kalgatgi 1983

COMBUSTION AND FLAME 52:91-106 (1983) 91

The Visible Shape and Size of a Turbulent Hydrocarbon Jet Diffusion Flame in a Cross-wind

GAUTAM T. KALGHATGI

Shell Research Ltd., Thornton Reseach Centre, P.O. Box 1, Chester CH I 3SH, UK

The results of an extensive wind-tunnel study into the shapes and sizes of hydrocarbon jet diffusion flames in a horizontal cross-wind are presented. The shape of a turbulent diffusion flame in a cross-wind can be described by the frustum of a cone, which, in turn, can be defined by five different parameters of shape. When the burner axis is normal to the wind, each shape parameter can be related to the burner diameter, the burner exit velocity, the cross-wind speed, and the density of the burner gas by one equation. When the burner axis is not normal to the wind, the experimental results still follow an identifiable pattern and can be used to estimate flame shapes and sizes.

1. INTRODUCTION

Prediction of the size and shape of a turbulent dif- fusion flame in cross-wind is of much practical in- terest-for instance, to engineers designing in- dustrial burners and flare systems in the petro- chemical industry. The problem has been studied by Brzustowski and coworkers [1-6], by Escu- dier [7], and more recently by Becker et al. [8]. The enormous difficulties involved in theoretically modeling such a complex turbulent flow and com- bustion problem have been highlighted in Refs. [1] and [3]. Hence, for the time being, engineers have to rely on empirical methods that predict some gross average features of the flame which, in many practical cases, are all that are needed.

Many such methods are used in the oil and gas industry (see, for example, Ref. [9] ) for predicting the position of the flame tip with respect to the burner tip in a normal cross-wind. Of all these methods, perhaps the one proposed by Brzustow- ski [2] has the soundest scientific foundation. However, as he pointed out, his procedure, which is mainly based on cold flow correlations, does not predict the flame length accurately (for laboratory- scale propane flames, for instance), though the tra-

Copyright © 1983 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, ICY 10017

jectory of the flame centre line can be described adequately [6]. Results from large-scale flare tests are not well reported and whatever evidence is available (see, for example, Ref. [ 10] ) is inconclu- sive. Becker et al. [8] have published a limited amount of experimental data for flames from a vertical burner in a normal cross-wind; they have also considered interesting variants of the prob- lem, viz. the flame from a horizontal burner in still air and the flame from a vertical burner in a body of air rotating about the burner axis. Again, there is not much information in the literature about flame widths. Hence, there has been a need for a systematic experimental study of the detailed shape and size of a jet diffusion flame in cross- wind; the results of such a study are described in this paper. The study leads to the formulation of empirical correlations based on extensive experi- mental data which allow the flame size and shape to be predicted in greater detail than before.

The main body of the work considers the stand- ard case of a vertical burner in a horizontal wind. Experiments were also conducted where the an- gle, 0j, between the burner axis and the wind di- rection was other than 90 °, though the wind was always horizontal. The visible flame can be de-

0010-2180/83/$03.00

92 G.T. KALGHATGI

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scribed by a frustum of a cone, which, in turn, can be defined by three lengths and two angles (see Fig. 1). The angle a a is the angle between the burner axis and the line OB joining the flame tip to the tip of the burner. The angle a is the angle made by the axis of the frustum with the burner axis. The flame tip is located with respect to the stack tip by a B, together with a length, either the length L n of the line OB or the normal distance L s v between the flame tip B and the burner exit plane. W 2 and W 1 are the widths of the frustum at either end. Note that the lower end of the frustum, PQ, passes through the point of intersection of the frustum axis and the burner axis. Thus the base of the flame, as described by the frustum, is lifted off the burner along, but not perpendicular to, the burner axis. We would have to introduce an ad- ditional length scale to describe the displacement from the burner tip of the flame base perpendicu- lar to the burner axis; such displacement was ac-

tually observed in many of the cases studied here. Since this would only introduce an extra shape parameter which would have to be empirically pre- dicted, it was decided to tolerate the small errors in the description of the shape of the flame near its base by sticking to a five-parameter description of the frustum.

It is possible to find an empirical formula for each of these parameters, at least for the 0j = 90 ° case, from analysis of the experimental results as described below.

2. EXPERIMENTS AND RESULTS

The experiments were conducted in a wind-tunnel belonging to Sheffield University. The test section of the wind-tunnel is 2.65 m high and 2 m wide and has a large window (2.3 m × 2.9 m) made of transparent heat-resistant plastic through which the flame can be observed. The air flow passes

JET DIFFUSION FLAME IN CROSSWlND 93

through a fine wire mesh, a contraction, and a honeycomb structure before it enters the test section and, hence, is expected to be uniform there.

Burners of 6, 10, 12, 14 and 22 mm diameters were used. Each burner was placed in the wind- tunnel section with its axis making the appropriate angle, 0j, with the horizontal, which was always the wind direction. The experiments were done at different cross-wind speeds (V), ranging between 2.7 m/s and 8.1 m/s, and at different burner exit velocities (Ue), ranging between 15 m/s and 220 m/s. Each burner is a straight tube and was mounted on a large settling chamber of 150 mm internal diameter. The tip of the burner was usually about 0.6 m from the floor of the tunnel. The pressure in the settling chamber was measured using either a water or a mercury manometer. This pressure was taken to be the upstream stagnation pressure of the flow and the velocity at the nozzle exit was calculated from it. The wind velocity was meas- ured at the level of the burner exit, using a micro- manometer. The gases used were commercial grade propane, ethylene, methane, and butane.

The flame shape was recorded using a color video system for each gas, burner and 0j for dif- ferent sets of V and U°. For each of the experi- ments, a frustum of a cone was fitted to the flame in each of five randomly chosen frames of the rele- vant video record. The average of these five shapes was taken to represent the flame shape for that particular case. There were a few cases where the flame shape fluctuated too much with time for such an average to be meaningful. These cases are not included in the final data reduction, which considers a total of 136 different experiments. It must be emphasized that, for any given case, there was very good agreement (to within 6% for any of the shape parameters considered) between the shapes fitted in this manner to the flame by two independent observers.

Before we come to the presentation of the re- suits, we will briefly discuss how we expect them to behave. Let us, for the sake of the following dis- cussion, consider LB, the length of line OB in Fig. 1 which is often taken to be the "flame length," as a characteristic dimension of the flame. At the tip of the flame, the concentration of the

fuel gas should have reached the stoichiometric mass fraction, C. The rate at which air is entrained into the flame to bring this about will determine the length LB. The entrainment rate in a jet in cross wind depends on the relevant aerodynamic param- eters, the momentum flux ratio pooV2/PeUe 2, where p~. and Pe are, respectively, the densities of the burner gas and air, and the Reynoids and the Richardson ratios. It will also depend on the burner source diameter D s = D(Pe/p~) o'5, where D is the actual burner diameter (e.g., Refs. [2, 11]). We can reasonably assume that the Reynolds number at the burner exit is sufficiently high, and the turbulence is sufficiently developed, so that the jet entrainment coefficients are independent of the Reynolds number. The Richardson ratio, which measures the importance of buoyancy, is defined as the ratio of the buoyancy to the input mo- mentum flux. Conventionally, the cube root of this ratio, termed the Richardson number, ~, is used in diffusion flame studies (see the Introduction in Ref. [11 ]). In the present context, it can be de- fined as

~= ~ - - ~ g 2~tl /alXLB \os2Vo !

where g is the acceleration due to gravity. Thus we can expect L B to depend on V, Uo, Ds, pc, p~, C, and ~. From simple dimensional analysis, we can expect LB/D s to depend on the velocity ratio R = V/U°, ~, C, and Pc~P**. We can extend this argu- ment to any of the length scales used to describe the flame and expect them to depend on the non- dimensional parameters discussed above when nor- malized with respect to D s. The angles describing the flame depend on the ratios of lengths and hence should be independent of Ds, but should depend on the same nondimensional parameters as the lengths.

We will show, from experimental results, that R is by far the most important nondimensional pa- rameter in the present problem. The results for the 0j = 90 ° case are described first.

2 .1 T h e 0i = 9 0 ° c a s e

This series of tests comprised 103 different experi- ments. The range of conditions considered, as well

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JET DIFFUSION FLAME IN CROSSWIND 95

as the symbols used in the subsequent figures, are listed in Table I.

The five parameters chosen to define the cone frustum in this case were ctB, a, LBv, W, and W2. It was found that a B and a depend only on the velocity ratio R. This is illustrated in Figs. 2 and 3, where ct B and t~, respectively, have been plotted against R. Also shown in Fig. 2 are the plots for a B for propane, methane,, and ethylene as pre- dicted by Brzustowski's procedure [2]. These are, in general, lower than the values from our experi- ments.

If any of the three length scales is normalized with respect to Ds, the data for all the experi- ments can again be collapsed on to a single curve when plotted against R. This is illustrated in Fig. 4 for (LBv/Ds), where the curves predicted by Brzustowski's procedure [2] for propane, methane, and ethylene have also been plotted. It can be seen that there is very good agreement between these curves and our experimental data. Thus, it can be seen from Figs. 2 and 4 that Brzustowski's pro- cedure [2] underestimates the flame length, LB, though it predicts the height of the tip of the flame above the tip of the burner very well. The plots for (W2/Ds) and (W1/Ds) in Figs. 5 and 6, respec- tively, show much more scatter than the plots in Figs. 2, 3, and 4. Best-fitting curves were found for the plots of each of the five shape parameters. Over the range 0.02 < R < 0.25, the equations that describe these curves are:

a B = 94 - (1.6/R) - 35 R (degrees) (1)

a = 94 - (1 . l /R) - 30 R (degrees) (2)

(LBv/Ds) = 6 + (2.35/R) + 20 R (3)

(W2/Ds) = 80 - (0.57/R) - 570 R

+ 1470 R 2 (4)

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+ 950 R 2. (5)

From these correlations, we can also deduce that the cone half angle, 13, for the frustum de- creases from a value of about 5 ° at R = 0.025 to a value of about 2.8 ° at R = 0.2. Thus at large rela-

tive wind speeds, the flame takes an almost cylin- drical shape. For diffusion flames in still air, the value of/~ appears to vary between 6 ° and 8 °.

The results show that the shape and size of the flame is independent of C and is determined only by the aerodynamics of the problem. We must, however, remember that the range of C considered in our experiments is small, from 0.063 for ethylene to 0.055 for methane. The results depend on the density ratio Pe/P~, which ranged from 1.86 for commercial butanes to 0.55 for methane, only to the extent that it appears in D s. In still air, the en- trainment of air into the diffusion flame is dom- inated by buoyancy [ 11 ] and flame lengths are de- pendent on ~. Our results show that in the presence of cross-wind, buoyancy is not important and flame size is independent of ~, which ranges from 1.5- 11.6 in this study, ascan be seen from Table I. The cross-wind is the dominant factor in the entrain- ment of air into the fuel jet and indeed enhances it considerably (e.g., Refs. [12] and [13]). This greatly shortens the flame length. For instance, in all our experiments (LB/Ds) was between 95 and 120, In still air, for the jet velocities considered in this paper, (LB/Ds) can be expected to be larger than 200 [11]. Brzustowski and co-workers [1-6] , as well as Becket et al. [8], have also noted that the visible flame shape, as determined by the tra- jectory of the flame centerline, is largely unin- fluenced by buoyancy. Buoyancy effects would become increasingly important as one moved downstream into the plume of hot gases beyond the tip of the flame. Entrainment in that region may be described by a conventional buoyant plume model (see Ref. [7] ).

The largest flame encountered in this study was 2.7-m long, comparable in size to a flame from an industrial burner. In large flames, such as those re- sulting from industrial flares (e.g., 1 m stack di- ameter, methane flare), ~ could vary between 4 and 20 depending on exit velocity. Thus, the present experiments do cover a range of ~ which is of practical interest and the correlations presented should be applicable to a large class of practically interesting cases. Indeed, some preliminary field tests with large flames (L B --- 15 m, /-,re between 100 m/s and 260 m/s) have confirmed that the correlations presented here predict the flame shape

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very well. However, we have also got a few results from field tests where the observed flame lengths are significantly lower than can be expected from the laboratory results. These field tests were done at large values of R (greater than 0.2) and low exit velocities. It is possible that at large relative wind- speeds, the structure of the wind turbulence ac- quires greater importance and results from uni- form wind tunnel streams do not give wholly reliable indications of performance under natural wind conditions, as suggested by Becker et al. [8]. These flames are also "lazy" and are unstable and meander a lot, thus making the idea of an "average" flame shape much less meaningful. A lot more reliable data from large scale field tests are needed either to satisfactorily confirm or to extend the flame shape and size correlations given in this paper, to large industrial flares.

2.2 Cases where Oj =/= 90 °

In this section, we present experimental results for when 0j = 45 ° , 66 ° , 114 ° , and 135 ° . The gases used were propane and ethylene. The wind speed, V, ranged between 2.7 m/s and 8 m/s and the exit velocity, Lie, ranged from 45 m/s to 1 I0 m/s. The data are not as extensive as in the 0j = 90 ° case, but they still follow an identifiable pattern as de- scribed below.

Here we have chosen aB, a, L B, W 2, and W 1 to define the cone frustum that describes the flame, In Fig. 7, the angle a B is plotted against R for dif- ferent burner inclinations. It again appears that for a given value of 0j, a B depends only on R, as in the 0j = 90 ° case. In Fig. 8, (LB/Ds) has been plotted against R for different values of 0j. Though there is a lot of scatter in the plots, we can assume

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JET DIFFUSION FLAME IN CROSSWIND 103

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JET DIFFUSION FLAME IN CROSSWlND 105

to a good approximation that (Ln/Ds) is constant for a given value of 0j. It can also be seen that the lower the value of 0j, the larger the value ofLn/D s. This is consistent with the observations o f Platten and Keffer [12] that as 0j increases, the total en- trainment coefficient increases.

In fact, we can now plot the variation of (Ln/Ds) against 0j, as in Fig. 9, and use this to esti- mate the flame length L n for 0j ~< 135 ° if R > 0.025. For larger values of 0j, when the wind is blowing almost into the jet, the flame can no longer be represented by the frustum of a cone and our model breaks down. A linear relation- ship between (LB/Ds) and 0 i given by:

(LB/Ds) = 163 - 0.64 0j (6)

where 01 is in degrees, appears to be adequate. Finally a has been plotted against R for differ-

ent values of 01 in Fig. 10. In general, a > aB, though this difference is much less noticeable for cases where 0j < 90 °. It can also be seen that a tends to 0j, as is to be expected, whenR increases Indeed, if (a + 90 - 0j), the angle between the center line of the frustum and the vertical, is plotted against R, the points in Fig. 10 will all collapse reasonably around the plot in Fig. 3, where a has been plotted against R for 0j = 90 °.

When normalized flame widths (W1/Ds) and (W2/Ds) are plotted against R for this second series of experiments, all the points fall within the scatter of the points for corresponding plots for 0j = 90 °. Thus we can use the correlations given in Equations 4 and 5 for all the values of 0j considered.

ner gas. In fact the shape and size of the flame ap- pear to be determined solely by the aerodynamics of the problem and in particular by the cross-wind which seems to dominate the entrainment process. Buoyancy appears to be unimportant, so that the most important nondimensional parameter in de- termining the flame shape and size is the ratio of the wind speed to the burner exit velocity.

Flame lengths of up to 2.7 m were encountered in these tests, so that the results should be directly applicable to industrial burners which usually pro- duce flames of comparable size. Preliminary re- sults from field tests also suggest that the correla- tions presented in this work predict the flame shape very well for large industrial flares if the stack exit velocity is large and the relative wind speed is small. Such flames could result from emergency flarings. For large relative wind speeds and small stack exit velocities, i.e., when "lazy" meandering flames are produced, the few results from field trials that we have made suggest that the present correlations are not very good. More reliable data from large scale tests are needed either to satis- factorily confirm or extend the present correla- tions to flames resulting from industrial flare.

Experimental data have been presented for four cases when the burner axis is not normal to the wind. These data also follow an identifiable pat- tern and can be used to estimate flame shapes and sizes. Thus, it is now possible to predict the shape and size of a hydrocarbon diffusion flame in a cross-wind for a jet injection angle 0j in the range of 45 ° ~<Oj ~< 135 ° .

3. CONCLUSIONS

The shape of a turbulent diffusion flame in a cross- wind can be described by the frustum of a cone, which, in turn, can be defined by five different shape parameters. When the wind is normal to the burner axis, the analysis of experimental data over a wide range of conditions has shown that there is one equation for each of these parameters relating it to the burner diameter, the burner exit velocity, the cross-wind speed, and the density of the bur-

The author wishes to thank Mr. R. J. Wade and Mr. J. F. Bennett o f Shell Research Ltd., Thornton for their help in the experimental work.

REFERENCES

1. Botros, P. E. and Brzustowski, T. A., Seventeenth Symposium on Combustion, The Combustion Insti- tute, 1979, p. 389.

2. Brzustowski, T. A. Prog Energy Combust. ScL 2:129 (1976).

106 G.T . KALGHATGI

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Received 28May 1982; revised 28 February 1983