spectra of flames with C/O ratios ranging from the stoichiometric (C/0=0.33) up to 0.5 show a high signal at =200 nm and yet they fall off near 230 nm. No ultraviolet laser induced fluorescence signal is detectable.

Flames with C/O ratios in the interval between 0.5 and 0.7 show an absorption spectrum extended from 200 nm up to 250 nm and a broad band UV fluorescence spectrum with a maximum around 320 nm. The scattering coefficient measured in these flames is appreciably higher than that due to gaseous combustion products. The strong dependence of the light scattering coefficient on the mean size of the scatterers suggests that high molecular mass structures are present in these flames. The high value of the band gap found in these flames indicates that the transparent particles contain islands with only few condensed aromatic rings.

Finally, flames with a C/0 ratio higher than 0.7 have an absorption spectrum which extends from the near UV down to the visible and a visible fluorescence signal in addition to the ultraviolet feature. Moreover, the scattering signal is much higher than that due to gaseous compounds thus indicating the presence of soot particles. These structures are characterised by a low value of the band gap that indicates a strong growth of the aromatic islands inside the particles. From the absorption spectra it appears that the class of structures with a higher band gap is still present.

The "in situ" absorption and fluorescence measurements have been compared with those obtained on particles sampled in flame and suspended in water. A very good agreement between the spectra was found in flame regions where only transparent nanoparticles are produced.

When soot particles are also present the comparison of the absorption spectra measured in flame with those of the soot particles collected on the quartz plate allows to separate the contribution of soot from that due to nanoparticles.


  1. A.D'Alessio, A.D'Anna, A.D'Orsi, P.Minutolo, R.Barbella, A.Ciajolo, "Precursors formation and soot inception in premixed ethylene flames". Proc. Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 973-980, 1992.
  2. P. Minutolo, G. Gambi and A. D'alessio, "The Optical Band Gap Model In The Interpretation Of The U.V.-Visible Spectra Of Rich Premixed Flames". Proc. Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, pp.951-957, 1996.


Rumynsky A.N., Katasonov A.A., Voronin V.V., Itina T.E.
Russia, Kaliningrad, Moscow Region, TsMIIMASh

It is well known that in exact mathematical formulation the problem of statistical simulation of radiation transfer in scattering substance can be reduced to the calculation of the following value [1]

where x is the phase vector (for example photon position r and direction of its movement v), collisions phase density is a decision of integral equation

k(x',x) may be regarded as a probability distribution of photon transition x'--> x, f(x) is phase density of initial collisions. The appearance of k(x',x), f(x) and function h(x) (for calculation of various physical values) is well studied.

If scattering medium contains reflecting surface S the appearance of k(x',x) has to be modified. We write it in the following form:

where among obvious and common indications R is a point where ray r = r'+vs crosses the surface S, ls(r',v) is a distance along this ray to the surface S, s(r) is surface -function, F(r',r) =1 if one point is seen from another one and F(r',r)=0 otherwise.

The most attractive feature of Monte-Carlo method is the possibility of calculation of radiation intensity, which is proportional to . The method of "double local estimator" [1] is the most universal one for this purpose. According to this method one constructs the function h(x) only for photons arriving to the selected ray through intermediate collision (calculations for other ones are trivial). The presence of reflecting surface results in necessity of calculation for three various functions, which for protuberant correspond to the following photons transitions

  1. from medium to the selected ray;
  2. from reflecting surface to the selected ray;
  3. from medium to the point where selected ray crosses reflecting surface;
The calculation of the second and third values is connected with "local estimators" for points on the surface S.

If one does not take some special precessions the dispersion of all three values is infinite [l, 2] this leading to inadequate accuracy of the calculations.

The infinity of the dispersion for the first value may be eliminated by re-selection procedure [2] for free point of integration along the selected ray.

The most convenient method for calculation of "local estimators" type for points in medium is proposed in the article [3]. It is constructed in such a way that combination of contributions from consecutive point of Markov's chain leads to final value of estimator dispersion. The application of this method for points on a surface is not obvious because "next" point of Markov's chain may be not seen from the point under consideration. We have shown that corresponding estimator has final value of dispersion also for points on the surface.


  1. Ermakov S.M., Mikhailov G.A. Statistical simulation. Moscow, "Science" 1986,
  2. Calos M., Steinberg H. Bounded estimators for a llux at a point in Monte-Carlo. Nuclear Science and Engineering 1971, 44, 406-412.
  3. Voronin A.F., Khisamutdinov A.I. Estimatíons with additional casual sample for calculation of particles flux "in a point". Journal of Calculation Mathematics and Mathematical Physics,1985, 25, 8,1155-1163.

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