I O N I Z A T I O N C U R R E N T M E A S U R E M E N T S AS A M E A N S O F

D E T E R M I N I N G T H E S T R U C T U R E OF A T U R B U L E N T F L A M E

E. K h o m y a k a n d Yu . Y a r o s i n s k i i UDC 536.468

The problem of establishing the s t ruc ture of a turbulent f lame, though one of the most important in combustion theory, is still far f rom having been solved. It can be formulated in the following simple form: Are there laminar fronts in the turbulent flame and under what conditions ? What is the s t ruc ture and con- figuration of these fronts? Is there a volume react ion zone in the flame? Under what conditions do in te rme- diate s t ruc tu res appear?

The principal difficulty l ies in the choice of method. Optical methods are ineffective, since the ob- served s t ruc ture can be a rb i t ra r i ly explained, while measur ing the t empera tu re and chemical composit ion of the gases is a difficult and complex process . Accordingly, we decided to t rea t the flame as a plasma. Although the origin and nature of the ionization in the flame are still debatable, there is much to support the assumption that the ionization mechanism is different at different points in the flame: in the react ion zone ion "production" is chiefly attributable to chemical p roces ses , e lsewhere thermal ionization prevails . The ionization in the reaction zone is at least an order higher than the thermal ionization (Fig. i).

The nonuniformity of ionization can be used to investigate the flame structure; if the turbulent flame consists of laminar flame fronts, the observed ionization intensity should vary from very high values (when the probe is in contact with the flame front) to low values (when the probe is outside the combustion zone). Intermediate values should occur relatively seldom. If, however, the turbulent flame consists of moles, in which at various stages a volume reaction takes place, the occurrence of the ionization current should be completely random in accordance with the random ion distribution. The duration of the signals should also vary depending on the structure of the combustion front.

E x p e r i m e n t a l M e t h o d s a n d R e s u l t s

Three types of probes have so far been used for investigating the turbulent flame. That used in [1-6] consisted of a platinum wire 0.5-0.8 mm in d iameter , to which the negative te rminal of a 90-V s torage ba t t e ry was connected. The positive terminal was connected to the tube of the bunsen burner; the probe was advanced up to 3 cm into the combust ion zone f rom the f r e sh -mix tu re side (Fig. 2). In this case the probe

acts as a modified c lass ica l Langmuir probe. A miniature, wel l -de-

luminous zone

\ c~ products

\_ thermal

Fig. 1. Distribution of t em- pera tu re T and ion concent ra- tion c i in a l aminar flame.

signed vers ion of this probe has recent ly been used to investigate laminar f lames [7]. The authors of [8] and [9] used the probe shown schemat ica l ly in Fig. 3. One pole of the probe is a thermocouple and its holder (thermocouple d iameter 0.018 ram, length 6.5 mm), the other a pointed tip of undetermined size. VCnich of these elements is the cathode and which the anode is not stated. The resul t s axe inter- preted as depending on the res i s tance of the medium in the gap be- tween them. A third type of probe was used for investigating a laminar f lame front in [10]. It consisted of two e lec t rodes ar ranged side by side in an insulating ce ramic sleeve (Fig, 4).

Warsaw. Translated f rom Fizika Goreniya i Vzryva, Vol. 6, No. 3, pp. 390-400, Ju ly-September , 197-0. Original ar t ic le submitted July 20, 1968.

�9 1973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

341

, . , o

to oscillo- graph

0

Fig. 2. Use of a ba re e l e c - t rode as ionizat ion probe.

thermocouple junction

Fig. 3. Combined ion- izat ion p robe and t h e r - mocouple.

~ J

Fig. 4. Ionizat ion probe with c e r a m i c - i n s u l a t e d e l e c - t rodes .

the e x p e r i m e n t s that:

All these p robes have a se r ious shor tcoming: the magnitude and durat ion of the signal a re affected by the d i rec t ion of mot ion of the ionization zone re la t ive to the probe. Moreover , they cannot be used for a local ana lys is of the f lame s t ruc tu re (except for the probe shown in Fig. 4). The la t t e r probe, however , has the disadvantage of an e x t r e m e l y smal l e lec t rode , so that the ionization signal is a lso ve ry smal l . This r equ i r e s an inc rease in the supply voltage, which in turn , r a i s e s the insulat ion r e q u i r e m e n t s and compl ica tes the m e a s u r e m e n t s . In o r d e r to avoid r e - s i s tance f luctuations and insulation breakdown assoc ia ted with heating, it b ecomes n e c e s s a r y to "shoot" the p ro b es through the m e a s u r i n g zone.

The r e su l t s obtained by these methods cannot be r ega rded as sa t i s fac tory . On the one hand, it follows f r o m

a) the ionization signal v a r i e s within wide l imi t s and in te rmedia te s t r u c t u r e s often appear;

b) the ionization c u r r e n t r a r e l y fa l ls to ze ro , which indicates the a lmos t continuous p r e s e n c e of ion- izat ion zones at the p robe location;

c) the m a x i m u m values of the ionization cu r r en t cons iderably exceed the values for a l amina r f l ame

[41;

d) the dura t ion of the s ignals exceeds the the cor responding t ime for a l amina r f l ame front [8, 9].

These findings m a y be cons idered to favor the hypothesis of volume combust ion.

On the other hand, it is known that:

a) the re a re many m o r e big s ignals than smal l ones;

b) the smal l and med ium s ignals may depend on the depth of i m m e r s i o n of the probe in the combust ion zone [1-3, 5, 6], which sugges ts the exis tence of l a m i n a r f ronts in that zone.

As a r e su l t of all this , d i f ferent in t e rp re ta t ions of the r e s u l t s obtained by dif ferent inves t iga tors under the s ame conditions have led some to suspec t the usefu lness of the method [12]. No one has yet succeeded in explaining the exis tence in the turbulent combust ion zone of ionization s ignals much g r e a t e r than in the l a m i n a r f l ame , where the mos t intense r eac t ions a re assumed to take place.

Accordingly , we have developed a spher ica l p robe for local m e a s u r e m e n t s that is insensi t ive to the d i rec t ion of mot ion and a co r respond ing method of in te rpre t ing the resu l t s .

342

" < ~ . \ o,[mm

q , , ~ ,,l:.i~il l:.if

Fig. 5. Miniature spher ica l probe.

Pt/dRh -~-

Fig. 6. D iag ram of the a r r a n g e m e n t for obtaining beads on Pt13Rh wire.

S p h e r i c a l P r o b e

Spherical p robes provide a r eady means of making local m e a s u r e m e n t s insensi t ive to the d i rec t ion of motion. Since under no rma l conditions the width of the l amina r combust ion f ront ~0.2 m m , the d i a m e t e r of the probe should be of the same order . Because of f abr ica t ion diff icul t ies and the mechanica l p r o p e r t i e s of the m a t e r i a l the d i ame te r of the p robe was taken equal to 0.5 mm. The sens i t ive e l emen t of the probe was made of P t l3Rh alloy, in view of the assumed l e s s e r cata lyt ic ac t iv- ity of PtRh al loys as compa red with pure plat inum. The sphe r -

ical bead was attached to a 0 .2 - ram wire (Fig. 5). Quartz proved to be a be t t e r insula tor than porce la in or A l z O 3.

A bead of specif ied s ize was obtained on the end of a thin wire by means of the a r r a n g e m e n t shown schemat i ca l ly in Fig. 6. This cons i s t s of a 25-V s torage ba t t e ry , a meta l tank filled with m e r c u r y and s i l i - cone oil, and a manipu la to r for d isplacing the wire. The e l ec t r i c a l c i rcu i t composed of these e l emen t s was c losed by advancing the wire through the l a y e r of oil until it made contact with the m e r c u r y and an e lec t r i c a rc was s t ruck at the contact point. The arc mel ted the end of the wi re , which assumed the shape of a bead. The p r e s e n c e of the oil led to rapid quenching of the arc.

T h e o r e t i c a l A n a l y s i s

The re l a t ions be tween the probe signal and the ionization densi ty in a turbulent f l ame at a tmospher i c p r e s s u r e s t i l l have not been es tabl ished. The explanat ions to be found in the l i t e ra tu re are intuitive in c h a r - ac t e r [1-8, 11] or based on the c l a s s i ca l theory of Langmui r p robes [7], which is suitable only for p r e s s u r e s at which the m e a n - f r e e path of the ions is much g r e a t e r than the d i a m e t e r of the probe. Under f lame condi- t ions, at above -a t m os phe r i c p r e s s u r e s , it is n e c e s s a r y to introduce co r r ec t i ons of the o rde r of the ra t io of p robe d i a m e t e r to ion m e a n - f r e e path, which is s e v e r a l o r d e r s g r e a t e r than the m e a s u r e d quantity. T h e r e - fo re , as a l ready pointed out in [10, 13], the c l a s s i ca l theory of Langmuir p robes is unsuitable for i n t e r p r e t - •ng the r e s u l t s of m e a s u r e m e n t s obtained fo r a p l a s m a that should be r ega rded as a continuum. The r e su l t s of [13], an analys is of ion diffusion in a Couette flow and in the boundary l aye r n e a r a s tagnat ion point, can be used to de t e rmine the magnitude and nature of the signal f r o m a spher ica l p robe located in a flow. The ion densi ty in the f lame is be tween 101~ and 1013 1 / c m 3 at an average mo lecu l e -number densi ty of m o r e than 1018 1 / c m ~. The the rmodynamic and t r a n s p o r t p r o p e r t i e s of a p l a s m a of this kind are not d i s tor ted by the p r e s e n c e of charged pa r t i c l e s . The re fo re the equations of motion of the ions can be separa ted f r o m the known equat ions of motion of the neut ra l gas.

We will de t e rmine the mot ion of the charged pa r t i c l e s (ion and e lec t rons) r e l a t ive to the neut ra l gas, a ssuming that the med ium in quest ion cons i s t s of a monatomic ionized gas with ions and e lec t rons , whose recombina t ion is r e t a rded , at the same t e m p e r a t u r e . Then the motion of the ions depends on the concen t ra - t ion gradient and the e l ec t r i c field f o r c e s and in the space of the probe boundary l ayer can be desc r ibed by the following equations:

-- ( D ~ ) Oc~ + g v Oe~ 0 ~) . . . . . p t f ~ E c i , (1) '~ ll --~x O y O y t O y

Oc e bee O ( D OCe ) ~ + ' Oy e dy < '

ov--gT~ . . . . o .~--oX~ec~ (2)

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O ~ e ~ ( c[ c e ) 0 y ~o Mi .44~ ' (3)

w h e r e x and y a r e c o o r d i n a t e s , and u and v a r e v e l o c i t y c o m p o n e n t s ( see F ig . 7); P i s the m a s s dens i ty ; D i s the diffusion coefficient; K is the ion mobility; E is the e lectr ic field strength; M is the part icle mass; e0 is the permit t ivi ty of the medium. The subscr ipts "i" and "e" relate to ions and e lect rons , respectively. In the space of the boundary layer there are regions of ambipolar diffusion, where c e = ci, and regions where the e lec t r ica l fo rces are s t rong and c e ~ c i. Since the react ion ra te has an Arrhenius tempera ture dependence and since in the boundary layer the gas is cooled, it may be assumed that ion "production" ceases at the edge of the boundary layer , where the t empera tu re drop begins. At this point the ion concentrat ion is equal to the ion concentra t ion in the f lame:

Ci ~ "is,

Ce \ M~ I " c~,. (4)

At the surface of the probe recombinat ion is instant:

c i . = c , ~ = O. (5)

The solution of Eqs. (1)-(3) given in [13] for conditions (4) and (5) in a Couette flow depends heavily on the p a r a m e t e r

A - a~ ' (6) L

where~ = S ~ dy-- is the reduced thickness (L is the distance between plates); and A 0 is the Debye radius. pc

o

When A --" ~ or, in prac t ice , > 1000, the dimensionless cur ren t

j~ _ f i M ~ c i A + 2

Ci~ '% ~ 1 -t- See ]e ' (7) Sc~ ]~

where j is the cur ren t per unit surface, Sc = U/po is the Sehmidt number, and 7 is a constant equal to pp / PoPe . The subscr ipt "0" denotes the p a r a m e t e r s at the upper plate in the Couette flow or the pa rame te r s of the undisturbed motion. A Couette flow is a quite good approximation of the motion in the boundary layer , so the resu l t s obtained can be applied to our problem. Since Sce << Sci, for negative probe potentials exceed- ing the Langmuir potential in absolute magnitude Je < Ji and Ji ~" 2. Assuming that ni= p(ci/Mi) , we obtain

edge of boundary layer

~edge of layer in which field strength

/

=o l . . . - - I , t �9 ~1 ~ . . . . _ u ~ ,

one of strong eieetric- s N al effgets

~ ambipolar diffusion zone

Fig. 7. Model of the motion around a spherical probe.

], : : 2~z--- (8)

S c i r 9~ A [J'(t

Instead of A we take the mean thickness of the boundary layer , which de termines the mass t r ans fe r in accordance with the relat ion

,Sh = k - Sc '/3Re m, (9)

where Sh is the Sherwood number, whence

d k �9 Sc 113 �9 Re ~12

(10)

Thus, we can write

j~ = :2ha,. k Re 'i: ( i i ) Sc~'a . d

or the total cur ren t f rom the probe

j , , ::: '2r~n m . k . Re U2 , d S,,,~l ~ (12)

This is an important relation in that it links the strength of the signal with the velocity and properties of the gas. As may be seen from the above expressions, the ion diffusion in the electric field

344

o I~ -i i -o-5ov t

~ - I

F i g . 8. D i a g r a m o f m e a -

s u r i n g system.

i • 1 o , 0 -

'<~ 5,0.-

"~ 2/- ~.j~" ..

.o o . . . . . . . . . . -~ ............ 7 - - 12 t i m e , m s e c

Fig. 9. Record of the ioniza- tion cur ren t detected by a probe t ravel ing through a laminar bunsen flame.

is twice the free diffusion, a known proper ty of diffusion in e lectrolytes [14], The total cur ren t f rom the probe is direct ly proport ional to its diameter and depends l inear ly on the ion concentrat ion at the edge of the boundary layer.

So far it has been assumed that the distance at which the ion concentrat ion is equal to that of the un- disturbed zone is determined by the thickness of the boundary layer around the cold spher ical probe. In real i ty , the probe is s trongly heated, since there is no means of effectively cooling its miniature elements. Therefore the point at which the ion concentrat ion is equal to the concentrat ion in the undisturbed zone will be displaced, and a cor rec t ion , a function of the probe tempera ture , must be introduced on the r ight side of Eq. (12):

J c 2 ~ ni(~ �9 k - Re l!~ - d =: . . . . . . . . . . . . . . . . . . . sc~;,~ - f ( T :~j.; (13)

We are now in a posit ion to understand why the turbulent exceeds the laminar ionization current .

The resul t s of the theoret ical analysis are highly sensitive to the assumption that there is no r e c o m - bination in the boundary layer around the probe. We will es t imate the co r r ec tnes s of this assumption by compar ing the charac te r i s t i c ion-e lec t ron recombinat ion t ime with the dwell t ime of the par t ic les in the boundary layer . Using the resu l t s of [7], we can take the following data for a s t0ichiometr ic p ropane-a i r mixture at a tmospher ic p re s su re : number of ions n i = 1.42.101~ 1 / c m 3, recombinat ion coefficient 7 = 2.2"10-7 em3/see; consequently, the charac te r i s t i c recombinat ion t ime m = 1/-/# = 3.2.10 -4 sec. In the general case this t ime is g rea te r than the mean-dwell t ime of the par t ic les in the boundary layer of a probe immersed in a turbulent flame; accordingly, recombinat ion may be neglected.

R e s u l t s o f t h e M e a s u r e m e n t s

We will determine the dependence of the ionization cur ren t on the probe potential for a laminar bunsen flame. The c i rcui t d iagram of the measur ing sys tem is shown in Fig. 8. During the measurements , as the probe was slowly displaced, it was observed that the ionization cur ren t depends on probe tempera ture . On the one hand, this may be related with a change in the boundary layer p r o c e s s e s or, on the other, with a change in the conductivity of the quartz. Since there was no possibil i ty of determining the t empera tu re of the measur ing element, the measuremen t s were made with a cold probe. The probe t raveled through the combust ion zone at 2.5 m / s e c attached to a pendulum 1 meter long. The resul t s of one pass are presented in Fig. 9. The probe f i rs t c rossed the combustion product zone, then the f lame front and the cold mixture, and again the f lame front and the combustion product zone. In p ierc ing the f lame front f rom the co ld-mix- ture side, the probe ca r r i ed a cer ta in amount of the mixture into the combust ion product zone, which is r e - flected in the charac te r i s t i c shoulder on the r ight of the figure.

The random differences in the ionization cu r ren t s on the left and right of the bunsen flame are of considerable interest . If the left side is taken as a re fe rence level, they may fluctuate by • Since the components were well mixed, while the combustion conditions were prac t ica l ly invariant during each mea- surement , we may conc]ude that the ion concentrat ion in the laminar f lame exper iences random fluctuations. The origin and nature of these fluctuations are not c lear , and the l i tera ture is silent on this point. The width of the ionization cur ren t signal in the laminar f lame is quite large; it considerably exceeds the width of the flame and is equal to approximately 5 ram. This compl ica tes the analysis of the s t ructure of a com- bustion zone, in which a ra ther large number of laminar fronts is located.

345

.~4-

.'~2-

voltage, V

Fig. I0. Current -vol tage cha rac - t e r i s t i c s of a laminar p ropane-a i r flame.

I 1

t 1 \ / I

Fig. 11. Diagram of com- bustion chamber.

In Fig. 10 the ionization signal is shown as a func- tion of the potential for two values of the a i r - fue l ratio. In the region of 22-30 V the curve has a point of inflection. Although at values above 30 V the curve is not a c lass ica l saturat ion curve, the potential dependence of the ioniza- tion current is weaker. The turbulent flame measurements were made at 30 V. Anhomogenous mixture of air and

propane was burned in the chamber shown schematical ly in Fig. 11 at mean mixture veloci t ies of 15-50 m / s e c at the chamber inlet and va lues of a f rom 0.9 to 1.2.

The chief object of the measuremen t s was to evaluate the proposed technique, not to make a sys t em- atic investigation of the s t ruc ture of the f lame front; accordingly, the experimental conditions were limited.

Ionization signals, s imi lar in shape to those obtained for a laminar flame, were recorded as the probe approached the f lame zone 2-5 mm f rom the apparent boundary of combustion (Fig. 12). Somewhat deeper, at the edge of the flame zone, the number of signals increases , sharply differentiated signals with much g rea t e r amplitude and g rea t e r duration than in the laminar flame are observed, and jogs appear on the spikes with eve r - i nc r ea s ing frequency. There are also zones where the cur ren t does not fall to zero over an extended period 9 suggesting that the spikes are superposed (Fig. 13). The presence of the differentiated signals make it appear doubtful that they cor respond to a p rocess of combustion in laminar fronts, though the nature of the signals suggests that the react ion takes place in thin layers .

In the inter ior of the turbulent combustion zone the signals take the fo rm of a large number of rounded folds. In addition to the t race of the ionization current , Fig. 14 shows the flame s t ructure in a slit 1 m m side r ecorded by means of a shadow system. The thin horizontal line denotes the location of the measur ing e lement of the probe re la t ive to the flame. The l inear speed of the f i lm was 25 m/sec ; the gas moved at approximately the same speed at the entrance to the combustion chamber. The scale of the photos was 1:1. A compar i son of the cur ren t t r ace and the flame s t ructure indicates quite good correspondence between the ionization peaks and the more heavily exposed areas of the photograph, i.e., density gradients. Consequently, the a reas with a density gradient cor respond to an intense chemical reaction. Sometimes the change in ion concentra t ion in these a reas is small , which may be attributable to intense ion diffusion along layers with high concentrat ion gradients.

On average, the number of more exposed areas is three t imes g rea te r than the number of ionization peaks. This is because the probe t r ansmi t s local signals corresponding to a width of 0.5 mm, while the photo shows the flame s t ructure superposed on the 30-ram width of the combustion chamber. As the probe moves deeped into the combust ion zone, a cur ren t t race without charac te r i s t i c breaks (zero values of the

i 12,5-

o ~, ~ ~ ~ "'~ o time, msec

Fig. 12. Record of the ionization cu r ren t near the apparent turbu- lent f lame front.

t i m e , m s e c

Fig. 13. Record of ionization �9 cur ren t at the beginning of the apparent turbulent f lame zone.

346

ionization current) is obtained. The signal becomes continuous and begins to resemble the typical t r ace of a random process . P a r t of such a r ecord is shown in Fig. 15 by way of i l lustration. The ionization signal may be explained as follows: the t race suggests the superposit ion of ionization peaks corresponding to chemical react ions in nar row layers or fronts on a cer ta in level of the ionization cur ren t corresponding co r respond- ing to the volume in which a volume react ion is taking place. During pulsating combustion the accelera t ion of the f lame front was observed to affect the ionization s t ructure .

S U M M A R Y

A probe has been developed for making local measurements of the ionization cur ren t in a turbulent flame. The probe signal depends l inear ly on the ion concentrat ion at the edge of the boundary layer on the measur ing element of the probe. The magnitude of the signal depends on the velocity of the gas and the t empera tu re of the measur ing element.

In a homogeneous laminar flame the ionization signal var ies between l imits of • The region corresponding to high ionization is several t imes thicker than the laminar com- bustion front.

In the turbulent flame zone the signal fluctuates within wide l imits, intermediate values of the signal being common. The maximum signal amplitudes in the turbulent flame much exceed those in the laminar flame. Inside the turbulent f lame there are regions where an e~:ended uniform ionization signal can be detected.

In the inter ior of the turbulent flame zone the ionization signal is continuous, it does not fall to zero, and its t race r e - sembles that of a random process . Accelera t ions acting on the flame front affect the ionization s t ructure .

All this suggests that in relat ion to a rea l turbulent flame the proposed method is a qualitative one. The method is suitable for investigating the flame front in a steady flow, when the mea- suring element of the probe is not heated and the p re s su re fluctuations are small.

Fig. 14. Trace of ion- ization cur ren t and s t ructure of turbulent f lame.

5/,5:

• J0,o-

,...2 22,s-

o t5,o

2

0 T ] W "~" 4 8 ~2

tin'le~ 1TI s e e

Fig. 15. Trace of ionization cur ren t in the inter ior of the turbulent f lame z o n e .

LITERATURE CITED

1. B. Karlovitz, D. W. Denniston, and others, Fourth Syrup. (Intern.) on Combustion, Bal t imore (1953).

2. R .S . Marsden, Four th Syrup. (Intern.), Bal t imore (1953). 3. D. Karlovitz, Selected Combustion Problems. Fundamen-

tals and Aeronaut ical Applications, AGARD, But terwor th ' s Scientific Publications, London (1954), p. 248.

347

4. M. Summeriield, S. H. Reiter, 17. Kebely, and R. W. Mascolo, Jet Propulsion, 25, 377 (1955). 5. J . K . Richmond, W. F. Donaldson, D. S. Burgess, and J. Grumer, Jet Propulsion, 28, 393 (1958). 6. D.W. Denniston, J. R. Oxendine, and others, J. Appl. Phys., 28, 70 (1957). 7. H . F . CMcote, Ninth Syrup. (Intern.) on Combustion, Academic P res s (1963). 8. E .S. Shchetinkov, in: Combustion in a Turbulent Flow [in Russian], Izd. AN SSSR (1959). 9. K .P . Vlasov, in: Combustion in a Turbulent Flow [in Russian], Izd. AN SSSR (1959).

10. C.H. Su and S. H. Lain, Phys. of Fluids, 6, No. 1 (1963). 11. N.N. Imozemtsev, Flame Stabilization and Development of Combustion in a Turbulent Flow [in

Russian], Oborongiz (1961). 12. F .A . Williams, Combustion Theory, Addison-Wesley (1965). 13. P. Chugh, Phys. of Fluids, ! , No. 1 (1964). 14. g . G . Levich, Physicochemical Hydrodynamics [in Russian], Fizmatgiz, Moscow (1959).

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