radiation from flames in furnaces - …...flow chart for the solution of a radiative transport...

RADIATION FROM FLAMES IN FURNACES

J. M. BEI~I[ AN[) C. R. ItOWARTtt

Departmettt of Fuel Tech,~ology and Chemical E,~giaeeri,tg, U,dversitg of Sheffield, She~ehl, England

Theoretical and experimental research on the radiative transport from flames in furnaces is reviewed. A "flow chart" of the procedure of solving a radiative transfer problem is presented. Banded and continuous emission in furnace flames is considered. Emission from particulate clouds is discussed in three groups according to the value of the Mie parameter X=rrd/X: for X<<I (soot in flames) where scattering is negligible, and calculated and measured optical constants are available, for X ~ I (cenospheres in flames) where scattering by individual particles is taken into account, and for X>>I (pulverized coal flames) where the scattering is multiple and anisotropic. Simplified furnace calculations: the well-stirred and the plug- flow furnace models and the zone method of analysis are discussed, together with approximate methods for the solutions of the transport equation when allowance has to be made for multiple scattering.

The experimental information smareyed is presented in two groups:

(a) Radiometric measurements on industrial size flames, and (b) Physical measurements of radiative properties of absorbing-emitting-scattering

media.

The experimental research reviewed includes data of radiant emittance and emissivity of flames as a function of design and operational input variables obtained at IJmuiden and discus- sions on the correlation of values of absorption coefficients determined from flame measurements with results of theoretical studies.

Further research is required on methods of predicting temperatures, gas-, and soot-concentration distributions in flames from input parameters; on the radiative properties of soots at flame temperatures, and of scattering characteristics of particles that are large compared with the wavelength of the incident radiation. Approximate methods for the solution of the transport equation for scattering media need checking experimentally.

1. Introduction

The purpose of this paper is to review recent advances in the field of radiative transfer in high-temperature systems, such as industrial furnaces and combustors. Reference is made to various areas of theoretical and experimental research that have made a contribution to predicting radiative heat transfer from flames. It is also intended to point to research areas in which further work is urgently required.

In solving problems of radiative heat transfer involving absorbing-emitting-scattering media, it is usual to assume that any small gas volume in the system is in thermodynamic equilibrium. The significance of this is that, when this assumption is valid, the fundamental laws of radiation such as Planck's law of spectral energy distribution, Wien's displacement law, and the Stefan-Boltz- mann law of blackbody radiation are applicable to the discussion of radiative transport. If thermo-

dynamic equilibrium cannot be assumed, radiant transfer problems become considerably more complex as the actual distribution of radiant energy with wavelength and the gas-absorption coetti- eients become functions of the population of the energy states in the gas, and detailed quantum statistical calculations are necessary for deter- nfining the emission and absorption of radiant energy. Conditions for radiative equilibrium are discussed by Gaydon and Wolfhard 1 in detail. In small clear flames, for example, the loss of energy by radiation may not be fully compensated for by collision processes within the flame, with the effect that, due to deactivation, the proportion of excited atoms and molecules falls below that determined from the Maxwell-Boltzmann distribution law. Other practical eases where non- equilibrium effects can be significant include those in shocks, rarified gases exposed to a strong radiation field, or systems in which transients of incident radiation are so rapid that there are

1205

1206 RADIATION FROM PRACTICAL FLAMES

Z LU b -

Z

Z O F - <

. < r r

LU

< _ J LO r

(1

2 - -

1 - -

1 2 3 4 5

WAVELENGTH - MICRONS

Fig. 1. Spectral emission of radiation from luminous and nonluminous flames at 1500 ~ K. (a) Black-body; (b) pulverized-coal flame (Ref. 71); (c) liquid-fuel flame (Ref. 70) ; (d) nonluminous exhaust gas from jet engine combustor (Ref. 72).

significant changes in incident radiation over periods of t ime commensurable with those required for electron and vibrational transition processes in the gas. 2-G In combustion processes in industrial-sized flames, the colliding molecules are not excited or ionized, because the ionization potentials of molecules or atoms are generally high and hence the chance of their excitation at normal combustion temperatures is low. Thus, industlial-sized flames can be regarded as systems in equilibrium with good approximation, and the

fundamental laws of radiation can therefore be applied to their discussion.

In furnaces fired by gaseous, liquid, or solid fuel the principal contributors to the radiation from the flame and from the fully burned combustion products are C02, H20, soots, and fly-ash particles. Figure 1 represents examples of infrared emission spectra of combustion products of various fuels compared with blackbody emission, illustrating the nature of these emissions (banded or continuous). The complexity of the radiative-

RADIATIVE TRANSFER PROBLEM

i I NON EQUILIBRIUM l_ [ CONDITIONS OF

�9 ,m----- SYSTEMS F I THERMODYNAMIC EQUILIBRIUM

t I 'PPL'CAT,DN OF FUNDAMENTAL LAWS OF RAD,AT,ON]

I ,NPU,S-I MATHEMAT,CA' I I ' FORMULATION OF I I [ I I A B_SO_.RP_T/ON SPECTRA_ TRANSPORT I I PARTICLE SIZE (d), SHAPE &l I ( ' ) MEASURE~ AS EQUATIONS I I VOLUME CONCENTRATION(N) I I f (p ,L ,T ) i OPTICAL PROPERTIES (n, k ) [ I (,t) PREDfCTED FROM SOLUTION OF l I &(n k) = f{~k,T) I I MOLECULAR STRUCTURE EQUATIONS FOR i { . . . . . . . I

A PROTOTYPE [ SYSTEM J

RADIOMETRY

MEASUREMENT OF

RADIANT ENERGY, TEMPERATURE & EMISSIVITY

MODEL LAWS OF f RAD AT VE TRANSFER i

J

PREDICTION OF

RADIATIVE TRANSPORT I FOR PROTOTYPE SYSTEM]

Fig. 2. Flow chart for the solution of a radiative transport problem for flame systems.

RADIATION FROM FLAMES IN FURNACES 1207

transfer problem is increased by the fact that banded and continuous emission from gaseous and particulate media are superimposed in most practical flames. A "flow chart" of steps in the solution of radiative transport problems is presented in Fig. 2.

2. Banded Radiation

The radiation from flame gases of conventional fuels is mainly due to carbon dioxide and water vapor. Both CO2 and H20 emit in bands of the infrared (CO: at 2.7 ~, 4.3 p, and 15 ~, and the H20 at 2.7 #, 6.3 p, and 20 #).~2 Radiation from nonluminous gases is dependent upon the number of molecules in the optical path and on temperature. Charts developed by Hottel 7 enable calculation of total emissivity of the gas e~ as a function of gas temperature To, and of the product of partial pressure and path length of the optical beam pL. These charts, covering ranges up to T=2800~ pL=0.001-1.7 m a t m , and pL= 0.002-6.0 m arm for C02 and H20, respectively, are mainly based on measurement both for CO2 (Refs. 8-10) and for H20 (Refs. 8, 10, 11). Radiation from nonluminous gases also can be computed from absorption spectra predicted from knowledge of molecular structure of the gas. '2-14 For purposes of determining absorptanee of C02 and H20, use was made of infrared band models in which tractable mathematical presentations were made of infrared bands consisting of many hundreds of spectral lines. Penzias and co- workers 15,'6 have fitted the statistical random band modeP 4 to experimental absorptance data and have determined band-model parameters for CO2 and It20 in the temperature range of 1273 ~ to 2400~

The significance of this semi-empirical method is that it offers improved accuracy and also that it enables extrapolation of gas emissivities to high temperatures and pressures--conditions not favorable for accurate experimentation.

The application of theoretical and experimental data of infrared-band spectra to the calculation of radiative performanee of combustion chambers is complicated by the fact that the contributions of different bands to the gas emissivity varies differently with the path length L. Kottel t7 sug- gested that the gas may be visualized as a mixture of grey gases and that the e~--L function may be represented in exponential series form

co= E a,,'[1-- exp (-- KnL ) ], (1) n

where a,~' is the fractional amount of a component

gas in the mixture having an absorption coefficient of K~.

A comparison of emissivities of a typical fur- naee gas, calculated from the basle emissivity charts of C02 and H20, with those obtained from Eq. (1) showed that the consideration of two terms in the exponential series (a single grey gas plus a clear gas with K = 0) gives an adequate answer in most practical cases. When four terms of the series have been considered, the curve so obtained fits the data of the basic enfissivity charts over a 2500-fold range of pLY

3. Continuous Radiation

The spectrum of radiation from solids such as furnace walls and particulate clouds in flames is continuous over a wide range of wavelengths.

3.1 Radiative Properties of Solid Particles in Flames

For any theoretical treatment of radiative transfer from luminous flames containing soot and larger solid particles, knowledge of radiative properties of the particles is necessary. The term radiative properties broadly covers the efficiency factors of absorption A, extinction E, and scattering S of a particle and, for purposes of this review, the angular distribution of the scattered intensity S (0) is also included.

The Mie theory is that describes the interaction of an electromagnetic wave with a spherical particle is the one generally used for determining the efficiency factors A, E, and S for carbon particles. ~9 The solutions of the Mie equations are given in terms of two parameters: the particle perimeter/wavelength ratio X=d@X, and the complex refractive index of the particle m= n(1--ik).

A concept generally referred to is the attenuation of a parallel beam after penetrating a distance dL into an absorbing/scattering medium. For a cloud of particles with varying sizes, the attenuation of a monochromatic parallel beam can be given as

IdL = [0 exp ( - - r)

--- Io expE cdL E E~xN.. (Trdj/4) ~. z

(2)

Extinction expressed by the factor Ez in Eq. (2) is due to absorption and scattering by the particles of the incident radiation. Because of the variation of the significance of scattering with the parameter X=rrd/X, three characteristic ranges of X are considered: X<<I, X ~ I , and X>>I.

1208 RADIATION FROM PI{ACTICAL FLAMES

3.1.1 X<<I (Very Small Particles Such as Soots in Flames)

Soot particles are very much smaller than the wavelengths important for thermal emission ir~ flames. 2~ For this case, scattering is negligible a,2~ and hence extinction equals absorption: E=A. The emissivity (absorptivity) of a cloud of particles can be calculated as a function of the mass concentration ~ and the optical constants of the particles: the real refractive index n and the absorption index k.

6x=l--exp[--~L 36(rip)f (n, k)/h], (3)

where

n2k f(n, k)= (n2+n2k2)+4(n~_n2k2+l). (4)

As shown by Eq. (3), the monochromatic emissivity in this size range is no function of particle size.

The values of n and k generally used ~2s for calculating 6x originate from experimental data on carbons in the visible range of the spectrum 25 theoretically extended into the infrared, u Experi- mental values of n and k obtained in the infrared at room temperature are now available for soo~s of varying carbon content 29 and have been theoretically extended to temperatures up to 2000~ ~

For determining the total emissivity eT, we write Eq. (3) in the form

ix = 1-- exp[-- cLKx] (3a)

and integrate ex over the whole spectrunl as

6r= foo~ / fo ~176

= 1-- exp[-- cnKm].

1(x, T) dX

(5)

I t was shown that substitution of the emission mean wavelength X0.5 into Eq. (3) yields good approximate values of 6T. The emission mean wavelength is given by },G.5 T=0.411 cm ~

Correlations of theoretically predicted flame emissivities and experimental data obtained on industrial-sized flames are discussed in Sec. 5.2.

3.1.2 X ~ I (Cenospheres, Chars, Fly Ash in Flames)

Scattering is no longer negligible. Calculations of the attenuation coefficient by Foster ~ showed that neglecting scattering in optically thin clouds c~n cause errors up to 50%.

Because scattering for the X-'-1 range can be considered isotropic/s a simple correction for the effect of scattering on 6x can be made.

6x=[1--exp(--~LK• (6)

3.1.3 X>>I (Pulverized Coal, Chars, Fly Ash in Flames)

Scattering is commensurable with absorption and is anisotropic. 32 Extinction E and scattering S can be calculated from simple relationships of geometrical optics which describes the scattering in terms of diffraction reflection and refraction. The value of E ten<is toward 2 and becomes independent of particle size, the absorption A nlay be taken as the emissivity of a plane surface, and the scattering S then can be determined as S=2-A. While S is independent of particle size, the angular distribution of the scattered intensity S(O) is dependent upon the size and shape of the particles and is forward directed. Because of this anisotropic nature of the scattering, measurements of attenuation coefficients in pulverized coal flames using narrow-angle instru- ments are open to error, a4

For predictions of radiative transfer, values of the scattering albedo co (ratio of the scattering to total extinction) and the phase function p(O) (normalized intensity distribution for single scatter) need to be known. Scattering intensity distributions of suspensions of coal particles have been measured by Hodgkinson, a~ from which the phase functions can be directly determined.

4. The Calculation of Radiative Transfer

With the information on the radiative characteristics of combustion products and solid surfaces as considered in Sees. 2 and 3, and by applying the laws of radiation geometry, the radiative heat transfer from the combustion products to heat sinks and walls of the combustion chamber can be calculated (see Fig. 2).

The emission of radiation from a volume of emitting absorbing fluid of specific shape to a specified portion of its bounding surface can be given as 17

f[ fv E4A.: (1)• v)dv]x Ed,J

x [exp(- (7)

Here the first bracketted term is: Total emission from volume dV; the second is: Fraction towards

IIADIATION FROM FLAMES IN FURNACES 1209

element of surface; and the third is: Fraction of emission transmitted towards element of surface.

The above integral can be solved for various enclosure shapes and for cases when the values of the coefficients E, and Az, and also the spatial distribution of the concentrations, are known. I t holds for cases of banded emission and emission from nonscattering particulate clouds, and for the case of a particulate cloud of small particles in which intermediate size particles are present as a small fraction of the total mass.

Because of the extensive computations required for a rigorous solution and the lack of some of the physical input data, combustion engineers relied on methods of calculation based on simpli- fying assumptions. The most widely used of these methods are the "well-stirred furnace model," the "long furnace model," and the "zone-method analysis."

The well-stirred furnace model is based on the assumption that mixing in the furnace is so effective that the gas temperature and concentration is uniform throughout the furnace volume. Hence, the mass of gas within the furnace can be assigned a single radiation temperature T,, which is the same as the exit-gas temperature. Hottel, in his Melchett lecture, ~ derived a relationship between nondimensional groups representing the heat-transfer efficiency or the proportion of input heat transferled in the furnace as a function of the input enthalpy, the heat-sink temperature, and a so-called total exchange area. This latter is a factor that incorporates flame and sink emissivities, and the fractional coverage of the wall by the sink. The relationship derived from heat balance considerations is given as

Q,D+r 4= ( 1 - Q~)4, (8)

where 0~ is the reduced furnace efficiency

QTR/Qi., r the reduced heat-sink temperature T~/TAF, D the reduced firing density

and (~in/ (~S)o'T AF 4,

AT <as)= (1/eo) + (1/Ce,) - - 1

and C is the coverage factor AJAT. Some of the important features of the "well-

stirred speckled-walled grey gas combustion chamber" can be seen in Fig. 3 where the curves represent Eq. (8) drawn for different values of the heat-sink temperature r.

(i) As the firing.rate D decreases the heat- transfer efficiency Qr increases and approaches the limit of 1--r as D--if).

(ii) When the furnace wall is completely covered by heat sink (C--+-- 1) and the heat-sink emissivity is high so that Ce,--~l, D becomes inversely proportional to eg. This means that for combustion chambers with high-combustion intensity (gas turbines, rockets), the heat transferred is directly proportional to the flame emissivity, while in furnaces with low firing rates the effecL of the flame emissivity on the heat transfer is slight.

(iii) When the refractory wall is sparsely covered by sink and/or the sink emissivity is low, the flame emissivity has only little effect oil the heat flux front the flame to the heat sink.

The long furnace model. The well-stirred furnace model yields the relationship between heat-transfer efficiency and important design variables, but does not give information on the heat flux distribution in the furnace.

Thring ~7 has developed an analysis based on the long furnace model. I t is assumed that the furnace

0 0

i z LU

LL U3

�89 LIJ (J

2 uJ r~

1"0

0'8

0'6

0"4

0.3

0"2

0-1

0-06

0"04

0.01

- - T = 0

_ _ % = 0 " 4

"~ :0 -6

"~: 0-7

I ~ soA.,.o P,TS

I I I I J 0'I 1"0 2"0 4"0 6-0 10

~REDUCED' FIRING DENSITY, D Fig. 3. T]mrma] perfornl'mce of a "well-stirred" furnace.


is long compared with its dimensions normal to the direction of flow, and that the gas temperature varies only along the gas path, but is constant across any cross section of the furnace. By setting up a heat balance for a short element of length of the gas path and integrating it along the furnace, the exit-heat losses have been determined. By considering the heat balance of the furnace, and by introducing dimensionless parameters, a relationship for the heat-transfer efficiency, as a function of varying heat input, of furnace wall, heat loss, and heat-sink temperature was derived. The comparison of the predicted data with those measured in industrial furnaces showed good agreement and have yielded information on the effect of design variables on furnace efficiency, s7 A similar method for determining the gas temperature distribution was proposed by Gurwich and Blokh ss and quoted by Dolezal. s9 Allowing for the nature of temperature-distance curves--they rise to a peak at some distance from the furnace entry and then the temperature drops along the furnace--they represent the T 4 - X function as

O 4= TVTAF 4-- exp (--o~X)-- exp (--/3X), (9)

where X is the dimensionless length, and a and/3 are constants dependent upon furnace cooling and on the variation of heat-release rate along the furnace respectively.

From Eq. (9), gas temperature at the furnace exit (X= 1) can be given as

OE= TE/TAF = [-exp (-- a) -- exp (--/3)]~/4, (t0)

and the position of the maximum flame temperature as

X,,= ( l n a - l n ~ ) / ( a - ~ ) . (11)

The long furnace model often referred to as the plug-flow combustor model was used by a number of research workers for both combustor design purposes ~7,4~ and also for the development theories of thermal flame propagation in strongly absorbing dust clouds. 42-~

The zone method of analysis. With increasing unit capacity of industrial furnaces and combustors, there is great interest in the detailed heat-flux distribution in the furnaces, information that cannot be obtained from the well-stirred and long-furnace-model calculations. Improved methods of predicting flow patterns and the progress of combustion and, thus, the concentration of the absorbing emitting species in the furnace enabling the use of the zone-method analysis 46-49 the most

useful procedure available for calculating detailed furnace performance.

The volume and surface of the furnace is sub- divided into zones assumed to be of uniform temperature and concentration, the number of which ~ill depend oll the accuracy required of the solution. Equations are then written for the energy balance of each zone. The setting up of these balances necessitates the description of emissivity and absorptivity of combustion products by the weighted sum of grey gases, and the calculation of so-called exchange-area coefficients, the latter of which represent the radiative interchange between two finite zones of gas and/or surface of any shape and relative dispo- sition. The exchange-area factors are evaluated between all zone pairs.

The simultaneous solutions of the energy- balance equations containing unknown temperatures yield the temperature distribution in the furnace. Substitution of these temperatures into equations containing unknown heat fluxes per- mits the calculation of wall heat-flux distribution. A check on the convergence of the solution of heat-balance equations is provided by the comparison of the sum of fluxes to the wall with the decrease in total enthalpy along the gas path.

In the zone-method analysis a complicated integral equation is replaced by a series of alge- braic equations. The solution usually requires the use of high-speed digital computers.

The further development of the zone method will greatly depend upon the progress that can be made in predicting velocity and temperature patterns in furnaces from input and design parameters.

For the case of multiple scattering, the mathematical description of the heat transfer from an absorbing emitting scattering medium to its bounding surface is more complex. The optical depth r may be considered as a criterion of multiplicity of scatter: if r~0.3 , i.e., e>_0.25, multiple scattering theory has to be applied, s~

The general integrodifferential equation for the radiant energy balance along a pencil beam can be written as

d~(r,O,~)_ I(r,O,r dr

f0 ~Tr f0 7r + (r I (r', 0', r (0, q~; 0', gb')

XsinO' dO' de'. (12)

Here, the left-hand expression is the net change in intensity over an optical depth dr, and the right-hand expressions are de-


crease in intensity due to a t tenuat ion+increase in intensity due to thermal emission+ increase in intensity due to scatter into the direction 0,6 from all other directions.

The mathematical task of solving the transport equation EEq. (12)-] is considerable even when the physical input data are available. For simpli- fying the analysis, it is usual to assume that the scattering is isotropic and to treat the problem as one dimensional. Merits of some simplified solutions St-s5 have been considered by Tien and Churchill, 56 and the effect of anisotropy on the solution has been discussed by Hottel e t a l . 57 and by Evans et al. 5s Approximate solutions closely relevant to the calculation of the effect of scattering in burning particulate clouds have been presented by Love and Grosh s9 and by Spalding3 ~ Calculating the scattering function from Mie theory for the unidimensional system of carbon particles between partially reflecting surfaces, Love and Grosh concluded that the assumption of isotropic scattering gave good approximate results for the over-all heat transfer. Since the size parameter considered in these studies was between X=rd/X= 1+6, it remains to be determined whether the assumption of isotropic scattering can be made for pulverized coal flames with a size parameter of X~-40.

Field et al3 s have applied the Schuster- I tamaker "two-flux" method 6~,62 proposed by Spalding r176 for determining the temperature distribution across a slab of burning pulverized coal between cold plane-parallel walls. Their calculation showed a distinct effect of scattering: the temperature distribution was more peaked as a result of scattering and the peak temperature in the center of the slab was closer to that computed for "black" particles then the temperature peak of a slab containing particles with an emissivity less than unity. The attraction of the Schuster- Hamaker technique is in its simplicity. A comparison of predictions by this simple method with those from more-rigorous theory would be of considerable interest.

5. E x p e r i m e n t a l

Radiometric measurements are discussed in two groups: (Sec. 5.1) Measurements on optically thick flames for determining radiative heat-transfer parameters as a function of design and operation variables; and (Sec. 5.2) Detailed measurements both outside and within flames with the objective of determining more fundamental flame properties by comparison of measurement data with theoretical predictions.

'-i �9

:E W t-, z ,< F, < ,,y

0 I-,

2 L 8

4 - -

0 I 1 I I I

0 . 8 - - a / ~ ~ b

0 . 6 - -

C

0.4--

o.2 I I l [ r 0 1 2 3 4 5

D I S T A N C E F R O M B U R N E R - M E T R E S

Fig. 4. The effect of carburetion on the emissivity and radiation from oil/coke-oven gas flames of varying mixture concentrations. (a) 100% oil/0% coke oven gas; (b) 40% oil/60% coke oven gas; 20% oil/ 80% coke oven gas; 0% oil/100% coke oven gas.

5.1 Radiometric Measurements on Industrial-Sized Flames

Since the beginning of the work of the Inter- national Flame Research Foundation at IJmuiden (Holland) in 1948, systematic measurements were made of radiant emittance and flame emissivity of gas, oil, and pulverized-coal flames. The measurement method most generally used in these trials is the "modified Schmidt method, 'm an emission-absorption method originally developed by Schmidt 64 for monochromatic radiation. The total absorptivity of the flame for a given blackbody background temperature can be determined from two readings taken with a narrow angle total radiation pyrometer: radiation from the flame alone (cold background) R1 and the com- bined radiation of flame and hot blackbody background R2. The effective flame absorptivity (emissivity) can then be given as

eT=I--E(R2--R1)/oTB4-]. (13)

Observations of the radiation from industrial-


"5 6 O

,g

I

h i r Z < t -- I -

:E ILl

I--

14

12

10

8

6

Z <

4 <

. . J

2 O

I I I I I I 0 1 2 3 h 5 6 7

DISTANCE ALONG F L A M E - M E T R E S

Fig. 5. The effect, of input particle size and coal rank on the total radiation from pulverized-coal flames. (a) Bituminous coal 70%<76 t* diameter; (b) Anthracite coal sized 100% <76 #; (e) Anthraeit,e 60% <76 t*; (d) Anthracite 20% <76 t*.

sized turbulent diffusion flames were interpreted to provide empirical curves of flame emissivity and radiant emit tance for the effect of variables, such as fuel-jet momentum, C / H ratio of the fuel, oxygen enrichment, and particle size and coal rank in pulverized-fuel flames. Figure 4 presents the results of an investigation in which coke oven gas was mixed with liquid hydrocarbon fuel to show the effect of the C / H ratio of the fuel on the radiation from and the emissivity of the flame. ~ These results are of particular interes~ to combustion engineers for their applications to the design and operation of gas-fired furnaces and boilers. Another set of typical results by I .F.R.F. is shown in Fig. 5, illustrating the effect of fineness of pulverized anthracite and of the volatile combustion on the radiation from the flame. Radiant emittance R~ is increasing with increasing fineness of the anthracite and the peak radiation is translated towards the burner. For a bituminous coal the volatile combustion associated with soot formation intensifies these trends. ~ Detailed results of the IJmuiden furnace trials, providing a wealth of data on the influence of

input parameters on flame radiation, are available in published reports of the I .F .R.FY

5.2 Mcasurcmctds of Radiative Properties of Luminous Flames

The Schmidt method 64 was used by a number of research workers 2~'2s':~5 to determine the mean absorption coefficient K,, in sooty flames. Effec- tive flame emissivities of liquid-fuel flames were correlated with soot-concentration distributions measured along the path of the optical measurements. The following relationship was used to determine the value of K,,:

ev=l--exp[--Km foLCdll(1--e~). (14)

Computed values of the parameter 36 (Tr/p)}~ f(n,k) [see Eqs. (3) and (4)] , plotted as a function of n and k, ~9 are presented in Fig. 6, and the ranges of n and k are shown where experimental or ~heoretical data are available.


Products of the experimentally determined ab- | sorption coefficient K~ and the emission mean wavelength M.~ are compared with the theo- ~0 retically predicted parameter in Fig. 6. Experi- mental values of K~ determined from pressure-jet oil flames at IJmuiden ~s and Sheffield ~ gave two :- distinct values for two different modes of flame s stabilization. For the case without stabilization ~ a near the burner, high values of K,, were obtained ~K,,= 0.03, X~=2.45~ (Ref. 28), and K,~= 0.032, Xm=2.79 # (Ref. 27)~, approaching the theo- ~E s retical maximum for small particles ( n= l . 0 , o_~e k=1 .6 ) . The lower values of K,~=0.014 and ~ 0.021, obtained in stabilized flames, are close to N the range of known values of n and k (Fig. 6). ~ �9

Figure 7 is an electron micrograph showing - ~ ~ soot particles from a plug-flow type oil flame ~ :~ (without stabilization) .~ The graphitic hexagonal o g structure of the soot particles may account for < the apparent high values of n and k associated ~ ~= 2 with the high value of K~ for this flame (Fig. 6). :~ I t is noteworthy that the graphitization of soot particles occurred here at temperatures very much lower (1600%1700~ than the range of 2500 ~ 0~ 3000~ reported by Walker. ~s

Measurements traversing the flame by a water- cooled pyrometer probe were made at IJmuiden to determine the contribution of radiation from finite layers a]ong the optical beam. Comparison of results of these measurements with traverses predicted from known temperature and concen-

[ ~ HOWARTH. (29) HOWARTH et al. (30)

[]T~STULL AND PLASS. (24)

IBIRICU.(27) ASHTON.(35~ - - IBIRICU.~

0.4 0-8 1'2 1-6 2.0 ABSORPTION I N D E X - k

Fig. 6. A comparison of calculated and measured absorption coefficient parameters 36(~/p)f(n, k) for clouds of smM1 particles. The shaded area refers to the regions of experimental values of optical constants of carbons.

iiiii!i i!i ii? iii? ii! �84 ~ ~ ~ ~ ~ ~ ~: ~ : ~ ~ ~ ~;~ ~ ~ : ~ i ~ : ~ ~ ~ ~ ~ ~ ~ ~ ~:~ Fig. 7. An electron micrograph ~)f graphitized soot particles from liquid-fuel flames

at t700~ (Ref. 27).


tration distributions, and by using the appropri- AT, As ate value of the absorption coefficient, showed good agreement39 A

Information on spectral absorptivity in industrial-sized flames is scarce. Weeks and Saunders 7~ have obtained spectral radiant emittance values and emissivities for liquid-fuel flames c in a gas-turbine combustor. They warned that the application of the Schmidt method to flames C with large temperature gradients can lead to d erroneous values of emissivities. D

Penzias 71 has recently made spectral measure- E ments of the radiation from pulverized-coal flames in the IJmuiden furnace. The information can be expected to provide useful data of spectral absorption coefficients measured at flame temperature.

6. Conclusions

Analytical solutions of radiative transfer problems are difficult even for systems of simple geometry. For many particular cases, however, simplified furnace model calculations, such as the well-stirred, the long furnace model, or the zone method of analysis suffice, the choice of type of the model depending upon the details of the solution required. The zone method can 3deld N detailed heat-flux distribution in the furnace p when the spatial distribution of gas temperature and of the concentration of the absorbing emitting p (0) media are known. The application of the zone method to luminous flames is made difficult by Q~ the uncertainty of the value of the absorption coefficient of soots. Further research is required S(0) on the effect of the composition and physical properties of soots (C/H ratio, agglomeration) on their optical properties at flame temperatures. Information is lacking also on the rate of for- S marion of soot in hydrocarbon flames, which is required for the prediction of soot concentration distribution in luminous flames.

For strongly scattering media, such as pulver- T ized-coal flames, the zone method of analysis V cannot be applied at present; therefore, solutions X of the transport equation have to be sought. Physical input data required include the radiative a, r characteristics of coal, char, and fly-ash particles e i-w, p(0), n, k, size and shape-]. The use of 0,4~ approximate methods (e.g., the two-flux method) can simplify the mathematical problem. Experi- 0 mental check of data so predicted is necessary ), for determining the magnitude and nature of p error due to these approximations, r

7. N o m e n c l a t u r e r

a'() weighting factor for calculating absorp- co tivity (emissivity) of gases, dimensionless ~2

(GS)

I

I(~, T) K

L m

area of a surface zone; T refers to total and S to sink area absorption, the ratio of energy absorbed per unit time to the energy incident on the projected area of a particle per unit time, dimensionless particulate concentration mass per unit volume, ~ refers to mean coverage factor As/AT diameter of the particle reduced firing density, Eq. (8) extinction, the ratio of energy absorbed and scattered per unit time to the energy incident on the projected area of the particle per unit time, dimensionless total interchange area between a gas and surface zone intensity of radiation (function of position) Planck's law, distribution function gas, solid absorption coefficient, re- ciprocal length path length along a pencil beam complex refractive index m= n (1-- ik ) , where n is the real refractive index and k the absorption index number of particles per unit volume partial pressure of radiating component of a gas phase function, normalized intensity distribution for single scatter reduced furnace efficiency QTR/QIn, Eq. (s) scattered intensity coefficient, the ratio of the light flux per unit solid angle in the direction 0 to the flux geometrically incident on the particle scattering, the ratio of energy scattered per unit time to the energy incident on the projected area of the particle per unit time, dimensionless tempera ture volume size parameter, X = 7rd/~; dimensionless length, Eq. (9) constants in Eq. (9) emissivity polar and azimuthal angles defining pencil-beam position dimensionless gas temperature T/TAF wavelength of radiation particle density, g/cc reduced sink temperature T~s/TAF in Eq. (s) optical depth, product attenuation coefficient and path length albedo of scatter, ratio of scatter to extinction S//E solid angle


Subscripts

AF refers to adiabatic flame temperaLure E refers to exit gas g refers to gas in refers to input n number of gas zones, also general (nth)

term in a series expression of emissivity (absorpt ivi ty) of gas

m refers to mean S refers to sink T refers to total TR refers to transferred z refers to zth particle

R E F E R E N C E S

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COMMENTS

H. C. Hottel, Massachusetts Institute of Tech- nology, Cambridge, Mass. The author has stated that the zone method of furnace performance prediction is not suitable for problems in which radiation scatter is important and that there is then the need to solve the transport equation ab initio. I disagree. The exchange area, (GG } or (GS}, that appears in the zone method is an expression of the radiation, per unit difference in black emissive power of the members of a zone pair, that goes from one of them to the other by any means. Scatter can be included, though admittedly the calculation of exchange area is enormously more complicated. There- after, the establishment of the temperature field and the wall-flux distribution is unaffected.

J. M. Bedr. In principle, the zone method of analysis can be extended for the detailed com- putation of radiative transfer involving strongly scattering media. Such computations, however, are not practicable at present because of the considerable complication in the calculation of the "exchange areas" as mentioned by Hottel. While the zone method of analysis is, in general, the most satisfactory method for detailed compu-

tation of heat-flux distribution in enclosures, both from the points of view of accuracy required for practical problem solving and economy of calculation, approximate solutions of the transport equation are worth considering for systems with strongly scattering media, because of increased complications and rising expense in computer time for calculating the "exchange areas".

H. C. Hottel. May I nmke a plea that, in review papers giving emissivity versus furnace length, the generality of the result be increased by using, instead of actual length, its dimensionless equivalent, such as the square root of the momentum rate divided by a dominant entrance velocity?

J. M. Bedr. We agree with Hottel that the use of dimensionless length parameters in Figs. 4 and 5 would have been preferable. In the experimental series represented by Figs. 4 and 5, respectively, the input momentum flux was maintained constant so that an equivalent nozzle diameter could be calculated from the ratio of

llAI)IATION FROM FLAMES IN FURANCES 1217

the mass-flow rate and the square root of the product of momentum flux and density for both eases. The value of the equivalent nozzle diameter for the results given in Fig. 4 is do' = 0.44 m, and for those in Fig. 5, do' = 0.156 m. The abscissa in these figures thus can be expressed in terms of equivalent nozzle diameter, instead of meters as given in the paper.

M. W. Thring, Queen Mary College, London. The object of flame-radiation studies is to provide designers with formulae for calculating the performance of a flame when they determine the input variables (fuel type, rate of firing, bm'ner and air register shapes, combustion-chamber size and shape). I believe that Hottel's zone method now gives a satisfactory calculation technique, that Be~r's paper ahnost completes the relationship between soot concentration and emissivity, but that the principal weakness is that we have no generalized empirical relationship from which the soot concentration can be predicted.

J. M. BeOr. We agree with Thring that our lack of knowledge about rates of soot formation in practical flames is the most serious obstacle to predicting radiative transport in combustors from design and operational input data. An empirical relationship giving soot-concentration distribution as a function of input parameters, such as jet momentum flux and fuel composition, would be of great value even if it was valid only for simple geometry and for a limited range of the variables. However, it is felt that, because of the complexity of the process the chances of developing a useful empirical relationship are, at present, rather slim. I t is hoped that the better understanding of the processes of nucleation and growth of particles in flames may help in the better formulation of experimental conditions for a future study leading to such an empirical relationship.

$

J. Rogier, Gaz de France. In the range of flame temperatures that we meet in industrial furnaces

(500 ~ to 1700~ I think the structure of soot formed as a result of vapor-phase cracking, is amorphous and not graphitie.

The samples we took in Toulouse inside industrial natural-gas flames and also heavy fuel- oil flames show, without a doubt, the amorphous structure of soot. This can be seen by micro- diffraction diagrams.

A. M. Godridge, C. E. G. B., Marchwood. With regard to the graphitized soot, I would be interested to know more about the test conditions and sampling technique. We have found that similar--although mostly larger--cokey ma- terial (I hesitate to say graphitized) can be obtained if the soot is not quenched rapidly enough in the sampling probe.

J. M. Be~r. The soot samples showing a graphitized structure were taken by Ibiricu using an Umuiden-type probe for soot sampling, in which quenching was fast (about 5 X 10s~ and the soot sample was collected in a sintered bronze filter close to the probe tip. I t is unlikely that the sampling conditions have contributed to the graphitized nature of the soot.

A. M. Godridge. Figure 3, which is taken from a paper by Hottel, would be more useful, I think, if it included data for water-tube boilers, since some 90% of the electricity produced in the U.K. is from steam generated in water-tube plants.

J. M. Be~r. Since the reduced firing density, the abscissa of Fig. 3, is a generalized form of heat-input rate per unit area of effective heating surface, the values representing large power- station boilers will not differ significantly from those of smaller boilers given in the graph by Hottel. This is because an increase in the heat input per unit area of built-in heating surface for larger boilers is compensated for by the improved radiating ability of the furnace gases when the combustion chamber is larger.

radiation from flames in furnaces - …...flow chart for the solution of a radiative transport...

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