The e�ect of an electric ®eld on the shape of co-¯owing andcandle-type methane±air ¯ames

Jing Hu *,1, Boris Rivin, Eran Sher

Department of Mechanical Engineering, The Pearlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev,

Beer-Sheva, Israel

Received 18 November 1999; accepted 18 November 1999

Abstract

The e�ects, which an electric ®eld exerts on ¯ames, have been observed and reported in the literature for a long time. Burning

velocity, ¯ame stability, ¯ame shape, ¯ame luminosity, extinction limit, and soot formation, are among the e�ects that have been

observed. Most of the studies in this ®eld were experimental observations. There is fairly limited information in the literature on

numerical studies in the area of electric ®eld and ¯ame interaction. Therefore, our fundamental understanding of the process and our

ability to use electric ®eld as a means to control the combustion process, are restricted. In the present work, co-¯owing di�usion

methane/air ¯ames and candle-type methane/air ¯ames under the electric ®eld e�ect have been observed experimentally. A numerical

model, which considers the more important physical and chemical phenomena associated with the ¯ame±®eld interaction process,

has been developed to explain the experimental observations. The model employs a two-dimensional cylindrical coordinate system

and assumes axial symmetry. A simpli®ed chemical reaction scheme for a methane±air mixture, which contains 19 chemical species

and 31 reactions is employed. It combines existing methane oxidation mechanisms with a series of chemiionization, ion-molecule,

and dissociative-recombination reactions, which are important for the ionic species. The mass, momentum, species and energy

conservation equations are solved numerically by an integrated version of the PHOENICS and CHEMKIN computer codes. It is

concluded that the e�ects of an electric ®eld on the ¯ame behavior are mainly due to ionic wind e�ects. Ó 2000 Elsevier Science Inc.

All rights reserved.

Keywords: Methane±air ¯ames; Electric ®eld e�ects on ¯ames; Ionic wind

1. Introduction

The e�ects of an electric ®eld on ¯ames have beenstudied extensively for many years [1]. Stabilizing¯ames, reducing carbon formation, increasing ¯amevelocity, extending ¯ammability limits, increasing ¯ameluminosity and extinction, are among the e�ects thathave been observed.

Many of the e�ects of an electric ®eld on ¯ames areknown to be due to ionic wind e�ects. This was sug-gested already by Guenault and Wheeler in 1931 (ascited by Bowser and Weinberg [2]). It has been however

shown, that the ion-driven ¯uid-mechanical e�ects,which are inevitably present and quantitatively calcula-ble, account for the experimental observations in manycases [1,2]. Early workers supposed that these phenom-ena were caused by chemical e�ects induced by trans-posing the charge carriers by the action of the electric®elds. Jaggers and von Engel [3] observed the e�ect ofdc, ac and high frequency (hf) electric ®elds, on theposition of ``¯oating'' ¯ames above simple burners, andthe rate of ¯ame propagation through tubes. Theyconcluded that the burning velocity of several hydro-carbon/air mixtures was increased by the direct action ofthe electric ®eld. However, subsequent attempts tomeasure changes in burning velocity induced by ac andhf ®elds applied to a ¯at ¯ame burner system, havefailed to show a statistically signi®cant e�ect [2,4].

It seems that two di�erent mechanisms are respon-sible for the interaction between electric ®eld and ¯ame:ionic wind e�ects, and chemical e�ects. Most of the

Experimental Thermal and Fluid Science 21 (2000) 124±133

www.elsevier.nl/locate/etfs

* Corresponding author. Tel.: +1-418-5455011; fax: +1-418-

5455012.

E-mail address: jhu@uqac.uquebec.ca (J. Hu).1 Present address: Dept. des sciences appliqu�ees, Universit�e du

Qu�ebec �a Chicoutimi, Chicoutimi, Qu�ebec, Canada, G7H 2B1.

0894-1777/00/$ - see front matter Ó 2000 Elsevier Science Inc. All rights reserved.

PII: S 0 8 9 4 - 1 7 7 7 ( 9 9 ) 0 0 0 6 2 - X

studies in this ®eld, however, are based on experimen-tal observations of the overall phenomena. Detailedcalculations are needed to quantify these e�ects in orderto provide a better insight and understanding.

There is fairly limited information in the literature onnumerical studies in the area of electric ®eld and ¯ameinteraction. To the author knowledge, no attempt hasbeen reported in the literature to investigate numericallymulti-dimensional ¯ames which are subjected to elec-trical ®elds. This is probably due to the multi-dimen-sional nature of the problem which is coupled withcomplexities associated with the combined e�ects oftransport phenomena, chemical processes, and electricalinduced forces. In the present study, we investigate ex-perimentally e�ects of a uniform electric ®eld on meth-ane±air ¯ames. A comprehensive model has been solvednumerically to explain the observed results. Co-¯owing¯ames and candle-type ¯ames have been selected be-cause they are the more important ¯ame types of mostpractical combustion devices.

2. Experimental observations

2.1. Co-¯owing ¯ames

The experimental system is shown schematically inFig. 1. For the co-¯owing ¯ame, it consists of a cylin-drical fuel (methane) jet which is surrounded by a co-

¯owing oxidizer jet. The radius of the inner fuel jet is 2mm and the radius of the outer oxidizer jet is 25 mm.Two horizontal electrically conducting plane mesheshave also been employed; the lower mesh is situated atthe burner aperture level, while the upper mesh is in-stalled at a distance �z1� of 50 mm above the burner(highly above the ¯ame tip). A direct-current high-voltage is applied between the two planes. A high volt-age power supply, regulated from 0 to 50 kV dc with 1MX damping resistor, is employed. The boundary con-ditions at inlet for (0 < r < RI) are given by T � 298 K,YCH4

� 0:696, YN2� 0:304, Yj � 0, j 6� CH4, N2, m � 0:0

cm/s, w � 35:0 cm/s and for (RI < r < RO) by T � 298K, YCH4

� 0:232, YN2� 0:768, Yj � 0, j 6� CH4, N2,

m � 0:0 cm/s, w � 50:0 cm/s.A typical behavior of a co-¯owing ¯ame which is

subjected to a gradually increasing electric ®eld is shownin Table 1. We estimate an experimental error in theorder of 5.5% (2% in fuel to air ratio, 3% in volumetric¯ow rate, 4% in the evaluation of the ¯ame geometry).

When a negative electric ®eld is gradually increased(negative burner), the ¯ame height shortens and slims.When the voltage reaches 25 kV, the ¯ame shortens by16.0%, its width slims by 21.7%, the ratio between the¯ame height to its width is marginally reduced, and thesurface area reduces by 40%. When the electric ®eldreverses its polarity, the ¯ame height ®rst stretches up-ward, in a monotonic manner up to 5 kV, and then itbecomes unstable. As the voltage reaches 5 kV, the¯ame height lengths by 6%, widens by 13.7%, the ratiobetween the ¯ame height to its width is marginally re-duced (in a similar manner as was observed for thenegative polarity ¯ame) and the surface area increasesby 13.5%.

2.2. Candle-type ¯ames

The experimental set-up for the candle-type ¯ames issimilar to that of the co-¯owing ¯ames (Fig. 1) exceptfor the burner which consists of a candle-type burnermade from brass having an aperture diameter of 8 mm.The fuel gas (methane) entering the burner, induces airinto the tube from its surroundings. As the fuel and air¯ow up the tube, they mix in a controllable mixing ratio,and before the top of the tube is reached, the mixture isassumed to be completely homogeneous. The volumetric¯ow rate of the mixture is kept constant at a value of26.3 cm3/s (1.587 l/min) for the candle-type ¯ame. Table2 shows the ¯ame height and width of candle-type¯ames, when an electric ®eld is applied between twoparallel plates. For a stoichiometric candle-type ¯ame,the above data show that when a negative electric ®eldof 3 kV is applied (negative burner), the ¯ame heightshortens by 11.8%, the ¯ame width slims by 8%, theratio between the ¯ame height to its width is marginallyreduced, and the surface area reduces by 16%. When theelectric ®eld reverses its polarity, the ¯ame heightlengths by 15%, widens by 19%, the ratio between the¯ame height to its width is again marginally reduced,Fig. 1. Experimental system and domain of solution.

J. Hu et al. / Experimental Thermal and Fluid Science 21 (2000) 124±133 125

and the surface area increases by 24%. Somewhat simi-lar trends for a stoichiometric propane±air ¯ame werealso observed by Nakamura [5].

As shown in Tables 1 and 2, it is clear that the be-havior of co-¯owing ¯ames and candle-type ¯ames un-der electric ®eld e�ect are similar and the electric ®elde�ects are signi®cant.

3. Numerical approach

The domain of solution is shown in Fig. 1, with thedimensions of 50 mm� 25 mm. It is found, a priori, thatthe spatial distribution of the temperature, velocity andspecies concentration inside and around the ¯ame zone,is insigni®cantly a�ected with a further expansion of thedomain.

3.1. Conservation equations

The conservation equations, which include the mass,momentum, species and energy balances, are solved bythe PHOENICS. The conservation equations may bepresented in the following general form:

oot

qw� � � r � qV wÿ ÿ Cwrw

� � Sw; �1�

where w is the dependent variable, Cw the transportcoe�cient of the property w, and Sw is the source term ofw. The relevant properties and associated transport co-e�cients and source terms are shown in Table 3.

When an electric ®eld is imposed, the net force [1] perunit volume, which exerted on charge carriers, is:

Sw � F � Ee�n� ÿ nÿ�; �2�where Sw is the source term of the momentum equationin the radial or axial direction, as applicable.

Substituting the current ¯ux in the form of:

I � l�n�Ee �3�into Eq. 2 yields an expression for the force per unitvolume in terms of mobility and current:

F � Il�: �4�

In the present work, it is assumed that the current Ihas no component in the radial direction. The binarymobilityÕs, ljk, can be related to the binary di�usivities,Djk, by the Einstein relationship [1]:

Djk

ljk� KbT

e: �5�

Table 3

Parameters of the relevant conservation equations

Conservation of Property, w Transport coe�cient Cw Source term Sw

Mass 1 0 0

Momentum (r) v v ÿop=or � Sv

Momentum (z) w v ÿop=oz� Sw

Energy T k=cp ÿPnspcj�1 Mjxjhj

Chemical species Yj qDjm Mjxj

Table 2

Flame height and width of candle-type ¯ames

Applied voltage (burner polarity) (ÿ) 3 kV 0 kV (+) 3 kV

/ � 1:0Stoic.

Di�. ¯ame / � 1:0Stoic.

Di�. ¯ame / � 1:0Stoic.

Di�. ¯ame

Flame height/aperture diameter 1.12 1.42 1.27 1.61 1.46 1.65

Flame width/aperture diameter 0.92 1.15 1.00 1.35 1.19 1.58

Flame height/¯ame width 1.22 1.23 1.27 1.19 1.23 1.04

Flame surface area/aperture area 6.98 7.76 8.31 10.21 10.29 11.31

Table 1

Flame height and width of co-¯owing di�usion ¯ames

Applied voltage (burner polarity) (+) 5 kV 0 kV (ÿ) 5 kV (ÿ) 10 kV (ÿ) 15 kV (ÿ) 20 kV (ÿ) 25 kV

Flame height/aperture diameter 8.88 8.37 8.44 8.30 8.00 7.63 7.03

Flame width/aperture diameter 2.15 1.89 1.85 1.78 1.70 1.63 1.48

Flame height/¯ame width 4.13 4.43 4.56 4.66 4.7 4.68 4.75

Flame surface area/aperture/area 171.71 151.20 153.00 130.59 134.92 112.43 90.72

126 J. Hu et al. / Experimental Thermal and Fluid Science 21 (2000) 124±133

Few experimental data are available concerning thedi�usion of the speci®c relevant ions. It is therefore as-sumed that the di�usivity of a speci®c ion is equal to thatof the corresponding neutral species. From these as-sumed ion di�usion coe�cients, the mixture mobility, l,can be determined [6]:

l �Xnspc

j�1k 6�j

Xk

ljk

0B@1CAÿ1

: �6�

When an electric ®eld is applied, an additional mass ¯ux,Jj, due to the electric mobility, has to be considered [6]:

Jj � �lqYjE: �7�The convection ¯ux in the ionic species conservation

equation has been modi®ed in order to consider theadditional mass ¯ux.

Jconv: � qYj�w� lEz� �8�The CHEMKIN is used to calculate the thermodynamicproperties and transport properties. This is based on theavailable JANAF data.

3.2. Boundary conditions

The system is closed with appropriate boundaryconditions on each side of the computational domain.For the co-¯owing ¯ame, the boundary conditions at theburner aperture correspond to the experimental condi-tion, as shown in Table 4. Identical boundary conditionsare employed for the candle-type ¯ame except for the

outer zone and inlet (Table 5). For the premixed candle-type ¯ame, w is parabolic distributed (well-developedlaminar ¯ow in a pipe) corresponding to a volumetric¯ow rate of 26.3 cm3/s through an 8 mm aperture di-ameter.

3.3. Chemical kinetic mechanism

In the present study, both neutral species and ionicspecies reactions are considered as shown in Table 6.Reactions 20±24 have been suggested by Green andSugden [7] and others [8] to represent the important ionprocesses in hydrocarbon ¯ames. There is no doubt thatthe major ions are formed through reactions which in-volve CH molecules. The CH molecules may be formedeither from acetylene and other C2 molecules, or via theoxidation of CH3. Green and Sugden [7] proposed thatthe main mechanism through which CH is produced in amethane/air stoichiometric mixture is via the oxidationof CH3 through CH3 �O! CH�H2O (reaction 20).Peeters et al. [8] have used this reaction successfully intheir computations, and Jones et al. [9] proposed mod-ifying the rate constant of this reaction to result in abetter correlation with their experimental observations.Pederson and Brown [6] examined a 13-step reactionscheme for the determination of the ion pro®les. Theirresults indicate that for a stoichiometric mixture, H3O�

is the most important ion; its maximum concentration ismore than two orders of magnitude higher than that ofC2H3O� and C3H�3 , and three orders of magnitudehigher than that of HCO�. The latter ion is, however, animportant component for the production of H3O� and,

Table 4

Boundary conditions for the co-¯owing ¯ame

Yj v w T

Inlet (z � 0)

0 < r < RI Yj0 0 w0 T0

RI < r < RO Yj0 0 w0 T0

Outlet (z � z1) rzYj � 0 rzv � 0 rzw � 0 rzT � 0

Axis of symmetry �r � 0� rrYj � 0 0 rrw � 0 rrT � 0

Outer zone �r � RO� rrYj � 0 rrv � 0 rrw � 0 rrT � 0

Table 5

Boundary conditions for the candle-type ¯ame

Yj v w T

Inlet (z � 0)

0 < r < R Yj0 0 w0 T0

R6 r < r1 YO2� �YO2

�A rzv � 0 rzw � 0 TA

YN2� �YN2

�AYj � 0; j 6� O2; N2

Outer zone �r � r1� YO2� �YO2

�A rrv � 0 rrw � 0 TA

YN2� �YN2

�AYj � 0; j 6� O2; N2

J. Hu et al. / Experimental Thermal and Fluid Science 21 (2000) 124±133 127

therefore, is the only ion (except the H3O� ion) which isconsidered in the present work. Reactions 21±23 havetherefore been adopted to evaluate the major ion con-centrations.

3.4. Mesh size

The grid size and the spatial distribution of the meshhave a crucial impact on the accuracy of the results andcomputation. Since most of the chemical reactions occurwithin a narrow zone surrounding the outlet of the fueltube, grid points are clustered in this region. The totalnumber of grid nodes, in each coordinate, has beendetermined by evaluating the e�ect of the grid size onthe mass±fraction-peak values of the species. This pa-rameter has been found to be very sensitive to the gridsize. Solutions with 40� 40 grid and with 20� 20 grid,have been obtained. Di�erences in peak mass fraction ofspecies were less than 2%. A grid of the size of 20� 20was found to satisfy our requirements and no bene®t isgained with a ®ner mesh. Based on these tests, whichwere carried-out for each case, a 20� 20 grid size meshhas been selected for all cases.

4. Results and discussion

4.1. Co-¯owing ¯ames

The results of the co-¯owing ¯ame model have beenvalidated against some available data obtained fromother numerical predictions. Fig. 2 shows a comparisonbetween isotherms under non-electric ®eld condition, aspredicted by Smooke [10], and those calculated in thepresent work, using the same computation domain andboundary conditions. For the sake of convenience, thetemperature is reduced by introducing the adiabatictemperature TF and ambient temperature TA. It seemsthat our predictions ®t quite well the SmookeÕs predic-tions, except for the aperture neighborhood regionThese discrepancies are attributed to the small di�er-ences in the chemical kinetic schemes and transportparameters.

In order to explore the mechanism by which anelectric ®eld a�ects the ¯ame shape, we will look into thedetails of a representative ¯ame and compare its rele-vant characteristics for two cases: with no electric ®eldand when the ¯ame is subjected to a 5 kV uniformpositive-burner electric ®eld.

Table 6

Chemical reaction mechanism scheme of CH4/air ¯amesa

Reaction A b Ea (cal/mol)

1 CH4 ! CH3 �H 4:23� 10�15 0.0 108:69� 10�3

2 CH4 �OH! CH3 �H2O 2:00� 10�14 0.0 8:41� 10�3

3 CH4 �O! CH3 �OH 3:48� 10�13 0.0 8:38� 10�3

4 CH4 �H! CH3 �H2 4:35� 10�14 0.0 13:74� 10�3

5 CH3 �O2 ! CH2O�OH 5:29� 10�11 0.0 1:70� 10�3

6 CH2O�OH! CO�H2O�H 5:87� 10�14 0.0 4:88� 10�3

7 CO�OH! CO2 �H 1:30� 10�12 0.0 1:53� 10�3

8 CO2 �H! CO�OH 1:45� 10�14 0.0 23:76� 10�3

9 O2 �H! OH�O 2:24� 10�14 0.0 16:80� 10�3

10 OH�O! O2 �H 1:71� 10�13 0.0 0:87� 10�3

11 O�H2 ! OH�H 1:74� 10�13 0.0 9:45� 10�3

12 OH�H! O�H2 7:70� 10�12 0.0 7:58� 10�3

13 O�H2O! 2OH 5:75� 10�13 0.0 18:10� 10�3

14 2OH! O�H2O 5:38� 10�12 0.0 1:05� 10�3

15 OH�H2 ! H2O�H 2:19� 10�13 0.0 5:15� 10�3

16 H2O�H! H2 �OH 8:41� 10�13 0.0 20:10� 10�3

17 H�OH�M! H2O�M 2:00� 10�19 ÿ1.0 0.0

18 O�O�M! O2 �M 8:90� 10�14 ÿ0.5 0.0

19 H�H�M! H2 �M 1:00� 10�18 ÿ1.0 0.0

20 CH3 �O! CH�H2O 2:80� 10�8 0.0 0.0

21 CH�O! HCO� � eÿ 5:75� 10�11 0.0 6:00� 10�3

22 HCO� �H2O! CO�H3O� 5:02� 10�17 0.0 24:00� 10�3

23 H3O� � eÿ ! H2O�H 1:44� 10�17 0.0 0.0

24 CH�O2 ! CO�OH 6:00� 10�10 0.0 0.0

25 O�N2 ! NO�N 1:36� 10�14 0.0 75:4� 10�3

26 NO�N! O�N2 3:10� 10�13 0.0 0:33� 10�3

27 N�O2 ! NO�O 6:43� 10�9 1.0 6:25� 10�3

28 NO�O! N�O2 1:55� 10�9 1.0 38:64� 10�3

29 NO�O�M! NO2 �M 1:05� 10�15 0.0 ÿ1:87� 10�3

30 NO2 �O! NO�O2 2:10� 10�12 0.0 0.0

31 NO2 �H! NO�OH 3:00� 10�14 0.0 0.0

a Reactions rates are in form of k � AT b exp�ÿEa=RT � and have units of cm mol s cal.

128 J. Hu et al. / Experimental Thermal and Fluid Science 21 (2000) 124±133

Fig. 3 shows the e�ects of the positive-burner electric®eld on the iso-mass-fraction curves at z � 32 mm, forthe major species (a), intermediate species (b), and thecharged particles (c). The e�ects on the spatial distri-bution of any of the species are quite observable. Itseems that the electric ®eld induces an upward move-ment of the neutral species and ions, such as H2O, CO,H2, H, O, OH, CH3, CH2O, CH, H3O� and HCO�,towards the cathode. Simultaneously, the electrons areshifted towards the anode (downward). Under a posi-tive-burner electric ®eld, the positive ions are acceler-ated preferentially toward the cathode while collidingwith neutral molecule, and a portion of their momen-tum is transferred to the neutral molecules. Since themean free path is small and the ions are reacceleratedby the ®eld after each collision [1], each ion is respon-sible for producing a large number of neutral moleculeswhich are displaced toward the cathode. The net e�ectis that the electric ®eld produces a signi®cant bodyforce or ``ionic wind'' (Eq. 4). Owing to these aerody-namic e�ects, the entire ¯ow ®eld is a�ected (Fig. 4),and the ¯ame shape contour, which is well known to bevery sensitive to the surrounding ¯ow ®eld, is thereforein¯uenced accordingly. A comparison between twoisotherm pro®les, is shown in Fig. 5. The left side showsthe temperature pro®le with no electric ®eld, and theright side shows the same isotherms when the ¯ame issubjected to a uniform positive-burner electric ®eld. The¯ame height is de®ned as the axial position of maxi-

Fig. 3. Mass-fraction pro®les of the major species (a), intermediate

species (b), and charged species (c), for a CH4/air co-¯owing ¯ame, at

z � 32 mm. Left: no electric ®eld, right: applied voltage � 5 kV (pos-

itive burner).

Fig. 2. Isotherms of a CH4/air co-¯owing ¯ame at zero electric ®eld.

Left: results from Smooke [10], right: present work.

J. Hu et al. / Experimental Thermal and Fluid Science 21 (2000) 124±133 129

mum ¯ame temperature. It is clear that the ¯ame heightincreases by 5% with applied an electric ®eld, a ®gurethat ®ts well the experimental observation (6% ± in

Table 1). The maximum temperature appears to be2248 K which is slightly above (by 1.7%) the corre-sponding adiabatic ¯ame temperature of a stoichio-metric methane±air mixture at standard conditions(2210 K). This di�erence is attributed to the shortenedchemical mechanism that we have adopted. Neverthe-less, this deviation seems to be quite acceptable for thepresent purposes.

4.2. Candle-type ¯ames

The numerical model of candle-type ¯ame has alsobeen validated against experimental observations [11].A representative stoichiometric candle-type ¯ame, withno electric ®eld and when the ¯ame is subjected to apositive burner electric ®eld, has been selected as anexample to show the details of the ¯ame±®eld inter-action. A comparison between two isotherm pro®les,at a height of 3.27 mm above the burner aperture, andat 26 mm, is shown in Fig. 6. The burner aperturediameter � 8 mm. The left side shows the tempera-ture pro®le with no electric ®eld, and the right sideshows the same isotherms when the ¯ame is subjectedto a uniform positive-burner electric ®eld. At thislevel above the burner, the temperature pro®le peaksat a radial distance of 3.6 mm, which corresponds tothe ¯ame width at this level. It should however benoticed that although experimental observations indi-cate that a uniform positive-burner electric ®eld af-fects the ¯ame height by a noticeable extent (15% ±Table 2), our computations show a much lower e�ect

Fig. 6. Temperature pro®les of a stoichiometric CH4/air candle-type

¯ame at z � 3:27 and 26.00 mm above the burner. Left: no electric

®eld, right: applied voltage � 3 kV (positive burner).

Fig. 4. Velocity ®eld for a CH4/air co-¯owing ¯ame. Left: no electric

®eld, right: applied voltage � 5 kV (positive burner).

Fig. 5. Temperature contour of a CH4/air co-¯owing ¯ame. Left: no

electric ®eld, right: applied voltage � 5 kV (positive burner).

130 J. Hu et al. / Experimental Thermal and Fluid Science 21 (2000) 124±133

(only a few percents), though trend is however thesame.

The e�ects of the electric ®eld on the iso-mass-frac-tion curves at z � 12 mm, for the major species (a), in-termediate species (b), and the charged particles (c),have also been investigated as shown in Fig. 7. It is notsurprising that the e�ect on neutral species is unnotice-able due to the slightly e�ected temperature distribution,but the e�ect on the ions is quite observable. As for theco-¯owing ¯ames, the electric ®eld induces ions to movetowards the cathode (upward) while the electron movetowards the anode (downward). Due to the body forcewhich is induced by the electric ®eld, as discussed for the

co-¯owing ¯ame case, the entire velocity ®eld increases(Fig. 8) and the ¯ame shape contour, which is sensitiveto the surrounding ¯ow ®eld, is therefore lengthens ac-cordingly.

Our experimental observations show that the ¯ameshape of co-¯owing ¯ames and candle-type ¯ames hasbeen a�ected signi®cantly by the electric ®eld, while ourpredicted co-¯owing ¯ame behavior under electric ®elde�ect, ®ts quite well the experimental data, our predic-tions for the candle-type ¯ame does not. For the latter,the boundary conditions at the inlet (R6 r < r1), and atthe outer zone �r � r1�, seem to be unrealistic and infact, can hardly be described accurately. Though the

Fig. 7. Mass fraction pro®les of the major species (a), intermediate species (b), and charged particles (c), for a premixed CH4/air ¯ame, at z � 12 mm.

Left: no electric ®eld, right: applied voltage � 3 kV (positive burner).

J. Hu et al. / Experimental Thermal and Fluid Science 21 (2000) 124±133 131

predictions for the candle-type ¯ame are quite far fromreality, the trend seems to be correct. It is thereforeconcluded that the mechanism of ¯ame±®eld interactionfor both co-¯owing ¯ames and candle-type ¯ames re-semble each other: the ionic wind e�ect is the moreimportant e�ect.

5. Conclusions

The e�ects of an electric ®eld on the behavior of co-¯owing and candle-type methane±air ¯ames have beenstudied. It has been concluded that the e�ects of theelectric ®eld on methane±air ¯ame behavior are mainlydue to the action of the electric ®eld induced volumetricbody forces. These forces result large-scale bulk ¯owmovements, known as ionic wind. Minor e�ects arepossible due to the re-distribution of the ionic species asa result of the applied electric ®eld. This, however, maynot a�ect the rate of the major reactions steps.

References

[1] J. Lawton, F.J. Weinberg, Electrical Aspects of Combustion,

Clarendon Press, Oxford, 1969.

[2] R.J. Bowser, F.J. Weinberg, The e�ect of direct electric ®elds on

normal burning velocity, Combust. Flame 18 (1972) 296±300.

Nomenclaturecp speci®c heat at constant pressure

(ergs/(mole K))D di�usion coe�cient (moles/(cm3 s))e electron charge (C)E electric ®eld intensity (V/cm)F force (ergs)h speci®c enthalpy (ergs/g)I electric current density (A/cm3)J mass ¯ux (g/cm3)k thermal conductivity (w/(cm K))Kb Boltzman constant (ergs/K)M molecular weight (g/mol)n number concentration (cmÿ3)nspc number of speciesp pressure (dynes/cm2)r Radial coordinater1 width of domain of solutionR burner aperture radius (cm)RI inner fuel jet radius (cm)RO outer oxidizer jet radius (cm), width of

domain of solutionS source termT temperature (K)v radial velocity (cm/s)V velocity vector (cm/s)V applied voltage (V)w axial velocity (cm/s)X molar fractionY mass fractionz axial coordinatez1 height of domain of solution

Greeks/ fuel/air equivalence ratiol mobility (cm/V/s)q density (g/cm3)t dynamic viscosity (cm2/s)x species production rate per unit volume

(mol/(cm3 s))w dependent variable

Subscripts+ positive charged particlesÿ negative charged particles0 initial valueA ambientj jth speciesjm between the jth species and mixturek kth speciesr radial directionz axial direction

Fig. 8. Velocity ®eld for a premixed CH4/air ¯ame. Left: no electric

®eld, right: applied voltage � 3 kV (positive burner).

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