49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
4 - 7 January 2011, Orlando, Florida
AIAA 2011-597
Dependence of the Bluff Body Wake Structure on Flame
Temperature Ratio
Benjamin Emerson1, Julia Lundrigan2, Jacqueline O’Connor1, David Noble3, Tim Lieuwen4
Georgia Institute of Technology, Atlanta, GA, 30318
This paper describes an experimental investigation of the wake and flame characteristics
of a bluff body stabilized flame. Prior investigations have clearly shown that the wake
structure is markedly different at “high” and “low” flame density ratios. This paper
describes a systematic analysis of the dependence of the flow field characteristics and flame
sheet dynamics upon flame density ratio, ρu/ρb, over the range 1.7< ρu/ρb <3.4. This paper
shows that two fundamentally different flame/flow behaviors are observed – characterized
here as Kelvin-Helmholtz and Von-Karman vortex street dominated - at high and low ρu/ρb
values, respectively. These are interpreted here as a transition from a convectively to
absolutely unstable flow. This transition manifests itself in several ways with decreasing
ρu/ρb values, including (1) the spectrum of the flame motion and flow field transitions from a
distributed to a narrowband peak at St~0.24, and (2) the correlation between the two flame
front branches monotonically increases. Finally, the intermittent nature of the flow field is
emphasized, with the relative fraction of the two different flow/flame behaviors
monotonically varying with ρu/ρb.
Nomenclature
A
D
ṁ
Re
StD
T
U
c
f
k
t
v
=
=
=
=
=
=
=
=
=
=
=
=
flow cross-sectional area
bluff body diameter
mass flowrate
Reynold’s number, UlipD/ν
Strouhal number, fD/Ulip
temperature
time-averaged axial velocity
modal wave propagation speed
frequency, Hz
wavenumber
time
instantaneous transverse velocity
Greek Characters
β
ζL
ζU
ν
ρ
ρf
ρU,L
ρt
τ
=
=
=
=
=
=
=
=
=
backflow ratio, -U(y=0)/U(y=∞)
lower flame edge position
upper flame edge position
kinematic viscosity
gas density
correlation coefficient between sine fit and original time signal
correlation coefficient between upper and lower flame edge positions
correlation coefficient threshold
temporal duration of a sinusoidal chunk of signal
1
Graduate Research Assistant, School of Aerospace Engineering, 270 Ferst Dr, AIAA Student Member.
Undergraduate Research Assistant, School of Aerospace Engineering, 270 Ferst Dr, AIAA Student Member.
3
Research Engineer, School of Aerospace Engineering, 270 Ferst Dr, AIAA Member.
4
Professor, School of Aerospace Engineering, 270 Ferst Dr, AIAA Associate Fellow.
1
American Institute of Aeronautics and Astronautics
2
Copyright © 2011 by Benjamin Emerson, Julia Lundrigan, Jacqueline O'Connor, David Noble, and Tim Lieuwen. Published by the American Institute of Aeronautics and Astronautics, Inc., with
φ
ω
= equivalence ratio
= frequency, rad/s
0
b
i
lip
max
ref
u
=
=
=
=
=
=
=
’
= unsteady component
Subscripts
zero group velocity
burned
imaginary component
bluff body trailing edge lip
maximum
reference velocity
unburned
Superscripts
I. Background
Bluff bodies are a common mode of flame stabilization in a variety of practical combustion devices 1. The
unsteady flow fields in bluff body flows, both with and without the presence of combustion, are often dominated by
large scale coherent structures, embedded upon a background of acoustic waves and broadband fine scale
turbulence. These large scale structures play important roles in such processes as combustion instabilities, mixing
and entrainment, flashback, and blowoff. The objective of this study is to experimentally characterize the role of
flame density ratio upon the appearance and characteristics of these structures in a reacting bluff body wake.
These large scale structures arise because of underlying hydrodynamic instabilities of the flow field 2. The
concepts of convective and absolute stability of the base flow3-5 upon which these flow disturbances are initiated,
and subsequently amplified or damped, will play an important role in the subsequent discussions, so it is helpful to
review a few key concepts. In an unstable flow, disturbances are amplified. These amplified disturbances in a
convectively unstable flow are swept downstream so that the response at any fixed spatial point eventually tends
toward zero. In contrast, perturbations in absolutely unstable flows increase in amplitude at a fixed spatial location,
even as the actual flow particles are convected downstream6.
The implications of this absolute/convective instability distinction are important. A “convectively unstable”
flow acts an amplifier, in that a disturbance created at some point grows in amplitude as it is convected out of the
system. However, the oscillations are not self-excited but require a constant disturbance source to persist. In any
real situation, there are a variety of background disturbances, such as broadband turbulence and harmonic acoustic
disturbances, that provide this consistent source of excitation. The flow then selectively filters these background
disturbances. For example, in convectively unstable shear flows, the spectrum shows a distributed peak around a
frequency associated with the most rapidly amplified mode7. When such systems are forced by external
disturbances, such as acoustic waves, these disturbances are easily discerned in the system response.
An absolutely unstable system is an oscillator – it exhibits intrinsic, self-excited oscillations and does not require
external disturbances to persist. In such a self-excited system, the amplitude grows before saturating into a limit
cycle oscillation. Moreover, the spectrum of oscillations shows a narrowband peak associated with this natural
frequency. When externally forced, the limit cycle behavior remains essentially independent of the external forcing,
unless the amplitude is high enough that the phenomenon of “lock-in” occurs8-9. In other words, in a convectively
unstable flow, there is a monotonic relationship between forcing amplitude and system response, while in an
absolutely unstable system, the limit cycle oscillations persist despite this forcing, except at high forcing levels.
These distinctions are important in combustion instability problems, where vortical structures excited by acoustic
waves play important roles in the feedback mechanism. In one case, low amplitude acoustic excitation will induce a
proportional response while in the other it may not. In turn, this has important implications on which type of flow
instabilities can be involved in linear combustion instability mechanisms.
As shown in Figure 1, there are two key flow features downstream of the bluff body, the separating free shear
layer10 and the wake, both of which strongly influence the flame. These two flow features are discussed further
next.
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Figure 1. Schematic of non-reacting flow past a bluff body at Re = 10,000.
Reproduced from Prasad and Williamson11
The separated shear layer evolves in a similar manner to a mixing layer given a sufficiently long recirculation
zone length. It is convectively unstable due to the Kelvin-Helmholtz mechanism for ReD> ~1200, leading to shear
layer rollup into tightly concentrated vorticity. In most practical configurations, the flame lies nearly parallel to the
flow and, thus, almost directly in the bluff body shear layer for practical high velocity flows. The separating
vorticity sheet on both sides of the bluff body rolls up, which induces a flow field that wraps the flame around these
regions of intense vorticity.
In non-reacting flows, the bluff body wake is absolutely unstable, and characterized by large scale, asymmetric
vortex shedding12 known as the Von Karman vortex street. This instability has a characteristic frequency of11
f BVK
StD
U
D
(1)
where StD is the Strouhal number. For circular cylinders, StD is independent of Reynolds number (StD = 0.21) in the
turbulent shear layer, laminar boundary layer regime, ~1000<ReD<~200,00013. Above ReD = ~200,000, the
boundary layer starts to transition to turbulence and there are some indications that this Strouhal number value
changes14-15.
This Strouhal number value is a function of bluff body shape9. In particular, StD is lower for “bluffer” bodies,
i.e., those with higher drag and wider wakes16. For example, StD ~ 0.18 for a 90 degree “v-gutter” and drops to 0.13
for a sharp edge, vertical flat plate17. Roshko suggests that StD fundamentally scales with the wake width16, 18 and,
therefore, care must be applied in inferring Strouhal numbers from one bluff body shape to another. For example,
flow separation is retarded for circular bluff bodies when the boundary layer transitions to turbulence, implying a
reduction in wake width and turbulent vortex roll-up19. In contrast, the flow separation point would not move in
bluff bodies with sharp separation points.
There is a large literature on the effects of wake heating18-21, splitter plates10, and wake bleeding on the absolute
stability characteristics of the wake. Of most interest to this study are analyses showing that a sufficiently hot wake
relative to the free stream eliminates the absolute instability of the wake, so that its dynamics are then controlled by
the convectively unstable shear layers. For example, Yu20 and Monkewitz6, 20 reported the results of a parallel
stability analysis in an unconfined domain. They show that the absolute stability boundary depends upon density
ratio between the outer flow and wake, and the ratio of reverse flow velocity in the wake to outer flow velocity, β,
defined below:
u( y
u( y
0)
)
(2)
The resulting convective/absolute stability boundary is plotted in Figure 2. For the purpose of this study, only
the sinuous (asymmetric) mode stability boundary is plotted, as it is more easily destabilized in wakes than the
varicose (symmetric) mode. This plot shows that absolute instability is promoted with lower density ratios, ρu/ρb,
and higher wake reverse flow velocities. In other words, as the reverse flow velocity in the wake increases, the flow
becomes more absolutely unstable. For this study, the density ratios plotted in the figure equal the temperature ratio,
Tb/Tu , to within a fraction of a percent.
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Figure 2. Dependence of convective/absolute stability limit upon backflow and
density ratio, as predicted by 2D parallel flow stability analysis
Figure 3. Illustration of the bluff body flowfield, showing region of reverse flow in
the wake centerline (ballistic bluff body at 50 m/s, ρu/ρb = 1.7)
Computations demonstrating this same effect in combusting flows have also been presented by Erickson et al.21.
Their results show that the BVK instability magnitude gradually grows in prominence as density ratio across the
flame is decreased below values of approximately 2-3. This observation is quite significant as it shows that the
dominant fluid mechanics in a lab scale burner with non preheated reactants, which have a “high” density ratio, can
be very different from that of a facility with highly preheated reactants. Similarly, other experiments have clearly
shown that the BVK instability becomes prominent either at low flame density ratios 22-23 or for flames close to
blowoff22, 24.
The objective of this study is to characterize the unsteady flow evolution as the flame density ratio is
monotonically varied across this bifurcation in flow structure. While other experimental studies have clearly
demonstrated the structural flow change at high and low density ratios, there does not yet appear to be a study where
density ratio is systematically varied, particularly while keeping other key flow parameters, such as flow velocity,
constant. Additionally, the experiments performed in this study have been designed in order to facilitate a
comparison to parallel stability theory. That comparison is presented in a companion work25.
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Figure 4. Computationally predicted vorticity field and instantaneous flame edge
for various flame temperature ratios, produced by Erickson21
II. Experimental Facility, Diagnostics, and Testing Procedures
The experimental rig, shown in Figure 5 and Figure 6, consists of two premixed, methane-air combustors in
series. The first combustor is swirl stabilized and used to vitiate the flow. The bluff body stabilized combustor
section consists of a rectangular section with a bluff body spanning the width of the combustor, creating a nominally
2D flow. The aspect ratio of bluff body height to chamber width is 0.15. This combustor has quartz windows for
optical access from all four sides. Two different bluff bodies were used in the test section: a 2D ballistic shape
(shown in Figure 7a), and a V-gutter (shown in Figure 7b). From here on, the 2D ballistic shape will be referred to
as the ballistic bluff body.
Vitiator
Test Section
Secondary Air Inlet
Secondary Fuel Inlet
Flow Direction
Figure 5. Schematic and photograph of the atmospheric pressure, vitiated, bluff
body rig
Figure 6. Schematic of test section with ballistic bluff body installed
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a)
b)
Figure 7. Schematics of bluff bodies, a) ballistic, b) V gutter
Primary air and fuel were premixed upstream of the vitiator. Secondary air and fuel were plumbed into the rig
and premixed in a 1.4 m long settling section aft of the vitiator, and upstream of the test section. The primary and
secondary air and fuel each have their flowrates adjusted individually. This design allows the flame density ratio
and bluff body lip velocity to be varied independently in the test section, by adjusting the air flowrate and
stoichiometry in the vitiator and test section separately. The test matrix was developed such that primary and
secondary air flowrates and primary and secondary equivalence ratio could be adjusted to achieve a variety of
density ratios at a fixed velocity.
Mass flowrates for the primary and secondary air and fuel were measured across calibrated knife-edge orifice
plates using the static upstream pressure and the differential pressure across the plate, measured with Omega PX209
solid state pressure transducers and Omega PX771A differential pressure transmitters, respectively. The
temperature just upstream of the vitiator (after addition of secondary air and fuel) was measured by a type K
thermocouple and an Omega TX13 Smart Temperature Transmitter. Values were recorded once every second for
ten seconds, and then averaged. During all tests, the measured primary air and fuel flowrates as well as the
measured temperature just before the test section were recorded. On average, the measured absolute temperature
entering the test section was 26% and 31% lower than the calculated adiabatic temperature for 50 m/s tests and 20
m/s tests, respectively. Bluff body lip velocity was calculated as Ulip=ṁlip/(ρlipAlip). For this lip velocity calculation,
the total measured mass flowrate and the flow cross sectional area at the bluff body trailing edge were used. The
density for the lip velocity calculation was determined from the temperature measured just before the test section
and the gas composition of the secondary air and fuel adiabatically mixed with the equilibrium vitiated gas. An
equilibrium gas solver was then used to calculate the adiabatic density ratio across the test section flame. For PIV
tests a reference velocity (Uref) was determined directly from the PIV velocity field as the time-averaged axial
velocity just aft of the bluff body, located transversely in the center of the bulk flow.
Samples of the design parameters used and the density ratios and lip velocities obtained are presented below.
For the 50 m/s cases, uncertainty was about 2% for the measured gas flowrates and the resulting temperature and
density ratios. For the 20 m/s cases, uncertainty was about 4% for the measured gas flowrates, about 9% for the
resulting density ratios, and about 10% for the density ratios. Uncertainties are bounded by worst case combinations
of maximum and minimum flowrates and thermocouple readings for a given test. Differences between Ulip (based
on flowrate measurements) and Uref (based on PIV measurements) are 0.6 m/s and 6 m/s for the 20 and 50 m/s cases,
respectively. Figure 8 shows the experimental air flowrates and equivalence ratios from the ballistic bluff body at
50 m/s. Uncertainty in thermocouple reading was less than 1%. The charts in Figure 8, shown for the ballistic 50
m/s cases, demonstrate how air flowrates and equivalence ratios in the two burners may be adjusted so that the
density ratio can be swept while lip velocity is held nearly constant.
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a)
b)
Figure 8. Experimental design parameters for ballistic bluff body at 50 m/s,
showing a) primary and secondary air flowrates and b) equivalence ratios in both
combustors
Test matrix design was motivated by Figure 2. Actual conditions tested are provided in Figure 9, where the
maximum backflow ratio max was determined from the maximum reverse flow velocity, and overlaid on the
absolute stability map from Figure 2. Note that the ballistic bluff body provides a lower maximum backflow ratio
than the V-gutter. Contours of constant ω0,iD/Ulip (corresponding to the temporal growth rate of the absolute
instability) are provided as well. Note that these are theoretical values that are deduced from assumptions of tophat
density and velocity profiles and inviscid flow; more complex hyperbolic tangent profiles have been investigated by
Monkewitz26.
Figure 9. Tested conditions overlaid onto map obtained from 2D parallel flow
stability analysis
Experimental diagnostics consisted of high speed, line of sight imaging of flame chemiluminescence and particle
image velocimetry (PIV). High speed video was captured for the ballistic bluff body only. High speed imaging was
performed with a Photron Fastcam SA3 camera to capture chemiluminescence at a 3000 Hz frame rate at a
resolution of 512 x 256 pixels. This CMOS camera operates nearly continuously at 3000 Hz. The flame was
imaged through a BG-28 filter for CH* chemiluminescence imaging. This filter transmission exceeds 10% for
wavelengths between 340 and 630 nm, and peaks at 82% transmission at 450 nm. The flame was imaged from the
bluff body trailing edge to approximately nine bluff body diameters downstream. A total of 8029 images were
stored in each run.
PIV was conducted for both the ballistic bluff body and the V-gutter at conditions identical to those for high
speed video. The PIV system is a LaVision Flowmaster Planar Time Resolved system that allows for twodimensional, high-speed velocity measurements. The laser is a Litron Lasers Ltd. LDY303He Nd:YLF laser with a
wavelength of 527 nm and a 5 mJ/pulse pulse energy at a 10 kHz repetition rate. The laser is capable of repetition
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rates up to 10 kHz in each of the two laser heads. The Photron HighSpeed Star 6 camera has a 640x448 pixel
resolution with 20x20 micron pixels on the sensor at a frame rate of 10 kHz. In the current study, 2000 PIV image
pairs were taken at a frame rate of 10 kHz with 12 s between image pairs. The DaVis 7.2 software from LaVision
was used to process the PIV data, performing background subtraction and then calculating the velocity fields. A
sample time-averaged velocity field from PIV is provided above in Figure 3.
III. Results - Flame and Flow Dynamics
A. Spectral and Correlation Analysis
This section will discuss several characteristics of the flame and flow dynamics for the ballistic bluff body at a
lip velocity of 50 m/s, which will be used as a representative case; data taken at other conditions show similar
trends. Flame dynamics, measured by high speed video, were quantified via the transverse position of the top and
bottom flame branch edges, ζU(x,t) and ζL(x,t), as a function of axial position and time (see Figure 10). This resulted
in time series for edge positions along both flame branches, at each axial position. These time series are Fourier
transformed to determine their temporal spectra, given by ζU(x,f) and ζL(x,f).
Figure 10. Coordinate system and instantaneous flame edge position definition
from edge tracking, 50 m/s, ρu/ρb = 1.7.
PIV data were used for corresponding analysis of flowfield dynamics. PIV data shown in this section were
taken from the transverse centerline velocity v’(x,y=0,t), whose Fourier transform is given by v’(x,y=0,f). The rest of
this section summarizes the key results obtained from analysis of the time series and spectra of both flame and flow
dynamics as a function of flame density ratio.
Figure 11a shows spectra from the upper flame branch at x/D=3.5 at three different density ratios as a function of
Strouhal number, St=fD/Ulip. At the highest density ratio shown, ρu/ρb=2.4, the spectrum is fairly evenly distributed
across all frequencies, with a small bump at St ~0.24. As the density ratio is decreased to 2.0, a clear feature appears
centered near St = 0.24. As the density ratio is further decreased to 1.7, the response at St = 0.24 becomes
narrowband and quite prominent. Figure 11b shows spectra of the unsteady transverse velocity for the same flow
conditions, and demonstrates that the flow similarly exhibits a growing narrowband spectral feature at St=0.24.
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a)
b)
Figure 11. Spectra for ballistic bluff body at 50 m/s and x/D = 3.5 for a) upper
flame edge and b) centerline transverse unsteady velocity magnitude
In order to focus on the characteristics near the frequency of peak response, the integrated power under the
spectral peak between Strouhal numbers of 0.20 and 0.28 as a function of density ratio is computed for the flame
response spectra in Figure 11a, and for the unsteady transverse velocity spectra in Figure 11b. This power is
converted to a root mean square (RMS) of the signal at the response frequency by use of Parseval’s theorem, using
the relation below that relates RMS of the time series s(t) of duration T and spectrum φ(f),
srms
1
f
2
( f ) df
(3)
f
These RMS values are presented in Figure 12 for both the flame and the flow. The flame data in Figure 12 show
that the normalized fluctuation in flame position has a value of roughly 4% over the 2.4<ρu/ρb<3.4 range. Below a
value of ρu/ρb=2.4, the response gradually increases to 18% at ρu/ρb=1.7. Comparing the flame to the flow data
again demonstrates similarities. This plot also indicates that the transition in flow and flame characteristics is not an
abrupt bifurcation with change in density ratio, but a more gradual increase in narrowband response as the density
ratio decreases.
Figure 12. Spectral energy vs density ratio for ballistic bluff body at 50 m/s and
x/D = 3.5, expressed as RMS flame edge fluctuation averaged over both flame
branches, and RMS centerline transverse unsteady velocity.
The correlation coefficient between the two flame branches, U,L (defined below), provides important
information on the scale and/or correlation between the underlying flow structures perturbing them.
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U ,L
U
( x)
(
( x, t ) L ( x, t )
(4)
2
( L ( x, t )) 2
U ( x, t ))
Note that negative and positive correlation coefficients mean an asymmetric and symmetric flame, respectively.
Furthermore, a near zero correlation coefficient implies that the flame is disturbed by uncorrelated structures much
smaller than their transverse separation distance, roughly the bluff body diameter.
The dependence of correlation coefficient upon ρu/ρb is plotted in Figure 13, showing that the correlation
coefficients are near zero, but possibly slightly positive, for ρu/ρb> ~2.5. The correlation coefficient monotonically
decreases towards values of ρU,L ~ -0.6, indicative of growing correlation and antisymmetric motion with decreasing
flame density ratio.
Figure 13. Correlation coefficient between top and bottom flame edge position for
ballistic bluff body at 50 m/s.
To summarize these data, Figure 12 shows that there is a gradual increase in spectral energy at the asymmetric
vortex shedding frequency, and Figure 13 shows a gradual increase in asymmetry and large scale structures in the
wake. The very narrowband spectral nature of the flow in Figure 11 suggests that the flow evolves to a limitcycling, absolutely unstable flow at low density ratios. These data also suggest that the limit cycle amplitude of the
absolutely unstable flow oscillator grows monotonically in amplitude with decreases in density ratio for ρu/ρb<2.4.
B. Intermittency
The above measures of the flame structures are averaged temporal attributes and do not illustrate that the flame
dynamics are actually highly intermittent in time. As will be shown next, it appears that rather than characterizing
the limit cycle amplitude as monotonically growing in amplitude with ρu/ρb, a better description is that the flow has
two possible states and intermittently flips between them. The relative fraction of time the flow spends in each state
monotonically varies with density ratio. This intermittent character is evident from Figure 14, which shows two
images of the flame at the same operating conditions, but different instances of time.
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a)
b)
Figure 14. Intermittent wake structure evident in two flame images from the same
high speed video for ballistic bluff body at 50 m/s, ρu/ρb = 1.7
In order to quantify this intermittency, the time series were locally fit to a sinusoidal fluctuation with a fixed
frequency of fo=0.24Uo/D=~630Hz over a two period window. Within each window, a correlation coefficient, f
(defined below), was calculated between the sine fit and the actual data, providing a measure of the goodness of fit.
f
U
( x)
(
( x, t ) sin(2 f 0t )
(5)
2
(sin(2 f 0t )) 2
U ( x, t ))
A sample plot of the temporal dependence of ρf at ρu/ρb =1.7 is plotted in Figure 15, illustrating that it spends a
significant fraction of time between 0.9-1.0 for flame edge position (slightly less for velocity), but also has certain
periods of time where it drops to values well below 0.5.
a)
b)
Figure 15. Correlation coefficient between sine fit and time signal for ballistic
bluff body at 50 m/s, x/D = 3.5, for upper flame edge position and centerline
transverse unsteady velocity at a) ρu/ρb = 1.7, b) ρu/ρb = 2.4
The fraction of time that this correlation coefficient exceeds a specified threshold value, ρt, was then computed at
each spatial location and density ratio. Figure 16 plots a typical result at two threshold values. Notice the
similarities between the spectral energy plot, Figure 12, and the intermittency plot, Figure 16.
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a)
b)
Figure 16. Percent of time that sine fit correlation coefficient is greater than the
threshold value for ballistic bluff body at 50 m/s, x/D = 3.5 for a) upper flame edge
and b) centerline transverse unsteady velocity. Results for two threshold values
are presented with symbol x for ρt = 0.5 and symbol o for ρt = 0.8.
Although not shown for reasons of space, results at other spatial locations indicate qualitatively similar results.
The fraction of time that the flow spends in the “periodic state” monotonically grows with downstream distance.
These data clearly support the notion that the rise in narrowband energy is associated with an increased fraction of
time that the flow spends in a limit-cycling state, manifested by asymmetric structures with length scales of the order
of the bluff body diameter. These results raise the question of how much the growth in amplitude with decreasing
density ratio shown in Figure 11 is due to intermittency effects, and how much to a rise in limit cycle amplitude.
The answer appears to be both, as shown next.
From the sine fits in the previous section, we determined the conditional amplitude of the fit averaged over the
time intervals where ρf>ρt, denoted by ζ’rms(ρf>ρt) in Figure 17. This may be compared to the density ratio
dependency of the intermittency as shown previously in Figure 16. From this figure, it is clear that the apparent
monotonic increase in the flame’s limit cycle amplitude is not due only to the intermittency, but that the limit cycle
amplitude of the sinusoidal configuration also grows as density ratio decreases.
Figure 17. Effect of density ratio and intermittency on limit cycle amplitude for
ballistic bluff body at 50 m/s, x/D = 3.5, shown by comparing a) amplitude of
flame edge fluctuation only during sinusoidal times, and b) percent of time that
flame edge fluctuation is in a sinusoidal configuration, based on ρt = 0.8
The statistics of the conditioned time intervals of the “sinusoidal” and “random” bursts in the flame edge time series
was also determined, suggesting that these behaviors are stochastic in nature. Although not shown, probability
density functions of these time intervals are log-normal in behavior; averages of the “sinusoidal” time intervals, τ,
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are plotted against density ratio in Figure 18. This result shows that the time length of the “sinusoidal bursts”
monotonically increases with decreasing density ratio.
Figure 18. Density ratio dependence of average duration of the times when ρf > ρt,
based on ρt = 0.8, at x/D = 3.5
IV. Concluding Remarks
These results clearly show that the bluff body wake structure is a strong function of density ratio, but that no
sharp bifurcation occurs with variations in ρu/ρb. Rather, at intermediate density ratios the wake exhibits two
structures intermittently. Further understanding of the flow intermittency at realistic density ratios and conditions is
a critical step in predicting bluff body flame response characteristics. A companion paper will describe comparisons
of these data with parallel stability analyses25, as well as the frequency and amplitude characteristics of the
externally forced flame and flow field as a function of ρu/ρb.
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14
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