Pressure hot-wire and laser doppler anemometer studies of flame acceleration in long tubes

C O M B U S T I O N A N D F L A M E 8 7 : 2 1 - 3 2 (1991)

21

Pressure Hot-Wire and Laser Doppler Anemometer Studies of Flame Acceleration in Long Tubes S. A. S. JONES* and G. O. T H O M A S + Department of Physics, UCW Aberystwyth, Dyfed SY23 3BZ, United Kingdom Results are presented from an experimental study of the propagation of premixed natural gas-air flames in a long rectangular duct closed at one end. Oscillations in pressure have been observed which arise from acoustic interactions between the flame and the open end. The measured frequencies and amplitudes are in good agreement with the values predicted using a theoretical model proposed by Jones [Proc. R. Soc. Lond. A 367:291 (1979)]. Flame front motion was monitored using photodiodes. These show that after an initial slow acceleration an oscillatory phase developed, corresponding to the observed acoustic interactions. This was followed by rapid flame acceleration during the final stages of propagation just prior to the flame front exiting the tube. Hot-wire and laser doppler anemometer determinations of the mean and turbulent flow field were also taken and the results compared. In general the laser doppler signals were consistently lower than the hot-wire values, and this is ascribed to the variations in the wire calibration due to temperature changes in the flow. In addition, and unlike the hot-wire, the laser technique continued to provide valid data as the reaction zone traversed the measuring point. From these velocity determinations it is concluded that, for the present experimental configuration, flame acceleration is not strongly dependent on the root mean square turbulent flow velocity. The onset of a final rapid acceleration phase is attributed to turbulence arising from interactions of the pressure waves propagating in the tube with the density discontinuity at the flame front. At later times, the relative importance of shear generated turbulence and that arising from the interaction of pressure and density fields is difficult to quantify.

INTRODUCTION The mechanisms that link fluid flow and combustion and that give rise to increased burning velocities in explosions have been the subject of numerous studies over the years. In general, only the gross effects of parameters such as turbulence levels have been studied, usually by measurements of the resultant enhanced flame speeds. Thus, for example, many studies, such as those by Moen et al. [1] and Chan et al. [2] on a laboratory scale and Hjertager et al. [3] on a larger scale, have been conducted on flame acceleration by obstacle arrays. Such investigations have demonstrated that induced turbulence can result in flame acceleration and have to some extent quantified the degree of acceleration that can be expected for a given physical configuration and mixture reactivity. There are, however, still significant areas where our comprehension of the fundamental mechanisms of turbulent flame acceleration is lacking.

*Present address: EASAMS Ltd., Leanne House, Avon Close, Weymouth, Dorset, UK. t To whom all correspondence should be addressed. Copyright © 1991 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc.

Currently our understanding of turbulent combustion is derived mainly from studies of wellstirred reactors and studies, such as those undertaken by Bradley and co-workers [4, 5], that have resulted in relationships between enhanced turbulent burning velocities and turbulence intensity levels. However, such data are obtained under as nearly isotropic conditions as can be achieved, with fully developed turbulence covering all possible scale lengths. There is some debate therefore as to whether such data are valid for the transient nonuniform flow fields generated during flame acceleration. The object of the current study was to measure velocity and turbulence parameters in the unburned gas ahead of and through a propagating flame confined in a tube. In this way it was hoped to define more precisely the importance of certain fluid flow parameters on flame acceleration under more realistic explosion conditions. In particular, a major objective was to investigate the validity of the relationship between the root mean square (rms) gas velocity and turbulent burning velocity under transient flow conditions. The present article reports on an experimental program in which a long rectangular tube has 0010-2180/91/$3.50

22

S . A . S . JONES AND G. O. THOMAS

been used to study the influence of gas flow parameters on flame propagation in natural gasair mixtures. Gross combustion front velocity measurements employed photodiode detectors, while pressure and hot-wire gauges were used to determine the flow field immediately ahead of the flame front. Further flow field measurements were obtained, both ahead of and behind the flame front, through the use of laser doppler anemometry. This article considers the acoustic oscillations that can arise in such tubes and the present experimental results are compared with a theoretical model proposed by Jones [6]. Finally, the mechanisms that could give rise to the observed rapid flame acceleration are discussed. EXPERIMENTAL DETAILS The flame tube was formed from 1.8-m-long sections of 76-mm by 25-mm rectangular wave guide reinforced using duralumin plate. It was fitted with numerous sensor ports and a 380-mmlong window section. The tube length used could be varied, and ranged from 6.9 to 8.7 m. One end was permanently closed and was fitted with a gas inlet port and a spark plug. The other end was fitted with a 10-cm isolating ball valve that allowed the tube to be opened to the atmosphere

just prior to ignition. In all tests ignition was at the closed end, effected by a 0.25-J spark, while the other end was always open to the atmosphere. Natural gas-air mixtures were used exclusively during the present study. The gas mixture was formed using a purge fill method and the methane concentration of the mixture composition monitored using a calibrated chromatographic system. The composition of the natural gas was determined to be CH4--91.950%, C2H 6 --3.525%, N2--3.075%, C3H8--0.875%, Can10--0.26%, and CO2--0.250%. A sequencer unit consisting of a number of linked, preset-delay trigger units provided automatic control during filling and ensured the correct sequence of valve operations prior to ignition. The gas-handling system is illustrated in Fig. 1. The open end was closed during purge filling by means of the 10-cm ball valve and, with both 2.5-cm ball valves open, gas was allowed to flow from a gas blender through the tube to an exhaust pipe located on the laboratory roof. A sample of the exhaust gas was diverted to the gas chromatograph via a needle valve. The chromatograph output was monitored continuously and the blender output adjusted until the desired fuel concentration was obtained. Ignition could only occur when the operation of these valves was re-

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Fig. 1. Schematicdiagram of flametube and associatedcontrol and measurementequipment.

FLAME ACCELERATION IN LONG TUBES versed, isolating the blender and exhaust and opening one end of the flame tube to air. Three Kistler type 701 piezoelectric pressure gauges could be deployed together with a maximum of 12 photodiodes to monitor flame propagation. In addition, extensive use was made of hot-wire anemometry to measure the gas velocities ahead of the flame front. The upper frequency response of the hot wires was in the range 50-100 kHz, and the calibrated velocity range was 0 - 5 0 m s - ~. Due to the surface oxidation that occurred during flame passage over the wire it was necessary to recalibrate the wires after each test. Further velocity data was obtained using a laser doppler anemometer (LDA) system that, unlike the hot wire, allowed measurements through the flame front of velocities up to 525 ms -1. The LDA system is described in greater detail in the next section. All LDA measurements were made at a distance of 6.2 m from the ignition point in a 8.9-m-long tube.

LASER DOPPLER ANEMOMETER SYSTEM The LDA arrangement used for the present studies, described in detail by Jones [7], was based on an RCA 15-mW H e - C d laser (441.6 nm) used with TSI modular optics operating in the forward scatter mode. The signal was processed by a TSI 1980 timer-counter and a HP2100S computer. The laser was mounted together with the transmitting optics on an optical bench on one side of the flame tube. The receiving optics were mounted on a second bench, inclined at 20 degrees to the horizontal, in the plane of the laser beam, on the opposite side of the tube. Access to the tube was through a special window section formed using two 2.5-cm-thick pieces of optical glass. The transmitting optics consisted of a mask, beamsplitter, and 250-mm focal length transmitting lens that, together with a beam angle reducer, gave a beam intersection angle of 4.83 degrees. This resulted in a fringe spacing of 5.2 × 10 -3 mm and a calibration constant of 0.19 MHz ms -1 relating the doppler frequency shift to the instantaneous particle velocity. As the signal processor was capable of dealing with signals up to 100 MHz, this provided a possible velocity measuring range of _ 520 ms-1. The

23 seeding used was 1-#m-diameter Al203 (aloxite) introduced into the purge flow just prior to ignition. The receiving optics consisted of a 250-mm focal length lens, a scattered light focusing lens (f = 200 mm), an angled mirror, and a photomultiplier. The signal output was processed by the TSI 1980 timer-counter that generated a velocity estimate by estimating the time for N cycles of the frequency burst in scattered light generated as a particle passed through the sampling volume. An input conditioner first amplified and then filtered the scattered light signal. In the present case a high-pass filter set to 100 kHz (equivalent to 0.5 m s - l ) was selected. High-frequency noise was not a problem, as a result of the low signal-tonoise ratio resulting from precautions taken with ambient light shielding. Once filtered, the signal was converted to a series of square wave pulses using a schmitt trigger and envelopes corresponding to the time for N and N/2 pulses were generated. A counter operating at 250 MHz then determined the duration of these envelopes, i.e., the time for N and N/2 pulses. The particle velocity could then be calculated based on the calculated calibration constant determined by the fringe spacing. The data were validated by a comparison of the velocity estimates calculated using the N and N/2 timings. Any data outside a preset accuracy was rejected. For the present tests, the percentage difference tolerated between the two estimates was set at 5% with N set at 16, half the predicted number of fringes present. The gain was adjusted so that fringes near the middle of the burst were detected by the schmitt trigger. The receiving optics was adjusted such that it viewed the center of the ellipse formed by the intersection of the transmitted beams. A TSI 1998H data interface module was used to couple the counter to an HP2100S minicomputer and data were transferred in the form of two sequential 16-bit words placed in the computer memory via a direct memory access. The first word contained the time between samples data in the upper 8 bits and the N-cycle count in the lower 8. The second word contained the burst time mantissa in the lower 12 bits and the exponent in the upper 14 bits. The computer had sufficient memory to store 5000 data bursts per test.

24

S . A . S . JONES A N D G. O. THOMAS

EXPERIMENTAL RESULTS

O

(a)

Pressure and H o t Wire Pressure and hot-wire records obtained with a mixture containing 9.7% methane in a 6.9-m-long tube are shown in Fig. 2. The negative phase on the pressure record is the result of insufficient thermal insulation of the quartz crystal from the hot combustion products. This gives rise to a thermoelectric effect that is of opposite polarity to the piezoelectric effect of interest. The main point to note is the oscillatory nature of the signals. This is shown even more clearly in Fig. 3, which was obtained with a leaner mixture. The repeatability in the peak of the initial pressure oscillation envelope between a number of tests at nominally the same initial conditions was poor, as shown in Fig. 4, where this parameter is plotted as a function of mixture composition. There is a clear maximum near stoichiome-

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Time (seconds)

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Time (seconds)

Fig. 3. Simultaneous pressure and hot-wire velocity measurements in a 6.9-m-long tube. Methane concentration--6.8%, gauge locations; pressure--4.76 m, hot wire--6.57 m.

d (a)

c5

try, but in general there is a great deal of scatter in the data. Average flame speeds, as measured using the time of arrival of the flame front at a photo diode are more repeatable, however, as shown in Fig. 5. The validity of such a measure-' 1000

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Time (seconds)

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~ 400

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0.2 0.3 0.4 015 Time (seconds) Fig. 2. Simultaneous pressure and hot-wire velocity measurements in a 6.9-m-long tube. Methane concentration--9.7%, gauge locations; pressure--2.13 m, hot wire--4.36 m.

8 I

I

I

I

I

I

2

4

6

8

10

12

Methane

(X}

Fig. 4. Peak-peak of pressure envelope measured over the first 200 ms of flame propagation as a function of methane concentration in air. Tube length; ( 0 - - 6 . 9 m, gauge location 4.76 m and (e) 8.7 m, gauge location 6.59 m.

F L A M E A C C E L E R A T I O N IN L O N G TUBES

25

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1.0

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9.7% (a)

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11.5%

tJ

.~" 0 . 6 ,1¢ +

@

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Z

i=l= , , . . . .

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8 9 10 11 Composition (%methane)

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400 600 Time (ms) Fig. 6. Normalized flame position as a function of time for

co

200

three methane concentrations in air. Tube length 8.7 m. t÷

÷ +,÷,.

%

t~

6

7

8

9

10

11

12

13

composition (%methane) Fig. 5. Flame arrival time as a function of methane concentration in air. Photodiode gauge locations were (a) tube length 6.9 m, x--0.6 m and + --5.0 m and (b) tube length 8.7 m, x --2.4 m and +--6.8 m.

ment is however open to question. Both the hot wire and the photodiode records indicate that the flame propagation is composed o f an oscillating flame superimposed on a mean forward flow. Further evidence of flame oscillations was obtained from schlieren cine films o f flame propagation past the window sections. Normalized flame positions versus time for three gas compositions are shown in Fig. 6. Three phases can be identified. An initial acceleration phase is followed by a second, oscillatory phase, which arises from acoustic interactions with the open end o f the tube. It should be noted that although the frequency and phase o f the oscillations were derived from the pressure records, their amplitude is purely illustrative. The final phase is a rapid acceleration to the tube exit. It is interesting to note that, as shown in Fig. 7, the final velocity is largely independent o f the mixture, with a mean value o f 96 m s - 1 for the 6.9-m tube and 127 m s - 1 for the longer tube.

The effect o f variation in mixture composition is to give a slower initial acceleration and a longer oscillatory phase as the mixture deviates from stoichiometry.

Laser Doppler Anemometer O f the 100 laser anemometer experiments undertaken, 20 of the signals contained some valid data, but only 9 o f these were suitable for further analysis. Using these data, estimates of mean velocity and rms velocities could be calculated as 125 1

.6%

100 "~ ~ 75 .~ (J o 50 > 25 0 0

I

I

I

I

100

200 Time (ms)

300

400

Fig. 7. Flame velocity development as a function of time for three methane concentrations in air. Tube length 8.7 m.

26

S . A . S . JONES AND G. O. THOMAS

a function of time. The rms velocities were calculated as the rms deviation from a quadratic fit to the data. This procedure was employed to remove both linear and nonlinear trends in the data. A comparison of the laser anemometer and hot-wire velocity measurements is given in Fig. 8. In all cases the hot-wire estimates are consistently higher, particularly at higher velocities. One possible cause of this discrepancy is an error due to the extrapolation of the wire calibration. Another possible explanation is a modification of the calibration due to an increase in the local gas temperature in the vicinity of the flame. A further feature of the hot-wire data are the fast velocity excursions in the reversed flow, which are believed to originate from an interaction of the probe support. The most significant difference, however, is that the laser system continues to give valid velocity data as the flame front passes the measuring station.

Mean and rms velocities derived from the instantaneous velocity estimates are shown in Fig. 9 for three tests at initial methane concentrations of 11.5%, 10.3%, and 9.7% in air. Flame propagation past the measuring station occurs for the two lower concentrations. These results indicate that the turbulence levels are low, with some dependence on the mean flow velocity. This is shown in Fig. 10, where the rms velocities are plotted as functions of the mean velocity for both the preflame and postflame passage measurements. In addition to evidence of an increase in the rms velocity in the reaction zone there is also an indication of an increase in the postflame turbulence. Before the flame passes the measuring station the rms velocities lie in the range 0.5-6.0 m s - i while measurements in the reaction zone always indicate velocities greater than 4.0 ms t. There is therefore some evidence of changes in the flow characteristics in the reaction

(a)

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620 640 Time since ignition (ms)

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Fig. 8. Comparison of LDA and hot-wire velocity measurements. Tube length 8.7 m, measurement location 6.7 from ignition point. Methane concentration in air (a) 11.5 % and (b) 7.5%.

FLAME

ACCELERATION

O0

IN LONG

--

TUBES

27

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Fig. 9. Mean RMS velocity estimates obtained from LDA measurements. Tube length 8.7 m. Methane concentration in air (a) 11.5%, (b) 10.3%, and (c) 9.7%.

28

S . A . S . JONES AND G. O. THOMAS

Q

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zone, although this increase may be attributable in part to the possibility of larger experimental scatter due to the effects of combustion on the seeding particles. The mean flow measurements also indicate a strong deceleration of the flow coincident with flame passage and there is evidence of possible fragmentation of the front.

continuous growth in wave amplitude unless balanced by some dissipative mechanism, which in the case of the present experiments is due to viscous drag at the tube walls. Replacing the flame front by a density discontinuity separating uniform burned and unburned gases, the normal modes of oscillations can be determined by applying continuity conditions in velocity and pressure across the interface. In this way a set of equations can be derived that give, the frequency and amplification of acoustic vibrations as a function of reduced flame position along the tube. The exact nature of these equa-, tions is determined by the boundary condition applied at both ends of the tube. The present experimental conditions correspond to a tube closed at the ignition end and open at the other. If the total length of the tube is taken as L and the lengths of burned and unburned gases as 12 and l I respectively, with corresponding sound speeds c~ and c 2, then the normal modes of oscillation for the present configuration are given by 1

tan 0 = -- cot ~b, q

(1)

where q = c 2 / q , 0 = ~oll/c 2, and ~b = ~ol2/c 2, and co = 27r f , where f is the frequency. It can also be shown that

DISCUSSION

(0 + q¢,) Acoustic

Oscillations

One important aspect of flame propagation in long ducts is that the flame motion induces acoustic oscillations that by a feedback mechanism involving the burning velocity then influence the subsequent flame behavior. This phenomenon is well known and has been reviewed by Guenoche [8]. Recent studies include those of Leyer and Manson [9]. A theoretical analysis of such behavior reported by Jones [6] allows the frequency of oscillation and amplification rate to be calculated as a function of flame position. In this analysis it is shown that for a slow-moving flame a small fraction (less than 10 -6 ) of its combustion heat supports sound waves that are a normal mode of vibration in the tube. The energy transfer rate is proportional to the mean square of the density condensation in the flame. This would imply a

o~ -

L

eI

(2)

and that the reduced distance ~ is given by l2 ~7- L -

1 (1 + 0 / q ~ b ) "

(3)

To calculate the oscillation frequency, ~b (or 0) is taken as a parameter and 0 (or ~b) calculated from Eq. 1. o~ is then calculated from Eq. 2 and ~7 from Eq. 3, giving the desired frequency variation with reduced distance. The first mode is calculated for ~b in the range 0 to 7r/2. Higher modes correspond to larger values of ~b. A comparison of the measured fundamental and the first two harmonic components of both hot-wire and pressure records with the results of predictions based on the above model is shown in Fig. 11. The normalized flame position was determined by interpolation of the photodiode

FLAME ACCELERATION IN LONG TUBES

29

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/Y

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J

0.2

0.4 Reduced

0.6

0.8

1.0

position

Fig. 11. Measured oxcillation frequency compared with predicted values as a function of reduced flame position along the tube. Tube length 8.7 m. Oscillation modes (a) fundamental, (b) first harmonic, and (c) second harmonic.

30

S . A . S . JONES AND G. O. THOMAS

records. In calculating the solid curves, it was assumed that the sound velocities in the burned and unburned gases were 950 and 340 ms-1, respectively, corresponding to temperatures of 1875 and 300 K. All display similar features, with an increase in frequency as the flame moves down the tube. The agreement with theory is very good for the fundamental, but less so for the first harmonics, where there was significant scatter in the experimental data. The differences are attributable partly to assumptions in the theory and to experimental errors. The theory assumes a thin planar flame, whereas schlieren visualization showed the flame front to be highly curved. It also assumes the flame speed to be small compared with the sound speed in the unburned gas, a condition that is only true during the early stages of propagation. The main experimental error is in the estimation of flame position, which is particularly large during the oscillatory phase. A further feature of the present results for moderate flame velocities is the initial growth and subsequent decay of the peak-to-peak variations in pressure and velocity, as shown, for example, in Fig. 3. The model of Jones [6] provides an estimate of the rate of growth of acoustic energy of the form -1

e dt

= C 1+

-L

I1 +

~2

12 cot 2 (3)

Here C is a constant that can be related to the thermodynamic parameters of the reactive system and T t and T2 are the temperatures of the unburned and burned gases, respectively. The relative growth of amplitude for the first and second modes of oscillation derived from this equation for the case of ignition at a closed end are shown in Fig. 12. For the fundamental, integrating Eq. 3 with respect to t and assuming a simple linear variation of flame position ~ with time, this gives an estimate of the variation in acoustic energy e as a function of ~ that is in qualitative agreement with the experimental observations shown in Fig. 3. Higher harmonics were also observed, as reported in Fig. 11, but for most tests, measurements could only be made over the first half of the tube and these did not give meaningful amplitude information.

0

oO o

o

g ~

fl

.o

~- c5

fo

<

0

"

0.2

0.4

0.6

0.8

1.0

Reduced Distance Fig. 12. Growth of acoustic amplitude as a function of reduced distance for fundamental and first harmonic of a flame propagating in a tube from closed towards open end.

Turbulent Burning and Flame Acceleration In an in-depth investigation of turbulent burning, Andrews et al. [4] found that the ratio of turbulent to laminar burning velocity u t / u t could be correlated with the ratio of rms turbulent velocity to the laminar burning velocity u ' / u t and to the turbulent Reynolds number based on the integral length scale L. Abdel-Gayed and Bradley [5] later presented a summary of turbulent burning data that supported this correlation. In the present study, for measurements in the preflame region, the rms turbulent velocity was determined to be in the range I to 5 ms-1. If the laminar burning velocity uz is assumed to be in the range 0.5-2.0 ms-1, then the ratio u ' / u t lies in the range 0.5 to 10.0. The correlations of Abdel-Gayed and Bradley suggest a value of u t / u l of 1-20 for this range of u ' / u t, and, using the same range of ut (0.5-2.0 m s - l ) , t h e turbulent burning velocity is "predicted" as 2.0-10.0 m s - '. This range of values is consistent with the present observations, within the limits of. experimental error. Experimental determinations of the turbulent burning velocity under conditions typical of those found during flame acceleration, require measurements of both the flame speed and the mean flow speed. In the present tests, the experimental data often showed LDA determined

FLAME ACCELERATION IN LONG TUBES flow velocities close to the flame speeds estimated using photodiodes. From this it can be inferred that the turbulent burning velocity is always small compared with the mean flow velocity, which is consistent with the "prediction" given above. This observation is supported by the results of Bjorkhaug [10] who found that the turbulent burning velocity was 3 - 4 times the turbulent rms velocity. The present results are unfortunately limited by the lack of accuracy in the measurement of the local flame velocity as a consequence of the large physical separation of the photodiodes. The LDA results also indicate some evidence of flame fragmentation because the mean flow velocity falls rapidly on flame arrival, again in a similar manner to that observed by Bjorkhaug [10]. In this region, pockets of higher velocity are observed and could correspond to entrained unburned mixture. It should be noted that the terminal velocities obtained in the present studies were comparable to those obtained by Bjorkhaug (of the order 100-180 m s - t ) . However, in the present tests, these velocities were achieved without the use of obstacles to promote acceleration, although a distance of 8.7 m was required compared with the 1-m-long obstructed section used by Bjorkhaug [10]. The exact cause of this final acceleration in the present studies is still uncertain. It is possible that it could arise from the amplification of pressure and velocity fluctuations predicted by the Jones model, as discussed in the previous section. There is a rapid increase in the amplification factor for the first harmonic at around a reduced distance > 0.5. Similar increases for the higher harmonics could thus lead to the observed flame acceleration. This is not inconsistent with present observations where pressure oscillation became apparent after r/ = 0.4. Unfortunately, the Jones model is no longer valid in those regimes where rapid acceleration is observed. It should be remembered that the Jones model gives the frequency and amplification as a function of flame position for a flame whose velocity is small compared with the velocity of sound in the medium. An insight into the mechanism responsible for the rapid acceleration can be obtained from the excellent photographic studies of Schmidt et al. [11], who monitored the flame behavior in tubes for a combination of ignition locations and end

31 boundary conditions. Their results using a 1-mlong tube closed at the ignition point are qualitatively very similar to those obtained in the present study. The general oscillatory nature of the flow can be clearly seen. Also of great interest is the change in the nature of the flame front once it has reached a reduced distance of approximately 0.4. At this point the flame is first decelerated and then accelerated again towards the open end. During this process there is a distinct change from a curved laminar flame to a more wrinkled and extended flame. The rapid acceleration phase would therefore appear to result from this change in the flame front structure. This would result in an increase in combustion rate as a consequence of the increase in flame surface area, unlike the simple change in the burning velocity that occurs in the initial acoustic phase as a result of the variation in pressure and density. Schmidt et al. [11] attributed the observed development of flame turbulence to turbulence in the unburned gas ahead of the flame resulting from wall boundary layer effects. There can be little doubt that this plays a role once flame acceleration is established, but it does not easily explain the rather rapid onset of acceleration that is observed. A possible explanation does arise, however, from the well-known Markstein instability, and Scarinci et al. [12] have recently repeated in greater detail experiments initially reported by Markstein [13]. These studies show that pressure wave interaction with a flame front can also lead to the generation of turbulence. Initially this is a purely gas-dynamic effect resulting from the interaction of the nonaligned pressure field and density change across the flame front. The subsequent growth or decay of these induced perturbations has been shown by Scarinci et al. [12] to be related to the mixture reactivity. In reactive mixtures the turbulence becomes self-sustaining whereas weak mixtures relax back to a nearly laminar flame. This is consistent with the present experimental observations, where little acceleration is observed with lean or rich mixtures, despite the fact that relatively large pressure and velocity fluctuations are observed. For more reactive mixtures acceleration is observed, always originating at ff of the order 0.4. Once acceleration has been initiated by this mechanism, sheargenerated turbulence due to wall interactions

32 could become of increasing importance as the mean flow velocity increases. Unfortunately, the relative importance of the two turbulence-generating mechanisms in maintaining the increased combustion rates cannot as yet be quantified. A final surprising observation is the constancy of the average exit velocity of the flame as function of the tube length, with little apparent dependence on reactivity. A possible explanation is that the mixture range over which acceleration is observed is relatively narrow and that, given the rapid acceleration that occurs, the flames may not have reached a maximum terminal velocity by the end of the tube. CONCLUSIONS Flame velocity studies using photodiodes have shown that, for propagation along a major portion of the tube, the observed velocities are low, with rapid acceleration only occurring over the latter half of the tube. Laser doppler anemometry has been used successfully to provide good mean and turbulent flow velocity data both ahead of and within the reaction zone of a rapidly accelerating flame. Measurements have been obtained for mean flow velocities approaching 200 m s - l . The rms turbulent velocities were observed to be always of the order of or less than 5 % of the mean flow velocity. Accurate determinations of the turbulent burning velocities in accelerated flames were, however, limited by a lack of resolution in the flame velocity measurements. The oscillatory nature of flames propagating in a long tube closed at one end can be modeled using a simple theory developed by Jones [6]. This accurately predicts that change in the acoustic frequency that results from the interaction of the modulated energy release at the flame front and the acoustic mismatch at the open end of the tube. Based on the observed flame acceleration and LDA turbulence measurements, there is a suggestion that another mechanism for flame acceleration should be considered in addition to that of shear induced turbulence. Evidence for this is provided by the fact that the rms velocity remains constant at around 5 % of the flame speed for

S . A . S . JONES AND G. O. THOMAS most of each test and that rapid acceleration only occurs towards the end. The primary cause of the rapid flame acceleration observed over the latter half of the tube is believed to be turbulence generated as the pressure waves associated with the oscillating flow field interact with the density discontinuity at the flame front. At later times both could contribute to maintaining high combustion velocities, although their relative importance is not clear at present.

This work was sponsored via an SERC Research Scholarship (SASJ) in collaboration with British Gas Midlands Research Station. The authors also wish to acknowledge the contribution o f Dr. D. R. Brown and thank him f or his constant advice and guidance during the course o f this work. REFERENCES 1. Moen, I. O., Donato, M., Lee, J. H., and Wagner, H. Gg., Prog. Astronaut. Aeronaut. 75 (1981). 2. Chan, C., Moen, I. O., and Lee, J. H., Combust. Flame 49:27-39 (1983). 3. Hjertager, B. J., Fuhre, K., Parker, S. J., and Bakke, J. R., Prog. Astronaut. Aeronaut. 94 (1985). 4. Andrews, G. E., Bradley, D., and Lwakabamba, S. B., Combust. Flame 24:285-304 (1975). 5. Abdel-Gayed, R. G., and Bradley, D., Philos. Trans. R. Soc. Lond. 301:1-25 (1981). 6. Jones, H., Proc. R. Soc. Lond. A 367:291 (1979). 7. Jones, S. A. S., Ph.D. thesis, UCW Aberystwyth, 1985. 8. Guenoche, H., in Non-Steady Flame Propagation (G. H. Markstein, Ed.), Pergamon, London, 1964, pp. 107-181. 9. Leyer, J. C. and Manson, N., Thirteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1970, p. 551. 10. Bjorkhaug, M., Ph.D. thesis, The City University, London, 1986. 11. Schmidt, E. H. W., Steinicke, H., and Neubert, U. Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1952, p. 658. 12. Scarinci, T., Lee, J. H., Thomas, G. O., and Bambrey, R., Paper presented at 13th International Colloquium on the Dynamics of Explosive and Reactive Systems, Nagoya, 1991. 13. Markstein, G. H., Sixth Symposium (International) on Combustion, Reinhold, New York, 1957, p. 387. Received 7 June 1990; revised 5 May 1991