Characteristics of Turbulent Nonpremixed Jet Flames under Normal- and Low-Gravity Conditions

Cherian A. Idicheria, Isaac G. Boxx and Noel T. Clemens∗

Center for Aeromechanics Research, Department of Aerospace Engineering and Engineering Mechanics,

The University of Texas at Austin

Running title: LOW-GRAVITY TURBULENT NONPREMIXED JET FLAMES

Full-Length article submitted to Combustion and Flame

∗ Corresponding Author: Prof. Noel T. Clemens, 210 E 24th St. WRW 313B, 1 University Station, C0604, Austin, TX-78712-1085, USA Phone: (512)-471-5147 Fax: (512)-471-3788 E-mail: clemens@mail.utexas.edu

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ABSTRACT

An experimental study was performed with the aim of investigating the structure of

transitional and turbulent nonpremixed jet flames under different gravity conditions. Experiments

were conducted under three gravity levels, viz. 1 g, 20 mg and 100 µg. The milligravity and

microgravity conditions were achieved by dropping a jet-flame rig in the UT-Austin 1.25-second and

NASA-Glenn Research Center 2.2-second drop towers, respectively. The flames studied were

piloted nonpremixed propane, ethylene and methane jet flames at source Reynolds numbers ranging

from 2000 to 10500. The principal diagnostic employed was time-resolved, cinematographic

imaging of the visible soot luminosity. Mean and root-mean square (RMS) images were computed,

and volume rendering of the image sequences was used to investigate the large-scale structure

evolution and flame tip dynamics. The relative importance of buoyancy was quantified with the

parameter, Lξ , as defined by Becker and Yamazaki (1978). The results showed, in contrast to some

previous microgravity studies, that the high Reynolds number flames have the same flame length

irrespective of the gravity level. The RMS fluctuations and volume renderings indicate that the

large-scale structure and flame tip dynamics are essentially identical to those of purely momentum

driven flames provided Lξ is less than approximately 2-3. The volume-renderings show that the

luminous structure propagation velocities (i.e., celerities) normalized by the jet exit velocity are

approximately constant for Lξ 8. The flame length fluctuation

measurements and volume-renderings also indicate that the luminous structures are more organized

in low gravity than in normal gravity. Finally, taken as a whole, this study shows that Lξ is a

sufficient parameter for quantifying the effects of buoyancy on the fluctuating and mean

characteristics of turbulent jet flames.

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INTRODUCTION

Becker and Yamazaki [1, 2] and Becker and Liang [3] were among the first to systematically

study the effects of buoyancy on the characteristics of turbulent nonpremixed jet flames, such as soot

formation, entrainment and luminous flame length. They proposed that the effects of buoyancy could

be quantified by a non-dimensional “buoyancy parameter”, Lξ (defined below), which is a measure

of the relative importance of the buoyancy force to source momentum over the entire flame length.

They concluded that the effects of buoyancy on the characteristics of the flame become negligible

when this non-dimensional parameter is less than unity. In their experiments they lowered Lξ by

increasing the Reynolds number; however, this raises the important issue of whether any observed

differences in the flame characteristics are due to the reduced importance of buoyancy or to the

larger Reynolds number.

In the past couple of decades, the microgravity environment has been used to investigate the

effects of buoyancy on a wide range of combustion systems. The microgravity environment offers

the advantage that buoyancy effects can be isolated, because gravity can be changed without having

to modify the Reynolds number. Bahadori et al. [4] and Hegde et al. [5,6,7] were among the first to

investigate nonpremixed jet flames in the laminar to turbulent regime in normal and microgravity

conditions. Their primary diagnostic was video-rate (30 fps) luminosity imaging, which was used for

flow visualization and to obtain flame length data over a range of Reynolds numbers. Their results

showed that there are significant differences in the characteristics of normal and microgravity

nonpremixed jet flames. For example, at a Reynolds number of about 5000 their microgravity flames

were more than twice as long as their normal-gravity flames, the latter of which had Lξ ≈ 6.5. This

indicates a much stronger dependence of flame length on Lξ than would be indicated by the results

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of Becker and Yamazaki [1]. Therefore, this raises the issue of whether Lξ is a sufficient parameter

for quantifying the effects of buoyancy.

With particular focus on the underlying turbulent structure, studies of transitional

nonpremixed jet flames have shown that disturbances originate at the base of the flame in

microgravity and propagate upwards as Reynolds number is increased, whereas in normal gravity,

the disturbances originate near the flame tip and work their way down [4]. Furthermore, normal

gravity studies of turbulent nonpremixed flames have shown that flame-tip burnout dynamics are

closely related to the large-scale organization of the jet flame [8], and hence are strongly affected by

buoyancy [9]. To date, there is no consensus as to the nature of the large-scale motions present in

purely momentum driven round jet flames, although there is evidence for both axisymmetric and

helical structures [5,8,9]. It has also been suggested that buoyancy can substantially influence the

large-scale structure of even nominally momentum-driven flames, since the low velocity flow

outside of the flame will be more susceptible to buoyancy effects [10]. Even subtle buoyancy effects

may be important because changes in the large-scale structure have implications for the fluctuating

strain rate, which influences the structure of the reaction zone.

There are evident limitations in the range of conditions that were achieved by Becker and

Yamazaki [1,2], Becker and Liang [3] and in previous microgravity studies [4-7]. For example, in

Refs. 1-3, they were not able to obtain values of Lξ less than 3 and so they could not study flames

that were momentum-dominated (according to their own criterion) over the full length of the flames,

whereas Refs. 4-6 investigated only a limited range of Reynolds numbers (250

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jet flames. We take advantage of an ability to study flames at a range of Reynolds numbers and

under three different gravity levels, viz. 1 g, 20 mg and 100 µg. The three gravity levels make it

possible to alter the value of Lξ through two orders of magnitude, while maintaining the same

Reynolds number. The reduced gravity levels are achieved by using the 1.25-second University of

Texas drop tower facility (UT-DTF) and 2.2-second drop tower at NASA-Glenn Research Center

(GRC). The primary diagnostic employed was cinematographic imaging of the flame luminosity.

The cinematographic imaging improves upon the video-rate (30 Hz) imaging used in previous

studies of microgravity nonpremixed jet flames [4-7] because it enables us to investigate the

evolution and dynamics of large-scale turbulent structures. Furthermore, the flame length results in

Refs. 4-7 seem to suggest that Lξ is not sufficient to quantify the effects of buoyancy, and so a major

objective of this work is to specifically address this issue, and to determine at what value of Lξ the

turbulent structure reaches its asymptotic momentum-dominated state.

EXPERIMENTAL PROGRAM

Drop-Rig

The experiments were conducted using a self-contained combustion drop-rig in the UT and

GRC drop towers. A schematic of the drop-rig is shown in Fig. 1. The drop-rig consists of a

turbulent jet flame facility and an onboard image and data acquisition system assembled in a NASA-

GRC 2.2-second drop tower frame. The fuel jet issues from a 1.75 mm (inner diameter) stainless

steel tube, surrounded by a 25.4 mm diameter concentric, premixed, methane-air flat-flame pilot

(operated near stoichiometric conditions). The pilot flame was used to ignite the main jet during the

drop and also to keep the jet flame attached. Flame luminosity was imaged using a Pulnix TM-6710

progressive scan CCD camera, capable of operating at 235 fps or 350 fps, at resolutions of 512×230

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pixels and 512×146 pixels, respectively. The camera was electronically shuttered, with the exposure

time depending on flame luminosity (1/235 to 1/2000 seconds), and was fitted with a 6mm focal

length, f/16 CCTV lens, chosen to maximize the field of view (typically 405 mm). The drop-rig was

fully automated through a custom configured passive back-plane type onboard computer

(CyberResearch Inc). The onboard computer had no monitor or keyboard due to space constraints in

the rig and was controlled remotely from a notebook computer. A program developed in LabVIEW

was used for timing and control of the experiment. A more detailed description of the drop-rig is

given in Idicheria et al. [11].

1.25-second drop tower

The 1.25-second UT-DTF is 10.7 m tall and has a 2.5 m square cross-sectional area. The

tower is equipped with a two-ton capacity electric hoist and a cargo hook at the end of the hoist's

chain that acts as the quick-release mechanism. At the base of the drop tower is a deceleration

mechanism consisting of a container 1.7 m long by 1.1 m wide by 1.8 m deep, filled with flame

retardant, HR-24 polyurethane foam. The floor of the container is lined with two 150 mm thick

sheets of foam, and the rest of the container is filled with 150 mm foam cubes. After allowing for the

space taken up by the electric hoist and the deceleration mechanism, the drop tower has a 7.6 m free-

fall section. This allows for approximately 1.25 seconds of low gravity time per drop. In order to

characterize the milligravity conditions, data were acquired using a Kistler model 8304-B2 “K-

Beam” capacitive accelerometer. These measurements acquired in the UT-DTF indicate the gravity

levels range from 0 mg at the beginning of the drop to 20 mg by the end (the latter value is due to

aerodynamic drag because no drag-shield is used). The g-gitter (defined as peak to peak variation)

from these measurements was typically ±3 mg. A Kistler Model 8303-A50 “K-Beam” capacitive

accelerometer was used to measure the deceleration of the drop-rig on impact at the end of each

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drop. Impact loading thus measured ranged from 25-30 g. In order to reduce the effects of outside

disturbances while performing the experiments in the UT-DTF, the sides of the drop-rig were closed

with aluminum sheets.

2.2-second drop tower

The 2.2-second drop tower at NASA-GRC is approximately 24 m tall. The drop-rig is

enclosed in a drag shield to minimize the aerodynamic drag on the experiment. The assembly

consisting of the drop-rig and drag shield is attached to a pneumatic release system at the top of the

tower prior to the drop. At this point, the drop-rig stands 191 mm from the base of the drag shield.

After the release, the drop-rig falls through the 191 mm inside the drag shield while the whole

assembly of drag-shield and drop-rig falls through 24 m. At the end of the drop the assembly impacts

an air bag and comes to rest. During the 2.2 second drop time microgravity levels of 100 µg is

attained. Impact levels during the deceleration are in the range of 15-30 g.

EXPERIMENTAL CONDITIONS

Three different jet fuels were studied (propane, ethylene and methane) and experiments were

conducted for a range of Reynolds numbers (2000

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mg and 100 µg; thus, for the different fuels studied, Lξ varied from 3.7 to 12.0 in normal-gravity,

1.0 to 4.0 in milligravity and 0.36 to 0.66 in microgravity conditions.

RESULTS AND DISCUSSION

Instantaneous, Mean and RMS Luminosity

The time-sequenced images of the luminosity acquired during the drops reveal the start-up

transient and the attainment of a steady state (i.e., a stationary state that is steady in the mean

properties). Sample startup sequences for ethylene flames at two Reynolds numbers of 2500 and

7500 in normal and milligravity conditions are shown in Fig. 2. In the low Reynolds number case,

the flame tip seems to reach a steady state in approximately 0.3 seconds in milligravity (Fig. 2a),

whereas in normal-gravity (Fig. 2b) it takes only 0.2 seconds. A more quantitative measure of the

flame tip time history for the higher Reynolds number case is shown in Fig. 3. It can be seen that for

the case that is presented the time to steady state is approximately 0.2 seconds for the normal and

milligravity conditions. However, in the case of propane flames, the startup transient is higher owing

to the lower jet exit velocities when compared to the ethylene flames. Nevertheless, the maximum

startup transient was less than about 0.4 seconds irrespective of the gravity level for all the cases

studied.

Mean and RMS luminosity images were computed from the time-sequences, excluding the

startup and shutdown transient frames. Sample mean flame images for ethylene and propane at

different Reynolds numbers and buoyancy parameters are presented in Fig. 4. For comparison,

sample instantaneous images, from which the mean images were computed, are shown in Fig. 5. The

instantaneous images were sampled from the steady state portion of the flame time history. Each set

of mean and instantaneous images (i.e., those separated by vertical lines in Figs. 4 and 5) is for the

same fuel type and Reynolds number. All of the cases with Lξ

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with 1< Lξ 3 were taken in normal-gravity.

Significant differences in the structure of the flames can be seen by comparing the high and low Lξ

cases. For example, Fig. 4d and 5d, compare ReD=5000 propane flames in normal, milli- and micro-

gravity. It is seen that the milli- and micro-gravity flames are significantly thicker than the normal-

gravity flame, both instantaneously and on average. This observation is consistent with previous

studies that compared the structure of laminar and transitional/turbulent jet flames in normal and

microgravity [4,5]. The thicker microgravity flames are likely a result of the convection/diffusion

competition that governs the growth rate of laminar jets. The jet growth rate is set by the broadening

effect of radial diffusion and the thinning effect of streamwise convection. In the presence of gravity,

the upward buoyant acceleration increases the convection length scales and hence reduces the

growth rate. As the flames become more turbulent with increasing Reynolds number, it would be

expected that the difference in the thickness of the flames should diminish, and this appears to be the

case.

Upon careful viewing of the instantaneous images and movie sequences, a few

generalizations can be made about the structure of the flames at the lower Reynolds numbers when

there is a large difference in the magnitude of Lξ . For example, the most obvious trend seen in the

luminous structure of the transitional flames is that in low-gravity they exhibit approximately

axisymmetric structures that extend over a relatively small scale (e.g., about 1-2 luminous jet widths)

and which exhibit a relatively regular spacing. In normal gravity, the structure is similar to that of

the low-gravity case in the lower portion of the flame, but farther downstream the flames tend to

exhibit a large-scale sinuous structure that is several jet widths in extent. Figure 6 shows highly

simplified cartoons of these differences in the luminous structure of the transitional flames. The

cartoons are meant to show an exaggerated view of the differences, but in reality, either type of

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flame can exhibit characteristics of the other; i.e., the buoyant flames can exhibit more axisymmetric

structures or the low-gravity flames can exhibit a sinuous structure. Nevertheless, the differences

discussed above are readily evident upon viewing the time sequences and correctly describe the

gross features of the two types of flames. Specific examples of these trends in the instantaneous

images can be seen by comparing high and low Lξ flames in Fig. 5c and 5d, and the startup

sequences in Fig. 2a,b. These differences in the structure also seem to have a bearing on the flame

tip dynamics as will be discussed below.

As Lξ approaches unity, the buoyant acceleration is overwhelmed by the jet momentum and

little difference is expected among normal and microgravity jet flames. This effect can be seen in

Fig. 4a, which shows the mean luminosity images for ethylene at ReD=10500 in normal and

milligravity environments. This image pair shows that the Lξ =3.7 flame is very similar to the Lξ =1

flame. A careful viewing of all of the images in Fig. 4 strongly suggests that flames with Lξ near

unity and below are essentially identical in their mean luminosity (flame height and width).

Differences start to appear as the Lξ values become farther apart as seen from Figs. 4b-4d.

Figure 7 shows the variation of the mean visible flame length (obtained from mean images)

normalized by the tube exit diameter for all the cases studied. Precision uncertainty levels (95%

confidence) computed from repeated runs are also shown. The confidence intervals are in the range

of ±4D to ±35D for all three flames, with higher differences in the lower Reynolds number cases. It

is evident from Fig. 7 that the flame lengths under different gravity levels converge with increasing

Reynolds number for ethylene and propane. Only low Reynolds numbers are shown for methane

because at higher Reynolds numbers the flames were lifted, which was not desirable for the purposes

of this study. For the different Reynolds number ethylene jet flames, the maximum variation in the

mean flame length is ±15% (ReD=2500 and 5000). However in the higher Reynolds number cases,

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the variation in flame length is less than ±10%. For propane, a difference of ±20% is seen only at the

lowest Reynolds number whereas in all the other cases the difference is less than ±10%.

There are some trends in flame length behavior for a particular fuel and across gravity

conditions that are evident in Fig. 7. The normal gravity propane flames are seen to increase in their

normalized mean luminous flame length (L/D) from a value of approximately 200 to 270 as the

Reynolds number increases from 2500 to 8500. The milligravity and microgravity propane flames

also show the same trends, i.e., increasing mean luminous flame length with increasing Reynolds

number. Substantial differences in the mean luminous flame length between gravity conditions are

seen only in the low Reynolds number propane flames (e.g. the low-gravity flame is longer than the

normal gravity flame by 45D at ReD=2500). However, a majority of the low-gravity propane flames

appear to be longer than their normal gravity counterparts by about 10%. The trend seen in the

ethylene flames is noticeably different from the propane flames over the entire range of Reynolds

number of 2500 to 10500. First, it can be seen that the ethylene flames are shorter than the propane

flames over the full range of Reynolds number. Furthermore, the normal-gravity ethylene flame

length is seen to increase from L/D of approximately 180 to 200 as the Reynolds number increases

from 2500 to 10500. Differences in flame length between gravity conditions for ethylene are seen for

Reynolds numbers less than 6000, as the majority of the normal gravity flames are longer than the

low-gravity flames. However, the flame lengths are very similar for Reynolds number higher than

6000. As mentioned previously, the methane flames were tested under milligravity and normal

gravity conditions only. The flames at the two Reynolds numbers investigated are longer in

milligravity than in normal gravity by approximately 12% and 5%, at Reynolds numbers of 2000 and

2500, respectively.

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Figure 7 also shows the data of Hegde et al. [6] for propane flames under normal and

microgravity conditions. Their microgravity data and the current milligravity data differ substantially

over the entire Reynolds number range. The normal-gravity data of both studies, however, show

better agreement, but still are significantly different in magnitude and trend with Reynolds number.

The computation of visible flame lengths will depend on the definition of the length, and therefore

absolute differences are not surprising. However, in contrast to the current findings, the differences

in trend between normal and microgravity flames are seen to be very large even for Reynolds

numbers greater than 4000. Note that similar differences in the flame lengths between normal and

microgravity conditions were also observed in methane and propylene jet flames [4].

The reason for the difference between the measurements of Hegde et al. [6] and the current

study is not known, but one other microgravity study [12] shows agreement with the current

measurements. Page et al. [12] studied pulsed, turbulent nonpremixed ethylene / oxygen-enriched-air

jet flames in microgravity, but they also included flame length measurements for steady, unpulsed jet

flames at a Reynolds number of 5000. Their normal and microgravity flame lengths did not exhibit

the large difference observed in Refs. 4,5,6, but the normal-gravity flame was actually slightly

longer than the microgravity one. This finding is consistent with the current study where the normal-

gravity ethylene-flame at ReD=5000 was also observed to be slightly longer than the milligravity

case.

Despite the agreement of the current results with those of Ref. 12, the difference with

Bahadori et al. [4] and Hegde et al. [5,6] could mean that the current setup is generating anomalous

results, even at normal-gravity. Therefore, to serve as validation of the current normal-gravity

results, Fig. 8 shows normal-gravity flame length data taken in the current study plotted together

with the data of Becker and Yamazaki [1] and Mungal et al. [9]. It can be seen that the present data

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agree quite well both in trend and in value with previously published work for the same fuel and the

same range of Reynolds number.

In order to give further confidence in the reliability of the normal-gravity results, a series of

tests were performed to see if the current normal-gravity flames were sensitive to the particular setup

used. First of all, tests were conducted at normal-gravity to see if non-piloted lifted propane flames

differed substantially in their length from the piloted attached flames. The differences seen in the

flame heights for these conditions were small. Secondly, tests were conducted with the burner in

various configurations; specifically, normal-gravity tests were conducted with the burner inside and

outside the drop rig, and with and without the pilot flame housing. In all of these tests, the difference

in observed flames lengths was small. This series of tests showed that the current normal-gravity

flames were not highly sensitive to how they were generated.

It seems likely, therefore, that the reason for the observed differences among the various

microgravity studies is that transitional low-gravity flames are particularly sensitive to the boundary

conditions under which they develop. The reason for this proposed increased sensitivity is that under

normal gravity conditions, buoyancy-induced fluctuations are the primary mechanism that triggers

the transition to turbulence. In microgravity, this source of disturbances is removed and therefore it

leaves the flame sensitive to other, possibly much weaker, disturbances. In other words, a

microgravity flame can be sensitive to the exact nature of the boundary conditions -- even when the

same flame under normal gravity would not be -- because the disturbances under normal-gravity

would be dominated by buoyancy. Under this argument, the reason for the increased flame lengths

of Refs. 4-7 is that they exhibit an extended laminar or transitional region as compared to the current

study and Ref. 12. The effect of buoyancy on the transition to turbulence is well known in laminar

flames. In fact, flames that are completely laminar in microgravity (e.g. [13]), can be highly

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wrinkled and turbulent in normal gravity owing to buoyancy-induced vorticity. In fact, a major

advantage of the microgravity environment is that it enables one to study low-strain rate laminar

flames that would be dominated by buoyant instabilities in normal gravity.

If this is argument is correct, then it would be expected that flame length data obtained in

microgravity would exhibit much more scatter than equivalent data obtained in normal gravity. For

example, whether a jet flame is piloted or not, or is enclosed or free, may have a greater impact on

the flow development under low-gravity conditions. Therefore, slight differences in the flow

configuration among the current work, Hegde et al. [5,6] and Page et al. [12], may lead to large

differences in the flame heights observed under low-gravity conditions. Given this possibility, the

differences between the experimental configuration of the current study and those of Refs. 4-7, and

12 are documented below. The jet flames in Refs. 4-7 were unpiloted and enclosed in a cylindrical

chamber (with a volume of 0.087 m3), whereas in the current study the jet flame issued into the

quiescent air inside the drop-rig (with an unoccupied volume of 0.24 m3). In general, the enclosure

around a flame can have an effect because it allows recirculation of products into the oxidizer

stream, and therefore can change the overall stoichiometry and density ratio. However, Refs. 4-7

state that the flame lengths were the same irrespective of the run time of the flame they investigated,

and so it appears that confinement was not an issue. Another important configuration difference

across the experiments is geometry near the jet exit. In the current study, the flames were piloted

with a 25 mm concentric laminar premixed flame, but otherwise the jet-exit region was

unobstructed. In Refs. 4-7, the flame was unpiloted, and a base plate was used that was located 5 to

10mm below the nozzle exit. According to the authors of Refs. 4-7, the presence of this plate could

have impeded the entrained air near the nozzle exit, and this could have led to lift-off and blowout at

moderately low Reynolds number. With regard to the experimental configuration used in Ref. 12,

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the flames were enclosed and stabilized by an igniter (which was always present) and issued into a

weak co-flow. It is not known if these differences are those that are most responsible for the

differences in the flame lengths, but the fact that such differences in geometry exist gives future

researchers specific issues to consider when designing experiments that will be used to study

transitional microgravity jet flames.

The RMS fluctuations of the flame luminosity time-sequences were computed to determine if

the trends that are observed in the mean images are also seen in fluctuating quantities. It is well

known that soot luminosity depends on many factors and so cannot be related in a simple manner to

a particular property of the soot, such as the soot volume fraction. As a consequence, if the RMS

fluctuations for two cases are different, it could be due to differences in the soot properties,

temperature or the underlying fluid mechanics. Nevertheless, the RMS fluctuations can provide

useful information because we are interested in detecting differences in the low- and normal-gravity

flames, regardless of the underlying mechanism. The RMS luminosity is useful toward this end

because it provides a more sensitive measure of the potential differences (as do all higher order

statistics) than the mean luminosity. Figure 9a shows RMS images for the ethylene flames at

ReD=10500 in normal and milligravity. The flames have noticeable similarities, but clear differences

are also apparent, such as the lower peak RMS values on the centerline of the Lξ =1.0 flame.

Furthermore, more drastic differences can be seen when comparing flames with a larger difference

in Lξ (Fig. 9b). Figures 9c and 9d compare the RMS luminosity for the propane flames (ReD=8500

and 5000). In Fig. 9c it is seen that the fluctuations are nearly identical for the Lξ =2.1 and Lξ =0.38

cases, however both differ substantially from the Lξ =7.8 case. A similar trend is observed for the

image set of Fig. 9d. It can be concluded that large fluctuations are present near the flame tip in the

large Lξ flames, which is expected since buoyancy acts on fluid volumes and so its effects are more

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prevalent near the flame tip where the large-scale vortical structures are formed. Interestingly,

regardless of fuel type or Reynolds number, the low Lξ flames all have qualitatively similar RMS

contours, i.e., the fluctuations peak near the periphery of the flame and remain low even at the flame

tip. This observation is consistent with expectations of a momentum-dominated jet where the largest

scalar fluctuations occur at the outer edges of the jet where the intermittency is largest [14].

Flame Length Time Histories

The time-histories of the instantaneous luminous flame length are shown in Fig. 10. These

data are for propane flames at varying Reynolds number, and were generated by computing the

instantaneous luminous flame length from the image-time-sequences. It is expected that the flame tip

fluctuation frequency will scale with the local large-scale time-scale δ/ Uc (with δ the local width

and Uc the centerline velocity) [15,9], but in the current study the local velocity is not known for all

conditions. Since δ/ Uc ∝ x2/(U0D) ∝ (D/U0)(x/D)2, then δ/ Uc ∝ (D/U0)(L/D)2 for a turbulent

momentum-driven flame of length L. For the same fuel (and hence stoichiometry), then L/D will be

nearly constant and the large-scale time (δ/ Uc ) will scale as D/Uo; therefore, the time axis has been

scaled by the characteristic time scale D/Uo. This scaling should be sufficient for removing the effect

of differences in the local convection velocity on the flame tip fluctuations for flames that are

momentum-dominated and of the same fuel type. Since the framing rate is not fast enough to detect

small-scale fluctuations in the flame tip, we expect Reynolds number effects will not be very

significant in these plots. These plots show that the flame tip fluctuations are very similar for Lξ

values of 2.8 and below, which indicates that the fluctuations are associated with the same type of

large-scale motions in all of the momentum-dominated cases. The Lξ =7.9 case seems to exhibit

higher frequency fluctuations, and this is clearly the case at Lξ =10.1 also. Since the time-scale

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normalization used does not account for buoyant acceleration, these higher-frequency fluctuations

are clear evidence of the effect of buoyancy on the flame tip dynamics. Careful inspection of Fig. 10

reveals some interesting trends in the nature of the flame tip fluctuations. For example, at the lower

values of Lξ the flame-tip time-histories exhibit “ramp-like” characteristic, whereby the flame

length gradually increases and then abruptly decreases. Similar “ramp-like” oscillations in the flame

length were observed in Ref. 9 and in the liquid-phase, acid-base “flames” in Ref. 15. The liquid-

phase flames are purely momentum-driven, and they exhibited a particularly high degree of quasi-

periodicity [15]. The movie sequences acquired in the current study show this behavior is associated

with the flame tip burnout characteristics. In particular, the movies show that a large-scale luminous

structure will form near the flame tip, propagate downstream, and then the entire structure will burn

out in a relatively uniform manner. It is the burnout of the entire structure that causes the flame

length to abruptly decrease. In Ref. 15 it is argued that the rapid burnout of the flame tip structure

indicates that the entire structure is mixed to a relatively uniform composition. In some cases, the

flame tip seems to burnout starting from its upstream edge, which was also observed in liquid flames

[15]. In Ref. 15, this upstream-to-downstream mode of burnout was attributed to the entrainment

motions, which sweep ambient fluid into the structure from the upstream side and so it is this side

that reaches stoichiometric proportions first.

The most buoyant case, Lξ =10.1, seems to deviate from this mode of burnout because the

flame length time history does not exhibit such obvious ramp-like time-traces. Indeed, observation

of the movie sequences shows that the burnout dynamics are different in the buoyant flames. In

particular, the large-scale structures near the flame tip are stretched out by the buoyancy forces, and

this causes them to exhibit an elongated, sinuous structure, and as a result the burnout is more

gradual. It appears that this stretching of the structures by buoyancy sufficiently modifies the

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entrainment motions to create a less uniform distribution of mixture fraction throughout the

structure. In addition to the difference in the ramp-like time-traces, careful observation of the movie

sequences indicates that the luminous structures at the flame tip in the momentum-dominated flames

seem to be more organized, or coherent, than the ones that exhibit strong buoyancy effects. The

more regular flame length fluctuations in low-gravity seem to be related to the more regularly spaced

structures as illustrated in Fig. 6. The flame tip fluctuations shown in Fig. 10 also suggest a lower

degree of organization with increasing buoyancy, since the fluctuations seem to be more random at

high Lξ . The observation that the liquid-phase flames, which are momentum-dominated, exhibit a

high degree of periodicity, even at higher Reynolds numbers, seems to add support to this

hypothesis. This issue will be discussed further below, but it should be noted that in Ref. 9 it was

remarked that the flame tip fluctuations seemed to be organized across the same range of Lξ as

considered here. In fact, it seems that their low and high Lξ cases all exhibit the ramp-like burnout

characteristics and arguably exhibit the same degree of organization. Since their data were taken at

higher Reynolds numbers than in the current study it is possible that this is the reason for the

apparent discrepancy.

Volume Rendering

Volume rendering of jet flame image sequences was used to investigate further the

characteristics of the large-scale luminous structures. In this image-processing technique, discussed

in Ref. 9, the two-dimensional (x,y) images are stacked along the time axis (t) as shown in Fig. 11. A

three-dimensional volume (x,y,t) of the jet flame edge is then generated using image processing. This

rendered volume enables qualitative and quantitative comparisons of features such as large-scale

structure evolution and celerity. The celerity is the propagation velocity of a structure and is not

18

necessarily a convection velocity, because a luminous structure can theoretically propagate at a

different speed than the local flow velocity. A simulated light source, usually to the left of the

stacked images, provides illumination of the rendered surface and shadowing for depth perception.

The advantage of the volume rendering technique is that the large-scale structures -- visualized as

wrinkles or bands in the renderings -- can be readily tracked over their entire lifetimes. The slope of

each band in the volume rendering is proportional to the celerity of the luminous structure. In these

renderings, higher celerity structures will exhibit bands that have larger slopes. In the current study,

the renderings were computed using a Pentium-III machine equipped with 1GB of RAM and a

commercial software package called ‘Slicer-Dicer’.

Using this technique, Mungal et al. [9] found the celerity of luminous structures to be 12 ±

2% of the jet exit velocity irrespective of the buoyancy parameter (up to Lξ = 9) and fuel type. This

observation that the celerity is constant is intriguing because the fluid velocities decay with

downstream distance, and it might be expected that the luminous structures velocities should

decrease also. Mungal et al. [9] suggest the reason for the constant celerity is that the stoichiometric

mixture fraction surface, on which the flame resides, is similar in shape to a constant velocity

surface, and so the luminous structures remain associated with nearly constant velocity fluid.

Sample renderings for ethylene and propane are shown in Fig. 12. The renderings are shown

from the side view and so the y-direction is into the page. The wrinkles represent luminous

structures that propagate up the flame with increasing time. The faster the structures propagate, the

larger will be the slope of the wrinkles. The flame length variations are seen by the “spiky” top

surface of the renderings. Figures 12a-12b show the rendering of ethylene flames at ReD=2500 for

Lξ values of 8.5 and 2.5. Figure 12b shows the entire duration of the 1.25 second drop, including

startup (t = 0) and impact. The impact of the drop rig into the deceleration system is marked by the

19

time when the flame length becomes very large. The movie sequences show this large flame length

is associated with the creation of a large super-buoyant, mushroom-like flame that is generated by

the 15-30g deceleration.

A comparison of Figs. 12a,b shows that there are significant differences between the two

cases. It can be clearly seen that the flame tip fluctuates at a higher frequency in normal-gravity than

in milligravity. Also, the wrinkles in the normal- gravity case have higher slopes than those for the

milligravity case implying higher celerities in normal-gravity than in milligravity. Renderings for a

higher Reynolds number of 7500 are presented in Figs. 12c ( Lξ =4.6) and 12d ( Lξ =1.2). The large

differences seen at the lower Reynolds number are not readily apparent in these renderings, and the

super-buoyant flame is less prominent in the milligravity case; however, subtle differences in the

flame tip oscillation frequencies are still visible on careful viewing.

Figures 12e-12g show renderings for propane at a Reynolds number of 5000 at three different

gravity levels, rotated by 25° about the y-axis. Owing to the high density of propane, at this

Reynolds number, the jet exit velocity is relatively low and so these flames take longer to reach a

steady state in low-gravity conditions. Figure 12f shows that this relatively long startup transient is

seen to take up about half of the drop time. Comparing the slopes of the bands between Figs. 12e-

12g, it is apparent that the buoyancy parameter has a dominant effect on the luminous structure

celerities for the propane flames also. The normal-gravity case (Fig. 12e) exhibits wrinkles that seem

to have a finer spacing and which exhibit larger slopes than the milligravity and microgravity cases

(Figs. 12f and 12g). The similarity in slopes between Figs. 12d and 12e indicate the negligible effect

of buoyancy when Lξ changes from 2.8 to 0.49, but the time at which the flow is stationary is so

short that the Lξ =2.8 (milligravity) case is not very convincing in this regard.

20

The nearly constant slope of the wrinkles in all of the renderings indicates that the structures

move downstream at approximately a constant velocity, in agreement with previous observations in

jet flames [9]. Occasional pairing of the structures can also be seen as a coalescence of the wrinkles

in the renderings. Although this might not be readily apparent to the reader, after looking at many

such renderings, and after watching the movies, we can conclude that the pairing of the structures is

more dominant in the strongly buoyant cases. In other words, the luminous structures in the

momentum-dominated flames seem to have longer lifetimes, or to maintain their identity longer,

than in the buoyant flames. Perhaps a related observation is that the difference in the nature of the

flame tip fluctuations, as discussed above, can also be seen in these renderings. For example, a

comparison of Figs. 12e and 12f shows that the variations in the flame length at normal gravity

appear to be much larger than in microgravity.

Celerity Measurements

Figure 13a shows a plot of the ratio of the luminous structure celerity to jet exit velocity,

Us /Uo (%), versus the buoyancy parameter, Lξ . The normal gravity flames (high Lξ values) are

associated with higher celerity, which can be attributed to the buoyant acceleration. This suggests

that luminous structure celerity is in fact buoyancy dependent, contrary to the findings of Mungal et

al. [9]. It should be noted, however, that since Mungal et al. [9] studied higher Reynolds number jet

flames, it is possible that the disagreement is due to a Reynolds number effect. For Lξ values less

than about 6, the celerity is independent of the gravity level and fuel type. In this regime, there is

reasonable agreement with the findings of Mungal et al. [9]. The bars shown on each data point

represent the standard deviation of the celerities measured at each condition and therefore are a

measure of the variation of measured values. It is interesting to note that high Lξ cases have higher

21

deviations which imply that the structures have a wider distribution of celerity. However, the

deviations become smaller with decreasing Lξ which suggests greater organization (or repeatability)

of the structure celerity. This conclusion of greater organization is consistent with the lack of

merging of the luminous structures described above, and the more regular fluctuations of the flame

tip that were observed under low-gravity conditions. This observation of a higher degree of

organization for momentum-dominated flames is a new one, because it is usually assumed that

buoyancy increases the large-scale organization of turbulent flames (e.g., the large billowing

structures observed in oil-well or pool fires) [16]. Although the pure buoyant-driven limit may

indeed exhibit strong organization, it appears that the first effect of buoyancy is to reduce the

organization by disrupting the hydrodynamic instability of the momentum-dominated jet.

The log-log plot (Fig. 13b) shows that for Lξ >8, the celerity values are consistent with a 23 /

Lξ scaling law. We can derive this result by the following analysis. If the structure celerity

essentially follows the local velocity at the stoichiometric contour then the celerity should be equal

to the local centerline fluid velocity at the stoichiometric flame length. Becker and Yamazaki [1] use

a quasi-1-D momentum analysis to show that in the buoyancy-dominated limit the entrainment rate

scales as 2/3xξ . We use this same procedure to show how the local velocity scales at the flame tip

under these same conditions. Consider the simplified geometry and control volume of a jet flame

issuing into quiescent ambient fluid as shown in Fig. 14. Let the jet fuel of density ρo exit the nozzle

into the ambient of density ρ∞ from a tube of diameter D with a velocity Uo and mass flow rate om& .

Assume the jet flame to be an inverted cone of width δ and height x, and that the density at each x-location can be approximated as an appropriate average density fρ (i.e. a mixing-cup density [1]).

Furthermore, the jet entrains ambient fluid with a mass flow rate em& , but assume that this entrained

fluid has no initial momentum in the x-direction and so it does not contribute to the momentum

balance. Owing to the presence of heat release the jet will experience a buoyancy force, BF as

22

shown in the schematic. At a particular downstream location x, let the mass flow rate and velocity be

given by )(xm& and Uc(x), respectively. Applying the momentum principle in the x direction gives

0)()( c =−+ xUxmFUm Boo && (1)

Now consider the case where the flame is buoyancy-dominated, in which case the buoyancy-induced

momentum is much larger than the initial source momentum. Following these assumptions, equation

(1) reduces to

cB UxmF )(&= (2)

The buoyancy force that is exerted on the flame, modeled as an inverted cone as discussed above, is

)(121 2

fB xgF ρρπδ −≈ ∞ (3)

Owing to the reduced density in a flame, we have ∞∞ ≈− ρρρ )( f and (3) simplifies to

∞≈ ρπδ xgFB2

121 (4)

The momentum at the downstream location, x, is approximated as follows

4

)(2

2 δπρ cfc UUxm ≈& (5)

and substituting (4) and (5) in equation (2) gives

412

1 222 δπρρπδ cf Uxg ≈∞ (6)

Note that (6) is not a function of the source conditions (Uo or Ds) because the source momentum was

assumed to be negligible. However, because the celerity is normalized by Uo, we introduce the

source parameters into (6) to obtain the relation for the normalized celerity

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛∝⎟⎟

⎠

⎞⎜⎜⎝

⎛ ∞fso

s

o

c

Dx

UgD

UU

ρρ

2

2

(7)

Now, 2o

ss U

gDRi ≡ and ( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛≡

ssx D

xRi 31 /ξ and hence, 3

3−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

sxs D

xRi ξ

23

Using these relations in equation (7) yields

211

23

/

/

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛∝ ∞

−

fsx

o

c

Dx

UU

ρρξ (8)

Following the nomenclature of Tacina and Dahm [17], we define a modified source diameter, D+,

which like Ds in nonreacting jets, is able to collapse velocity and mixture fraction decay data in

turbulent flames. For our purposes, we define 21 /

⎟⎟⎠

⎞⎜⎜⎝

⎛≡ ∞+

fsDD ρ

ρ , which differs somewhat from that

of [17] and was used because it was found to work better for scaling mixture fraction data measured

in the current facility [18]. With this definition of D+ we can write

1

23−

+ ⎟⎠⎞

⎜⎝⎛∝

Dx

UU

xo

c /ξ (9)

To obtain a scaling in terms of the flame length parameters, x is replaced with L in equation (9).

Furthermore, it is assumed that the celerity (Us) will scale with the local centerline velocity (Uc) and

therefore at the flame tip we have

231

23 // ~ LLo

s

DL

UU ξξ

−

+ ⎟⎠⎞

⎜⎝⎛∝ (10)

Equation (10) shows that the normalized celerity near the flame tip will approximately scale as 23 /Lξ

provided the flame is buoyancy-dominated. Figure 13 shows the celerity data plotted with a line that

follows the 23 /Lξ scaling. It is seen that this scaling seems to be appropriate for 23 /

Lξ > 8 or so. Note

that equation (10) suggests that the celerity will depend on L/D+ and Lξ but the effect of the former

term will be small in Fig. 13 if L/D+ is approximately constant. Specifically, the L/D+ value for the

flames in the current study were measured to be approximately 90 [18]. This suggests that the

normalized celerity will be a function of Lξ only.

A similar analysis can be used to explore the scaling of celerity at the momentum-dominated

limit ( Lξ →0). The normalized centerline velocity of a momentum dominated jet flame is found to

scale as [17]

24

1−

+ ⎟⎠⎞

⎜⎝⎛∝

Dx

UU

o

c (11)

At the flame tip it is again assumed that the celerity scales with the centerline velocity and hence for

a momentum-dominated flame

1−

+ ⎟⎠⎞

⎜⎝⎛∝

DL

UU

o

s (12)

Equation (12) shows that the normalized celerity is (obviously) independent of Lξ and will have a

constant value if L/D+ is constant. Figure 13 shows relatively good agreement with this scaling law

because the celerities are independent of Lξ for Lξ < 5, and seem to exhibit similar values over this

same range of Lξ .

The analysis above shows that the celerity seems to scale with the local mean velocity, but

whether it has the same value as the local mean velocity is another issue. To explore this further

consider the measured centerline velocity decay in a turbulent nonreacting jet [14], which is given by

1

2.6−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

so

c

Dx

UU (13)

Assuming that the velocity decay in a momentum-dominated reacting jet can be obtained by

substituting Ds with D+ [17] in (13) gives

1

2.6−

+ ⎟⎠⎞

⎜⎝⎛=

Dx

UU

o

c (14)

Furthermore, assuming the celerity is the same as the centerline velocity at the flame tip and that the

normalized flame length L/D+ is approximately 90 [18], (14) will predict a constant normalized

celerity (Us /Uo) of approximately 7%. Figure 13 shows that the mean celerities measured in this

study range from about 8−18% at the low Lξ limit, and those of Ref. 9 were measured to be 12%.

Both of these studies, therefore, suggest that the luminous structures propagate faster than the local

mean fluid velocity. The reason why the celerity is different from the local fluid velocity is not

25

known but it is possible that the luminous structures exhibit a wave-like behavior, with a wave-speed

that differs from the local fluid velocity. For example, consider an essentially steady laminar flame

surface that is located in a region of low speed flow, but which surrounds a column of fast moving

jet fluid. If a velocity perturbation were to be introduced into the high-speed jet fluid, then this

disturbance would propagate downstream at the local jet fluid velocity. As the disturbance

propagated downstream it would cause a “bulge” in the laminar flame surface, which would

propagate at the same velocity as the disturbance. The bulge in the flame surface would have a larger

propagation velocity than the local fluid velocity. We do not know if this discussion correctly

describes the physics of the flow, but at least it emphasizes the point that although the celerity may

scale with the local fluid velocity, there is really no obvious reason why it should be equal to it.

CONCLUSIONS

The characteristics of turbulent nonpremixed jet flames were studied at Reynolds numbers

ranging from 2,000 to 10,500 and at three levels of gravity, viz., 1 g, 20 mg and 100 µg. The flames

were piloted with a small concentric premixed methane-air flame to keep them attached to the flame

base for all Reynolds numbers considered. Time-resolved (cinematographic) imaging of the natural

soot luminosity was used to investigate the mean and RMS luminosity, flame tip dynamics, and

evolution of large-scale structures. The relative importance of buoyancy over the entire length of the

flame was quantified with the Becker and Yamazaki [1] “buoyancy parameter,” Lξ .

The mean flame luminosity data show that the normal and low-gravity flames exhibited

approximately the same flame lengths for all Reynolds numbers tested. This result is different from

some previous studies in the literature that have shown large differences in flame lengths between

normal and microgravity flames. It is conjectured that the reason for this difference is that the

26

microgravity flames in the previous studies may have exhibited an extended laminar/transitional

region owing to the absence of turbulence-induced vortical perturbations. This emphasizes the

importance of documenting the boundary conditions under which the flames develop when

conducting microgravity studies. Furthermore, the mean and RMS luminosity, and flame tip

fluctuations suggest that the structure of the large-scale turbulence reaches its momentum-driven

asymptotic state for values of Lξ less than about 2. Volume renderings of image time-sequences

show that the large-scale luminous structure celerity depends on the value of Lξ . In particular, the

celerity was found to be nearly constant for momentum dominated flames ( Lξ < 6), but to scale as

Lξ3/2 in the buoyancy-dominated limit ( Lξ > 8). It is argued that the celerity should scale with the

local fluid velocity, although not necessarily be equal to it, and a simple momentum-equation

analysis supports this view. Taken as a whole, the results of this study indicate that Lξ is sufficient

to quantify the effects of buoyancy on both the mean luminosity and different measures of the

fluctuations, provided the flame is turbulent.

Another interesting finding of this work is that the visible flame tip time-histories, volume

renderings, and movie sequences, support the view that the luminous structures of the jet flames are

better organized, or coherent, when the flames are momentum-dominated than when they are

influenced by buoyancy. This result contradicts the view that buoyant instabilities should cause the

flame-structures to become more coherent. Although this latter view may be true at the buoyancy-

dominated limit, it appears that as buoyancy effects first become non-negligible, the buoyant

acceleration disrupts the Kelvin-Helmholtz instability of the jet, and this causes reduced coherence

of the turbulent structures.

27

ACKNOWLEDGEMENTS

This research was supported under co-operative agreement NCC3-667 from the NASA

Microgravity Sciences Division. We would like to thank our technical monitor Dr. Zeng-Guang

Yuan of NCMR for his hard work in facilitating the NASA GRC 2.2-second drop tower

experiments. Furthermore, we would also like to acknowledge useful discussions with Dr. Uday

Hegde regarding the effects of boundary conditions on microgravity flames.

28

REFERENCES 1. Becker, H. A. and Yamazaki, S., Combust. Flame 33 (1978) 123-149.

2. Becker, H. A. and Yamazaki, S., Proceedings of the Combustion Institute, Vol. 16, (1977),

681.

3. Becker, H. A. and Liang, D., Combust. Flame 32 (1978) 115-137.

4. Bahadori, M.Y., Stocker, D.P., Vaughan, D.F., Zhou, L. and Edelman, R.B., Modern

Developments in Energy, Combustion and Spectroscopy, Pergamon Press, 1995, p. 49.

5. Hegde, U., Zhou, L., Bahadori, M. Y., Combust. Sci. Technol. 102 (1994) 95-100.

6. Hegde, U., Yuan, Z.G., Stocker, D.P. and Bahadori, M.Y., Proc. of Fifth International

Microgravity Combustion Workshop, 1999, p. 259.

7. Hegde, U., Yuan, Z.G., Stocker, D.P. and Bahadori, M.Y., AIAA Paper 2000-0697 (2000).

8. Mungal, M.G. and O’Neil, J.M., Combust. Flame 78 (1989) 377-389.

9. Mungal, M.G., Karasso, P.S. and Lozano, A., Combust. Sci. Technol. 76 (1991) 165-185.

10. Roquemore, W.M., Chen, L.D., Goss, L.P. and Lynn, W.F., Lecture notes in Engineering Vol.

40, Springer-Verlag, 1989, p. 49.

11. Idicheria, C.A., Boxx, I.G. and Clemens, N.T., AIAA paper 2001-0628 (2001).

12. Page, K.L., Stocker, D.P., Hegde, U.G., Hermanson, J.C. and Johari, H., Proc. of Third Joint

Meeting of U.S. Sections of the Combustion Institute, 2003.

13. Chen, S.-J. and Dahm, W.J.A., Proceedings of the Combustion Institute, Vol. 27, (1998) 2579-

2586.

14. Chen, C.J., and Rodi, W., Vertical Turbulent Buoyant Jets - A Review of Experimental Data,

(Ed. Chen) Permagon Press, London (1980).

15. Dahm, W.J.A. and Dimotakis, P.E., AIAA J. 25 (1987) 1216-1223.

29

16. Zukoski, E.E., Cetegen, B. and Kubota, T., Proceedings of the Combustion Institute, Vol. 20,

(1984) 361-366.

17. Tacina, K. M. and Dahm, W. J. A., J. Fluid Mech., 415 (2000) 23-44.

18. Idicheria, C.A., Boxx, I.G. and Clemens, N. T., “The Turbulent Structure and Entrainment of

Nonpremixed Jet Flames in Normal- and Low-Gravity Conditions,” Proceedings of the Spring

2004 Technical Meeting of the Central States Section of The Combustion Institute (2004).

30

Table 1 Experimental Conditions

Fuel Uo (m/s)

ReD Lξ (1g)

Lξ (20 mg)

Lξ (100 µg)

6.2 2500 12.0 4.0 0.66 12.5 5000 10.1 2.8 0.49 18.7 7500 8.3 2.3 0.38

Propane

21.2 8500 7.9 2.1 0.36 12.4 2500 8.5 2.5 - 24.8 5000 6.6 1.6 - 37.2 7500 4.6 1.2 -

Ethylene

52.2 10500 3.7 1.0 - 19.5 2000 8.0 2.4 - Methane 24.4 2500 7.3 2.1 -

31

LIST OF FIGURE CAPTIONS Figure 1 Schematic diagram of the drop-rig. Figure 2 Flame-luminosity image-sequences of ethylene jet flames showing the startup

transient. (a) normal-gravity, ReD=2500 (b) milligravity, ReD=2500 (c) normal- gravity, ReD=7500 (d) milligravity, ReD=7500.

Figure 3 Flame tip time history for ethylene flame at ReD=7500. Figure 4 Sample mean luminosity images: (a) Ethylene ReD=10,500, x/D=43−279, normal

(left) and milligravity (right), (b) Ethylene ReD=5000, x/D=43−279 normal (left) and milligravity (right), (c) Propane ReD=8500, x/D=76−308, normal (left), milligravity (center) and microgravity (right) and (d) Propane ReD=5000, x/D=76−308, normal (left), milligravity (center) and microgravity (right).

Figure 5 Sample instantaneous luminosity images: (a) Ethylene ReD=10,500, x/D=43−279,

normal (left) and milligravity (right), (b) Ethylene ReD=5000, x/D=43−279 normal (left) and milligravity (right), (c) Propane ReD=8500, x/D=76−308, normal (left), milligravity (center) and microgravity (right) and (d) Propane ReD=5000, x/D=76−308, normal (left), milligravity (center) and micro-gravity (right).

Figure 6 Cartoon of the luminous flame structure of transitional flames in (a) normal-gravity,

and (b) low-gravity. Figure 7 Variation of normalized flame length with Reynolds number at different gravity

levels. Figure 8 Comparison of current normal-gravity flame length data with other published data. Figure 9 Sample RMS luminosity images: (a) Ethylene ReD=10,500, x/D=43−279, normal

(left) and milligravity (right), (b) Ethylene ReD=5000, x/D=43−279 normal (left) and milligravity (right), (c) Propane ReD=8500, x/D=76−308, normal (left), milligravity (center) and microgravity (right) and (d) Propane ReD=5000, x/D=76−308, normal (left), milligravity (center) and microgravity (right).

Figure 10 Instantaneous flame tip location for propane flames at various Lξ .

Figure 11 Illustration of volume rendering technique

Figure 12 Sample volume renderings: (a) Ethylene, ReD=2500, normal-gravity ( Lξ = 8.5), (b)

Ethylene, ReD=2500, milligravity ( Lξ = 2.5), (c) Ethylene, ReD=7500, normal-gravity ( Lξ = 4.6), (d) Ethylene, ReD=7500, milligravity ( Lξ = 1.2), (e) Propane, ReD=5000,

32

normal-gravity ( Lξ = 10.1), (f) Propane, ReD=5000, milligravity ( Lξ = 2.8) and (g) Propane, ReD=5000, microgravity ( Lξ = 0.49).

Figure 13 Normalized celerity of large-scale structures vs. Lξ : (a) linear plot (b) log-log plot. Figure 14 Schematic diagram of the control volume used in the celerity scaling analysis.

33

Figure 1

Battery packs Burner

Onboard computer

GPDM

Gas panel

CCD camera

34

(a)

(b)

(c)

(d)

Figure 2

35

0 0.2 0.4 0.6 0.8 1 1.20

50

100

150

200

250

300

Time (seconds)

L/D

Normal−gravityMilligravity

Figure 3

36

ξL=3.7 ξ

L=1.0

ξL=6.6 ξ

L=1.6

ξL=7.9 ξ

L=2.1 ξ

L=0.36

ξL=10.1 ξ

L=2.8 ξ

L=0.49

(a) (b) (c) (d)

Figure 4

37

ξL=3.7 ξ

L=1.0

ξL=6.6 ξ

L=1.6

ξL=7.9 ξ

L=2.1 ξ

L=0.36

ξL=10.1 ξ

L=2.8 ξ

L=0.49

(a) (b) (c) (d)

Figure 5

38

(a) (b)

Figure 6

39

0 2000 4000 6000 8000 10000 120000

100

200

300

400

500

600

Reynolds number (ReD

)

L/D

Propane 1gPropane 20mgPropane 100µgEthylene 1gEthylene 20mgEthylene 100µgMethane 1gMethane 20mgHegde et al. 1gHegde et al. 100µg

Figure 7

40

0 0.5 1 1.5 2

x 104

0

50

100

150

200

250

300

350

Reynolds number (ReD

)

L/D

Current data (Propane)Becker and Yamazaki (Propane)Current data (Ethylene)Mungal et al. (Ethylene)

Figure 8

41

ξL=3.7 ξ

L=1.0

ξL=6.6 ξ

L=1.6

ξL=7.9 ξ

L=2.1 ξ

L=0.38

ξL=10.1 ξ

L=2.8 ξ

L=0.49

(a) (b) (c) (d)

Figure 9

42

xiL=10.1

ξL=10.1

ξL=7.9

ξL=2.8

L/D

ξL=2.1

ξL=0.49

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

x 104

150

225

300

Non−dimensional time τ=tUo/D

ξL=0.36

Figure 10

43

Figure 11

x

y

t

Image processing

x

t

Light source

y

44

45

0 2 4 6 8 10 12 140

10

20

30

40

50

60

70

ξL

Us/

Uo

(%)

PropaneEthyleneMungal et al.Us/Uo=ξL

3/2

(a)

10-1

100

101

101

102

ξL

Us/

Uo

(%)

PropaneEthyleneMungal et al.Us/Uo=ξL

3/2

(b)

Figure 13

46

Uo,

Uc

ρ

ρο

δ

x

ρf

FB

g

ρ

Figure 14