Stationary flames in cylindrical flow of homogeneous air-hydrogen mixtures

736

KINETICS OF COMBUSTION REACTIONS

83

STATIONARY FLAMES IN CYLINDRICAL FLOW OF HOMOGENEOUS AIR-HYDROGEN M I X T U R E S By

C. FOURI~

Introduction The theoretical study of the aerothermodynamic development of flows in which chemical reactions occur requires schematic representations 1. Generally speaking, it is rather difficult to develop experimental setups that meet, even approximately, the requirements for such ideal representations. Accordingly, any device which

a flow as possible through a cylindrical tube of a mixture brought to a temperature high enough for spontaneous ignition. With the very lean mixtures used in these experiments, the reaction zone extends over several inches, making temperature change and gas composition readily observable.

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FIG. 1. Diagram of experimental apparatus. permits systematic exploration of a reaction zone is of great help in obtaining new data. It seemed of interest to obtain combustion in homogeneous cylindrical flow of a combustible mixture (air-hydrogen, for instance) without superposition of the heat transfer phenomena on the chemical reaction of the initial mixture. The setup used in these experiments is based to some extent on that of Mullins 2, in which the heterogeneous flow prevented any correct interpretation of the chemical reaction of the mixture. Our purpose was to maintain as homogeneous

I

FIG. 2. Probes used. A, thermoelectric probe with exposed junction; B, thermoelectric probe with single flow over the junction; C, water-cooled probe for collecting gas; D, probe combining A and C. Experimental Procedure The main difficulty encountered in a setup of this type is the problem of selecting a mixture which can react spontaneously but where the chemical reaction does not set in prematurely. This was solved by using a high-speed mixture and aerodynamic recompression. Air and hydrogen are supplied from separate

STATIONARY FLAMES IN HOMOGENEOUS CYLINDRICAL FLOW

tanks and are preheated separately to about 900~ The air is accelerated to a high speed (275 m/sec), in a convergent, after which it passes to a mixing tube (inner diameter 0.6 cm, length 50 cm) at the inlet of which hydrogen is injected (Fig. l). Additional heating of the mixture may be provided through the tube walls without bringing them to the total stagnation temperature. The mixture which is now homogeneous a leaves the mixing tube at approximately sonic velocity.

737

The probe-holder was equipped simultaneously or successively with various thermoelectric probes, as well as pressure and gas cocks for determining the local composition of the mixture (Fig. 2). The electromotive force of the thermocouple is recorded by a Speedomax electronic potentiometer. The proportion of hydrogen in the gas samples is measured with an I.F.P. No. 3 apparatus ~.

Experimental Results In this experiment, the reaction takes place inside a tube such that neither direct nor photo-

(A) (B) FIG. 3. Appearance of the chemical reaction zone (A) and the free jet of the mixture just before reaction (B) made visible by increasing the exposure time. In both cases, copper oxide was added to increase emission. (A) exposure 3 seconds; (B) exposure 18 seconds. During deceleration in a divergent provided a t the mixing tube cutlet, the static temperature rises about 150~ and for the mixtures used (hydrogen concentration, 1 to 3/1000 by weight), a zone of spontaneous reaction appears in the cylindrical experimental tube (length 100 cm, inner diameter 1.9 cm) placed after the divergent. This reaction zone is investigated by means of a probe-holder, which moves along the axis of the tube at constant speed. Probe readings and signals from electric contacts at 10 cm intervals are recorded simultaneously and indicate the position of the probe. a Length/diameter ratio of 83 and the Reynolds number of 50,000 ob(ained confirmed this.

FIG. 4. Reaction as observed for three different positions of the thermoelectric probe (exposure 6 seconds; copper oxide). graphic observation is possible. In the course of a series of special experiments, the phenomenon was reproduced in the free jet from a shorter tube (5 cm). The chemical reaction zone is characterized by a pale blue flame whose outline is blurred. To make it possible to observe and photograph this flame, its intensity was increased by the addition of metal salts. Depending on the exposure time, photographs of the same phenomenon show either the chemical reaction zone alone (Fig. 3, 3 sec) or the entire hot free jet together with the reaction zone (Fig. 3, 18 sec). The appearance of the zone is not affected by the presence of the probe along its axis (Fig. 4). (The picture on the right was taken during a temporary lack of cupric oxide.)

738

KINETICS OF COMBUSTION REACTIONS

The lack of characterization generally shown by strioseopie images of flame fronts seems to confirm the progressive character of the reaction (Fig. 5). T E M P E R A T U R E C H A N G E S INDICATED BY THE P R O B E

At initial temperatures below 910~ there was no noticeable increase in temperature irre-

recording: (1) The temperature curve includes a constant temperature section OA, whose length, i.e., time of travel downstream, decreases when the temperature and/or the hydrogen concentration of the initial mixture increases (Fig. 7). Point A, which marks the end of an ignition lag, can be defined only arbitrarily, as for instance in Figure 6. The

(A) (B) FIG. 5. Strioscopic pictures of phenomenon. (A) horizontal knife edge; (B) vertical knife edge. spective of the hydrogen concentration of the mixture and the position of the probe in the 100 cm tube. Above this initial value, the temperature was observed to change throughout the length of the tube. Figure 6 is a good example of this and shows a direct Speedomax recording, taken during an upward displacement of the probe (lower half), followed by a downward displacement (upper half). A time scale in msec was added, which was computed on the basis of the flow velocity at the tube inlet. The following can be observed on this type of

choice of the tube inlet (point O) as the origin of the abscissae and lags is also arbitrary, but convenient. (2) Over a region of abscissae of several inches, the temperature increases along the curve AC whose maximum slope (dT/dx or dT/dt) (Fig. 6, line 2) increases with the hydrogen concentration of the initial mixture (Fig. 7). (3) In the first fractions of the reaction, an unexplained anomaly (B) appears systematically: the slope of the double tangent (Fig. 6, line 1) increases with the hydrogen concentration (Fig. 7).

STATIONARY FLAMES IN HOMOGENEOUS CYLINDRICAL FLOW

(4) The temperature reaches a maximum (C) and then levels off with a slight downward trend. This decrease in temperature beyond the maximum is due to heat loss by the tube, which is compensated only for the initial temperature of the mixture, and not for temperatures reached after the chemical reaction. (5) The temperature curves obtained by axial displacement of the probe along increasing and decreasing abscissae coincide if the probe is displaced slowly enough so that there is no effect due to thermal inertia of the probe. For a displacement velocity of 0.37 cm/sec, the thermal inertia effect is slightly perceptible, but it can be corrected by taking the arithmetical value of abscissae and slopes in both directions. (6) If, for a fixed longitudinal position of the probe, the hot junction is moved along a diameter of the tube, the temperature changes do not exceed 2~ and 10~ respectively, for the region of level stretches and maximum slope of the curve. PRESSURE CHANGES A static pressure probe was displaced axially in the tube. As expected in view of the moderate flow velocities (40 m/sec), the small temperature variations (less than 250~ and the small diameter of the tube, the pressure drop due to the chemical reaction was found to be low, as compared with the drop due to friction at the walls and on the probe itself. This method of experimentation was not precise enough and therefore was abandoned. VARIATIONS

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CONCENTRATION

Because the overall response time of the apparatus for hydrogen determinations is about 15 to 25 sec, a direct recording cannot be obtained by continuous displacement of the probe. It was necessary to move the probe discontinuously from point to point, maintaining each position long enough for the concentration recorded by the Speedomax to reach equilibrium. The resulting values are plotted against the corresponding abscissae (Fig. 8). There is no hydrogen reaction in the probe. The small diameter of the sampling tube and the low temperatures maintained by circulating water around it lead to heat losses at the rate of about 106~ Moreover, quenching at the cold wall tends to quench any such reaction. The overall hydrogen concentration fluctuates with the temperature (an increase in temperature cor-

739

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740

KINETICS OF

COMBUSTION

responds to a decrease in the hydrogen concentration), except for changes in the slopes of the initial fractions.

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REACTIONS

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To compare these two parameters accurately, a special probe was used (type D, Fig. 2) to make simultaneous measurements, thus eliminating possible discrepancies in the readings. In plotting the points, allowance was made for the longitudinal shift between the junction of thermocouples and the gas sampling outlet. Figure 9 shows the correspondence between these two measurements, with the local temperature increment as abscissa and the fraction of hydrogen consumed as ordinate. The experimental points from a number of experiments fallalong a single curve, which is entirely differentfrom the straight line (firstbisecting line),which would have been obtained if the reaction had been single and adiabatic, and the measurements had been free of error. W e shall now consider various hypotheses by which this difference can be explained. Nonadiabaticity of the phenomenon might be a cause. Because of insufficientcompensation for heat loss at the wall in the reaction zone, the temperature incrementsAT measured in this zone are all smaller than those which w'ould have been obtained for an adiabatic reaction. It can therefore be assumed, as a first approximation, (if these A T remain less than 250~ that the negative errors for individual AT's increase linearly with the value of AT. This means that the values of the AT/ATmax ratio are not affected by the nonadiabatic character of the phenomenon. In the simplified case of a single reaction promoted at the surface of the hot junction or in its boundary layer, the curve obtained would be entirely below the first bissecting line, as the temperature increases would have been ahead of the decreases in hydrogen concentration. In a probable case' of a reaction involving intermediate species such as H, O, OH, H2, 02, H02, the concentration of these species would necessarily increase to a m a x i m u m and then decrease within the reaction zone. The heat of formation of these species being positive or lower in absolute value than that of water, the curve obtained for ideal temperature measurements would lie entirely above the firstbissecting line. Subject to reservations, anomaly B which appears on the temperature curve (Figs. 6 and 8) and the lower part of the curve in Figure 9 situated below the first bisecting line might be

OXYGEN UPTAKE BY CYCLOHEXENE IN LIQUID PHASE

741

REFERENCES 1. RoY, M.: Thermodynamique des syst~mes propulsifs ~ rOaction et de le turbine d gaz, p. 26-41. Paris, Dunod, 1947. 2. MULLINS, B. P.: Third Symposium on Combustion, Flame and Explosion Phenomena, p. 704-713. Baltimore, The Williams & Wilkins Company, 1949. 3. MONICARD, R.: Rev. l'Indust. Frangaise du P4trole, 6, 324, 379 (1951). 4. LEwis, B., AND YON ELSE, G.: Combustion, Flames and Explosions of Gases, p. 27. New York, Academic Press, Inc., 1951.

explained by chain breaking at the thermocouple junction entailing liberation of energy which affects the measurements. I t is to be noted that this perturbation seems to be limited to the first quarter of the evolution. To make the fullest use of the possibilities of such a flame for the study of the reaction kinetics, it would be interesting to determine the evolution of the intermediate compounds and the temperature by spectro-optical methods.

84

KINETICS OF OXYGEN UPTAKE BY CYCLOHEXENE IN THE LIQUID PHASE~ By ANIS T. TOUMA AND FRANK H. VERHOEK

This chapter reports the results of a study of the oxidation of cyclohexene, both as the pure liquid and in benzene solution, without shaking or stirring. The rates were measured manometrically by measuring pressure changes at constant volume. Oxygen-enriched air was used. Early experiments were carried out in Pyrex glass vessels. For 10 ml volumes of cyclohexene, the plot of oxygen absorbed against time showed a slowly accelerating rate followed by a period of steady reaction. The length of the period during which the rate was accelerating varied in irregular manner from one experiment to another. If Pyrex beads were placed in the liquid so that they lay partly above and partly below the surface, the length of this period was decreased. When a liquid-gas interface of constant area was maintained, by using Pyrex cylinders of constant cross-section, the reaction for amounts of cyclohexene less than 1 ml proved to be decelerating at the start, with an initially faster reaction, the smaller the volume of cyclohexene used. It was concluded that the glass surface was exerting a a This investigation was carried out as one phase of a research project on the mechanism of combustion, directed by Prof. Cecil E. Boord and sponsored by the Air Research and Development Command (Contract No. AF 33(038)22959) in cooperation with The Ohio State University Research Foundation.

catalytic influence on the initial stages of the reaction. The difficulties encountered in Pyrex vessels were avoided by using Teflon cups, bored out as cylinders of 2.22 cm inside diameter with flat bases, as containers for the hydrocarbon. These were inserted into 125 ml Pyrex flasks, which were in turn connected to mercury manometers. Care had to be taken to avoid contact of liquid with the glass portions of the apparatus, as by condensation, in order to obtain reproducibility. The experiments were started by pipetting the liquid to be studied into the Teflon cylinders in the thermostat, closing the apparatus, and admitting oxygen until the total pressure was of the order of 900 mm. The oxygen-nitrogen ratio in the atmosphere above the liquid was thus of the order of 40: 60 depending upon the vapor pressure of the liquid at the temperature used. The surprisingly long time of several hours was required to establish vapor pressure equilibrium; this makes the very early portions of the reaction somewhat uncertain. The pressure was allowed to fall as oxygen was absorbed until near to atmTspheric pressure; then more oxygen was added and observations continued. No dependence upon oxygen pressure was observed at partial pressure greater than about 40 mm; all experiments were made in this oxygen-independent region.