Effect of initial mixture temperature on the burning velocity of benzene-air, n-heptane-air, and isooctane-air mixtures

296

STRUCTURE AND PROPAGATION OF LAMINAR FLAMES

37

EFFECT OF INITIAL MIXTURE TEMPERATURE ON THE BURNING VELOCITY OF BENZENE-AIR, n-HEPTANE-AIR, AND ISOOCTANE-AIR MIXTURES By SHELDON H E I M E L AND ROBERT C. WEAST Introduction Theories of flame propagation introduce temperature-dependent properties of the combustible mixture such as thermal conductivity and reaction rate. Consideration of the effect of initial temperature on such properties for a given combustible should make it possible to determine how well theoretical and experimental burning velocities agree as this parameter is varied. Dugger ~ has shown that, for the gaseous fuels, propane, ethylene, and methane, maximum burning velocities predicted by both a thermal and a diffusion theory agreed with experiment to within 20 per cent in the temperature range of about 200 ° to 615°K. The same order of agreement was obtained by Dugger and Graab 2 for 2,2,4-trimethylpentane (hereinafter called isooctane) in oxygen-nitrogen mixtures at 311 ° and 422°K, with oxygen-nitrogen mole ratio ranging approximately from 0.205 to 1.000. The present investigation reports burning velocities for the liquid fuels, benzene, n-heptane, and isooctane, as a function of composition at initial temperatures ranging from 300 ° to 700°K. A comparison was made between the experimental data for each fuel and the relative effects of temperature on burning velocities predicted by the thermal and diffusion theories. Activation energies fitted to the initial temperature data were used rather than values from slow oxidation used previously?

burned in an open flame, which was photographed using schlieren optics• FUELS AND AIR

Some data relative to the fuels are listed in Table 1. Fuel-air ratio by volume was calculated on the basis of air consisting of 3.76 volumes N2 to 1.00 volume O~. For this investigation, laboratory service air containing approximately 0.3 volume per cent water was used.

C 0 M B U S AT IBC O N ~D E A,~ ~1 \L_

,,ill

FIG• 1. Experimental apparatus. A Air filter B Nullmatic pressure regulator C Thermocouple D Critical-flow orifice E Combustion-air valve F Upstream manometer G Downstream manometer H Glass capillary tee

I Vertical extension of capillary J Burner tube K Gauge, 0-100 lb/sq in. L By-pass valve M Precision-bore tube N Plenum chamber O Fuel storage bulb P Helical vaporizing coil Q Mercury reservoir R Three-way stopcock S Drain

Experimental Procedure The liquid fuel was vaporized in a turbulent air stream and the mixture passed through a heated burner tube. The fuel-air mixture was T A B L E 1. F U E L PROPERTIES Fuel

Molecular Weigh~

"~.2 •

d vol %

C,H6

Source

mole

78.1 ~.879 1176.2 L791 98•9 Barrett n-CTHI~ [00.2 •684 1209.2 .903 99.6 Phillips i-C8Hls [14.2 •692 12]0.6 .674 99.5 P h i l l i p s

METERING SYSTEM

The liquid-fuel feed system was of the Calcote type2 Liquid fuel was driven up through a precision-bore tube M (Fig. 1) by air pressure from the plenum chamber, N. The rate of pressure rise in the plenum was held constant by a critical flow orifice, D. 4 Thus, the liquid fuel from the tube, M, was forced into the side arm of a glass capillary tee, H. The metered combustion air was divided b y the valve, E, so that part flowed into the capillary (H and I) and the remainder went directly into the helical copper coil, P. The first part broke

INITIALMIXTURETEMPERATURE AND BURNINGVELOCITY up the stream of liquid fuel into droplets. The second part vaporized the droplets in the coil and formed the vapor-air mixture. 5 The resulting vapor-air mixture then flowed into the heated burner, J (see below). The fuel feed tube was a 80-cm length of precision-bore glass tubing, with an inside diameter of 6.602 ram. The tube was calibrated with each fuel by timing the rise of the mercury-fuel interface at various pressures upstream of a given orifice at a known upstream temperature. Fuel vapor flow at downstream temperature and pressure was calculated from the straight-line relation between upstream pressure and linear feed rate.

297

flow orifices were required. As a result, the stream-flow Reynolds number was limited between 380 and 1300. I t is believed that no preflame reaction occurred during the short periods ( < 1 sec) necessary to preheat benzene-air, n-heptane-air and isooctaneair to their respective maximum temperatures of 700 °, 579 °, and 707°K. This conclusion is supported by the fact that only the usual amount of data scatter was actually observed up to and including the higher temperatures used. This can be interpreted on the basis of the large scatter and eventual decrease in burning velocity obtained with propane-air flames when preflame reaction did oceurY Since the preflame reactions

B U R N E R T U B E AND T E M P E R A T U R E CONTROL

The heated burner tube detailed in Figure 2 received the mixture from the vaporizing coil after the mixture passed through a connecting length of tubing which contained a flashback arrester, F. The burner was a stainless steel tube of 0.998 cm i.d. The upright portion of the tube above the the thermocouple, C, was about 100 diam. long, insuring laminar flow. The burner tube was wrapped with four individually controlled lengths of asbestos-covered heating wire, G, to permit regulation of the tube-wall temperature. Temperatures were measured at the following positions: A: gas temperature at the port by an aspirating thermoeouple 6 positioned as shown between runs; B: lip temperature; C: gas temperature about half-way up the vertical tube; D: wall temperature; E: gas temperature. In addition, a bare wire thermocouple was used to monitor gas temperatures between the port and thermoeouple, C, between runs. All thermocouples were iron-constantan, except C which was chromel-alumel to withstand the thermal effect of flashback. Gas temperatures from A to C were maintained within 15°F of one another. Burning velocity was determined from schlieren photographs of the flame by a total area method. 2 Measurements were based on the outside edge of the image. Results and Discussion BURNING VELOCITIES

In Figure 3, burning velocity for each fuel is plotted against two composition variables: (1) equivalence ratio, O, and (2) mass air-fuel ratio, A/F. The over-all range of initial mixture temperatures was 298 ° to 707°K. The mass flow did not vary greatly. Thus, only very few critical-

I00 DIAMI B BURNERI.D.=0.998 CM C

FI~. 2. Burner Thermocouples (A-E) D A Aspirating E B Lip F C Bare ChromelG Alumel

~

(Or)

assembly. Wall Gas Flashback arrester Heating wire (4 sections)

which affect the burning velocity are very sensitive to temperature variations, it seems reasonable to relate the absence of large data scatter for the liquid fuels with the absence of preflame reaction. Norrish and Taylor s have carried out complete analyses of the products of oxidation of benzene in a flow system at atmospheric pressure. They observed no evidence of low-temperature oxidation in the temperature range 473 ° to 873°K, which is well above the range of the present investigation. The curves for benzene-air (Fig. 3a) show a maximum burning velocity at an average • = 1.046. The corresponding O's for n-heptane-air and isooetane-air are 1.060 and 1.033, respectively (Figs. 3b and e). The burning velocity

298

STRUCTURE STREAM-FLOW REYNOLDS NUMBER 6 5 0

200 180

AND

PROPAGATION

TEMPERATURE, °K 700

~

160 t4oi 12c BURNING VELOCITY, ioc CM/SEC

8

8c

9

0

0

/

2

~

0

~

'

~

~

u

1300

.

.

I

.7

I

1

20C

]

.9

I

1.0

I

1.1

1.2

I

I

I

18C

]

16C

1.3

EOUIVALENCE RATIO

I

I

IB.l . 16.7 14.8 13.3 12.t ILl 10.8 MASS AIR-FUEL RATIO, A/F

TEMPERATURE,

oK

120 8

2

0

~4C MAXIMUM t2C BURNING

STREAM-FLOW REYNOLDS 130 -NUMBER

I10

~

579

°

6(

I00

4(

B

~-HEPTANE i

I$OOCTANE

/

//

~"

2¢

90

(B)

VELOCITY, CMXSEC TO( 8(

0

BURNING VELOCITY, 8 0 CM/SEC 7O

(3)

b 4- cT$

298

1

I

,8

=

was fitted to the data by plotting log10 (u - b) against log10 To. For each fuel, b, c, and n are constants. The constant, b, was determined by trial and error. Least-square t r e a t m e n t of c and n

500

6o--

~o --IA) I

FLAMES

maxima from Figure 3, as well as maxima from replicate runs, are plotted against initial mixture temperature in Figure 4 to illustrate the reprodueibi!ity of the maxima. An empirical equation of the form

588

(A) 4o

OF LAMINAR

650

I pJ l p I ~o ~ I ; 200 400 600 800 200 400 6OO 2 0 400 600 8 0

499

INITIAL MIXTURETEMPERATURE,*K

q

FIG. 4. Effect of initial temperature mum burning velocity.

o

__ I

O

G

~

427

on maxi-

6O

gave the following equations: for benzene at To = 298 ° to 700°K,

50 4O --

508

~

u = 30.0 4- 7.910 X 10-7T~"°2

90O

30

(4)

for n-heptane at To = 308 ° to 579°K, .8

.9 1.0 L; L2 1.3 EQUIVALENCE RATIO

I

[

I

I

I

u = 19.8 4- 2.493 X 10-5T~ "~9

[

I9.I 17.0 I5.2 13.9 12.7 II.7 MASS AIR-FUEL RATIO, A/F

and for isooctane at To = 298 ° to 707°K, u = 12.1 Jr- 8.362 X 10-~To2"19

180 -STREAM-FLOW REYNOLDS NUMBER

TEMPERATURE, oK

38

(5)

707

(6)

E q u a t i o n (6) m a y be compared with the analogous equation from Dugger and Graab :2

140

u = 0.01193T~ "4°

(7)

I20

4 BURNING VELOCITY, I00 CM/SEC

'

0

~

576

780

8O

(c)

For example, at To = 700°K, Equation (6) gives 154.4 cm/sec, Equation (7) gives 114.7 cm/sec, and the experimental burning velocity is 158.4 cm/sec. Consequently, Equation (6) is applicable over a much wider temperature range t h a n Equation (7). The least-square burning velocity maxima are given in Table 2. The data of Table 2 m a y be

599

502

6O -- 530 6O0 40-20--

419 298

75O

~(cll

.8

I

I

i

I

I

I

I

I

,9 1.0 I.I 1.2 EQUIVALENCE RATIO

m.o m.9 ,5.2 ~ 3 . 8 ~2.7 MASS Am-FUEL RATm. A / E FIG.

3.

_'

FIG. 3. Burning velocity as function of equivalence ratio and mass air-fuel ratio at various initial mixture temperatures. (A) Benzene-air flames; (B) n-Heptane-air flames; (C) Isooctane-air flames.

299

INITIAL MIXTURE TEMPERATURE AND BURNING VELOCITY

used to show the variation of burning velocity with equilibrium flame temperature. (See below for calculation of flame temperature.) In contrast with initial temperature, a small increase in flame temperature is accompanied by a large increase in burning velocity.

This is reasonable since the per cent of fuel by volume does not exceed three per cent at maximum burning velocity. Since the mixtures being considered are substantially stoiehiometric, the following form of Semenov's bimolecular equation 9 was used:

T A B L E 2. FREDICTED R E L A T I V E B U R N I N G VELOCITIES OF BF~NZENE 1 ~ - H E P T A N E , AND ISOOCTANE :m/see

Fuel

Experimental leastsquares

Benzene

43.6 66.6 91.8 129.2 195.1

n-Heptane

41.9 43.0 72.5 96.6 129.5

Zsooc-

35.( 61.I 84.~ 110.( 118.7 164.

tane

* Fraction of stoichiometric fuel-air ratio at which maximum burning velocity occurred. t Theoretical adiabatic flame temperature computed by method of Huff, Gordon and MorrellY :~ Computed by method of Huff, Gordon and Morrell: 3 § Obtained from Figure 4 by extrapolation. ESTIMATION OF ACTIVATION ENERGY FROM EFFECT OF

INITIAL

TEMPERATURE

ON

MAXIMUM

.o~,

\:::/ \~:D/:

BURNING VELOCITY

. ( R f ~ ) , e x p (-- E / R T : ) To estimate the over-all or global activation energy of the flame reaction, the thermal himolecular equation of Semenov ° and the activeparticle diffusion equation of Tanford '° and Tanford and Pease 1~ have been reduced to functions of temperature. In tile final forms of the Semenov and Tanford-Pease equations, the temperatureindependent properties of the mixture have been eliminated, and the temperature-dependent properties have been made proportional to powers of T corresponding to the same properties for air:

(S)

(T: -- To) 3

Dugger 1 has shown that this equation can be closely approximated by u2

2 5 exp ( - E / R ~ )

The reduced form of the Tanford-Pease equation1 was modified to include the variation of k: with temperature.: D u : D o : D o H = 6.5:1:1 from Linnett and Hoare. 12

300

STRUCTURE AND PROPAGATION

Each reduced equation was solved for that activation energy which would equate the predicted and experimental burning velocities at the extreme values of initial temperature. This procedure minimized the influence of small changes in burning velocity on the calculated activation energy. At the maximum burning velocity, flame temperature and active-particle concentrations were calculated by a matrix method la with heats of formation published by the Bureau of Standards. 14 The largest uncertainty in the calculation of the relative active particle concentrations is the two per cent uncertainty in the original choice of the concentration of hydrocarbon in air for maximum burning velocity25 For example, a 1.8 per cent decrease in heptane concentration from 2.26 per cent produces a 3.8 per cent increase in relarive particle concentration. Table 2 shows that the activation energies calculated from the Tanford-Pease equation are about half of those calculated from the Semenov equation.

200

180 --

/

160

MAXIMUM BURNING VELOCITY, CM/SEC

t4C --

~//11~1

J2C - -

I0C - -

BC 6E

i II -- "0"

4¢

I

200

1

I

300

I

400

500

THEORY EXPERIMENT

--

I

I

600

700

INITIAL MIXTURE TEMPERATURE, °K

(a) 14C

/

12C

MAXIMUM IOC BURNING VELOCITY, CM/SEC 8C

OF LAMINAR FLAMES

COMPARISON OF E X P E R I M E N T A L DATA W I T H R E L A TIVE

VALUES

PREDICTED

BY

THEORETICAL

EQUATIONS 6C

4C

r~ x*"

(B)

~ ~ --0,- --

I 200

300

THEORY EXPERIMENT

t

1

400

500

t 600

I N I T I A L M I X T U R E T E M P E R A T U R E , °K

(B) 180

--

160 L-

14C

12C MAXIMUM BURNING VELOCITY,

IOC

CM/SEC 80' i

6O

4C 2(

-

-

THEORY

0

EXPERIMENT

{CI

t

200

I

300

I

400

t

500

I

600

t

700

(

800

INITIAL MIXTURE TEMPERATURE, °R

(C) Fza. 5. Effect of initial mixture temperature on maximum burning velocity. Comparison of predicted curves (based on 298°K) with experiment. (A) Benzene; (B) n-Iteptane; (C) Isooctane.

In order to validate the activation energies, predicted burning velocities, normalized with respect to the experimental burning velocities at the extreme initial temperatures, were calculated from the two theoretical equations using the calculated values of E. Figure 5 illustrates comparisons of the relative effect of initial mixture temperature on maximum burning velocities as predicted by the reduced equations for benzene, n-heptane, and isooctane. The values used in plotting both the experimental dashed curve and the predicted points are presented in Table 2. The extremities of each expermental curve are marked X to indicate that the method of calculation forces the predicted burning velocities to coincide with the experimental data at these initial temperatures. Figure 5 and Table 2 show that the burning velocities predicted by both the thermal theory equation and the diffusion theory equation did not deviate by more than 5.1 per cent from those obtained experimentally, for benzene, n-heptane, and isooctane in the temperature ranges studied. In the entire range of temperatures, the values predicted by the two theories are essentially the same. The goodness of fit of the theoretical burning

INITIAL MIXTURE TEMPERATURE AND BURNING VELOCITY

velocities, in order of increasing goodness, is benzene; n-heptane; isooctane. The predicted burning velocities for benzene and n-heptane are higher than the experimental values whereas the predicted burning velocities for isooctane are slightly lower than the experimental values.

Concluding Remarks Dugger ~ obtained linear correlations between maximum burning velocity and either (6.5 PH + Pon + Po) or PH alone for gaseous mixtures of constant composition but varying initial temperature. I n the current investigation such correlations were found only for isooctane. Isooctane also showed linear correlations between maximum burning velocity and Po as well as P o a . Longwell and Weiss16 were able to correlate blow-off limits in a stirred reactor burning isooctane in air. A good correlation was obtained with an E of 40 kcal/mole and a bimolecular mechanism, using the same rate constant for both the lean and rich data. (A somewhat better fit of the rich blow-off limits was obtained with an E of 42 kcal/mole and a 1.8 reaction order.) The E of 40 kcal/mole compares well with the E of 39 kcal/mole obtained in the Semenov theory correlation. Except for the aforementioned agreement in activation energy, the assumptions made in reducing both the Semenov and Tanford-Pease equations, and the absence of independently measured flame temperatures, radical concentrations and activation energies make it impossible to decide the relative merits of the two theories.

S u m m a r y of Results An investigation of the effect of initial mixture temperature on the laminar burning velocities of benzene-air, n-heptane-air, and isooctane-air mixtures gave the following results: (1) Empirical equations for maximum burning velocity u (cm/sec; based on the outer edge of the schlieren image of the flame cone) for use in the temperature ranges indicated were: for benzene, at an initial mixture temperature To of 298 ° to 700°K, u = 30.0 + 7.910 × 10-TT~'92 for n-heptane, for To = 308 ° to 579°K, u = 19.8 + 2.493 X 10-5ToT M and for isooetane for To = 298 ° to 707°K, u = 12.1 + 8.362 X 10-ST~"19

301

(2) Relative burning velocities predicted by both the thermal bimolecular equation presented by Semenov and the diffusional equation of Tanford and Pease did not deviate by more than 5.1 per cent from the experimental burning velocities for the temperatures and fuels studied. Isooctane gave the best, and benzene the poorest agreement. The values predicted by the two theories were essentially the same. (3) When maximum burning velocity was plotted against effective concentration of active species, a straight-line correlation was found for isooctane. Benzene and n-heptane gave linear correlations only over a limited range of burning velocities and effective radical concentrations.

Nomenclature

A/F

mass air-fuel ratio number of molecules of combustible per unit volume b, c constants in empirical equation for a given fuel cp specific heat at constant pressure, cal/(g)(°K) ~ mean specific heat at constant pressure, To to TI , cal/(g)(°K) d diameter of burner tube, cm D diffusion coefficient, cm2/sec Di,r relative diffusion coefficient of i th radical with respect to other radicals, cm2/sec E activation energy, kcal/g-mole exp base of Napierian logarithmic system raised to power in parentheses following exp i.d. inner diameter of burner tube, cm K frequency factor from specific rate equation, em3/(two molecules) (see) k~ specific rate constant for reaction between i th radical and combustible material, cm3/(two molecules) (sec) n constant exponent in empirical equation for given fuel nffn2 moles of reactants per mole of products from stoichiometric equation P~ equilibrium mole fraction or partial pressure of i th species at the flame front P~D~,r effective relative mole fraction or partial pressure of i th species at the flame front R universal gas constant, kcal/(g-mole)(°K) Re stream-flow Reynolds number, d~p/#, dimensionless T absolute temperature, °K T/ adiabatic flame temperature, °K u maximum burning velocity, varying ¢ at constant To, cm/sec average stream velocity, 4V/~d 2, cm/sec a

302 V t~ p

STRUCTURE AND PROPAGATION OF LAMINAR FLAMES

volumetric stream velocity, cm3/sec thermal conductivity, cal/em (sec) (°K) absolute viscosity of mixture, poise, g/(cm) (sec) density of mixture, g/cm 3 equivalence ratio, fraction of stoichiometric fuel-oxygen ratio

SUBSCRIPTS

0 f

property of reactants at initial conditions property of products at flame temperature

7.

8.

9. 10. 11.

REFERENCES 1. DUGGER, G. L. : NACA Report 1061, 1952. 2. DUGGER, G. L., AND GRAAR, D. D.: Fourth Symposium (International) on Combustion, pp. 302-310. Baltimore, The Williams & Wilkins Co., 1953. 3. CALCOTE, H. F.: Anal. Chem., 22, 1058-1060 (1950). 4. ANDERSON, J. W., AND FRIEDMAN, R.: Rev. Sci. Instruments~ 20, 61-66 (1949). 5. CLARK, T. P.: Ind. Eng. Chem., 45, 2786 (1953). 6. WHITESEL, H. A. : In Temperature. Its Measurement and Control in Science and Industry,

12.

13. 14. 15.

16.

p. 851. New York, Reinhold Publ. Corp., 1941. DUGGER, G. L., WEAST, R. C., AND HEIMEL, S. : Fifth Symposium (International) on Combustion, p. 593. New York, Reinhold Publ. Corp., 1955. NORRISH, R. G. W., AND TAYLOR, G. W.: Proc. Roy. Soc., A234, 160-177 (1956). SEMENOV, N. N.: NACA TM 1026, 1942. TANFORD, C., AND PEASE, R. N.: J. Chem. Phys., 15, 861-865 (1947). TANFORD, C.: Third Symposium on Combustion, Flame and Explosion Phenomena, pp. 140-146. Baltimore, The Williams & Wilkins Co., 1949. LINNETT, J. W., AND HOARE, M. F.: Third Symposium on Combustion, Flame and Explosion Phenomena, pp. 195-203. Baltimore, The Williams & Wilkins Co., 1949. HUFF, V. N., GORDON, S., AND MORRELL, V. E. : NACA Report 1037, 1951. RoSsINI, F. D., et al.: Circular C461, Nat. Bureau Standards, 1947. SIMON, D. M.: J. Am. Chem. Soc., 73, 422-425 (1951). LONGWELL, J. P., AND WEISS, M. A.: Ind. Eng. Chem., 47, 1634 (1955).