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 imion 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@Jield and the scalar Jield will be highlighted and implications for 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

Introduction

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

287

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.

Evidence 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.

288

Large-scale structures in turbulent difision flames

Figure 2. Technique applied to jet d imion flame showing tip burnout, [II].

(a) Schematic illustration of volume rendering technique, [12]. (b)

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 [ 1 1 1 . 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

289

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 300 jet diameters, [I I ] .

Figure 4 shows similar results [9] for a non-reacting jet (field of view from 120 to 600 m) at very high Re = 2 x108 and is compared to a hydrogen jet 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 of the camera). The non-reacting jet shows trajectories of the structure which slow as they move downstream (owing to momentum

290

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. Viewing angle 8 = 7 9 , [9].

Volume rendering of high Re (a) non-reacting jet, (b) reacting jet.

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", p2 ] .

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.

291

M.G. Mungal

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-reacting j e t in crossflow, (1 61.

292

Large-scale structures in turbulent d i f i ion flames

Implications

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.

Flame-sheet Reactor Reactor - Surroundings

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

293

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.

2 5

2 0

1 5

1 0

5

0 - 0 2 0 4 0 6 0 8 0 100 120

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 ~ 9 1 .

294

Large-scale structures 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.

295

M.G. Mwzgal

Figure 9. PIV veloci&field for (a) left: non-reacting jet, (b) right: reacting jet. Field of view extend ?om 20 to 30 jet diameters downstream, [21/.

Origins

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)

296

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.

0.1

....._ .... ...... 0.05 ..-.-..... ..... -

-0.05 -

0 1 2 3 4 5 6 -0.1

X

Figure 10. Representative pathlines fiom origin for a = 0.015.

0.1

0.05

P O

-0.05

-0.1 6 x 4 2

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

297

M.G. Mungal

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

motion.

Several authors have suggested that instability waves are the source of the large-

scale 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 ke 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 non-

reacting 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.

Conclusions

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 time-

averaged 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

298

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].

Acknowledgments 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.

References 1. 2. 3. 4.

5.

6.

7. 8.

9.

10.

11.

12.

13.

14.

15.

Roshko, A. 1976. Structure of turbulent shear flows: a new look. AIAA Jr., 14 (lo), 1349-1357. Cantwell, B.J. 1981. Organized motion in turbulent flow. Ann. Rev. Fluid. Mech., 13,457-515. Fiedler, HE 1988. Coherent structure in turbulent flows. Prog. Aero. Sci., 25,231-269. Dimotakis, PE 1991. Turbulent free shear layer mixing and combustion. High-speed Flight Propulsion Systems, Prog. in Astro. and Aero., Vol 137, S.N.B. Murthy and E.T. Curran (Eds.), 265- 340. Broadwell, J.E.; Mungal, M.G. 1990. Large-scale structures and molecular mixing. Phys Fluids A, 3 - (S), 1193-1206. Roshko. A. 1993. Instabilitv and turbulence in shear flows. Theoretical and Applied Mech. 1992, .. S.R. Bodner et al. (Eds), Elsevier, 1-24. Coats, C.M. 1996. Coherent structures in combustion. Prog. Energy Combust. Sci., 22,427-509. Dahm, W.J.A. 1985. Experiments on entrainment, mixing and chemical reactions in turbulent jets at large Schmidt number. Ph.D. Thesis, Caltech. Mungal, M.G.; Lozano, A,; van Cruyningen, 1. 1992. Large-scale dynamics in high Reynolds numberjets and jet flames. Expts. Fluids, 12, 141-150. Dahm, W.J.A.; Dimotakis, PE 1987 Measurements of entrainment and mixing in turbulent jets, AIAA Jr., 25 (9), 1216-1223. Mungal, M.G.; Karasso, P.S.; Lozano, A. 1991. The visible structure of turbulent jet diffusion flames - large-scale organization and flame tip oscillation. Comb. Sci. & Tech., 76, 165-185. Mungal, M.G.; Lozano, A. 1996. Some observations of a large, burning jet in crossflow. Expts. Fluids, 21,264-267. Yoda, M.; Hesselink, L. Mungal, M.G. 1992. The evolution and nature of large-scale structures in the turbulent jet. Phys. Fluids A, 4 (4), 803-81 I. Newbold, G.J.R.; Nathan, G.J.; Luxton, R.E. 1997 Large-scale dynamics of an unconfined precessing jet flame. Comb. Sci. Tech., 126, 71-95. Fric, T. F.; Roshko, A. 1994. Vortical structure in the wake of a transverse jet. J. Fluid. Mech. 279, 1-47.

299

M.G. Mungal

16.

17.

18.

19.

20.

21.

22. 23.

24.

25.

26.

Smith, S.H.; Mungal, M.G. 1998. Mixing, structure and scaling of the jet in crossflow. J. Fluid Mech.,

Broadwell, J. E. 1988. A model for reactions in turbulent jets: effects of Reynolds, Schmidt, and Damkohler numbers. Turbulent Reacting Flows: USA-France Workshop on Turbulent Reactive Flows, R. Borghi and S. N. B. Murthy, Eds., Springer-Verlag Lecture Notes in Engineering 40, 257- 211. Broadwell, J.E.; Lutz, A.E. 1998. A turbulent jet chemical reaction model: NOx production in jet flames. To appear, Comb. Flame. Turns, S. R.; Myhr, F. H. 1991. Oxides of nitrogen emissions from turbulentjet flames: 1. fuel effects and flame radiation. Comb. Flame 87,319-335. Everest D.; Driscoll, J. F.; Dahm, W. J. A.; Feikema, D. 1995. Images of the 2-D temperature field and temperature gradients to quantify mixing rates within a non-premixed turbulent jet flame. Comb. and Flame 101,5848 MuAiz, L.; Mungal, M.G. 1995, A PIV investigation of turbulent diffision flames. Fall Meeting, Western States Section I The Combustion Institute, 30-31 October 1995, Stanford, CA. Hama, F.R. 1962. Strcaklincs in a perturbed shear flow. Phys. Fluids, 5 (6), 644650. Shin, D. S.; Feniger, J. H. 1991. Linear stability of the reacting mixing layer. AIAA Jr., 29, 1634- 1642. Day, M.J.; Reynolds, W.C.; Mansour, N.N. 1997. Linear stability analysis and structure of the compressible reacting mixing layer. AIM-97-0761, 35th AIAA Aerospace Sciences Meeting, Reno, NV. Morris, P.J., Giridharan, M.G. and Lilley, G.M. 1990 On the turbulent mixing of compressible free shear layers. Proc. R. SOC. Lond. A, 431,219-243. M. G. Mungal & J. E. Broadwell (1998). “On Scalar Mixing and Chemical Reaction in Turbulent Free Shear Flows”, in preparation.

357,83-122.

300