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: [email protected]
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, ξ L , 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 ξ L 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 ξ L <6, but scale as ξ L 3/2 for ξ L >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 ξ L 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”, ξ L (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 ξ L 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 ξ L ≈ 6.5. This
indicates a much stronger dependence of flame length on ξ L than would be indicated by the results
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of Becker and Yamazaki [1]. Therefore, this raises the issue of whether ξ L 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 ξ L 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<ReD< 5800). This
study aims to improve upon and add to our knowledge of turbulent nonpremixed jet flames by
investigating a wider range of Reynolds number and ξ L than these previous studies, and to
specifically investigate the effect of buoyancy on the large-scale luminous structures observed in the
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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 ξ L 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 ξ L 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 ξ L 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 NASAGRC 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 freefall 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 “KBeam” 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
5
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<ReD<10500). The Reynolds number
(ReD=UoD/ν) is based on the jet exit diameter (D), the jet exit velocity (Uo) and the kinematic
viscosity (ν) of the fuel at room temperature. The primary experimental conditions that are referred
to in this paper are shown in Table 1. More cases were also studied to obtain finer resolution in
Reynolds number, primarily for the flame length measurements. The “buoyancy parameter” [1] is
defined as ξ L =Ris1/3L/Ds, where Ris is the source Richardson number (Ris=gDs/Uo2) based on the
source diameter Ds=D(ρo/ρ∞)½, and source velocity Uo (assuming a top-hat velocity profile), L is the
average luminous flame length, g is the acceleration due to gravity, ρo is the jet fluid density and ρ∞
is the ambient density. The experiments were conducted for three different gravity levels of 1 g, 20
6
mg and 100 µg; thus, for the different fuels studied, ξ L 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 ξ L <1 were taken in microgravity, cases
7
with 1< ξ L <3 were taken in milligravity, and cases with ξ L >3 were taken in normal-gravity.
Significant differences in the structure of the flames can be seen by comparing the high and low ξ L
cases. For example, Fig. 4d and 5d, compare ReD=5000 propane flames in normal, milli- and microgravity. It is seen that the milli- and micro-gravity flames are significantly thicker than the normalgravity 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 ξ L . 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
8
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 ξ L 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 ξ L 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 ξ L =3.7 flame is very similar to the ξ L =1
flame. A careful viewing of all of the images in Fig. 4 strongly suggests that flames with ξ L near
unity and below are essentially identical in their mean luminosity (flame height and width).
Differences start to appear as the ξ L 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,
9
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 normalgravity 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
11
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
12
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,
13
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 ξ L =1.0 flame.
Furthermore, more drastic differences can be seen when comparing flames with a larger difference
in ξ L (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 ξ L =2.1 and ξ L =0.38
cases, however both differ substantially from the ξ L =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 ξ L flames, which is expected since buoyancy acts on fluid volumes and so its effects are more
14
prevalent near the flame tip where the large-scale vortical structures are formed. Interestingly,
regardless of fuel type or Reynolds number, the low ξ L 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 ξ L
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 ξ L =7.9 case seems to exhibit
higher frequency fluctuations, and this is clearly the case at ξ L =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 ξ L 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 liquidphase flames are purely momentum-driven, and they exhibited a particularly high degree of quasiperiodicity [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, ξ L =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
16
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 ξ L . 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 ξ L as
considered here. In fact, it seems that their low and high ξ L 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
17
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 ξ L = 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
ξ L 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
18
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 ( ξ L =4.6) and 12d ( ξ L =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. 12e12g, 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 ξ L changes from 2.8 to 0.49, but the time at which the flow is stationary is so
short that the ξ L =2.8 (milligravity) case is not very convincing in this regard.
19
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, ξ L . The normal gravity flames (high ξ L 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 ξ L 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 ξ L cases have higher
20
deviations which imply that the structures have a wider distribution of celerity. However, the
deviations become smaller with decreasing ξ L 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 ξ L >8, the celerity values are consistent with a
ξ L3 / 2 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 ξ x3 / 2 . 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 m& o .
Assume the jet flame to be an inverted cone of width δ and height x, and that the density at each xlocation can be approximated as an appropriate average density ρ f (i.e. a mixing-cup density [1]).
Furthermore, the jet entrains ambient fluid with a mass flow rate m& e , 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, FB as
21
shown in the schematic. At a particular downstream location x, let the mass flow rate and velocity be
given by m& (x) and Uc(x), respectively. Applying the momentum principle in the x direction gives
m& oU o + FB − m& ( x)U c ( x) = 0
(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
FB = m& ( x)U c
(2)
The buoyancy force that is exerted on the flame, modeled as an inverted cone as discussed above, is
FB ≈
1
πδ 2 xg ( ρ ∞ − ρ f )
12
(3)
Owing to the reduced density in a flame, we have ( ρ ∞ − ρ f ) ≈ ρ ∞ and (3) simplifies to
FB ≈
1
πδ 2 xgρ ∞
12
(4)
The momentum at the downstream location, x, is approximated as follows
m& ( x)U c ≈ ρ f U c2π
δ2
(5)
4
and substituting (4) and (5) in equation (2) gives
1
δ2
πδ 2 xgρ ∞ ≈ ρ f U c2π
12
4
(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
⎛ Uc ⎞
⎛ gD ⎞⎛ x ⎞⎛ ρ ⎞
⎜⎜ ⎟⎟ ∝ ⎜⎜ 2s ⎟⎟⎜⎜ ⎟⎟⎜ ∞ ⎟
⎜
⎟
⎝ Uo ⎠
⎝ U o ⎠⎝ Ds ⎠⎝ ρ f ⎠
2
gD
1/ 3 ⎛ x
Now, Ri s ≡ 2s and ξ x ≡ (Ris ) ⎜⎜
Uo
⎝ Ds
⎞
⎛ x
⎟⎟ and hence, Ri s = ξ x3 ⎜⎜
⎠
⎝ Ds
22
(7)
⎞
⎟⎟
⎠
−3
Using these relations in equation (7) yields
⎛ x ⎞
Uc
∝ ξ x3 / 2 ⎜⎜ ⎟⎟
Uo
⎝ Ds ⎠
−1
1/ 2
⎛ ρ∞ ⎞
⎜
⎟
⎜ρ ⎟
⎝ f ⎠
(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
⎛ρ
turbulent flames. For our purposes, we define D ≡ Ds ⎜ ∞
⎜ρ
⎝ f
+
⎞
⎟
⎟
⎠
1/ 2
, 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
Uc
⎛ x ⎞
∝ ξ x3 / 2 ⎜ + ⎟
Uo
⎝D ⎠
−1
(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
−1
Us
⎛ L ⎞
∝ ξ L3 / 2 ⎜ + ⎟ ~ ξ L3 / 2
Uo
⎝D ⎠
(10)
Equation (10) shows that the normalized celerity near the flame tip will approximately scale as ξ L3 / 2
provided the flame is buoyancy-dominated. Figure 13 shows the celerity data plotted with a line that
follows the ξ L3 / 2 scaling. It is seen that this scaling seems to be appropriate for ξ L3 / 2 > 8 or so. Note
that equation (10) suggests that the celerity will depend on L/D+ and ξ L 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 ξ L only.
A similar analysis can be used to explore the scaling of celerity at the momentum-dominated
limit ( ξ L →0). The normalized centerline velocity of a momentum dominated jet flame is found to
scale as [17]
23
Uc ⎛ x ⎞
∝⎜
⎟
Uo ⎝ D+ ⎠
−1
(11)
At the flame tip it is again assumed that the celerity scales with the centerline velocity and hence for
a momentum-dominated flame
Us ⎛ L ⎞
∝⎜
⎟
Uo ⎝ D+ ⎠
−1
(12)
Equation (12) shows that the normalized celerity is (obviously) independent of ξ L 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 ξ L for ξ L < 5, and seem to exhibit similar values over this
same range of ξ L .
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
⎛ x ⎞
Uc
= 6.2⎜⎜ ⎟⎟
Uo
⎝ Ds ⎠
−1
(13)
Assuming that the velocity decay in a momentum-dominated reacting jet can be obtained by
substituting Ds with D+ [17] in (13) gives
Uc
⎛ x ⎞
= 6.2⎜ + ⎟
Uo
⎝D ⎠
−1
(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 ξ L 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
24
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,” ξ L .
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
25
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 ξ L less than about 2. Volume renderings of image time-sequences
show that the large-scale luminous structure celerity depends on the value of ξ L . In particular, the
celerity was found to be nearly constant for momentum dominated flames ( ξ L < 6), but to scale as
ξ L 3/2 in the buoyancy-dominated limit ( ξ L > 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 ξ L 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 buoyancydominated 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.
26
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.
27
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) 25792586.
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.
28
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).
29
Fuel
Propane
Ethylene
Methane
Uo
(m/s)
ReD
6.2
12.5
18.7
21.2
12.4
24.8
37.2
52.2
19.5
24.4
2500
5000
7500
8500
2500
5000
7500
10500
2000
2500
ξL
(1g)
12.0
10.1
8.3
7.9
8.5
6.6
4.6
3.7
8.0
7.3
Table 1 Experimental Conditions
30
ξL
(20 mg)
4.0
2.8
2.3
2.1
2.5
1.6
1.2
1.0
2.4
2.1
ξL
(100 µg)
0.66
0.49
0.38
0.36
-
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) normalgravity, 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 ξ L .
Figure 11
Illustration of volume rendering technique
Figure 12
Sample volume renderings: (a) Ethylene, ReD=2500, normal-gravity ( ξ L = 8.5), (b)
Ethylene, ReD=2500, milligravity ( ξ L = 2.5), (c) Ethylene, ReD=7500, normal-gravity
( ξ L = 4.6), (d) Ethylene, ReD=7500, milligravity ( ξ L = 1.2), (e) Propane, ReD=5000,
31
normal-gravity ( ξ L = 10.1), (f) Propane, ReD=5000, milligravity ( ξ L = 2.8) and (g)
Propane, ReD=5000, microgravity ( ξ L = 0.49).
Figure 13
Normalized celerity of large-scale structures vs. ξ L : (a) linear plot (b) log-log plot.
Figure 14
Schematic diagram of the control volume used in the celerity scaling analysis.
32
Gas panel
GPDM
Onboard computer
Battery packs
CCD camera
Figure 1
33
Burner
(a)
(b)
(c)
(d)
Figure 2
34
300
Normal−gravity
Milligravity
250
L/D
200
150
100
50
0
0
0.2
0.4
0.6
Time (seconds)
Figure 3
35
0.8
1
1.2
ξL=3.7
ξL=1.0
(a)
ξ =6.6
ξ =1.6
L
L
ξ =7.9
ξ =2.1
L
L
(b)
(c)
Figure 4
36
ξ =0.36
L
ξ =10.1
L
ξ =2.8
L
(d)
ξ =0.49
L
ξL=3.7
ξL=1.0
(a)
ξL=6.6
ξL=1.6
ξL=7.9
ξL=2.1
(b)
(c)
Figure 5
37
ξL=0.36
ξL=10.1
ξL=2.8
(d)
ξL=0.49
(a)
(b)
Figure 6
38
600
Propane 1g
Propane 20mg
Propane 100µg
Ethylene 1g
Ethylene 20mg
Ethylene 100µg
Methane 1g
Methane 20mg
Hegde et al. 1g
Hegde et al. 100µg
500
L/D
400
300
200
100
0
0
2000
4000
6000
8000
Reynolds number (ReD)
Figure 7
39
10000
12000
350
300
250
L/D
200
150
100
Current data (Propane)
Becker and Yamazaki (Propane)
Current data (Ethylene)
Mungal et al. (Ethylene)
50
0
0
0.5
1
1.5
Reynolds number (Re )
D
Figure 8
40
2
4
x 10
ξL=3.7
ξL=1.0
(a)
ξL=6.6
ξL=1.6
ξL=7.9
ξL=2.1
(b)
(c)
Figure 9
41
ξL=0.38
ξL=10.1
ξL=2.8
(d)
ξL=0.49
ξL=10.1
xi =10.1
L
ξL=7.9
L/D
ξL=2.8
ξL=2.1
ξ =0.49
L
300
225
150
0
ξL=0.36
0.25
0.5
0.75
1
1.25
1.5
Non−dimensional time τ=tUo/D
Figure 10
42
1.75
2
4
x 10
x
x
Light
source
Image
processing
t
y
Figure 11
43
t
y
44
70
Propane
Ethylene
Mungal et al.
3/2
Us/Uo=ξL
60
Us/Uo (%)
50
40
30
20
10
0
0
2
4
6
ξL
8
10
12
14
(a)
2
10
Us/Uo (%)
Propane
Ethylene
Mungal et al.
Us/Uo=ξ3/2
L
1
10
-1
10
0
10
1
ξL
10
(b)
Figure 13
45
δ
Uc
ρf
ρ
ρ
FB
Uo, ρο
g
Figure 14
46
x