Experimental studies on spinning waves in mesoscale combustion

Bo Xu and Yiguang Ju

Department of Mechanical and Aerospace EngineeringPrinceton University, Princeton, New Jersey 08544, USA

bxu@princeton.edu

Corresponding author:Bo XuDepartment of Mechanical and Aerospace EngineeringPrinceton University, Princeton, New Jersey 08544, USAPhone: 1-258-1411, Fax: 1-609-258-6233, Email: bxu@princeton.edu

Colloquium topic: New Technology Concepts

Short running title: Meso and microscale combustion

Paper length: 5929 (main text + references + figures)

Main text: 3597 (word tool)

References: ((27+2) x2.3x7.6) = 507

Figures: 1574 (Fig.1 + … + Fig.9)

10 single-column figures=1400

Figure captions =174

Equations: (28 equation lines +5 blank lines) x 7.6 words/line x 1 column=251

Paper length=3597+507+1574+251=5929

Experimental studies on spinning waves in mesoscale combustionBo Xu and Yiguang Ju

Department of Mechanical and Aerospace EngineeringPrinceton University, Princeton, New Jersey 08544, USA

bxu@princeton.edu

Abstract

A laminar premixed flame thermally coupled with the wall is studied in a mesoscale

diverging quartz tube. For the first time a spin flame is experimentally observed for both methane

and propane-air mixtures within a large range of Lewis numbers. The spin flame rotates in the

direction of clockwise or counterclockwise with equal probability and at a frequency roughly

proportional to the flame speed. The experimental results show that there exists a critical spin

diameter below which no spin flame exists for a fixed equivalence ratio. A transition between

spin flames and stables flames can be induced by cooling or heating up the outside wall, which

implies that the spin flame is a result of the strong thermal coupling between the flame and the

wall. The present study introduces a new mechanism of flame instability in small scale

combustion.

Key words: Mesoscale, instability, premixed flame, spin flame.

1

1. Introduction

The instability phenomena of combustion fronts have received considerable attention in an

effort to better understand the intrinsic mechanisms in both gaseous and gasless premixed

combustion. In gaseous combustion, there are basically two intrinsic instability mechanisms

associated with premixed flame propagation, namely hydrodynamic instability due to the density

variation across the flame front, and diffusive-thermal instability induced by the disparities

between mass and thermal diffusivities of the combustible mixture. Hydrodynamic instability

was originally introduced by Landau [1] and Darrieus [2]. Diffusive-thermal instability was first

theoretically investigated by Barenblatt et al. [3] and then subsequently analyzed by Sivashinsky

[4] and Joulin and Clavin [5]. The linear stability analysis showed that cellular instability occurs

when the Le of the mixture is smaller than a critical value slightly less than unity, while pulsating

instability occurs when Le is larger than a critical value [4] satisfying the criterion Ze(Le − 1) >

10.9 for the adiabatic flame, where Ze is the Zeldovich number. Joulin and Clavin [5] showed

that heat loss can significantly reduce the critical value and extended the pulsating instability

regime. Pulsating plane fronts have been observed experimentally in gases [8]. Pulsating

instability of 1D propagating flames was also studied for rich hydrogen/air [9] and lean

heptane/air [10] flames using detailed chemistry. In addition to the pulsating and cellar

instabilities in the gaseous combustion, spinning fronts have also been observed experimentally

in the gasless combustion of solids [11, 12] (Le ~ ∞). Theoretical analysis and numerical

simulations in a cylindrical domain [13-15] showed that spinning waves occur when the diameter

exceeds a critical value for solid combustion. Matkowsky and Olagunju [16] and Booty et al. [17]

considered a diffusional-thermal model describing a premixed gaseous combustion in a

cylindrical domain with or without heat loss and showed that a uniformly propagating plane

2

flame is unstable when the Lewis number or heat loss exceeds a critical value. Various bifurcated

analytical solutions describing pulsating or spinning flames were found. Experimentally, the

high-Lewis number diffusive-thermal instability in premixed gas combustion was studied in

tubes using lean C4H10-O2-He mixtures and a combined spiral wave and radial pulsation and a

pure radial pulsation were observed [18]. As is seen, most of the work is focused on diffusive-

thermal instability which occurs for sufficiently low or sufficiently high values of the Lewis

number at macro scales.

In small scale combustion, the increase of larger surface to volume ratios dramatically

increases the wall heat loss and leads to flame extinction. On the other hand, the reduction of

thermal inertia at small scale significantly reduces the response time of the wall and leads to

strong wall flame coupling. This flame-wall interaction can dramatically change the nature of

flame propagation in small scale devices. In particular, at small scale, the heat recirculation

through the wall heat conduction yields new flame regimes and instabilities [19-21]. In mesoscale

combustion with constant-area tube, there exist two different flame regimes, a slow flame regime

and a fast flame regime. In the fast flame regime, the propagation speed of the flame is fast

relative to the propagation speed of thermal wave of the wall. Flame speed is modified mainly by

the heat loss effect and the wall temperature remains almost unchanged due to its large thermal

inertia and long response time. In this case, the flame is said to be uncoupled with the wall. In the

slow flame regime, the propagation speed of the flame is in the same order as the propagation

speed of thermal wave of the wall. The wall temperature is much higher than the previous case

and heat loss is reduced. In addition, part of the energy is pumped back to preheat the reactants

through the heat recirculation effect of the wall. As such, the flame is strongly coupled with the

wall due to the heat recirculation effect. The thermal feedback effect may modify the local Lewis

number of the flame or flame head and change the flame dynamics and instability may occur at a

3

moderate Lewis number. However, in a constant-area tube, coupled slow flame only exists within

a very narrow flow rate at certain equivalence ratio. On the other hand, a diverging tube has a

velocity gradient such that the flame can always find a stabilization position. As such, the flame

is always coupled with the wall within a large range of flow rates and equivalence ratio. So the

objective of this work is to study the instability of phenomena induced by the coupling between

the flame and the wall using a mesoscale diverging tube.

2. Experimental setup

The spinning propagation flame due to the coupling of wall heat transfer and flame

propagation in a mesoscale channel is investigated using the methane and propane-air mixtures

burning in a vertical quartz tube. Experimental setup is schematically shown in Fig.1. The tube

(Fig. 1 b) has four sections: two constant-area sections A and D, a converging section B and a

diverging section C. The inner diameter of the constant-area sections is 10 mm and that of the

throat is 4 mm. The wall thickness is 1 mm. The lengths of the diverging and converging parts

are 50 mm and the D section is 600 mm long to ensure the flow is fully developed before entering

section C. A mesh grid is placed near the inlet of the tube to eliminate any vortex. Methane or

propane-air mixtures are introduced from the right hand side of the tube, and are ignited at the

exit of tube by a flame torch (on the left hand side). The flow rates of fuel and air are controlled

by two mass flow controllers (Brooks 5850E) with the maximum mass flow rates of 100 SCCM

and 500 SCCM respectively. The signal inputs and outputs of the mass flow controllers are

implemented using the Labview and A/D board (DAQ NI PCI-6014). To ensure the sufficient

mixing of methane and air, a mixing cylinder with the volume 150 cm3 is used. In addition, a

Flash arrester is used between the mixing cylinder and the quartz tube for the security issue. The

flame propagation history was recorded by a high-speed video camera at 500 frames per second.

3. Numerical simulation

To examine the thermal coupling effect between the flame and the wall, we seek numerical

simulations with detailed transport properties and chemical kinetics in a diverging vertical quartz

tube. We also simplify the problem using the one-dimensional model. CH4 is used as a sample

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fuel and GRI3.0 [25] is employed to model the flame. The transport properties are computed

using Chemkin [26] code. The governing equation for gas phase can be found elsewhere [26]. In

the simulation, the parameters of the quartz tube are the same as in the experiment.

Fig.2 shows the structure of coupled methane steady propagation flames in a diverging quartz

tube. It is seen that ahead of the flame front, the wall temperature is higher than that of the gas

reactants. As such, the premixture is preheated by the wall and the temperature increases by 50

degrees before reaching the flame front and flame speed is significantly increased due to this

preheat effect. Fig. 3 shows the flame speed of decoupled, coupled and adiabatic flames as a

function of equivalence ratio with di=4 mm. It is seen that the decoupled flame speed is much

lower than the adiabatic case and flammability limit is much narrower due to the heat loss effect.

However, with heat recirculation as well as heat loss, the coupled flammability limit is broadly

extended and the flame speed is even higher than the adiabatic flame speed. In one dimensional

simulation, any 2-D or 3-D flame structure is eliminated. However, in the real coupled flame, the

preheat effect is mainly constrained within the thermal boundary layer and has much stronger

effect on the flame head, which is close to the wall. As a result, the heat recirculation of the wall

can significantly enhance the thermal transport of flame head and change the flame dynamics and

induce instability by increasing the local effective Lewis number. As such, 2-D or 3-D simulation

is necessary for studying the instability phenomena induced by the flame-wall thermal coupling.

4. Experimental results

Two different propagation flames were observed in our experiment: a steady flame and a

spin flame. Both of the two flames exist for a large range of equivalence ratios and flow rates.

The tube was placed in different positions including horizontal, vertical, upside down or in a

random angle with the table and similar phenomena was observed, which implies that the spin

flames were not caused by the asymmetric flow induced by the buoyancy effect. In our

experiment, the tube was placed vertical to eliminate the buoyancy effect. Another quartz tube

with only a diverging section was also tested and similar results were also obtained, which

indicated that the spin flame was a result of the coupling between the flame and the diverging

tube instead of the tube itself. Before each recording, a sufficient long time was waited to ensure

a steady state of spin or stable flames.

5

In the experiment, both clockwise and counterclockwise spin flames were observed and the

spin direction was randomly selected during the initiation of the instability process and

maintained the same direction afterwards. This implies that the spin is not caused by the vortex of

the flow since no mechanism exists to generate such a strong vortex to drive a flame spinning in

random directions at a very high frequency (up to 70 Hz). The spin frequency was calculated

from the time history of flame front luminance of the images with FFT. The effective diameter dh

is the inner diameter of the tube where the flame head locates. An average flame speed Sa can be

estimated from the volume flow rate divided by the effective cross-section area. The traveling

speed of the flame head can be estimated by , where f is the spin frequency.

Fig.4 shows the structures of propane and methane steady propagation flames. It is seen that

flame is flat at low flow rates or high burning rates. It curves towards the reactants near the tube

wall due to the quenching effect and away from the reactants (towards the products) at the center

of the tube especially when the flame is weaker or the flow speed is higher.

Initially when the wall is cold, there is no coupling between the flame and the wall. When the

premixture is ignited, a stable flame is formed. Fig.5 shows the initialization process of a stable

flame in the divergent tube within the first 200 micro seconds. It is seen that the propagation

velocity is almost constant in the constant-area section and continue to decrease in the diverging

section due to the increase of the flow velocity and the decrease of the surface area of the flame

front and a stabilized flame is formed. As the wall is heated up in the following several seconds,

the thermal coupling becomes stronger and the flame head tends to move downwards. However,

the center of the flame is restricted by the flow velocity and cannot move downwards any further

because the center velocity is much higher in a diverging flow. As a result, the flame tilts and a

flame head is formed. The flame head heats the wall in both axial and azimuthal directions. The

flame head cannot move downwards anymore due to the increase of the flow velocity. However,

it tends to move in the azimuthal direction where the wall is also preheated and there is unburned

premixture. As it rotates, it continues to heat up the wall epicyclically until to a steady state. The

wall heats up the premixture after the flame head and the increased velocity blows the flame tail

further downstream. When a steady state is reached, an axisymmetric spin flame is formed shown

in Fig. 5. The spin direction is randomly selected during the initiation of the spin wave. When the

outside wall is cooled with cooling water, the flame head moves downstream and flame tail

moves upstream and eventually the spin flame shrinks to a stable flame. This phenomenon clearly

6

shows that the spin flame is a result of strong thermal coupling between the wall and the flame.

However, in a constant-area tube, no spin flame was observed even for coupled flames due to the

difference of the flow field.

Spin flames were observed for different fuels of both lean and rich cases. The structures of

lean (Le >1) and rich (Le<1) propane spin flames are shown in Fig.6 and the corresponding time

sequences in one period are shown in Fig. 7 for equivalence ratios at 1.6 and 0.8, respectively. In

a spin flame, the flame front is a 3-D surface and Fig. 6 only gives a side view of the flame

structure. For rich propane spin flames, the burning intensity of the flame head is much stronger

than that of the flame tail, while for lean cases the difference is indistinguishable. Since the head

of spin flames has a positive stretch due to the wall quenching effect, a Lewis number less than

unity will strengthen the burning flux. Oxygen, as the deficient reactant, has a larger mass

diffusivity and is easier to diffuse to the flame head and react with abundant propane, leaving the

flame tail lack of oxygen. As such, the burning intensity of the flame tail is weakened and even

becomes open, like an “L” shaped structure. Similar structure was observed for lean methane spin

flames, in which methane, as the deficient reactant, has a higher diffusivity and is easier to be

consumed at the flame head. For lean propane flames, a positive stretch will actually weaken the

burning intensity. Furthermore, propane, as the deficient reactant, has a smaller mass diffusivity

and is difficult to diffuse to the flame head. As such, there is still sufficient propane left at the

flame tail. As the flame tail approaches the wall, there is a decrease of the flow velocity and the

flame curves back towards the wall, forming an “S” shaped structure. Again similar flame

structure was obtained for a rich methane spin flame.

Fig. 8 shows change of flame structure throughout the transition process from spin flames to

stable flames. At sufficiently large flow rates, a spin flame is established with a flame head

thermally coupled with the wall and the flame sheet is tilted. As the flow rate decreases, both the

flame tail and flame head move upstream. However, the flame tail moves more because it is

decoupled with the wall and more strongly affect by the flow field. As a result, the flame sheet

becomes less tilted. To a certain position where the flame tail is almost at the same level as the

flame head and is also thermally coupled with the wall, a spin flame transforms to a stable flame.

As such, for a fixed equivalence ratio, there exists a critical spin diameter ds below which no spin

flame exists. As the flow rate is further decreased, the stable flame will either quench or pass

through the throat. As the burning flux increase, the burning flux becomes stronger and the flame

7

head can move further upstream. One would expect that this transition happen at a smaller critical

diameter when the burning velocity increases, which is clearly shown in Fig. 9. It is seen that spin

flames exist for both methane and propane within a large range of equivalence ratio. The critical

spin diameters for methane and propane have the same tendency and are inversely proportional to

the flame speed. The critical spin and quenching diameters of methane are consistently higher

than of propane due to its lower burning velocity.

Fig. 10 shows the frequency of methane flames at different flow rates with φ =1.05. A

frequency of zero represents a stable flame. It is seen that there exists a bifurcation region where

stable flame and spin flame coexist. This bifurcation phenomenon reflects the thermal history

effect of the wall. Even though the slow flame and the spin flame share the same equivalence

ratio and flow rate, they have different flame structures and wall temperature distributions. One

also sees that the frequency of spin flames is only slightly modified by the flow rates when the

equivalence ratio is fixed.

The frequencies of methane and propane spin flames at different equivalence ratios and flow

rates are shown in Fig. 11. And the averaged flame speeds for both stable and spin flames are

shown in Fig. 12. The spin frequency highly depends on the equivalence ratio instead of the flow

rate. It is seen that the spin frequency is highly proportional to the flame speed while it is only

slightly modified by the flow rate. It is reasonable in realizing that the flame spinning

propagation is guided by the traveling of the flame head at the flame speed. Fig. 13 shows the

ratio of the traveling speed of the flame head over the averaged flame speed. One sees that the

traveling speed of the flame head is in the same order as the flame speed. The big variation may

result from the elimination of any 2-D or 3-D structure in estimating the laminar flame speed.

5. Conclusions

Laminar premixed flame propagation in a mesoscale diverging quartz tube was studied and

two different propagation waves were observed: a stable flame and a spin flame. A large range of

equivalence ratio and flow rate was examined for methane and propane and the results showed

that the spin flame existed for both lean and rich methane or propane-air mixtures. The spin wave

was caused by a strong thermal coupling between the flame head and the wall and it occurred at

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various Lewis numbers. The spin direction was randomly selected during the initiation of the spin

flame and remained unchanged afterwards. The stable flame and spin flame could coexist within

a narrow range of bifurcation region caused by the thermal history effect of the wall. The critical

spin diameter highly depended on the equivalence ratio and was inversely proportional to the

flame speed. The spin frequency was also proportional to the flame speed and the traveling speed

of the flame head was in the same order as the flame speed.

Acknowledgement

Nomenclature

Cp: specific heat at constant pressure

ds: critical spin diameter

dq: quenching diameter

: differential operator:

E : activation energy

f : spin frequency

Le: Lewis number

Nu: Nusselt number

Q: Volumetric flow rate

r: radial direction

Sh: traveling speed of the flame head

Sa : average flame speed

Ze: Zeldovich number,

: thermal diffusivity

: azimuthal coordinate

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References

1. L. Landau, Acta Physicochim (URSS) 19 (1944) 77.2. G. Darrieus, Propagation d’un front de flamme. Essai de Theorie des vitesses arnoles de

Deflagration par developpment spontanne de la Turbulence. Sixth International Congress of Applied Mathematics, 1946.

3. G.I. Barenblatt, Y.B. Zeldovich, A.G. Istratov, J. Appl. Mech. Technol. Phys. 4 (1962) 21.4. G.I. Sivashinsky, Combust. Sci. Technol. 15 (3–4) (1977) 137–146.5. G. Joulin, P. Clavin, Combust. Flame 35 (2) (1979) 139–153.6. B. Rogg, N. Peters, J.Warnatz (Eds.), Numerical Methods in Laminar Flame Propagation,

Vieweg, Braunschweig/ Wiesbaden, 1982, pp. 38–48.7. D.G. Lasseignet, T.L. Jackson, L. Jameson, Combust. Theory Modelling 3 (1999) 591–

611.8. S. B. Margolis, Combusiton Science and Technology 22 (1980) 143-169.9. E.W. Christiansen, C.J. Sung, C.K. Law, Combust. Flame 124 (1–2) (2001) 35–49.10. E.W. Christiansen, C.K. Law, C.J. Sung, Proc. Combust. Inst. 28 (2000) 807–814.11. A. G. Merzhanov, A. K. Filonenko and I. P. Borovinskaya, Phy. Chem. Sec. 208 (1973)

122-125.12. Y. A. Maksimov, A. T. Pak, G. B. Lavrenchuk, Y. S. Naiborodenko and A. G.

Merzhanov, Explosions and Shock Waves 15 (1979) 415-418.13. G. Sivashinsky, SIAM J. Appl. Math. 40 (3) (1981) 432-437.14. T. P. Ivleva, A. G. Merzhanov, Doklady Physics 45 (4) (2000) 136-141.15. J. H. Park, A. Bayliss and B. J. Mathkowsky, SIAM J. Appl. Math. 65 (2) (2005) 521-549.16. B. J. Matkowsky and D. O. Olagunju, SIAM J. Appl. Math. 42 (5) (1982) 1138-1156.17. M. R. Booty, S. B. Margolis and B. J. Matkowsky, SIAM J. Appl. Math. 47 (6) (1987)

1241-1286.18. H. G. Pealman, P. D. Ronney, Phys. Fluid 6 (12) (1994) 4009-4108.19. P. D. Ronney, Combust. Flame135 (2003) 421-439.

20. Y. Ju, W. Choi, Combust. Flame 133 (2003) 483-493.

21. Y. Ju, B. Xu, Proc. Combust. Inst. 30 (2005) 2445-2453.

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Figure Captions:

Fig.1 Schematic of the experimental setup

Fig.2 Numerical simulation of the structure of coupled methane steady propagation flames with

φ =1.0, Q=18.84 cm3/s.

Fig.3 Calculated flame speed as a function of equivalence ratio for CH4-air flame with di=4 mm.

Fig.4 Structures of propane and methane steady propagation flames.

Fig.5 Time history of flame location for C3H8-air flame withφ =1.0, Q=6.87 cm3/s.

Fig.6 Structures of lean and rich propane spin flames.

Fig.7 Time sequences of spin flames in one period for C3H8-air mixtures. (a) φ =1.6, Q=8.84

cm3/s, Le < 1; (b) φ =0.8, Q=6.9 cm3/s, Le > 1.

Fig.8 Propane spin flame to stable flame transition atφ =0.8.

Fig.9 Critical spin diameters and quenching diameters at different equivalence ratio. (a)

Methane; (b) Propane.

Fig.10 Spin frequency at different flow rates for CH4-air flame withφ =1.05.

Fig.11 Frequencies of methane and propane spin flames at different equivalence ratio. (a)

Methane; (b) Propane.

Fig.12 Average flame speed Sa of methane and propane spin and stable flames at different flow

rates. (a) Methane; (b) Propane.

Fig. 13 Ratios of flame head traveling speed to the averaged flame speed. (a) Methane; (b)

Propane.

11

(a)

(b)

Fig.1

Fuel

Air

High speed cameraQuartz tube

Mass flow controllers

Mixing cylinder

Flash arrester

PCA/DBoard

4mm 10mm

100mm

600mmA

B C D

Inlet Outlet

12

Fig.2

Fig.3

(a) (b) (c) (d)

Fig.4

Methane φ =1.3, Q=8.8

Methaneφ =1.4, Q=8.8

Propaneφ =0.7, Q=4.9

Propaneφ =0.7, Q=6.9

ms 0 20 40 60 80 100 120 140 160 180 200

13

Fig.5

z

θ

r

tail

head

Propane, φ =1.6

z

θ

r

tail

head

z

θ

r

z

θ

r

z

θ

r

tail

head

Propane, φ =1.6Propane, φ =1.6

z

θ

r

tail

head

Propane, φ =0.8

z

θ

r

tail

head

z

θ

r

z

θ

r

z

θ

r

tail

head

Propane, φ =0.8Propane, φ =0.8

(a) (b)

Fig.6

(a)

(b)Fig.7

0 ms 8 ms 16 ms 32 ms24 ms

40 ms 48 ms 56 ms 72 ms64 ms

0 ms 4 ms 6 ms 8 ms

20 ms16 ms14 ms12 ms10 ms

2 ms

14

Fig.8

(a) (b)

Fig.9

Fig.10

Q=8.8 6.9 4.9 3.9 2.9 1.9

Spin Spin Spin Spin Stable Stable

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

Dia

met

er (c

m)

Eqivalence Ratio

ds

dq

Spin flame

Stable flame

0.6 0.8 1.0 1.2 1.4 1.6 1.8

0.4

0.5

0.6

0.7

0.8

Dia

met

er (c

m)

Equivalence Ratio

ds

dq

Spin flame

Stable flame

15

(b)

Fig.11

(a) (b)

Fig. 12

(a) (b)

Fig. 13

0.7 0.8 0.9 1.0 1.1 1.20

1

2

3

4

Sh/S

a

Equivalence ratio

Q=9.8 Q=8.8 Q=7.9 Q=6.9 Q=5.9

0.6 0.8 1.0 1.2 1.4 1.60

1

2

3

4

5

Sh/S

a

Equivalence ratio

Q=8.83 Q=7.85 Q=6.87 Q=5.89 Q=4.9

16