Buoyancy effects on the flame structure in the wakes of burning liquid drops

COMBUSTION A N D F L A M E 29, 21-31 (1977)

21

Buoyancy Effects on the Flame Structure in the Wakes of Burning Liquid Drops SUBRAMANYAM R. GOLLAHALLI* Thermal Engineering Group, Department of Mechanical Engineering, University of Waterloo, Waterloo Ontario. Canada. N2L 3G1

Data are presented on the structure of the flames m a wakes of model (6 mm and 3 mm diam. porous spheres) methanol and n-heptane drops burning in a downward air flow. The following measurements were made: axial and radial temperature profiles; axial and radial composition profiles showing H20 , CO2, N2, 02, CO, NO, fuel and pyrolysis products; radiant power emitted from the flame; flame length; extinction velocity and burning rate. The results show that buoyancy has a significant effect on the flow pattern and structure of these flames. The inverted envelope flames exhibit a structure similar to that of envelope flames in upward air flow, but the structure of the inverted wake flames is significantly different from that of the upright wake flames. Diffusion-controlled interface combustion is seen to be the dominant mechanism in inverted wake flames, as opposed to the premixed burning in the upright wake flames.

INTRODUCTION Although a vast amount of information is available in the literature [1] on the combustion of liquid drops, only a few experimental studies on the structure of droplet flames have been published [ 2 - 7 ] . Of these, the earlier investigations performed at the author's laboratory [ 2 - 4 ] , are related to the structure of the flames in the wakes of drops burning in an upward air stream. It was concluded that the near wakes of envelope flames over burning spheres were similar to laminar gas diffusion flames, whereas the near wakes of wake •flames corresponded to premixed gas flames. Also, it was shown that in the far wakes of both envelope and wake flames the heterogeneous combustion of soot was the dominant mechanism. A model [8] based on these findings was shown to predict the experimentally observed variations of flame length with various operating parameters. Since buoyancy was shown to be a signifi-

* Present address: School of Aerospace, Mechanical and Nuclear Engineering,TheUniversity of Oklahoma, Norman, OK 73019.

cant factor influencing the flow pattern and stabilization of flow in the wakes of the burning drops [9], the above stated conclusions derived from experiments where natural and forced convection fields were always augmenting each other, may not hold in general. This paper describes the results of some studies on tire flame structure in the wakes of droplets burning in a downward air flow, where natural and forced convection fields oppose each other. Data are presented on temperature profiles. composition profiles extinction velocity, flame length and radiant power of methanol and nheptane flames and compared with those in the wakes of flames burning in an upward air flow presented earlier. For brevity the flames in upward air flows are referred to as upright flames~ and those in downward air flows are referred to as inverted flames.

EXPERIMENTAL PROCEDURE The apparatus was essentially the same as in the previous work [2] performed at atmospheric pressure, except for the following modifications. Copyright © 1977 by The Combustion Institute Published by Elsevier North-Holland, Inc.

22 In this study the fuels were methanol and nheptane. Two porous bronze spheres of 6 mm and 3 mm diameter were used as model drops. The air nozzle-drop assembly was inverted such that the air was flowing vertically downwards over the spheres. Gas samples were taken by means of a horizontal uncooled quartz microprobe with a 50/Ira orifice and were analyzed by means of a gas chromatograph. On-line gas analysis was carried out using Mol-Sieve 5A and Porapak T columns, whose temperature was varied between 20-110 °C with a temperature programmable oven. The concentrations of nitric oxide were determined using a chemiluminescent analyser calibrated using the standard calibration gases supplied by Union Carbide Co. The temperature field was probed with a coated Pt-PtRh thermocouple as described earlier [2]. Measurements were also made of the transition velocity at which the envelope flame was transformed to a wake flame. The flames were photographed on panchromatic films through three narrow pass filters, peaking at 4315 A, 5160,8, and 6300 A with corresponding half widths of 38 A, 76 A and 130 A, respectively. These wave lengths were chosen to detect the regions of CH, Swan bands and luminous radiation, respectively. Radiation emitted from the flames was measured using a thermopile. For flow visualization, particle track photography was used as described in Ref. [2]. The best estimates of error in the data are -+1% for temperatures, -+5% for composition, -+1% for velocities and -+5% for burning rate, respectively.

OBSERVATIONS Appearance and Flow Pattern of the Flame Figure 1 shows the particle tracks around the 6 mm sphere in cold flow and with methanol flames at various downward air velocities. The white region on the sphere is caused by the light reflected from the sphere. In the cold flow a recirculation structure is noticed in the wake of the sphere, similar to the flow pattern in an upward air flow observed earlier [2]. In the presence of a flame, a stagnation plane is established in the

SUBRAMANYAM R. GOLLAHALLI upstream zone of the sphere between the flame and air stream. As the air stream velocity is gradually increased this stagnation plane moves towards the sphere and the flame assumes an inverted dish shape. Even after the flame is extinguished at the upstream part of the sphere, the particles are deflected sideways and do not enter the wake region of the sphere. A comparison of these photographs with those presented in Ref. [2] for the flames under mutually supporting natural and forced convection conditions brings out the following significant points. In the envelope flame under both conditions, air is not convected into the wake region. In the upright wake flame, particles penetrate the near wake region, whereas most of them are deflected sideways in the inverted wake flame. Hence, it appears that the combustion in the near wakes of envelope flames under both conditions is diffusion-controlled. The combustion in the near wakes of upright wake flames corresponds to that in a premixed flame, but the diffusion-controlled burning is dominant in the inverted wake flames. The flow pattern observed in the methanol flame around the 3 mm sphere is similar to that described above. N-heptane flames in a downward air flow resemble the corresponding upright flames described in Ref. [2], except that the luminous regions in the inverted flames are very much shorter than those in the upright flames. The photographs shown in Fig. 2 indicate the stagnation region between methanol flames around the 6 mm sphere and the white smoke rising from a smoking incense stick placed below. In both envelope and wake flames the stagnation region lies outside the flame region and is located on the air side of the edge of the flame. This is in contrast to the flow pattern near methanol cylinders [10] and n-heptane spheres [5] burning under natural convection, where the stagnation region was seen to be located on the fuel side of the reaction zone. This difference is presumably caused by the additional forced convection in this case, augmenting the outward diffusion of fuel vapour and products that balanced the natural convection in the experiments described in Refs. [5] and [10]. This figure clearly indicates the absence of any convective flow of oxygen into the flame zone in the

FLAME STRUCTURE

OF LIQUID DROPS

(a)

(d)

23

(b)

(c)

(e)

(f)

Fig. 1. Particle track photographs o f methanol flames on a porous sphere of 6 m m diameter at various downward air velocities: (a) cold flow without flame V - 0.50 m/s; (b) envelope flame V = 0.15 m/s; (c) envelope flame V = 0.40 m / s ; ( d ) envelope flame V - 0.55 m/s; (e) transition flame V 0.75 m/s; (f) wake flame V = 0.80

m/s.

(a)

(b)

Fig. 2. Smoke flow pattern downstream of the inverted m e t h a n o l flames on a porous sphere of 6 m m diameter: (a) envelope flame V = 0.50 m / s ; (b) wake flame V = 0.78

m/s.

24

SUBRAMANYAM R. GOLLAHALLI 160C

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Fig. 3. Axial temperature profiles in the wakes of inverted methanol and n-heptane flames on porous spheres: d = 3 mm: methanol (env.) F = 0.50 m/s; methanol (wake) F = 0.55 m/s; n-heptane (env.) F = 0.45 m/s; n-heptane (wake) F = 0.48 m/s. d = 6 ram: methanol (env.) F = 0.68 m/s; methanol (wake) F = 0.76 m/s; n-heptane (env.) F ~- 0.60 m/s; n-heptane (wake) F = 0.64 m/s.

wakes of inverted flames. A similar smoke pattern was noticed in the methanol flames around the 3 mm sphere. Temperature Profiles The axial profiles of the temperatures corrected for radiation losses in the inverted envelope and wake flames over 3 mm and 6 mm spheres are shown in Fig. 3. The following points emerge from the results shown in this figure: (a) the heat release zones are larger in envelope flames than in wake flames, similar to the behaviour observed earlier in the upright flames. But these zones in both envelope and wake flames in downward air flow are shorter than those in the corresponding upright flames. (b) There is no significant difference in the peak temperatures of envelope and wake flames, which is in agreement with the results of Ref. [2]. (c) The methanol flames have shorter heat release zones than the corresponding n-heptane flames. Figures 4 and 5 show the transverse temperature profiles at various axial distances in the

flames corresponding to Fig. 3. An examination of these profiles brings out the following: (a) the transverse temperature profiles in the envelope flame of the n-heptane drop show significant humps in the near wake region and these humps become flatter towards the end of the flame. This broadening of temperature peaks is not marked in methanol flames. The close resemblance of the temperature profiles in Figs. 4 and 5 with those presented earlier [2] indicate that similar mechanisms could be operative in both inverted and upright envelope flames. (b) Significantly large humps are seen in the transverse temperature profiles in the near wakes of the inverted wake flames, but the humps were absent in the transverse temperature profiles of upright wake flames [2]. This variation is probably a consequence of the different fluid dynamics in these two types of flames. In the upright wake flames, a mixture of fuel vapour and air is formed because of the air convected in to the wake and hence the temperature profiles resemble those of a premixed flame,

FLAME STRUCTURE OF LIQUID DROPS

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Fig. 4. Transverse temperature profiles in the wakes of inverted methanol and nheptane flames on a porous sphere of 6 mm diameter: methanol (env.) V = 0.68 m/s; methanol (wake) V = 0.76 m/s; n-heptane (env.) V = 0.60 m/s; n-heptane (wake) V --0.64 m/s.

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Fig. 5. Transverse temperature profiles in the wakes of inverted methanol and nheptane flames on a porous sphere of 3 mm diamter: methanol (env.) F = 0.50 m/s; methanol (wake) V = 0.55 m/s; n-heptane (env.) V = 0.45 m/s; n-heptane (wake) V = 0.48 m/s.

26

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Fig. 6. Axial and transverse composition profiles in the inverted envelope flames of methanol and n-heptane on a porous sphere of 6 mm diameter: methanol V-- 0.68 m/s; n-heptane V = 0.60 m/s.

Fig. 7. Axial and transverse composition profiles in the inverted wake flames of methanol and n-heptane on a porous sphere of 6 mm diameter: methanol V = 0.76 m/s; n-heptane V = 0.64 m/s.

but the absence of oxygen in the wakes of inverted wake flames makes the combustion diffusion-controlled, resulting in humps in the transverse temperature profiles. (c) The peaks in the transverse temperature profiles of the envelope and wake flames of both methanol and nheptane on the 3 mm sphere are flatter than those on the 6 mm sphere, probably because of the smaller effect of buoyancy in the former.

centration levels of the pyrolysis products are in conformity with the findings of Aldred et al. [5]. (b) In the inverted wake flames the axial composition profiles of all species except 0 2 are quite similar to those in the corresponding upright flames.

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Composition Profiles The axial and transverse composition profiles in the inverted envelope flames of n-heptane and methanol around the 6 mm sphere are shown in Fig. 6 and the composition profiles in the corresponding wake flames are shown in Fig. 7. Also Fig. 8 shows the composition profiles in both envelope and wake flames of n-heptane over the 3 mm sphere. In these figures the pyrolysis products are represented collectively a s C a l l m. By comparing these profiles with the composition profiles in the corresponding upright flames [2, 4 ] , the following points are observed: (a) the concentration profiles of CO2, H20, (C7H16 or CH3OH ) and CnH m in the inverted envelope flames around the 6 mm sphere are significantly similar to those in the corresponding upright flames. Also, the con-

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Fig. 8. Axial and transverse composition profiles in the inverted envelope and wake flames of n-heptane on a porous sphere of 3 mm diameter: (env.) V = 0.45 m/s; fwake) V = 0.48 m/s.

FLAME STRUCTURE OF LIQUID DROPS In the inverted wake flames the concentration of 02 near the surface of the drop is very small and slowly increases to the ambient value, hut in the upright wake flames 02 concentration near the drop is considerably higher and decreases to a trace value at the point where the fuel concentration becomes zero and then sharply increases to the ambient value. As explained earlier, this difference is caused primarily by the effect of buoyancy which opposes the convection of air into the wakes of inverted flames. {c) The composition profiles of the flames around the 3 mm sphere, although similar to those of corresponding flames around the 6 mm sphere, exhibit broader peaks presumably because of the smaller effect of buoyancy. These profiles are not compared with those in the corresponding upright flames since the flames over the 3 mm sphere were not investigated earlier.

Extinction Velocity The relative velocity between the drop and air stream at which the flame is extinguished in the upstream part of the drop is an important parameter since it determines the nature of combustion in the wake part of the flame. Udelson [11 ] found that the extinction velocities for kerosene spheres of diameter 6 to 25 mm were about 20% higher in the downward air flow than in the upward air flow. Table 1 shows the extinction velocities measured in the present study for n-heptane and methanol flames in upward and downward flowing air streams over the 6 mm and 3 mm spheres. The results support tile findings of Sjogren [12] and Agoston et al. [13] on the variation of extinction velocity with diameter (Ve cc v-d)and not those of Spalding [14] and Udelson [11] (Ve cod). Also, methanol flames have higher extinction velocities than n-heptane flames, which is in conformity with the results of Sami and Ogasawara [15]. The effect of the direction of the air stream on extinction velocity is in agreement with that documented by Udelson [11].

Burning Rate Since it was not possible to measure the flow rates of methanol with the capacitance transducer used,

27

TABLE l Extinction Velocities of Methanol and n-Heptane Flames on Porous Spheres (m/s) Ve

Ve

d (mm)

In upward air stream (m/s)

In downward air stream (m/s)

Methanol

6 3

0.55 0.40

0.76 0.55

n-heptane

6 3

0.50 0.34

0.64 0.48

only the burning rates of n-heptane flames could be determined, which are presented in Table 2. Also, the burning rates in upright flames over the 6 mm sphere determined earlier [16] and the burning rates calculated for envelope flames using the correlation of Agoston et al. [13] obtained for butyl alcohol are shown in this table. In this calculation the fluid properties are taken as those of air at a temperature corresponding to the arithmetic average of the adiabatic flame temperature and the ambient gas temperature, as suggested by Agoston et al. It can be seen that the burning rates of n-heptane in the inverted flames are not significantly different from those in the corresponding upright flames and also are in the range of predicted values.

Flame Length The visible flame lengths in the wakes of burning spheres measured from colour photographs are shown in Table 3. It is evident that the inverted flames are significantly shorter than upright flames, as a result of the mutually opposing forced and natural convection, which results in smaller axial velocities in the former case. It is also noticed that the lateral dimensions of the inverted flames are considerably larger than those of upright flames. Hence, although the flame length decreases by a large factor in the inverted flames, the surface area and the volume of the flame are not decreased to the same extent. For instance, for the 6 mm spheres with n-heptane, the length decreases by about 70%, whereas the surface area

28

SUBRAMANYAM R. GOLLAHALLI TABLE :2

Mass Burning Rates of Inverted and Upright Flames of n-Heptane over Porous Spheres In the upward air streama d (mm)

Flame type

In the downward air stream

V (m/s)

(mX 106) (kg/s)

V (m/s)

(m X 106) (kg/s)

6

Env.. Wake

0.45 0.50

6.2 1.9

0.60 0.64

5.8(7.6) b 2.1

3

Env. Wake

-

-

0.45 0.48

2.4(2.9) b 1.0

a From Ref. I16]. b Calculated using the correlation given in Ref. [13], using the properties of air at a temperature which is the arithmetic mean of the adiabatic flame temperature and the ambient gas temperature.

TABLE 3

Flame Lengths (L/d) in the Wakes of Methanol and n-Heptane Flames on Porous Spheres In downward air stream

In upward air stream Env.

Wake

Env.

Wake

d (ram)

V (m/s)

(L/d)

V (m/s)

(L/d)

V (m/s)

(L/d)

V (m/s)

(L/d)

Methanol

6 3

0.48 0.35

5.5 6.5

0.55 0.40

3.0 3.0

0.68 0.50

1.5 2.2

0.76 0.55

1.3 1.6

n-Heptane

6

0.46

15

0.50

8.3

0.60

0.64

3

0.30

18

0.34

9.5

0.45

4.0 (5.2)a 4.5 (6.6)a

2.5 (1.9)a 3.0 (2.4)a

Fuel

0.48

a Values calculated using the method of Ref. [8]. and volume decrease by 55% and 45% respectively when the upright flames are transformed to inverted flames by changing the direction of the air stream. Methanol flames are considerably shorter than n-heptane flames, presumably because of the smaller u n b u r n t fraction of the pyrolysis products and the absence of the relatively slow combustion of soot particles. The smaller unburnt fraction of pyrolysis products is a consequence of the smaller mass transfer number and lower oxygen requirement for stoichiometric combustion [17] of methanol as compared to n-heptane. The lengths of inverted flames calculated using

the model developed earlier [8] are also shown in Table 3. The values of the average stream velocity required in that prediction model was taken as the difference of the velocity computed using the burning rate and flame area [8], and the natural convection velocity induced by the burning drop. The natural convection velocity was estimated using the measured values of velocity given by Jaluria and Gebhart [18] for heated spherical surfaces and extrapolating them to the heat release rates of the burning spheres using the relation given by Fujii [19]. In view of the approximation involved in the calculations, the agreement

FLAME STRUCTURE OF LIQUID DROPS between the predictions and the measured values appears to be satisfactory. Predicted values for methanol drop flames are not shown since the burning rate required as an input in the prediction model was not measured as explained earlier. Radiation

The total radiant power emitted by the nheptane flames expressed as a fraction F of the heat release rate is shown in Table 4. The heat release rate was computed using the measured burning rate, assuming complete combustion. It is seen that F is significantly smaller in the inverted flames than in the upright flames, which presumably is the result of smaller flame volumes and soot concentration in the former. Since 11o measurements to separate the contribution of gases and soot to the emitted radiation were taken in this study, it is not possible to determine the relative dominance of those contributors. When the envelope flames are transformed into wake flames the radiant power decreases as reported earlier [2], but the fraction F does not decrease by the same extent, because the burning rate also decreases. The photographs of n-heptane drop flame exposed through narrow band pass filters show significant amounts of blue and green radiation near the upstream and side edges and continuous radiation over the entire wake of the inverted flame, which suggests that the formation and burning of soot begin quite close to the surface of the drop. Condensed Products

The condensed products sampled on stainless steel foils from the ends of the inverted n-heptane flames show much finer particles than those sampled at the ends of the upright flames, indicating smaller coagulation and growth of soot. Nitric Oxide Concentrations

Since the measurements of nitric oxide concentrations in the upright flames were not carried out in our studies reported earlier, the axial concentrations of nitric oxide were measured in both upright and inverted flames of n-heptane. Figure 9 shows the concentrations of nitric oxide in the

29 TABLE 4

Fraction of Heat Release Radiated from n-heptane Flames over Porous Spheres F In upward air stream

In downward air stream

d = 6 mm Env. Wake

0.26 0.23

0.16 0.14

d = 3 mm Env. Wake

0.25 0.19

0.17 0.13

Flame

flames over the 6 mm diam. sphere. It is seen that the peak concentrations of nitric oxide in the wakes of n-heptane spheres are significantly lower than those found by Hart et al. [20] in the forward stagnation region of 9.2 mm diameter porous cylinders burning n-heptane. This decrease is probably caused by the lower temperatures in the wakes than those in the upstream regions. The upright wake flame shows a slightly higher peak concentration of nitric oxide than the upright envelope flame, presumably because of the higher oxygen concentration in the near wake of the former. The peak concentrations of nitric oxide occur much closer to the surface of the drops in the inverted flames than in the upright flames, and are consistent with the locations of the peak temperatures. The peak concentrations of nitric oxide in the flames over the 3 mm sphere are smaller than those in the flames over the 6 mm sphere, which is in conformity with the size effects predicted by Kesten [21]. DISCUSSION

The differences in flame structure in the wakes of hydrocarbon drops burning in upward and downward air streams clearly demonstrate the importance of fluid dynamic parameters on the nature of combustion processes occurring in those regions. It is evident that the concentration of oxygen in the wakes of burning drops is primarily determined by the resultant of forces due to forced and natural convection. Under conditions

30

SUBRAMANYAM R. GOLLAHALLI n - HEPTANE d = 6rnm

20-

o

a + v

ENV (UPRIGHT) WAKE (UPRIGHT) ENV ( I N V E R T E D ) WAKE (INVERTED)

&

¢,1 1 5 n

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I

I

I

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L

2

4

6

8

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12

14

A X I A L DISTANCE

( x/d )

Fig. 9. Nitric oxide concentration prifiles along the axes in the wakes of uptright and inverted flames of n-heptane on a porous sphere of 6 m m diameter: upright flames: (env.) V = 0.46 m/s; (wake) V = 0.50 m/s; inverted flames: (env.) V = 0.60 m/s; (wake) V = 0.64 m/s.

where buoyancy and forced convection are augmenting each other, there is a significant difference between the wakes of envelope and wake flames, but when they are opposing each other that difference appears to be quite small. Since both buoyancy and forced convection act in the vertically upward axial direction in upright flames the radial component of velocities in the wake are negligible as noticed earlier [16]. Hence, molecular diffusion is the only mechanism for transporting the gaseous pyrolysis products formed in the near wake radially outwards to meet oxygen at the edges. This results in a small cylindrical surface where interface combustion occurs. A much longer luminous zone follows this region, because of large axial velocities due to the additive effects of buoyancy and forced convection and slow heterogeneous combustion of soot. But in the wake of an inverted envelope flame, the combined effects of smaller axial velocity, larger surface area, and larger radial velocity that augments molecular diffusion, shorten the flame considerably. The inverted wake flames are shorter than inverted envelope flames, mostly because of the smaller burning rates in the former.

The reasonably good agreement between the measured and predicted flame heights, taking natural convection into account, lends a significant support to the above explanation. The smoke pattern at the bottom edges of inverted flames show considerable resemblance to the flow pattern near the stagnation region of flat counterflow diffusion flames [22]. Since oxygen is not convected into the wakes of inverted flames, either from the sides or from the bottom edges, it appears that combustion in these regions can be modelled as a diffusion-controlled process. Recent evidence [23] suggests that liquid spray combustion can be modelled by combining the details of turbulent gas diffusion flames and single drop combustion. But there are numerous complex effects associated with the burning of sprays that are not present with single drop burning, such as droplet interactions, and fluctuating composition, temperature and velocity fields surrounding the droplets. The present study has demonstrated that a change in the relative flow around the burning drop alone can sufficiently affect the structure of the flame such that its chemistry is altered. Hence, enormous care should be exercised

FLAME STRUCTURE OF LIQUID DROPS when attempting to apply single drop data to spray combustion systems, particularly in modelling the processes like pollutant formation and radiation. The relative dominance of buoyancy and forced convection in flow systems is indicated by the ratio of the Grashof number to the square of the Reynolds number. An exact comparison between the values of this parameter in the present experiments and in practical spray combustion systems cannot be drawn because of the complex composition, temperature and velocity fields in sprays. But it can be easily seen that the effect of buoyancy in practical systems could be about 2 - 3 orders of magnitude smaller than that in the present study, because of higher relative velocities and smaller droplet diameters in the former. Moreover, the sprays may not contain droplets with individual flames as has been suggested recently [24], although that suggestion remains controversial. Hence, scaling of the structural data obtained from porous sphere experiments to practical systems is not direct.

CONCLUSIONS The structure of the flames in the wakes of burning spheres is significantly affected by the relative magnitudes and directions of buoyancy and forced convection. The combustion in the inverted envelope flame is diffusion-controlled and is somewhat similar to that in the upright envelope flame. On the other hand, the structure of the inverted wake flame is significantly different from that of the upright wake flame. Diffusion-controlled interface combustion is dominant in the inverted wake flame, whereas the combustion in the upright wake flame is similar to that in a premixed gas flame. The inverted flames are much shorter, produce less soot and emit less radiation than upright flames. The scaling of these results to burning sprays is not direct. The author acknowledges the financial support o f the National Research Council o f Canada in the f o r m o f an operating grant, and thanks Professor T. A. B r z u s t o w s k i Jbr his suggestions.

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