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Large-Scale Structure in Turbulent Diffusion Flames - Evidence Implications Origins.

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Dev. Chem. Eng. Mineral Process., 7(3/4),pp.287-300,1999.
Large-Scale Structure in Turbulent Diffusion
Flames - Evidence, Implications, Origins
M. G. Mungal
Mechanical Engineering Department
Stanford University,Stanford, CA 94305-3032, USA
This work reviews some evidence for the existence of large-scale structures in
turbulent d i m i o n flames, at low and high Reynolds numbers, for p e e jets and jets
in crossflow over a range of buoyancy conditions. The striking dferences between
the veloci@Jieldand the scalarJield will be highlighted and implicationsfor mixing
and reaction are explored The origins of these diferences are discussed by analogy
to simple large-scale wave motions in the velocityfield leading to complex mixing
patterns in the scalar field
The discussion of organized structure in turbulent flows is one which has been around
for several decades with a number of reviews on the subject [ 1-61. On the matter cf
organized structures in reacting flows, relatively less work has been done, but the
recent review of Coats [7]provides a good starting point for the present discussion.
Coats presents an overview of ideas on linear stability applied to turbulent flows, and
experimental observations of coherent structures in both non-reacting and reacting
flows. The larger part of his discussion dealt with two-dimensional mixing layers,
with a lesser part concerning turbulent jets. In the present work, we will concentrate
entirely on turbulent jets (fie jets, jets in coflow, and jets in crossflow) to
demonstrate observations of organized structure. We will attempt to contrast some
essential dif€erences between the velocity field and the scalar field, discuss these
M.G. Mungal
implications, and finally suggest that wave-like motions in the velocity field lead to
organized structure in the scalar field. Implications for modeling reacting flows will
also be discussed.
Figure I .
Jet visualization under jlood illumination (lefl) and laser sheet
illumination (right). Re = 5,000, [&‘I.
While organized structure in two-dimensional mixing layers has been readily revealed
using shadowgraphkhlieren or dye injection techniques, the same has not been true
in turbulent jets. A good illustration of this can be seen in Fig. 1 fiom Dahm [S]
where a dyed water jet (Reynolds number, Re = 5 x lo’) is shown under flood
lighting and also when illuminated by a thin laser sheet through the centerline plane.
The fonner image is seen to be dominated by exterior, small-scale features and so
appears quite structureless,while the latter, by nature of the laser sheet to provide an
interior view, shows the large-scale clumping of dye that is characteristic of organized
motion. A second example can be seen in Fig. 1 of [9] where two images of a large
jet plume (Re = 2 x lo8) are shown; in one image the overhead sun “slices” the jet
analogous to the laser sheet, revealing interior, large-scale features, while in the other
image, diffuse ambient lighting reveals a jet dominated by small scales.
Large-scale structures in turbulent difision flames
Figure 2. (a) Schematic illustration of volume rendering technique, [12]. (b)
Technique applied to jet d i m i o n flame showing tip burnout, [II].
Two additional factors that are important to revealing organized structure in jets
are also demonstrated in [ 101. These are: (1) chemical reactions can be used to reveal
details of the interior concentration field and (2) high-speed movie sequences of the jet
can be used to show the evolution and the dynamics of the organized structure. These
approaches have been used by Mungal et al. [9, 1 1 , 121 (nonreacting and reacting
gaseous jets including effects of buoyancy, and jets in crossflow), Yoda et al. [13]
(non-reacting liquid jets at low Re) and Newbold et al. [14] (reacting, precessing,
buoyant jets) to reveal the dynamics of the organized structure in jet flows. Examples
of these observations will be presented now.
The flow evolution is best revealed using the technique of volume rendering,
illustrated in Figs. 2% b. Here high-speed movie sequences of x-y-images of jet flows
are stacked as a function of time, t, on a computer to generate a solid object in x-y-t
space, Fig. 2a. A traveling “bump” in the flow becomes a “band” in the rendered
object, and illustrates the evolution of the organized structure when viewed fiom an
angle 0. Figure 2b illustrates the technique when applied to images of the visible
emission fiom a free jet flame [l 13; the burnout of the flame tip as the organized
structure convects downstream is readily visible.
Figure 3 illustrates three cases of free jet diffusion flames fiom [ 111. The field of
view extends from the jet lip to about 300 diameters downstream at the maximum
visible flame height. The leftmost image is a case where the discharge velocity is low
M.G. Mungal
(16 m / s , ethylene, Re = 5,700 ) so that buoyancy is strongly coupled to the evolving
jet flow, the middle image is intermediate (60 m/s, ethylene, Re = 21,400) while the
rightmost image is a case where the high discharge velocity (250 d s , acetylene, Re =
86,500) negates the effects of buoyancy leading to a momentum driven jet flame. The
traveling bands are clearly revealed in all cases, irrespective of buoyancy and Re.
Some pairing of structures is visible as bands merge into each other. The structures
are also seen to travel long distances relative to the flame length, suggesting extended
lifetimes, much longer than the local timescale as &lined by the centerhe velocity
and jet width. The repetitive nature of the flame tip bumout associated with the final
consumption of the fuel in the structure is also clearly revealed when comparing to
Fig. 2b.
Figure 3. Volume rendering of (a) buoyant, (b) intermediate, (c) momentum driven
flame. Viewing angle 8 = 70." Field of view @om jet lip to flame tip extends over
300jet diameters, [I I].
Figure 4 shows similar results [9] for a non-reactingjet (field of view from 120 to
600 m) at very high Re = 2 x108and is compared to a hydrogenjet flame at Re = 3 x
lo7 (field of view from 0 to 60 m). The flame looks strikingly similar to the
laboratory flame of Fig. 3b (each having similar levels of buoyancy) even though the
Re is three orders of magnitude higher (the flame base does appear structureless owing
to the inadequate h i n g rate ofthe camera). The non-reacting jet shows trajectories
of the structure which slow as they move downstream (owing to momentum
Large-scale structures in turbulent dimion flames
conservation) and is essentially similar to observations by Yoda et al. [I31 at Re =
4,000 which is more than four orders of magnitude smaller than Fig. 4a.
Figure 4. Volume rendering of high Re (a) non-reacting jet, (b) reacting jet.
Viewing angle 8 = 7 9 , [9].
Figure 5. Volume rendering of burning jet in crossflow. Viewing angles defined by
(a) ,p = @, e = 60°, (b) 6 = o", e = 250°, (c) ,p = 504 e = go", p 2 ] .
Similar phenomena are found when we examine renderings of a large (30 m overall
height) burning jet in crossflow [121 derived from video sequences of a large, unabated
oilwell discharge. Figure 5 shows three views of this as the rendering is rotated about
its vertical and horizontal axes. The development of structures as defined by the
upstream edge is similar to the straight jet (Fig. 5a), with similar tip burnout fealues
(Fig. 5c). The downstream side ofthe jet contains considerably more small scale
structure (Fig. 5b), and is likely associated with the complexity of the wake region d
the jet in crossflow [ 151.
Finally we note that another characteristic of the organized structure is an
instantaneous scalar field which tends to be considerably more top-hat than the
corresponding mean, which is more Gaussian [ 5 ] . Figure 6 illustrates this for a jet in
crossflow [I61 at Re = 30,000 for jet to fieestream velocity ratio, r = 20. The image
is obtained using planar laser induced fluorescence and is a slice through the centerline
plane. The large indentations on the upstream edge show the instantaneous organized
structure, while the small scales on the downstream edge associated with the wake are
clearly seen. The instantaneous scalar concentration profiles are compared to their
corresponding ensemble averages and show the large discrepancy between these two.
Figure 6. Instantaneous PLIF image of non-reactingj e t in crossflow, (1 61.
Large-scale structures in turbulent d i f i i o n flames
The results shown above are provided to suggest that organized structure is evident in
turbulent reacting jets and jets in crossflow irrespective of Re.and buoyancy. Given
this, one may ask of what importance is the observation. The flame tip oscillation
and burnout shown in Figs. l b and 2 is one consequence of this underlying
organization, such that the instantaneous flame length is a sawtooth function of time
with quasi-periodicity, rather than a purely random variable [9, 101.
When one
considers that the scalar field within structures tends to be more uniform
instantaneously, rather than Gaussian, the suggestion of Broadwell [ 171 is that the
process of mixing and burning in a jet appears to be more closely related to addition
of outside air to a well-stirred-reactor (WSR)which becomes progressively diluted as
the organized structure proceeds downstream. Eventually, the WSR is stoichiometric
at the flame tip and burns out as seen in Fig. 2b; this burnout process occurs over a
length scale roughly equal to the local jet width, and over a timescale which equals
the local width divided by the local velocity [9, 101. This description is to be
contrasted with one of turbulent diffusion through the flame brush by which fuel and
air react to form products.
Figure 7. Schematic illustration of the Two Stage Lagrangian (TSL) model, [18].
The physical description of mixing and reaction described above formed the
underpinnings of the Two Stage Lagrangian (TSL) combustion model of Broadwell
and Lutz [ 181, illustrated schematically in Fig. 7. Here air is entrained into a unit
quantity of fuel which is described in a Lagrangian sense. The initial fuel/air int&
leads to a flame sheet (in the flame sheet reactor) whose products mix with the excess
fuel and heat it (in the core reactor). This hellproduct mixture is assumed to be
homogeneously mixed throughout the jet and it reacts subsequently with the
entrained air (again in the flame sheet reactor), with the core reactor continuously
M.G. Mungal
accumulating the products of combustion. The process continues until the flame tip
at which point all of the fuel is consumed.
The simplicity of the fluid mechanical description of this model, which is thought
to contain the essential physics, allows full chemistry to be carried in NOx
predictions. The model has successfully predicted NOx production in hydrogen and
methane flames, and is also able to show the very significant effects upon NOx due to
radiation (controlling the temperature) and buoyancy (controlling the entrainment, and
hence the temperature history of the core reactor) with detailed results in [ 181. A
typical result is shown in Fig. 8 where the NOx Emission Index is shown for
methane flames and compared to the data of Turns and Myhr [19]. The uppermost
curve shows the model under adiabatic conditions and no buoyancy. The middle
curve shows the reduction in NOx due solely to the addition of buoyancy. The
lowest curve shows the prediction including buoyancy when the model is adjusted for
the radiant loss observed in the experiments; the agreement with experiment is seen to
be quite good.
100 120
Velocity (m/s)
Figure 8, Radiation and buoyancy effects on methaneflame NOx emissions
predicted by the TSL model, [18]. - - - adiabatic, no buoyancy; - - - - adiabatic, with buoyancy;-with radiation loss, with buoyancy. 0 , &tapom
Large-scalestructures in turbulenr d@ksionflames
Some additional physical justification for the TSL description is found in the
measurements of Everest et al. [20]. Using planar Rayleigh scattering to measure the
instantaneous temperature in a jet diffusion flame at Re = 4,000 to 16,000, they
conclude that “two types of thermal regions are observed in turbulent nonpremired
jet flames: relatively broad, homogeneous temperature zones in which the thermaI
gradients are small, and thin thermal mixing layers in which the gradients (and
thermal mixing rates) are large”. We believe that the dynamical evolution shown
above and the instantaneous temperature described by PO] are consistent
manifestations of the underlying organized structure.
Thus far our discussion of structure has focused primarily on the scalar field. Now
we wish to include some fe-
of the velocity field which will be relevant to the
subsequent discussion. Figure 9 shows instantaneous velocity fields obtained using
Particle Image Velochetry (PIV) through the centerline plane of ajet in coflow at Re
6,000 each measured approximately 1/3 ofthe way along the length of the flame
[21]. The left image corresponds to the non-reacting case, while the right images
corresponds to the reacting case. While the velocity magnitude has increased in the
reacting case, the observation to be made here is that in both cases, the velocity field
shows a large-scale meandering or zigzag appearance. This can be seen as the velocity
vectors oscillate to the left and then to the right as one proceeds downstream along the
centerline. To a single point probe in the flow, such as a hot-wire or LDV, the
passage of such velocity vectors would be recorded as a signal of continuously
fluctuating values leading to the traditional mean and rms component. What we
allude to here is the underlying waviness in the flow at the largest scales. We note
that no PIV images ever show a set of vectors which are which are more-or-less
randomly fluctuating and devoid of the large-scale oscillation; in fact the images
shown in Fig. 9 are fairly typical.
Figure 9. PIV veloci&field for (a) left: non-reactingjet, (b) right: reactingjet.
Field of view extend ?om 20 to 30 jet diameters downstream, [21/.
The suggestion made above thus far is one in which there exists organized structure in
jets as manifested by regions of similar scalar concentrations which convect
downstream and eventually burn out at the flame tip. Associated with this is a
velocity field which shows a wavy or meandering appearance at the large-scales. We
now wish to illustrate the connection between these seemingly disparate ideas by
consideration of a simple analytic problem first presented by Hama [22] in 1962. His
paper was written as a cautionary warning to researchers who use dye injection to
search for vortical regions in a flow. Here we seek a different interpretation, namely,
that a simple underlying wave motion on a shear flow can lead to a well organized but
complex scalar mixing field.
The base shear flow velocity components are given by
u0 = l + t m h y ,
v0 = O
to which traveling wave-like perturbation eigenfunctions are added
u' = 2a sech y tanh y sin a(x - ct),
v' = 2a sech y cos a(x - ct)
Large-scale structures in turbulent difision flames
where a is a measure of the amplitude of the velocity fluctuations, a (= 2 d 5 ) is the
wave number, 5 is the wavelength and c the wave velocity. The normalization is
such that a = 1, X = x/5, Y = y/h and T = cdh.
..-.-.......... ......
.... ....._
Figure 10. Representative pathlinesfiom originfor a = 0.015.
Figure 11. Streaklinesfiom various locations in shear layer for a = 0.015,
Figure 10 shows individual pathlines released from the origin at different phases in
the passage of the wave for a total elapsed time of T = 5 ; the order of release is: solid
line (T = 0), dotted (T = 0.2) and dashed (T = 0.4). Each pathline shows an inherent
up/down motion associated with the passing wave. Figure 11 is most interesting and
shows a set of streaklines (continuous release of dye) from various Y positions in the
layer. If one envisions an initial distribution of scalar at the inlet plane, one can use
the streakline pattern to infer the subsequent scalar distribution. This distribution of
the scalar due to the unsteady stirring, which represents the integrated effect of the
velocity field, is remarkable when considered in the context of the simplicity of the
underlying non-amplifying wave, and the motion of individual particles as seen in the
pathlines. This example shows that scalar mixing under the presence of large-scale
wave motion leads to broad regions of distributed scalar or organized structure.
Consideration of the large-scale wave motion is an essential element as random
fluctuations would not produce such organized scalar fields; while a random walk of
an individual fluid particle might result in such a particle exhibiting large-scale
displacement, it is clear that organized scalar structure requires a large-scale wave-like
Several authors have suggested that instability waves are the source of the largescale structure. An excellent discussion and review is given by Roshko [6] where it
is suggested that such instabilities
the turbulence rather than & fiom it.
Furthermore, stability analyses show that most k e shear flows contain an inflection
point instability resulting in primarily long-wavelength instabilities. Heat release
(and compressibility) do modify such instabilities [23, 241 so that reacting and nonreacting flows will likely have different unstable patterns.
Finally, we note that Moms et al. [25] have proposed solution methods where the
large-scale structures are modeled as sets of inviscid instability waves which are used
to formulate the velocity perturbations and hence the Reynolds stress for avenged
equations of motion. For the two-dimensional turbulent mixing layer, the resulting
prediction of the growth rate as a function of velocity ratio, density ratio and
convective Mach number are in very good agreement with experimental observations.
Non-linearity in the wave motion was not found to be necessary in the formulation.
This approach thus appears to contain some of the essential physics for describing the
time-averaged evolution of the flow.
However, chemical reactions, though not
explicitly included, can also be derived from the time-dependent, unsteady motion of
the shear layer, with streakline patterns that capture the instantaneous mixing field.
We have presented evidence for the existence of organized structure in jets and jets in
crossflow, from low to high Re, and for a range of buoyancy conditions. Associated
with the structure is a uniformity of the instantaneous scalar field unlike the timeaveraged Gaussian shape. The velocity field on the other hand displays a large-scale
wave-like behavior. A simple analytical model due to Hama illustrates how wave-like
Large-scale structures in turbulent d i m i o n jlames
motions lead to an organized but complex scalar field.
These experimental
observations allow a simplification in modeling for NOx predictions as illustrated by
the TSL model. This model is able to incorporate full chemistry within a simplified
mixing and reaction framework, explicitly shows the effects of radiation and buoyancy,
and shows good agreement with experimental results. The incorporation of large-scale
behavior through inviscid instability waves in the calculation of [25] suggests a
physically based alternative to prediction of turbulent flow. Further development cf
these ideas can be found in [26].
We wish to acknowledge countless conversations with J. E. Broadwell;
E. F.
Hasselbrink for bringing the Hama work to our attention; W. D. Urban for repeating
the Hama calculations; and the help of W. D. Urban and L. MufIiz in preparation cf
the manuscript. Aspects of the work have been sponsored in part by the GRI,
AFOSR and the NSF.
Roshko, A. 1976. Structure of turbulent shear flows: a new look. AIAA Jr., 14 (lo), 1349-1357.
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