Aerodynamic and flame structure within a jet-stirred reactor

AERODYNAMIC A N D FLAME STRUCTURE WITHIN A JET-STIRRED REACTOR

DEREK BRADLEY, S. B. CHIN, M. S. DRAPER,* AND G. HANKINSON**

Mechanical Engineering Department, University of Leeds, LEEDS LS2 9JT., U.K.

Computer modelling of a conical, jet-stirred reactor is described. Premixed methane-air enters in a central jet and the chemistry is modelled by two global reactions, one for the disappearance of methane, the other for the oxidation of carbon monoxide. To eliminate the need for a third, buffer, reactive zone, the water gas equilibrium is assumed. The restrictive nature of this is discussed. Turbulence is modelled by reference to hot wire anemometer measurements in air flow. Certain difficulties were experienced in deriving the length scale.

Computed results reveal a flame structure within the reactor, which is not homogeneous. Computed gas compositions and temperatures are compared with experimental measurements of these under identical conditions. Agreement is fairly good, but the global reaction rates which gave the best match are lower than those of previous workers. Chemical heat release rates are obtained from the programme and the profiles of these compare with those of positive ion concentrations, measured by an electrostatic probe. There is a wide scatter in measured electron temperatures.

1. Introduction

Early work on the "well-stirred" reactor of Longwell and Weiss 1 assumed a homogeneous structure within the reactor. Experimental measurements of blow-out points were, on the basis of this assumption, able to yield global reaction rate data. 2 Subsequent techniques, which involved measurement of gas temperature, were less dependent upon blow-out. 3'4 It was, however, becoming clear that the flame structure within the reactor was not homogeneous.5-7.

The mathematical forms of the necessary conservation differential equations, and their computational solutions, both of which have been developed over a number of years by Professor D. B. Spalding and co-workers, s may be applied to reveal something of this structure. The present paper applies this type of approach to numerical ly modelled combust ion of premixed methane-air in a jet-stirred conical

reactor, and compares the solutions with experimental measurements made on a reactor for identical conditions.

The aims of the work were two-fold. First, to reveal something of the structure wi thin such a reactor and second, to add to the accmnulat ing experience of computer modelling, through experimental and theoretical in- vestigation of a well defined combust ion system. In the pursuit of these aims, there a ~ four principal areas of uncertainty, involving:

(i) The derivation of turbulent parameters. (ii) Tile relation of these to turbulent trans-

port coefficients. (iii) A knowledge of relevant chemical ki-

netics, either of a fully detailed kinetic scheme, or of sufficiently accurate global reaction rates.

(iv) A knowledge of the inf luence of turbulence upon reaction rates.

2. Experimental Apparatus and Techniques

*Present address: National Gas Turbine Estab- lishment, Pyestock, Farnborough, Hants.

**Present address: Department of Mechanical Engineering, Lanchester Polytechnic, Coventry.

The experimental reactor, shown in section in Fig. 1, was manufactured from bonded a lumina chippings. Four sampling ports were provided, through which a variety of probes

1571

1572 HIGH OUTPUT COMBUSTION SYSTEMS

A B

90

160

FIG. 1. Conical reactor. Dimensions in ram.

could be traversed across the vessel. When ports were not in use, they were closed by Nimonic plugs. Dried, premixed, methane-air entered by a single, water-cooled, stainless steel nozzle, and the burnt gases exhausted concentr ical ly a round it. Combust ion took place at almost constant pressure, which was found to be close to atmospheric. The inlet temperature of the gas was mainta ined at 288~ by heat ing the h igh pressure gas lines, wh ich fed the orifice meter ing system.

A water-cooled, stainless steel probe of 0.5 mm bore, sampled the reactor gas at a constant velocity. The gases were dr ied and analysed by a twin-column chromatograph, us ing si l ica gel and a molecular s ieve as separat ion media, with argon as the carrier gas. The equ ipmen t al lowed for the measurement of H2, 0 2, Nz, CH 4, CO and CO 2. The concentrat ion of H 2 0 was deduced by stoichiometry.

Gas temperatures were measured by a s i l ica coated p l a t i n u m - - 4 0 % rhodium v p l a t i n u m - - 20% rhodium thermocouple of 1 mm diam. The hot junction was power driven across the reactor and the e.m.f, was d isp layed on a Moseley 7030 A x-y plotter. A radiat ion cor- rection 9 was app l ied to the hot junction temperatures, using es t imated values of reactor wall temperature and computed values of gas velocity.

A spherical, p l a t i n u m - - 4 0 % rhodium elec- trostat ic probe of 0.25 mm diam. measured posi t ive ion concentrat ions and electron temperatures. The wire from the probe was insu-

lated by two concentr ic a lumina tubes, which were suppor ted wi th in a water-cooled stainless steel tube. This ar rangement min imised leak- age currents. To avoid cool ing of the probe, its dis tance from the jacket was never less than 2 mm. The stainless steel nozzle, e lectr ical ly grounded, acted as the other electrode.

Current-vol tage characteristics, which were analysed to yie ld electron temperatures, were obtained by us ing a purpose bui l t e lectronic ramp (voltage) generator. Sweep rates wi th a rise t ime of 3 ms volt -1 could be obtained. Great care was taken to ensure that all stray capacitances, a cause of t ransient currents, were e l iminated from the probe leads and circuit. The characteris t ics were d i sp layed on an osci l loscope coupled to the generator us ing a high input impedance amplif ier . Photo- graphed traces were digi t ised and analysed by digital computer to y ie ld electron temperatures.

Posit ive ion concentrat ions were obta ined from profiles of ion saturat ion currents across the reactor, as d i sp layed on the x-y plotter. The thin sheath theory of Clements and Smy 10 was used.

The aerodynamic structure could only be s tudied with cold air flows, up to a mean entry velocity of 230 m see -1. Disa hot wire anemometry electrical equ ipment was used in associat ion with a pair of p la t inum pla ted tungsten crossed wires of 5 ~xm diam. Travers- ing measurements were obtained of mean flow veloci ty and tu rbu len t kinetic energy. The integral length scale of turbulence was obta ined through the use of a Hewlet t Packard Model 3721A correlator. The value of the length scale ranged from 7.6 mm in the central jet to 3.6 mm in the recirculat ion zone.

3. Theoretical and Numerical Model

The computer s imula t ion was based upon seven, steady state, part ial differential conservation equat ions, in the form given by Gosman et al.s These gave rise to equations in which the dependen t variables were methane concentrat ion, carbon monoxide concentration, enthalpy, vorticity, stream func- tiofi, turbulent kinet ic energy, and turbulen t length scale. Turbu len t Prandtl and Schmidt numbers were taken to be uni ty and thus stagnation entha lpy was a conserved property. The equations were solved by finite difference techniques, us ing the Gauss-Siedel i terative method. A L G O L computer language was em- p loyed and the bounda ry condit ions, a long with other details are given in Ref. 11. The

STRUCTURE WITHIN A REACTOR 1573

Arrhenius type source terms in the species conservat ion equations can exhibit severe spatial gradients, and a l lowance was made for this by assuming a parabol ic d is t r ibut ion of the term over the e lemental mesh volume. Typica l mesh sizes can be seen in Fig. 2.

3.1. Modell ing the Turbulence

The various conservat ion equations under condi t ions of turbulent t ransport have a similar form to those for molecular transport , but with " 'effective" viscosities, thermal conductivi t ies , and dif fus ion coefficients rep lac ing the corre- spond ing molecular t ransport properties. A key requirement in the solut ion of the equations is a knowledge of the values of the effective viscosity, b%ft, at different points. Fo l lowing the notat ion of Ref. 8, the ratio of p,~tf to the molecular viscosi ty is C • Rt, where C is ~t

some funct ion of the turbulen t Reynolds number , B c This funct ion has been der ived for isotropic turbulence from experimental data for non-react ing flows with turbulent t ransport ~2,xa and is

Io) NOR MAI_ISED STREAM ~ ' ~

(b) A EFFECTIVE ~ . 6 _~ VISCOSITY /~/--'-'~ ~\

F1c. 2. Methane-air, r = 0.84, (a) Normalised stream functions. (b) Effective viscosities. (Newton sec. m -2 • 10 2 )

C = 18.61 R t ~ (1)

Thus, in order to evaluate i.Ltt, it is necessary to know the value of R t. This is def ined by

k 1/2 l 11, - ( 2 )

11

where k 1/z is the square root of the turbulent kinetic energy, I is the turbulent length scale, and v is the kinematic viscosity. To evaluate R~, it is necessary to obtain the r.m.s, turbulent velocities, or turbulent kinetic energy, and the length scale at each point. Conservat ion equations were appl ied to these parameters, in accordance with the "'k-r' hypothesis of Ref. 8. These equations involved further constants: Co, related to energy diss ipat ion, Cs, related to s tretching of the length scale, and C w associated with length diminut ion. From a considerat ion of data from different types of non-react ing flow, some interre la t ionships between C and these three constants could be discerner

Those numerical values were ass igned to these constants which gave the best agreement be tween the computed values of k, l, and mean velocity, and the experimental values for the condi t ions of cold f low wi th in the reactor, whi ls t also sat isfying Eq. (1). These values of the constants were used in the combust ion computer programmes. In the evaluat ion of Bt, viscosities were obta ined from a series of polynomials in temperature 26 and mixture viscosities from the equat ion of Wi lke? 7

The nozzle inlet condi t ions to the reactor were model led us ing empir ical equations of p ipe flow. The variations of mean velocity, stream function, and vort ici ty were developed from the experimental results of Nikuradse. as The parameter k was obta ined from the data of a number of workersa2 and Ix~tf from the equat ion given by Reichardt. 19 The length scale was matched to that just beyond the end of the nozzle, wi th in the reactor.

3.2. Model l ing the Chemistry

In view of some of the uncertaint ies in the computer model and the lengthy comput ing times, any at tempt upon a ful ly detai led kinetic scheme was neither warranted nor possible. Instead, two global rate equat ions were employed; the first control led the d isappearance of CH4, and the second the oxidat ion of CO. Many workers 4,7'2~ have expressed these rates in the form of Arrhenius type equations:


d [ C H 4 ] ACHa T a [CH4 ] b

dt

d[CO] [02] c [ H 2 0 ] u exp (-EcH4/RT)

_ _ _ Aco Te [COl f [O2] g dt

[ H 2 0 ] h exp ( -Eco/RT)

There is a full review of the CO global rate data in Ref. 25. The different reported values o f the " A " factors, activation energies E (in kcals, gin m o l e - l ) , and exponents, with concentrations measured in moles cm -3, temperatures in ~ and t ime, t, in seconds, are given in Tables I and II.

Considerat ion was given to the possible use of a third global react ion which would l ink the above two. An intermediate hydrocarbon would be p roduced by the d isappearance of CH4, and the rate of formation of CO would be expressed, in terms of such an intermediate, by a third equation. However, no data were available in a form which enabled this idea to be pursued, and an alternative approach, chemical ly less satisfactory, was adopted to link Eqs. (3) and (4). This assumed that Eq. (3) p roduced CO, H 2 and H20 , whils t Eq. (4) oxidised the CO to CO 2. The amount of H 2 present was found by the appl ica t ion of the water gas equ i l ib r ium

C O + H 2 0 ~ C O 2 + H 2

The various coefficients in Eqs. (3) and (4)

were treated as the pr incipal unknowns in the problem. Numerical values were assigned to them by a combina t ion of theoretical reason-

(3) ing, reference to previous data, and the matching of present computed and experimental results. Thus, for Eq. (3) it was dec ided to use the values of a, b, c, and d presented by Dryer and Glassman, 22 whils t Ac~ and E c h 4

(4) were selected on the basis of the ~est match of computed and experimental composi t ion and temperature profi les, at equivalence ratios, +, of 0.74 and 0.84. Such matching was not easy, in view of the coupl ing of the two global rate equations, and the inf luence of the turbulent parameters.

With regard to Eq. (4), values of e, f, g, and h were chosen to be the same as suggested by Westenberg and Fr is t rom 26,23 and other workers, because of an under ly ing theoretical basis for such values. Again, values of Aco and E c o were selected for the best match of computed and exper imental profiles.

Solution of the entha lpy equation enabled the temperature d is t r ibut ion to be found. The enthalpy of each species was obta ined from the polynomials in temperature of Ref. 27, which were based upon JANAF data. The value of temperature at a point was that which matched the summed enthalpy, over all the species, with that given by the enthalpy equation. The net volumetr ic rate of chemical product ion of a species at a point was mult i - pl ied by the cor responding value of enthalpy

(5) and such products , for every species, added together. This gave the volumetr ic rate of chemical heat release at that point.

TABLE I Coefficients for methane global reaction, eq. (3)

ECH 4 Conditions (P = Reference logl0AcH4 a b c d k. cals. pressure in atmos.)

20 8.845 - I -0 .5 1.5 0 60 1203 < T < 1393

21 8.778 0 -0.4 1.4 0 57 T > 1200

7 18.724 0 1 0.5 0.5 57 1450 < T < 1750 0.3 < P < 0.8

22 13.204 0 0.7 0.8 0 48.4 1100 < T < 1400 0.05 < 4, < 0.5

P = I

Present work 13.477 0 0.7 0.8 0 47

STRUCTURE WITHIN A REACTOR

TABLE II Coefficients for carbon monoxide global reaction, eq. (4)

1575

Eco Conditions (P = Reference logmAco e f g h k. cals pressure in

atmos.)

20 12.017 -2.5 1 0.25 0.5 32 No hydro- carbons

23 12.526 0 1 0.25 0.5 39.08 Semi-theoretical (26)

4 11.079 0 1 0.3 0.5 16 1280 < T < 1535 0 . 2 5 < P < 1.0

24 12.255 0 1 0.25 0.5 28.3 1063 < T < 1593 P = I

7 13.255 0 1 0.5 0.5 25 1450 < T < 1750 0.3 < P < 0.8

25 14.114 0 1 0.5 0.5 30 840 < T < 2360

22 14.6 0 1 0.25 0.5 40 1030 < T < 1230 0.04 < ~b < 0.5

Present work 11.653 0 1 0.25 0.5 39

4. Computed Results

Results are shown in Figs. 2-4, for ~b = 0.84 and a mean inlet velocity of 130 m see -~, using those values of "A" factors and activation energies in Eqs. (3) and (4) which gave the best agreement with experiment. These values are listed on the last lines of Tables I and II. Stream functions, normalised to the peak value of inlet stream function, are shown in Fig. 2(a) and these show the expected flow pattern, as has been derived previously. ~

At the nozzle exit, where the jet discharges, a region of high shear is created and this generates high turbulent kinetic energies and associated high effective viscosities, shown in Fig. 2(b). In the recirculation region, values of these are somewhat lower. The region of high Ix~ff exerts a primary inf luence upon the flame structure within the reactor. In this region hot gases are transferred by the high turbulence to the central jet, the mean temperature of which is raised. By the same mechan- ism, reactants are transferred into a hotter

region away from the jet. The significance of these turbulent exchanges can be appreciated by reference to the computed isotherms in Fig. 3(a) and the lines of c o n s t a n t C H 4 and CO concentrations in Fig. 4. At high inlet velocities it was found that the values of fxff within the reactor were determined largely by the turbulence generated by the shearing of the jet. They were not much inf luenced by wall generated turbulence within the inlet pipe. On the other hand, at low inlet velocities the latter source of turbulence became important. It exerted a significant inf luence for the conditions now reported.

The volumetric chemical heat release rate is shown in Fig. 3(b). There is a well defined reaction front extending through a large proportion of the volume. This figure, along with the isotherms of Fig. 3(a), shows a structure which is far from homogeneous, although the recirculation zone does not exhibit large temperature gradients. Reference to Fig. 4 indicates the two-stage nature of the global reactions, with the C H 4 reacting first, to produce CO which then is oxidised.


(a) T E M PERATURE . . / / " ~ooc o K

~00

r500

(o) CH4

\

8 0 7.0

(b)

Flc. 3. Methane-air, ~b = 0.84, (a) Isotherms. (~ (b) Volumetric chemical heat release rates. (Watts m-3 • 10 -7)

6. Computed and Exper imenta l Profi les Compared

The best agreement between computed and experimental profi les was obta ined for two equivalence ratios and some of the results for cb = 0.84 and an inlet velocity of 130 m see -1, using the global rate constants given on the last lines of Tables I and II, are shown in Fig. 5. This shows computed and experimental profiles of the variat ions of mole percentages of CH 4 and CO 2 with distance, b, from the axis of symmetry, for traverses at posi t ion B, shown in Fig. 1. Comparab le gas temperature profiles are shown in Fig. 6. It was not poss ib le to obtain a sat isfactory match of both composi- tion and temperature profiles.

Computed temperatures are higher than those of experiment and this cannot be ex- p la ined by heat losses to the reactor walls. It was est imated that these would reduce the mean temperature by no more than 40~ In the central jet of reactants, where apprec iable chemical reaction is unlikely, the computed temperatures and CO z concentrat ions are

(b) co MOLE %

~ ~ ~ 0.5

0.1

FIG. 4. Methane-air, ~b = 0.84, (a) CH 4 mole percentage. (b) CO mole percentage.

higher than measured. This suggests poss ible errors in ae rodynamic model l ing, leading to overest imation of ~,~ff.

Another explanat ion is in terms of the steep spatial gradients at the boundar ies of the jet. Any at tempt to def ine gradients more ac- curately involves an increase in the number of mesh points, not only in this region, but also throughout the whole reactor. This is because the i terations tended to become unsta- ble if the ratio of adjacent mesh intervals was greater than 1.5:1.

The measured values of electron temperature shown in Fig. 6 exhibit a large scatter. The voltage sweep rate was not rap id enough to give temperatures on a t ime scale comparable to that of the turbulence and the effect of this appears to render this method of temperature measurement unrel iable.

The measurement of mean posi t ive ion saturation currents appears to be rather more use- ful. F igure 7 shows for a traverse, again at posi t ion B, the normal i sed variation of posi t ive ion concentration, n+. Values are normal ised to the maximum concentrat ion value on the


7

6 \x

5 N klJ4 __J 0 ~ - 3

2

1

0 0

/ / "

15 I

3O b mm

--COMPUTED

- - - -MEASURED

I I 45 60

Fro. 5. Methane-air, 4) = 0.84. Traverse at position B of computed and experimental profiles of CH 4 and CO 2 mole percentages.

traverse of 7.59 x 1016 m -3. Also shown, by the full l ine curve are the computed values of the logari thm of volumetr ic chemical heat release rate at the same section, q- These also are normalised, to a maximum value of 810 x 106 watts m -a. Chemi- ions are produced in flame reaction zones and there is evidence from laminar flames that the peak rate of ion production occurs close to the posi t ion of peak chemical heat release. In view of this, the similari ty of the two profi les in Fig. 7 is not surprising. It suggests a general method of indicat ing relative chemical heat release rates, at different posit ions, from probe saturation current measurements.

7. Discuss ion

With regard to the chosen "'k-l'" turbulent model, part icular d i f f icul ty was experienced in der iving values of constants which gave satisfactory agreement be tween computed and measured length scales for both cold and combust ion flows. It seemed, in fact, to be just if iable to use cold values of length scale

in the combust ion programme, for there is evidence from other turbulent systems that length scale is almost independen t of density. -~ Onr experience emphasises the need for measurements of turbulent t ransport parameters in combust ion systems. In the present combust ion studies there were no means of em- p loy ing any' form of anemometry technique. It might be possible to arrive at a more accurate value of P-~.tt by matching computed and measured concentrat ions of an inert gas. Because of the l imitat ions of the "k-l'" model, there has been a move towards the "k-e" model, :9 in which the length scale equation is replaced by one for the rate of turbulent energy dissipa- tion.

The combinat ion of these diff icul t ies at the central jet, where CH 4 decays, with the inac- curacies of f inite mesh sizes makes accurate mode l l ing of this part of the structure very difficult . The appl icat ion of the "eddy-break- tip" m o d e P ,3~ suggested that the rate of reaction was de termined predominant ly by chemical rate equations and not the decay rate of the turbulence. Only in the region where the jet struck the end of the cone was the latter


o K

2000

1800

1600

1400

1200

1000

800

60C

400

200 0

X

X

/

/ / x ELECTRON TEMPERATURE

/ ~ C O N P U T E D -

/ / - - MEASURED ,, / / /

- !

I I I I 15 30 45 60

b mm Flc. 6. Methane-air, s = 0.84. Traverse at position B of computed and experimental profiles of gas

temperature.

rate l imiting, in this case for the methane reaction.

Another source of error is the use of global rate expressions which use t ime-mean averaged values. The f luctuat ions of temperature and concentra t ions at a poin t give rise to non-l ineari ty in the reaction rates. These effects are most marked in the jet boundary region. The general effect is to increase the reaction rate above that given by t ime-mean temperature in the reaction rate expression.

Reference 31 discusses the effect of mixedness in the wel l -s t i r red reactor and in it the authors conclude that the formerly conven- tional methods of de te rmining a pressure ex- ponent and act ivat ion energy in a global expression would give reasonable values only if the fraction of the fuel reacted was be low 0.8. If more fuel than this were reacted the apparent act ivat ion energy would increase greatly, due to mix ing imperfection.

In the course of the present work it became clear that, as the mixture inlet veloci ty was increased the region of high volumetr ic chem-

ical heat release rate moved from predomi- nantly the edge of the central jet, as revealed by Fig. 3(b), into the main body of the reactor. The present paper concentrates on the data for a l ightly loaded condit ion, in which the fraction of fuel reacted is greater than 0.8. The model l ing technique demonstrates both the departure from well-mixedness and, under condit ions in which the reaction rate is not l imited by eddy break-up, that global rate expressions can be ob ta ined from a match of experimental and computed parameters, des- pite the l ight loading.

Reference to Table II shows both apprecia- ble differences be tween the different global rates for the oxidat ion of CO, and also that the present one is less than that of any previous workers. The two pr incipal categories of rate expressions, given by Refs. 22, 23, 24, 26 on one hand, and by Refs. 7 and 25 on the other, rest theoret ical ly upon different assumpt ions of partial equi l ibr ium. In practice, the degree of overshoot of OH concentrat ion, beyond that impl ied by the part ia l equ i l ib r ium assump-


1.00 I

0.98

0.96

0.94

0.92

0.90

0.88

0.86

0.84

0.82

0.80 0

log d] )gdtma:

/ / " ' \ \

/ \ / \

! I \ / \

/ I

/

/ I

I / I I

I I

I I I

I I

/ I I /

/ I

I I 15 30

bmm

l l l I l I l

\ \\ jlI

n +

n+ma x

I I 45 60

, \ \

\ \ A

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

FIG. 7. Methane-air, ~b = 0.84. Traverse at position B of normalised measured positive ion concentration, n+, and computed volumetric chemical heat release rate, q (Log scale).

t ions, can produce a cor responding change in the " A " factor of the global rate expression. Reference to the results from the laminar fiat f lames of Ref. 25, which are free of the compli- ca t ing influences of turbulence, show that the "A'" factor can fall by almost two orders of magni tude downstream from the reaction zone. A l ight ly loaded reactor is chemical ly more akin to post-f lame gases than is a heavi ly loaded one and, to some extent, different exper imenta l ly de r ived global rates can be ex- p la ined by the extent of the departure from partial equ i l ib r ium in the deta i led reaction scheme. This demonstrates basic l imitat ions in the use of global rate expressions, despi te their utility.

Not unconneeted with this p roblem is the restrictive assumption in the present work of water gas equi l ibr ium, as a subst i tute for a model of rate processes involv ing intermediate species. Both measurements in the flat flames of Ref. 25 and in the present reactor reveal

this to be erroneous. This is p robab ly the greatest h indrance to better agreement between computed and exper imental profiles in the present work.

Acknowledgments

The authors acknowledge support from the Science Research Council for M.S.D. and G.H. and from Leeds University for S.B.C.

REFERENCES

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4. HOTrEL, H. C., WILLIAMS, C. C., NERHEIM, N. M., AND SCHNEIDER, G. R.: Tenth Symposium (International) on Combustion, p. 111, The Combustion Institute, 1965.

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8. GOSMAN, A. D., PUN, W. M., RUNCHAL, A, K., SPALDING, D. B., AND WOLFSHTEIN, M.: Heat and Mass Transfer in Recirculating Flows, Academ- ic Press, 1969.

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13. ABDEE-GAYED, R. G. AND BRADLEY, D.: this Symposium.

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15. DRAPER, M.: Ph.D. Thesis, Leeds University, 1976.

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17. WILXE, C. R.: J. Chem. Phys., 18, 517 (1950). 18. N~KUrtADSE, J.: VDI-Forsch. No. 356 (1932). 19. RElcrtARtrr, H,: Z. Angew. Math. Mech., 31, 208

(1951). 20. KOZLOV, G. I.: Seventh Symposium (Internation-

al) on Combnstion, p. 142, Butterworths, 1959. 21. NEMETH, A. AND SAWYER, R. F.: J. Phys. Chem.,

73, 2421 (1969). 22. DRYER, F. L. AND GLASSMAN, 1.: Fourteenth

Symposium (International) on Combustion, p. 987, The Combustion Institute, 1973.

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24. LAVROV, N. V.: Nank Uzb.SSR, 25, 9 (1968). 25. HOWARD, J. B., WILLIAMS, G. C., AND FINE, D.

H.: Fourteenth Symposium (International) on Combustion, p. 975, The Combustion Institute, 1973.

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27. PSOTHERO, A.: Combust. Flame, 13, 399 (1969). 28. ABDEL-GAYED, R. G., BRADLEY, D. AND McMAHoN,

M.: in preparation. 29. SEKAG-ELDIN, M. A. aND SPALDING, D. B.: Third

International Symposium on Air Breathing En- gines, Munich, 1976.

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31. HOTTEL, M. C., WILLIAMS, G. C., AND MILES, G. A.: Eleventh Symposium (International) on Combustion, p. 771, The Combustion Institute, 1967.

COMMENTS

E. E. Khalil, Imperial College, England. Would you please comment on the effect of the probe disturbance on the obtained results, also did you include ~he effects of turbulence in your reaction model calculations?

At~thors" Reply. It would be instructive to do so, but we have not developed a computer program for the geometrical configuration which occurs with the probe in position. Reference to Fig. 1 and the streamlines of Fig. 2(a) suggests but small effect due to probe disturbance on the measurements at stations "A" and "B." For position "B" the probe occupies approximately 3% of the 'reactor cross section area in the plane of measurement.

We are unable to overcome the formidable difficulties involved in including the effects of turbulence in our global reaction rate expressions. The paper shows that the expressions employed are not entirely satisfactory, for purely chemical reasons.

Bernard T. Wolfson, Air Force Office of Scientific Research, USA. You indicate you plan on using ionization probes to determine turbulence levels and the influence of turbulence on chemical reaction rates.

I feel that such interference type techniques will indeed not give you sufficiently accurate measurements to permit you to reliably ascertain this influ-


ence sufficiently to permit you to evaluate your analytical models. I suggest you consider using more accurate and more reliable non-interference techniques such as LDV (laser doppler velocimetry).

Authors" Reply. Of course, the laser Doppler technique has many unique advantages and we do

not suggest ionization probes are in any way com- petitive. The use of such probes is comparatively simple and we draw attention to two possible ap- plications in practical eombustors. First, ion currents can indicate reaction zones and second, ion current intermittency factors seem to be related to turbulent Reynolds numbers.

Aerodynamic and flame structure within a jet-stirred reactor

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