Structure and similarity of nitric oxide production in turbulent diffusion flames

Eighteenth Symposium (International) on Combustion

STRUCTURE

The Combustion Institute, 1981

AND SIMILARITY OF NITRIC OXIDE PRODUCTION TURBULENT DIFFUSION FLAMES

IN

N. PETERS AND S. DONNERHACK

Institut fiir Allgemeine Mechanik Rheinisch-Westfiilische Technische Hochschule Aachen, Germany On the basis of Favre-averaged equations a similarity solution for the flow field and the mixture field is derived. Using the p.d.f. (probability density function) formulation and an asymptotic expansion for large activation energies of the NO reaction, an algebraic expression for the mean turbulent NO production rate is obtained. The result explains the "rich shift" of NO production by the influence of mixture fraction fluctuations. Integration over the flame yields a formula for the emission index. In the experimental part, the total NO production in vertical diffusion flames of H z, CH4, C3Hs, natural gas and a C O / H a mixture was measured. When the experimental emission index is compared with the theoretical index, a dependence on the diameter appears. This points to an influence of the turbulence length scale. Large coherent structures may be responsible for a reduction in NO production.

1. Introduction

analysis of natural gas flames. Theoretical papers that threat NO formation in cylindrical diffusion flames are due to Quan [5], Kent and Bilger [6], Bilger [7] and Janicka and Kollmann [8]. An attempt to explain the experimentally observed Reynolds number dependence of the emission index was made by Bilger [9]. The combined influence of the Reynolds number and the Froude number was also considered by Buriko and Kutsnetsov [10] who claim to be able to explain these effects by gaseous radiation alone, at least for hydrogen flames. The present paper summarizes the theoretical and experimental efforts of the authors [11]-[14] aimed at deriving a closed form theoretical expression for the emission index and verifying it experimentally.

Considerable advances have been made over the last decades in our understanding of the kinetics of nitric oxide formation in gaseous diffusion flames. It has been recognized that there are two major contributions: the thermal NO formed through the extended Zeldovich mechanism, and the "prompt NO" mechanism wherein hydrocarbon fragments attack bimolecular nitrogen, producing atomic nitrogen, cyanides, and amines, which subsequently oxidize to nitric oxide. Which one of these mechanisms predominates depends mainly on the flame temperature. Prompt NO is not very sensitive to temperature, it contributes between ten to thirty ppm to the total NO production in hydrocarbon flames, while thermal NO may contribute up to several hundred ppm. It is clear that the high NO levels that occur in practical systems can only be reduced by reducing thermal NO formation. There are several papers on NO formation in round vertical diffusion flames. Lavoie and Schlader [1], and Bilger and Beck [2] have performed systematic measurements of the NO emission index for hydrogen flames for constant Reynolds number and constant Froude numbers, respectively. Takagi, Ogasawara, Fujii and Daizo [3] studied the effect of nitrogen addition and preheating the air in hydrogen and propane flames. Recently Paauw, Stroo and van Koppen [4] made a theoretical and experimental

2. Governing Equations In the present paper the following approach will be adopted: 1. The turbulence balance equations are derived using density-weighted averages rather timemean averages [15]. A quantity a is written as a = pa/~

+ a" = fi + a"

(1)

where the dash denotes a time average. Note that by this definition d' r 0 but pa" = 0 [16], [17]. 33

34

COMBUSTION GENERATED POLLUTION

2. A density transformation will be used to derive a set of equations that has the same form as their constant density counterpart. 3. Rather than using second order modelling which would make the equations analytically intractable, empiricism will be introduced in two consecutive steps: First the concept of a constant eddy viscosity for a constant density jet, applied successfully by Sehlichting [18], will be used. Second the effect of density changes on the flow field will be accounted for by using the flame length formula of Hawthorne, Weddel and Hottel [19] to determine the Chapman-Rubesin parameter that appears as an outcome of the density transformation.

one obtains with ti = v,,Fd~j,

~6r = - p|

+ F - Fjq)

(7)

the equations IF

0F~

OF O ( ~ _ ) ]

an

O (FF

/

\n/

+ ( ~ o ) 3"qRe'2sr (P|

(8)

The steady state time-averaged boundary layer equations for a cylindrical turbulent diffusion flame for large Reynolds numbers are given by: continuity - - + - - + - Ox

r

=0

Or

momentum

(2)

~ t i - - + ~6 . . . . 8x

Or

v,

+g(p| - ~ )

r Or

Here r = 2/Z~ stands for the mixture fraction normalized by that on the centerline. A modified Chapman-Rubesin parameter has been introduced 1111 C = ~2v, r2

/( I ) 2p|

~rdr

(9)

o

fuel element mass fraction (mixture fraction)

~,(, -

+

Ox

~~

Or

....

v ,r

Pr r Or

(3)

where vt, is the turbulent viscosity of an inert let, taken as a reference viscosity. The turbulent viscosity may be assumed to be a constant [18] v,, = uodo/Re,,

In these equations the turbulent Prandtl number has been assumed constant and the Lewis number equal to unity. The fuel element mass fraction Z is the sum of the element mass fractions contained in the fuel. Under the assumption of Lewis number unity, the element mass fractions and the enthalpy are linearly related to Z. A similarity transformation which includes a density transformation is introduced [11] (cf. [20] for the planar jet).

~=x+a,

r" \'"~ / ",1= 2 }o~,lp.rdr) / ~

(4)

With the stream function defined by ~,ar = al,/or,

~r

=

-

0,/0x

(5)

the continuity equation is satisfied. Introducing the nondimensional stream function F(~,'q) = r174

(6)

Re, = 70

(10)

A similarity solution exists only for a constant value of the Chapman-Rubesin parameter, a zero freestream velocity and in the limit Fr ---* oo. Then one obtains F = C-t2~2/(1 + (~pl)2/4)

(11)

r = (1 + (yq)2/4)-~P'

(12)

where the constant of integration ~/~

3 Re~

Po

64

p| ~

(13)

is obtained from the requirement of momentum conservation. The conservation of the mixture fraction on the centerline gives l + 2 P r Po Re, d o 2o = - -

32

p| C ~j

(14)

Defining the flame length L by the position where

STRUCTURE OF NITRIC OXIDE PRODUCTION the mixture fraction on the centerline has the stoichiometric value Z,,, one obtains (~) F--|

=--Re' ( l + 2 P r ) 1 po 32 Z,, p - ~

35

I a-10-~

30

SNo

(15) 3

The comparison of this result with the flame length formula of Hawthorne, Weddel and Hottel [19] for negligible buoyancy yields for Pr = 0.71 a condition for the Chapman-Rubesin parameter

c = (0o0,,)

1/2

20

2

/p.

(le)

Thus the turbulent flow field and mixing field in the similarity region of the jet may be calculated.

10

1

3. The Turbulent Mean NO Production Rate It will be assumed that the combustion reactions are locally in chemically equilibrium and that the only kinetically controlled process is the production of NO. If one assumes that the first reaction of the Zeldovich mechanism O +N2~NO+

I/)NO SNO ~ - -

p

P 02

MN2 ~

BNo =

exp -

(17)

5.74 101. (cma/mol)*/2/sec, ENo = 66 900 K

Due to the equilibrium assumption for the combustion reactions the concentrations, density and temperature and thus the NO production rate are functions of the mixture fraction only. The turbulent mean production rate is expressed as

0.06

0.98

0.1u Z

FIG. 1. NO-reaction rate and p.d.f, for a hydrogen-air mixture

mixture fraction. In Fig. 1, SNo(Z) and P(Z) are plotted over Z for a hydrogen-air mixture. The production rate has a very sharp peak close to the point Zb where the equilibrium temperature is maximum. This is due to the high activation energy of the reaction rate, which makes the production rate decrease rapidly as the temperature decreases. As in [12] we make use of this fact by using a large activation energy expansion to evaluate the turbulent mean reaction rate. A similar approach was made by Lififin [21]. The independent variable is stretched around Z b

1(88 )

4=--

-1,

E

(19) =

1

~.o =

0.04

N, N + O 2 ~ N O + O

is rate determining and that O is in equilibrium with 02, the NO production rate is [11]

YN 2 = BNO M N O - -

0.02 Z b

PS = 0 Io SNo(Z)P(Z)dZ

(is)

where r'(Z) is a probability density function for the

E.od2T/dZ

2 .

A Taylor expansion of the temperature, the product of the density and concentrations and the p.d.f. around Z b yields

T = T b + ~2Z~(d*T/dZ2)J2

yN~(pyo2) 1/2 = YNzb(PYo2)b ,/~ + ~Zb~IdY~(PYo,)'/*/dZlb P(Z) = I)(Z~) + ~Zs~(dD/dZ) b

(20)

36

COMBUSTION GENERATED P O L L U T I O N

If this is introduced into Eq. (18), the turbulent mean reaction rate is in the limit e ~ 0

WNo=PSNo'bf'(Zb) eZbIi|

exp(--~2)(l + A~)d~

= ~SNo.~P(Z~) ~Z~r '/~

i15

(9.])

Thus the reaction rate cuts a very narrow region out of the p.d.f, close to Z = Z b and only this value will be needed. The p.d.f, can be related to the first n moments of Z, if an n-parameter functional form is assumed. Thus the turbulent mean NO production rate is a function of kinetic parameters contained in SNO.b and c, and via P(Zb) of the turbulent mean mixture fraction and the higher moments. In Fig. 2 S~_ plotted for a hydrogen-air flame over Z with Z "2 as a parameter. Here a beta function p.d.f, has been assumed [12]. It is seen that for growing fluctuations, the turbulent reaction rate spreads over a larger region of Z and that the maximum shifts to the rich side. This rich shift has been observed experimentally by Bilger and Beck [2]. It can be attributed to the influence of turbulent scalar fluctuations. For hydrogen and methane-air flames the "rich shift," i.e. Zm,~ at which the maximum mean reaction rate occurs, is plotted over ' ~ in Fig. 3.

4. The Total NO Production Rate For practical purposes the total NO produced by a flame is of primary importance. The total produc-

4'102 ~NO z~ ' 2 o

[

H2

o

15 <_

1.0 i

0.5-

0 106

10 5

10 '~

103

1

)2

FIe. 3. Integral H and "rich shift," hydrogen and methane-air flames tion rate in the flame is obtained by integration over the radial coordinate and the flame length. At the flame length the line of stoichiometric mixture reaches the axis. Beyond this point, NO production takes place around the axis only under fuel-lean conditions in the mean. This contribution is negligible compared to the production further upstream in the flame, which takes place in a circular source at a finite radial distance, predominantly under fuel rich condition (cf. Fig. 2). Using the similarity transformation, the total production rate is

Ii =2~rp~, J

L~2 If S,qd,qd~ (24) o

With Eqs. (12)-(15) and (21) the integral over -q for Z b - Z,, becomes

I| Snd'q

3

0

0.02

0.04

0.06

0.08

o11o

SNo.b~'n'/2(~lL)-t/2P'Hl (er7~)

(25)

The integral

H = FIc. 2. Mean reaction rate for a hydrogen-air flame

=

I"

~(Z~)(~/Zb)-'~P'+'>/2e'~/2

o

(26)

STRUCTURE OF" NITRIC OXIDE PRODUCTION on the right side of Eq. (25) depends on the Prandtl number, the value of Z at the centerline, and via P(Zb) on Z . According to Fig. 2the upper boundary may be replaced by Zc = 1, except for large fluctuations and at positions close to the flame length, where Zc approaches Z~. The integral H has been plotted in Fig. 3 over _ . ~L , , , 2 rro r ~"~c = 1 and Pr = 0.71. Measuretlae variance ments in flames by Kennedy and Kent [22] show scalar variances between 1.5 910 -4 and 6' 10 -a for x/do between 40 and i00 on the axis of the jet9 The corresponding value of H deviates from one by around 25%. To proceed further we take H equal to one and integrate Eq. (24) over ~ to obtain the total NO production as CNo = 4 ~r3/2 p|

_

37

|

_

f

|

i

---~110

oo 6o

- 1)"/2] (27)

Using Eq. (13) and (15), the theoretical emission index (= NO production rate normalized by the fuel mass flow rate Go = powd2ouo/4) finally is

GNo[

| |

[ tar32(l+2Pr)~ ]

9 |

2

L z,, 3 \ L F ~ . / - o

,

This formula is similar to the one derived in [11], except that the ratio ( L / L F ~ ) has not been set equal to one. Values for the quantities in the second term are given in Table II.

5.

Experimental

The experiments were performed in a co-flowing fuel-air-stream. The experimental apparatus used consists of a 110 mm diameter flame tube of 800 mm length placed on a ground plate (Fig. 4) into which the air distribution system and the nozzle are inserted. The air-fuel flow ratio was chosen between 1.5-3.7 of stoichiometric in order to meet the contradictory requirements of low air velocity and sufficient air supply. The nozzle diameter d o varied between 1.0 and 8.5 mm. The nozzle exit flow velocity uo adopted was such that series at constant Reynolds or constant Froude number could be measured. Samples were withdrawn at several radial positions at the top of the flame tube by a hot water-cooled probe. The NO in the samples was analysed using Saltzman's method [23], which had been tested against other methods and was adopted for the expected NO concentration range of the exhaust gases [24]. The emission index GNo/Go/exp was measured for hydrogen, methane, natural gas (82% CH 4, 14% N~, 3.3% CmH., plus impurities),

|

O FL6. 4. Experimental apparatus. (Numerals in the figure are in mm.) 19 air, 2. fuel, 3. sieves with glas-beads, 4. pyrex tube support, 5. jet-nozzle, 6. flame, 7. pyrex-tube, 8. water-cooled probe sampling propane and a mixture of CO with 10% (volume) hydrogen. The ranges of the measured series are given in Table I. The flame length was determined visually. It depended mainly on the Froude number, but a slight additional dependence on the diameter was also observed (cf. Hess [25] ). The mean Froude number dependence of the data is given by the expression (29)

LFr~ where LF~| is the flame length calculated from Eq. (15). The parameters Fr o and n used to calculate the theoretical emission index are given in Table II. The ratio of the experimental to the theoretical emission index was determined as a function of the Reynolds or the Froude number.

COMBUSTION GENERATED P O L L U T I O N

38

TABLE I Ranges of measured series Fixed value

Fuel H2

Re Re Re Fr Fr Fr Re Re Fr Fr Re Fr Fr Fr Fr Re

CH 4

natural gas

C3H 8

CO/10%H 2

= = = = = = = = = = = = = = = =

2500 7000 3200 1000 4000 10000 2500 4000 4000 10000 3200 1300 3250 10000 32500 5700

Range Fr: Fr: Fr: Re: Re: Re: Fr: Fr: Re: Re: Fr: Re: Re: Re: Re: Fr:

In Fig. 5 values for H 2 are plotted over the Froude number for Re = 2500 and 6000. A series at Re = 4500 is due to Lavoie and Schlader [1]. It is seen that a Fr~ fits both series. Constant Froude number series are shown in Fig. 6 for propane, the Reynolds number dependence here is Re -~ In Fig. 7 all measured ratios of the emission indices have been plotted against Fr ~ Re - ~ The solid lines go through the data with a slope one.

6. Discussion The large activation energy of thermal NO kinetics, combined with the rather sharp temperature maximum in the fluctuating diffusion flamelets, limits NO production to narrow regions around the local temperature maxima. This indicates a depen-

Number

61 000943 000 7 200 000-17 100 000 1 8404 110 2 3702 670 2 5703 580 2 6304 070 72030 000 4 94022 900 2 5603 600 2 6504 600 1062 200 3 4206 930 3 8708 960 4 4309 830 7 90012 100 1 100925 000

4 2 6 2 3 3 6 3 2 2 8 4 3 3 2 9

dence of NO production on the maximum temperature rather than on the turbulent mean temperature. Thus, the chemical kinetics can be uncoupled from the influence of turbulence. This allows us to derive a closed form solution for the emission index. The formula takes into account the main influence of the chemical kinetics, the dependence on flame length and the residence time. The integral H that accounted for the scalar fluctuations was set equal to one, due to lack of more detailed knowledge about the turbulence characteristics of the flame. The experiments show, that there exists a Reynolds and a Froude number dependence of the emission index. If one considers the Reynolds number dependence separately, it is difficult to explain. As the ratio of the molecular viscosity to the turbulent viscosity is in view of Eq. (10) of the order 70/Re, the molecular viscosity can be neglected in the governing equations. Thus there is no theoretical

TABLE II Values for calculating the theoretical emission index of measured fuels

fuel H2 CH 4

natural gas C~H s CO/10%H~

Zb [--]

T,,ax IK]

SNo.b" 10a [sec-Xl

~ I--!

v' 10~ [m2/sec]

Fr o [--1

n I--I

0.0284 0,0550 0.0550 0.0601 0.2526

2404 2240 2240 2286 2419

38.0 5.5 5.5 10.8 61.6

0.147 0.096 0.096 0.109 0.190

109 19.5 19.5 4.1 25.0

2.0 107

0.052 0.081 0.068 0.156 0.09

Pr = 0.71 for all fuels

5.6 10 4

4.0 105 1.0 104 355

STRUCTURE OF NITRIC OXIDE PRODUCTION

39

t (GNo/ Go)exp [ONo/G~th

1o

t (GNdcC)exp (GNo/Go)th

5-

0.01

/

,4~,/'~"

F r 033 Re-0 66~

o1 1

J

j,P

2 84

'

o ........ so.o*r AA,,~ / ""

9"

1'05

1'06

1'07

1'0e

Flc. 5. Ratio of experimental to theoretical emission index over Froude number for hydrogen-air flames with Re = konst. 9 Re = 2500, 9 Re = 4500 (Lavoie and Schlader), 9 Re = 7000

t

Re

.poo

~poo 6poo ,

~poo,~ooo

0100

0075

9

7akog, et el

.~

H2

Th,s wor#

a

n a t u t o l gcss

9

CH~.

9

C0.I0~H2

9

C2H8

,,

ool

Fie. 7. Combined Reynolds and Froude number dependence

way to predict a Reynolds number dependence of the emission index on the basis of the governing equations. If one analyzes the assumptions made, one finds the following possible sources of this failure:

(O~,~/ Go )e• IO~olGo)th

~ .~A

" " e a a u w et el

\,

\

0050

Fzc. 6. Ratio of experimental to theoretical emission index over Froude number for propane-air flames with Fr = konst. 9 Fr = 32 500, 9 Fr = 10 000, 9 Fr = 3250, 9 Fr = 1300

1) the fast chemistry assumption 2) neglect of the radiative heat loss 3) neglect of prompt NO or inadequate simplification of the Zeldovich mechanism 4) turbulence modelling According to ref. [8], nonequilibrium effects may account for not more than 25% deviation from the value calculated under the fast chemistry assumption. This effect is thus not important enough to explain the deficiency. As the dependence of the reaction rate on the temperature is very strong, Buriko and Kutsnetsov [10] have good arguments to support the second point. However, these authors predict a different Reynolds number dependence for propane than for hydrogen based on the different radiation mechanisms of these flames. This is not confirmed by the present experiments. The same objection applies to the third point: the Reynolds number dependence should be remarkably different for hydrogen and hydrocarbon flames, if kinetic effects are responsible for the observed differences between theory and experiments. Thus the fourth argument remains the most attractive. If one combines the Reynolds number and the

40

COMBUSTION GENERATED POLLUTION

Froude number dependence, the influence of the velocity drops out and only a diameter dependence remains. If one assumes for a given fuel a geometric similarity between the diameter and the local length scale, the present results call for an additional decrease of NO production with the length scale. Large length scales may be associated with turbulent mixing by large coherent structures. The flow is highly intermittent and the p.d.f, is bimodal under these conditions. The beta p.d.f, function assumed in the theory is not capable of approximating such a shape. Bimodal p.d.f.'s in flames were reported in [22]. Large coherent structures introduce large strain rates and may thus quench the combustion reaction locally [26]. Thus the turbulent reaction rates of the combustion reaction are considerably reduced also leading to lower NO production. Air pockets are convected deeply into the flame by coherent structures. This effect, often discussed as "unmixedness," may be responsible for the additional decrease in NO production.

7. Conclusions

With a certain number of simplifying assumptions, a theoretical expression for the NO-emission index in vertical diffusion flames can be derived. This formula predicts the influence of the kinetics, the residence time and the flame length. Experimental values indicate an additional influence of the nozzle diameter, which can be explained by large scale fluctuations. When this influence is taken into account empirically by a Fr ~ Re - ~ dependence, scaling laws for the NO-emission index are obtained. Nomenclature

A a BNo C ENo F Fr

first order terms from eq. (20) apparent origin of the jet frequency factor modified Chapman-Rubesin parameter activation temperature non-dimensional stream function u~o/dog,Froude number do jet nozzle diameter G o fuel mass flow rate GNo total NO production rate g gravity H integral, eq. (26) L flame length M, molecular weight of species i P probability density function (p.d.f.) Pr turbulent Prandtl number r radial co-ordinate Re uodo/vReynolds number Re, turbulent Reynolds number S production rate

T u v w, x Y, Z

temperature axial velocity component radial velocity component mass production rate per unit volume of species i axial co-ordinate species mass fraction mixture fraction

Greek Symbols a,fl "t

v

v, p d/ to

parameters of the p.d.f. integration constant expansion parameter stretched co-ordinate non-dimensional radial co-ordinate kinematic viscosity turbulent kinematic viscosity axial coordinate from apparent jet origin density stream function reduced inert quantity

Subscripts b c exp O r

st th 00

at maximum temperature on the axis experimental at jet nozzle exit plane reference at stoichiometric conditions theoretical in the external stream

Acknowledgements The authors are indebted to Dr. R. Borghi from the ONERA, France, for calling their attention to the paper by Buriko and Kutsnetsov and providing them with a translation. They also appreciated the fruitful discussion with R. Bilger during his visit at Aachen. REFERENCES 1. LAVO1E, G. A. AND SCHLADER, A. F.: Comb. Sci.

Techn. 8, 215 (1974). 2. BILGEa,R. W. ANDBECK,R. E.: Fifteenth Symposium (International) on Combustion, p. 541, The Combustion Institute, 1975. 3. TAKAG1,T., OGASAWARA,M., FUJU, K. AND DAIZO, M.: Fifteenth Symposium (International) on Combustion, p. 1051, The Combustion Institute, 1975. 4. PAAUW,TH. T. A., STBOO,A. J. AND VAN KOPPEN, C. W. J.: An effective probabilistic simulation of the turbulent flow and combustion in axisymmetric furnaces. Paper presented at the AGARD Conference "Combustion Modelling"

STRUCTURE O F NITRIC OXIDE PRODUCTION AGARD CP-275, Oct. 1979. 5. QUAN,V.: Acta Astronautica, 1,505, 1974. 6. KENT,J. H. ANDBraCES, R. W.: Sixteenth Symposium (International) on Combustion, p. 1643 (1977). 7. BINGES, R. W.: Prog. Energy Combust. Sci., 1, 87, (1976). 8. JANICKA,J. ANDKOLLMANN,W. : A prediction model for turbulent diffusion flames including NOformation. Paper presented at the AGARD Conference "Combustion Modelling" AGARD CP275 Cologne, Oct. 1979. 9. BILGER, R. W.: Combust. Flame 26, 115 (1976). 10. BURIKO, I. AND KUTSNETSOV, V. R.: P h y s i c s o f combustion and explosion 3, 32 (1978), in Russian. 11. PETERS, N.: Comb. Sci. Techn. 19, 39 (1978). 12. JAN1CKA,J. ANn PETERS, N.: A s y m p t o t i c e v a l u a t i o n of the mean NO-production rate in turbulent diffusion flames (1979), unpublished. 13. DONNERHACK, S.: *hnlichkeitsuntersuchungen zur NO-Bildung in turbulenten Diffusionsflammen. Diplomarbeit, Institut fiir Allgemeine Mechanik, RWTH Aachen (1979). 14. PETERS, N.: VDI-Berichte 346, 285-292 (1979). 15. FAVRE,A.: In "'Problems of Hydrodynamics and Continuum Mechanics" p. 231, Society for Industrial and Applied Mathematics, Philadelphia, 1969. 16. LIBBu P. A.: "Studies in variable-density and reacting turbulent shear flows" in "Studies in

41

convection, Vol. 2, p. 1, Academic Press, 1977. 17. BILGER, R. W.: Combust. Sci. Techn. 11, 215 (1975). 18. SCHUCHTINC, H.: Grenzschichttheorie, p. 690, Braun, 1965. 19. HAWTHORNE,W. R., WEDDEL, D. S, AND HOTTEL, H. C.: Third Combustion Symposium, p. 266 (1949). 20. BUSH, W. B., FELDMAN, P. S., FENDELL, F. E.: Combust. Sci. Techn. 18, 59 (1978). 21. L ~ N , A.: Nitric Oxide production in laminar and turbulent diffusion flames, Scientific Report 4, Air Force office of Scientific Research, Febr. 1977. 22. KENNEDY, I. M. AND KENT, J. H.: Seventeenth Symposium (International) on Combustion, p. 279, The Combustion Institute, 1979. 23. SALTZMAN, B. E.: "Colorimetric Microdetermination of Nitrogen Dioxide in the Atmosphere," Analyt. Chem. 26 (1954) pp. 1949-1955. 24. DONNERHACK,S.: "Aufbau eines Versuchsstandes zur Bestimmung der NO-Bildung in turbulenten Diffusionsflammen.," Studienarbeit, RWTH Aachen, Institut fiir Allgemeine Mechanik, 1979. 25. HEss, K.: Flammenliinge und Flammenstabilifiit, Ph. D. thesis, Karlsruhe, 1964. 26. PETERS,N.: Local quenching due to flame stretch and non-premixed turbulent combustion, paper WSS 80-4, presented at the 1980 spring meeting of the Western States section of the Combustion Institute.

COMMENTS Christopher Priddin, Rolls Royce, Ltd., England. Your discussion showed that a turbulent length scale seems to be an important parameter which you are not taking into account. Where in your analysis would you try to incorporate this effect?

Author's Reply. It could be incorporated by the integral H if we were able to model the p.d.f, of the conserved scalar by taking into account the effect of large structures. At this time there is not enough knowledge about the shape of these p.d.f.'s, in particular about their bimodal character. This is the reason why the integral H was set equal to one, and thus specific turbulence effects were omitted.

your predictions are affected by the assumption of chemical equilibrium? Do you think that the radiative emission from the flame and its effect on temperature in the reaction region can explain the Reynolds number dependence of your measurements?

Author's Reply. There is no doubt that radiative heat loss would affect the NO formation to some extent, but this would probably be more important in preheated-air flames. The conclusion of the present analysis is that radiation does not explain the Reynolds number dependence, but that the combined Reynolds number, Froude number effect is due to turbulence.

@

F. Tamanini, Factory Mutual Research Corp., USA. Since the magnitude of the temperature in the NO forming region critically affects the rate of production of NO, to what extent do you think

M. A. Delichatsios, Factory Mutual Research, USA. The use of flame height correlations in turbulent jet flames (e.g., Hottel et al.) to adjust the

42

COMBUSTION GENERATED POLLUTION

parameter C in your model seems to me to be inappropriate because of the notorious ambiguity concerning flame height determination. Furthermore, Becker and Liong (Combustion and Flame) indicate that the Hottel et al. flame height correlating underestimates experimental values in turbulent jet diffusing flames.

Author's Reply. The use of a different flame length formula would imply slightly different values of the turbulent Prandtl number. Values less than 0.71 have been used in the literature before and may in fact be more realistic. The formula for the theorectical emission index would not be affected by this change, since it turns out to be insensitive to the Prandtl number.

L. D. Smoot, Brigham Young University, USA. Were you able to compare your closed form solution results with numerical solution results in order to determine the accuracy of your solution method? How much of the differences observed were due to limitations in the solution technique?

Author's Reply. Comparisons with K-E-type calculations as well as with experimental data have been made. They show differences up to about 10 percent. Those differences are certainly not responsible for the systematic discrepancies between prediction and experiments observed in the present analysis.