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Flame Propagation Along a Vortex: the Baroclinic PushWM. T. ASHURST aa Combustion Research Facility, Sandia National Laboratories , Livermore, CA, 94551-0969Published online: 19 Apr 2007.

To cite this article: WM. T. ASHURST (1996) Flame Propagation Along a Vortex: the Baroclinic Push, Combustion Science andTechnology, 112:1, 175-185, DOI: 10.1080/00102209608951955

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Flame Propagation Along a Vortex: the Baroclinic Push

WM. T. ASHURST Combustion Research Facility,Sandia National Laboratories, Livermore, CA 94551-0969

(Received Apri/24, 1995)

Abstract-Flame propagation into a swirling flow allows the creation of burnt gas vorticity which mayenhance the forward motion of the flame. This baroclinic push on the flame differs from the axial pressuremodel suggested by Chomiak (1976).In particular, the baroelinic enhancement willdepend upon the locationof the burnt gas with respect to the flame, as shown by two vortex configurations: straight and curved.Additionally, the baroelinic effect, depending upon the flame density gradient and the swirling flow radialpressure gradient, will provide an enhancement that is proportional to the ambient pressure.

INTRODUCTION

What governs the propagation of a flame in a direction parallel to the axis of a vortextube? Chomiak (1976) suggested that the pressure minimum, created by the vorticalswirling flow, would draw a flame along the vortex; he assumed that the burnt gasswirling motion is reduced (due to volume expansion increasing the swirl radius, called'bursting') and the resulting static pressure difference in the axial direction would pullthe flame into the vortical core. Recently, a numerical simulation of this flame-vortexconfiguration shows that the flame speed does depend upon the magnitude of thevortical swirling velocity. We present a vortical model of flame propagation along theaxis of a vortex, this model is based on the baroclinic production of vorticity due to thecoupling of the density gradient across the flame and the radial pressure gradient in theunburnt, swirling gas ahead of the flame. The swirling motion in the burnt gas plays nopart in this baroclinic model. Comparisons are made with the numerical simulationsgenerated by Hasegawa et al. (1995) and experimental observation of flame propaga­tion around a vortex ring by McCormack et al. (1972).

BAROCLINIC PRODUCTION OF VORTICITY

The vector curl of Newton's equation of motion for a fluid produces an equation forangular momentum, known as the fluid vorticity. Helmholtz investigated vortexmotion in 1858 and showed the analogy with the scalar and vector potentials thatdescribe electric and magnetic fields (see Chapter 7 in Lamb). The vorticity equationdoes not include a pressure term when the fluid density is constant, or is only a functionof pressure. However, in reacting flow, the density is not constant and density gradients,

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176 W. T. ASHURST

which are not aligned with the pressure gradient, change the local vorticity. This effect,known as baroclinic production, was developed by Bjerknes in 1898 for atmosphericflow and is

~~ = G2) VP x Vp

(seeArticle 85 inPrandtl and Tietjens, 1934; Eliassen, 1982).With flame propagation inthe axial direction of a vortex, the density gradient across the flame combines with theradial pressure gradient to create azimuthal vorticity - the rotational sense of thisazimuthal vorticity creates a flow which enhances the convective velocity of the flametowards the unburnt gas, see Figure I. Thus, the burnt region is filled with azimuthalvorticity, confined within some radial region comparable to the initial vortical coresize, and the sign of this azimuthal vorticity is antisymmetric with respect to the initialaxial location of ignition. What is the magnitude of this baroclinic push? That is, howmuch does the flame speed increase in comparison to flame propagation withina constant cross section tube? We use the numerical simulations of Hasegawa et al.(1995) to first describe a baroclinic model or flame propagation in a straight vortex;later, we note the differences that will occur when the unburnt vortex is curved.

The numerical simulation of a straight vortex has an imposed symmetry: the initialflame is created over the vortex cross section at an axial location in the middle of thevortex tube. The tube length spans the periodic distance within the cubical computa­tional volume. The resulting two flames propagate away from each other, but they arealso moving towards each other and meet at the periodic boundary. For our modelestimate, we assume that the shrinking, finite unburnt vortex tube does not alter itsswirl velocity and so, the radial pressure gradient in the unburnt gas is assumed to beconstant during the flame propagation. The density ratio across the flame is 7.5, theflame thickness is <5, and in the simulations of Hasegawa et al., the estimated flamethickness is 0.17 L, where L is the computational cube edge length and L equals onemillimeter(the number grid cells in each periodic direction is 64). We use our baroclinicmodel to describe the initial behavior as the two flame surfaces move away from eachother, the length of the unburnt vortex is assumed to be infinite in the model estimates.Hence, in our model results, the two flames will not slow down, as is evident in thenumerical simulations due to the periodic boundary interaction.

The vortex swirling motion, in terms of the angular velocity, is

v r--i =--2 [I - exp( - r2Irt)]r 'Inr

where the lie radius of vorticity is at rM . We define an approximate maximum swirlvelocity by setting the circulation as r = 2nrM VM and at r = rM , we have V. = 0.63 VM'

Thus, the diameter of the maximum swirling velocity is ~ 2rM • With I) = r2lrt, thereduced angular velocity is rM V.lrVM = [I - exp( - 1)2)]/1)2. This swirling motioncreates a radial pressure gradient of

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FLAME PROPAGATION ALONG VORTEX

Straight Vortex

177

CutVed Vortex

I

Ignition PlaneI

I

I

I

FIGURE I Flame propagation along a vortex creates azimuthal vorticity in the burnt gas, shown by thecircular arcs; this baroclinic effect is maximum when the flame density gradient, Vp, is normal to the radialpressure gradient VP,existing in the unburnt swirling flow. The velocity produced by this baroclinic vorticitywill enhance the flame speed, but the enhancement depends upon the shape of the burnt gas and its locationwith respect to the flame.

and this gradient is assumed to remain constant, independent of viscous decay and theshrinking length of the unburnt vortex. The density gradient across the flame isassumed to be

where (j is the flame thickness, and the 1/P term is approximated as the geometric meanof the burnt Pb and unburnt P. densities, and 1:, the heat release parameter equals the

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178 W. T. ASHURST

density ratio minus unity. The flame normal is considered to be in the axial directionand so the production of baroclinic vorticity at the flame surface is simply the productof the above density gradient times the radial pressure gradient.

This product of gradients is integrated over the cross sectional area of the vorticalcore. We find that most ofthe baroclinic production is within r < 3rM , that is, the valueof Vilr at larger radii is very small. Therefore, we integrate from the vortex axis out to3rM and obtain

dw _ 4.5, r V2dt <5~ M M

where the numerical value of 4.5 is a result of the selected domain of integration, andwith the area integration, the equation now has dimensions of V~. This resultrepresents the vorticity created per unit time over the flame surface that has significantproduction of vorticity.

We now convert from a per unit time basis to vorticity per unit length of burnt gas.With respect to the flame, assuming no radial expansion, the burnt gas is moving awayfrom t~e flame at the rate of SL(' + 1)and so the value of dt is replaced with IJdtIIB) andthe expression IBldt is considered to be the burnt velocity with respect to the flame, orequal to SL(' + 1).The baroclinic vorticity, still integrated over the cross section, is nowon a per length basis, as

and the equation now has dimensions of circulation, VMIB' We can change theexpression rMVMI(<5SL ) to rMVMIl' where the product of flame thickness and burningvelocity is approximately the thermal diffusivity, and hence, the kinematic viscosity.Therefore, Rr = rMVMIl',which is the notation of Hasegawa et al., but we stress that thisapparent vortex Reynolds number is not describing the ratio of inertia to viscous forcesin our baroclinic model. Instead, R; describes the coupling of flame thickness (densitygradient) with radial pressure gradient induced by the swirling motion with circulationrM V M' We do not currently include the viscous spreading of the unburnt vortex, but if

.we did, then the radial growth estimate would be given as

41' tVM 4 tVM----=---rMVM rM Rr rM

and the Rr would be the parameter that affects the rate of viscous spreading. Thisspreading would reduce the pressure gradient and thus the amount of baroc1inicvorticity produced by the flame.

We now convert the baroclinic vorticity per unit length wBIIBinto discrete vortexrings, each ring will have the same circulation r B which is based on the selected axialspacing of the rings. This conversion to discrete rings is only for numerical simplicity, aswe can now use a collection of vortex rings, each with circulation r B, to describe theinduced velocity effect of the baroclinic vorticity which is actually distributed through­out the burnt gas. (This is not a bad exchange, as the comparison of a vortex ring andHill's spherical vortex, which has distributed vorticity (Lamb, Section 165), indicates

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FLAME PROPAGATION ALONG VORTEX 179

that the translation velocity of the spherical and ring vortex is very similar in terms ofthe size and circulation parameters and thus, their long-range induced velocity shouldalso be similar.) From Lamb (Section 161), a single vortex ring creates a streamfunction, in cylindrical coordinates X, R, of

r'f'(X, R) = 2n(r 1 + r 2 ) [K(A) - £(A)]

where X is the axial distance from the vortex location and R is the radial distance fromthe centerline of the cylindrical coordinate system. The functions K (A) and £(A)are thecomplete elliptic integrals ofthe first and second kind, and A= (r2 - r,)/(r2 + r1)' wherethe two distances, for a ring with radius RB, are defined as: ri= X 2 + (R - RBJ', andr~ = X 2 + (R + RBJ', thus, they are the least and greatest distances to the vortex ringfrom the point X, R.

In the numerical simulation, two flames are initiated, and as they propagate awayfrom each other, the burnt gas between them will contain vorticity created by thebaroclinic term, see sketch in Figure 1. We want to estimate the axial velocity,produced by the baroclinic vorticity, at the flame location X r- We select the baroclinicring radius as RB = 3rM and find the axial velocity created by these rings. This axialvelocity, denoted as UB, will change as the length of the burnt gas increases, that is, X p

starts near zero and increases - the total axial length of burnt gas is 2Xr- To model thiseffect, we use the growing number of discrete vortex rings, and sum their effect at theexpected flame location, X p • We obtain

UB - ~ VMRrJXplrM(r + 1) r + 1

where a numerical constant of order unity will be included to display the model resultsin a manner similar to the simulation results. The square root dependence of UB uponflame position is an approximation of the model results, valid when X r < 20R B• Beyondthis distance, the enhancement created by the baroclinic effect diminishes in compari­son to the growing square root. As the length of the vortical region becomes largecompared to the ring radius, the velocity enhancement continues to increase, but therate of increase decreases as 1IX~, which is the long-range behavior of the inducedvelocity given by a ring or a doublet. The flame speed is UB + SL(r+ 1); the assumptionof no radial expansion contributes the r factor.

To compare with the numerical simulation results given in Figure 4 of Hasegawa etal. (1995), we integrate the flame speed and determine distance as a function of time

X p = 1(uB + (r + 1)s Jdt

where time will now be scaled as tcolL, where L is the computational cube edge lengthof one millimeter and Co is the acoustic velocity (coiSL = 387/0.54). Figure 2 presents theflame trajectories for the seven cases, labeled as 3 to 9 in Hasegawa et at. (1995). Theratio of swirling velocity to burning velocity is VMISL= 1.8for Case 3, = 18.0for Cases4-6 and =36.0 for Cases 7-9. The product of VMRr/SV which determines themagnitude of the flame speed (U BISL) within the vortical core, and hence, the ordering

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180 w.T. ASHURST

~"T""---------e--"""'!r-------'

"-"'d...J

<,X

o 2 4 6TIme (t Co / L)

8 10

FIGURE 2 Model results for flame propagation within a straight vortex, the flame location versus time isgiven as scaled in the simulations of Hasegawa et al.; the value of the swirling motion, VMRr/SL' increasesfrom bottom to top, the flame speed enhancement is U8 - V"R r - V~/SL (see Figure 3).

of the model results, VMRr/SL = 8,85,440,800,340, 1800 and 3200 for Cases 3 to 9.Notice that Case 7 has a value between those of Cases 4 and 5 - and notice also, thatCase 7, shown as a dashed line, does produce a response which is between those twocurves. This same ordering is seen in the simulation results. (Note, for cases 4 and 7, wehave increased the stated value of the unburnt vortex core, by a factor of five, since theinitial core only spans two numerical grid points and so the actual core size is clearlymuch larger than the stated value, as is evident in their Figure 5 which shows the coresize time development.) The flame speed versus flame location is given in Figure 3,where the square root behavior is clearly evident, but remember that this power-law isnot a general result, it is only an approximation of the model results over a restrictedregion of flame motion.

The 'push' produced by the baroclinic vorticity that enhances the flame speed alongthe axis of the vortex can be summarized as

where the factors, from left to right, are: density gradient, radial pressure gradientproduced by swirl velocity V M' volume density ofbaroclinic vorticity in burnt gas, andthe dependence upon the length of burnt gas in the axial direction (valid forX F < 60rM ) . Thus, the flame speed enhancement does not depend upon a viscous flow

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FLAME PROPAGATION ALONG VORTEX

o~ .....--------------------,

§l...JVl<,

alo0. 0Vl-Q)

Eoc:;:

:il

181

0.0 0.2 0.4

Xfront ( X / L )0.6

FIGURE 3 Flame speed enhancement U';SL' model results for a straight vortex. see Figure 2.

effect (neglecting the reduction in pressure gradient due to viscous spreading). Theapparent Reynolds number, Rr, used to describe the simulation results generated byHasegawa et al. is not the complete description of the flame speed enhancement, but it isone factor in the baroclinic push on the flame.

EXPERIMENTAL FLAME-VORTEX CONFIGURATIONS

Straight Vortex

Ishizuka (1990) has produced enhanced flame speeds within a long tube (31 mmdiameter and one meter long) in which swirl motion is created at the closed end of thetube and flame propagation is initiated at the open end. The flame photographsindicate a surface which is many tube diameters long (flame normal not in the axialdirection) and thus, one may suspect that the unburnt stream lines are curved wherethey meet the flame. This curvature creates a pressure gradient and so, in addition tothe radial pressure gradient, there also may be a component along the flame surface.Lacking detailed knowledge of the complete flow, we do not try to estimate thebaroclinic effect in this configuration.

Experimental results obtained by Hanson and Thomas (1984) appear to agree withthe baroclinic model given above. They conducted laminar flame studies withinrotating cylinders, the cylinder height was either large (two times the diameter) or small

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182 W. T. ASHURST

(one-seventh of the diameter); the smaller one, called a disk, has an aspect ratio similarto an engine piston-cylinder at the ignition time. Within the large cylinder, using centralignition to create a spherical flame, they observe a smooth flame which is elongated inthe axial direction and the amount of deformation increases with the rotation speed, orwith a leaner mixture (which has a smaller burning velocity than a stoichiometricmixture). The elongated shape is a result of baroclinic vorticity production whichinduces increased flame convection in the axial direction but creates no effect at theequator of the flame surface. This follows from the vector product of Vp x VP beingequal to sin OIVpi IVPIwhere 0 is measured from the equator and has ± n/2 value at thepoles - thus, the starting spherical flame has burnt gas vorticity where the azimuthalcomponent varies as sin 0,and the magnitude is proportional to (r M/fJ )(VM/SL)2 whereVM/rM is the rotation rate. Decreasing the burning velocity, by using a leaner mixture,increases the density of baroclinic vorticity in the burnt gas, and thereby increases theflame elongation (assuming that the change in r/(r + 1)3/2 is small). Using ignition sitesthat are off the cylinder axis, they observe that the leaner mixture has a greatercentripetal effect by comparison to a stoichiometric mixture. Using the disk cylinder,with central ignition, they now observe that leaner mixtures have a longer combustionperiod than stoichiometric. This follows because in the disk configuration, during theflame travel to the cylinder ends (a distance of diameter/fourteen) there is baroclinicproduction, but the resulting flame shape, after the flame touches the cylinder end walls,is a cylindrical shell, which will have almost no baroclinic production, because now thevalue of sin 0 is close to zero over most of the flame surface - and so, the leaner flame,with smaller SL' does take longer to propagate out to the cylinder walls. However, offcenter ignition allows flame growth with baroclinic production proportional tosin OVplVPI (assume that the pressure gradient direction is constant over the wholesurface and let 0 be measured from that direction) - and they observe that again, theleaner flames are faster with off-center ignition. Hanson and Thomas comment that thepenciling effect (the apparent enhancement of flame motion along the axis) is "no morethan the normal action of a centrifuge" in moving the denser fluid to the outside and thelighter inward. However, it is much more than just a centrifugal effect because the flameis not just a passive surface between a light and heavy fluid, the flame is activelyproducing vorticity when the acceleration is normal to a density gradient - and theresulting distribution of vorticity in the burnt gas helps govern the future shape of thisactive flame surface.

Curved Vortex

Instead of a straight unburnt vortex, the unburnt mixture can be created withina vortex ring, and with point ignition, two flames will propagate around the vortex,within the ring's vortical core, and meet on the opposite side from the ignition site.Experiments like this were conducted by McCormack et al. (1972) in which propane­air mixtures were forced out of an orifice to create a traveling vortex ring. When the ringpassed a fixed igniter, the resulting two flames were seen to propagate around the ringat very high velocities in comparison to the burning velocity. The apparent flame speedwas proportional to the circulation contained within the unburnt vortex ring (usingtranslation velocity times the ring radius to determine circulation), but they could

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FLAME PROPAGATION ALONG VORTEX 183

propose no mechanism to explain flame speeds in excess of 10m]s.A baroclinic modelof this curved vortex configuration can provide a flame speed which is proportional tothe ring circulation.

We start with the circulation flux at the chamber orifice which forms the vortex ring,see Article 93 in Prandtl and Tietjens (1934) and discussion in Nitsche and Krasny(1994). A piston, which is three times larger than the orifice diameter, moves during thetime period Tp to create the flow at the orifice. The piston is driven by a pressure supply,and this pressure was varied in order to vary the strength of the vortex ring. In terms ofthe exit velocity, Ue' the circulation flux is (dr Idt) = U;/2, where the velocity at theorifice edge iszero and, at the outer edge of the boundary layer formed at the orifice, thevelocity is Ue- The vorticity within this boundary layer will roll-up to form the vorticalcore of the vortex ring. In the experiments, the apparent ring radius R is approximatelythe orifice diameter and the apparent vortex core radius 'e is one-tenth of the ringradius. We assume that U e is an upper bound for the maximum swirling velocity in thevortical core. Therefore, let the maximum swirling velocity be VM = Uelk, where k > 1,because the core may also entrain opposite sign vorticity from the boundary layer onthe external surface of the orifice plate. As before, the swirling radius is r M - 'e' and sothe pressure gradient times the density gradient will produce the same vorticity withinthe burnt gas as in the straight vortex configuration. However, the induced velocityeffect is now different, since as the flame propagates around the unburnt ring it does notremain in front of the burnt gas vorticity, see sketch in Figure 1. The effect of thiscurving path is such that only the burnt gas vorticity which is contained within an arcsegment of about fivecore radii contributes to the 'push' on the flame. The flame speedenhancement is estimated to be

t 9'MrUB - [r + 1)3/2 e5S

LTpk2

and using the experimental values, UB - 1,000cmls for r -7,600cm2/s, we obtain anestimate for the product Tpk

2- 100s. If the time period Tp to create the vortex ring is

one second, then the swirling velocity is one-tenth of the orifice exit velocity. Assumingthat the time period and constant k do not change when the pressure magnitude isvaried, in order to vary the ring circulation, would imply that the flame speedenhancement UB is proportional to the ring circulation, r.

DISCUSSION

Chomiak's model (1976) of flame propagation along a vortex was based on axialpressure differences to drive the flame. Atobiloye and Britter (1994)discuss Chomiak'smodel and re-examine the analysis with a two-fluid viewpoint. They determine how thefluid-fluid interface will change with the swirl rate and density ratio in a tube with fixedcross section. Their model does not include baroclinic vorticity, but like Chomiak, usesradial pressure gradients, and their axial difference to create a steady state fluid-fluidinterface. No unsteady behavior is considered. Flame propagation is treated as a casewhere the burning velocity is much smaller than any axial flow velocity created by axialpressure differences.

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184 W.T. ASHURST

It IS Important to notice that the fate of baroclinic produced vorticity is quitedifferent in flame propagation in comparison with the two-fluid interface problem. Theflame, like a shock wave, has a non-zero mass flux through the surface which separatesthe two different densities (Hayes, 1957). Thus, the mass which moves through thesurface acquires vorticity from the baroclinic effect, and so, the second fluid may befilled with vorticity at a rate dependent upon convection. In the other case, where thetwo fluids do not mix across the interface, then vorticity is restricted to region near theinterface until viscous diffusion has time to spread this vorticity (Tryggvason, 1989).

In the present work, by considering the flame to be an active surface of vorticityproduction, then those vortex-flame configurations which have a component of theflame density gradient normal to the radial pressure gradient in the unburnt vorticalcore, are configurations which generate an enhanced flame speed. The mechanism is theinduced velocity field of the distributed baroclinic vorticity which pushes the flame.And, the enhancement will be dependent upon the shape of the burnt gas. Othermodeling approaches, which only consider local axial pressure differences, do notdistinguish between flame propagation along a straight vortex from propagationaround a vortex ring. The baroclinic model obtains a growing enhancement for thestraight vortex, as seen in numerical simulations, and a constant enhancement for thering configuration which is dependent upon the ring circulation, as seen in theexperiments.

Flame propagation at high pressure may reveal a different flame speed enhancementfactor between a baroclinic effect and the vortex bursting model of propagation, thelatter depends upon the swirl rate and the density ratio across the flame, but not uponthe ambient pressure level. The baroclinic effect does depend upon the pressure levelbecause the flame thickness and the burning velocity are both reduced with increasedpressure. In the baroclinic estimate for the enhanced flame speed, UB, the product offlame thickness and burning velocity is ~SL - V - J1./P and so, the estimated convectionvelocity UB is proportional to the ambient pressure (P - pl. Kobayashi et al. (1995),using high-speed laser tomography, have observed turbulent flame motion overa range of pressure levels, from one to twenty atmospheres, and they notice a small­scale flame feature moving into the unburnt gas which may correspond to flame motionalong a vortex; note however, that they do not yet have any direct knowledge about theflow structure associated with these quickly moving flame features.

Flame propagation along a vortex may occur in reactingjets and mixing layers whenthe flame is far away from any walls, this suggestion is made because the knownstreamwise vorticity in these flows might provide an enhanced pathway for flamepropagation from one vortical structure to its upstream neighbor. Inlifted turbulent jetflames, Miake-Lye and Hammer (1988)comment that the flucuations in flame locationare consistent with propagation from one structure to its upstream neighbor. The exactmanner of this upstream propagation is not known, nor is the verticalstructure verywell known. The average flame location does correlate with a strain rate estimate basedon the large-scale features of the jet, but this same scaling does not describe the longertime periods associated with fluctuations in flame location (Hammer, 1993).The liftofflocation, and its movement, could depend upon the vortical structure of the unreactedportion of the jet: a ring mode with its streamwise vorticity would differ from a helicalvortical structure. Thus, the time period of ring versus helical jet structure could

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FLAME PROPAGATION ALONG VORTEX 185

determine the temporal behavior of the liftoff location. The flame photographs given byHammer (Appendix E) indicate flame tongues for conditions where the estimatedbaroc1inic effect should be larger. We suggest that these flame tongues could be flamepropagation along a vortex. Recent descriptions of streamwise vorticity in nonreactingflows is given by Liepmann and Gharib (1992),Abid and Brachet (1993)and Lopez andBulbeck (1993); addition of flame propagation with consideration of the baroc1iniceffect would be most interesting..

ACKNOWLEDGEMENTS

This work supported by the United States Department of Energy through the Office of Basic EnergySciences, Division of Chemical Sciences. Discussions with loge Gran and Tatsuya Hasegawa have beenhelpful.

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Abid, M. and Brachet, M. E. (1993). Numerical characterization of the dynamics of vortex filaments in roundjets. Phys. Fluids A 5, 2582. .

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Chomiak, J. (1976). Dissipation Fluctuations and the Structure and Propagation of Turbulent Flames inPremixed Gases at High Reynolds Numbers. Sixteenth Symposium (lntemational) on Combustion, TheCombustion Institute, Pittsburgh, p. 1665.

Eliassen, A. (1982). Vilhelm Bjerknes and His Students. Ann. Rev. Fluid Mech. 14, I.Hammer, J. A. (1993). Lifted Turbulent Jet Flames. Ph.D. thesis, California Institute of Technology,

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and Flame 55, 255.Hasegawa, T., Nishikado, K. and Chomiak, J. (1995).Flame Propagation Along a Fine Vortex Tube. Comb.

Sci. and Tech., 108,67.Hayes, W. D. (1957).The vorticity jump across a gasdynamic discontinuity. J. Fluid Mech. 2, 595.Ishizuka, S. (1990).On the Flame Propagation in a Rotating Flow Field. Combustion and Flame 82, 176.Kobayashi, H., Nakashima, T., Tamura, T., Maruta, K. and Niioka, T. (1995). Turbulence Measurements

and Observations of Turbulent Premixed Flames at Elevated Pressures up to 3.0 MPa. Submitted toCombustion and Flame.

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