Reignition Regime

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Combustion of Foamed Emulsions in the Quenching/Re-ignition Regime Boris Kichatov, Alexey Korshunov, Alexey Kiverin, and Eduard Son Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 06 Jun 2017 Downloaded from http://pubs.acs.org on June 10, 2017

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Combustion of Foamed Emulsions in the Quenching/Re-ignition Regime Boris Kichatov*, Alexey Korshunov, Alexey Kiverin, and Eduard Son Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow 125412, Russia

ABSTRACT: The paper considers the problems of combustion of foamed emulsion consisting of oxygen bubbles dispersed in the emulsion which represents a water solution of surfactant with oil drops distributed in it. The interest to study such problems is caused by the perspective of obtaining a new type of fuel based on water-oil blend as well as by the need to solve ecological issues related with oils spill on the water surface. At significant content of water in the combustible foam the irregular regime of flame propagation can be established that is related with sequential quenching and re-ignition of the foam. On the basis of experimental research we study the influence of magnesium oxide particles fraction, fuel concentration and tube diameter on the speed of flame propagation in the foamed emulsion in the quenching/re-ignition regime. It is obtained that the presence of magnesium oxide particles in the foam leads to the increase in total burning rate of the foam. The reducing in tube diameter and the use of leaner foam favor the onset of the quenching/re-ignition regime.

1.

INTRODUCTION Foamed emulsion or foamulsion is a multiphase system consisting of oil drops and gaseous bubbles distributed

in the water solution of surfactant. Due to the widespread in our everyday life, e.g. as detergents, this class of foams is of a wide research interest.1-3 When studying the issues related with combustion traditionally foams are treated as materials for fire suppression.4 However unique properties of foams can brightly manifest themselves in the elaboration of combustible systems. For the first time the opportunity to use foamed emulsion as a combustion system was proposed by Kichatov et al. in 2016.5 The interest of studying such systems is caused by the perspective of development of a new type of fuel on the basis of water-oil blend. Nowadays there is an increase in the research interest to the issues related with an opportunity to use the emulsive combustible systems of oil-in-water and water-in-oil as a fuel.6-16 This is due to a number of reasons associated first of all with the issues of decrease in emission of NOx and soot, as well as with changes in the reological properties of hydrocarbon fuels for increasing on spray combustion efficiency.17-23 For example the use of emulsifying crude coal tar with water to form water in oil emulsions is a good way to improve the combustion of coal tar and reduce environmental problems.24

1 ACS Paragon Plus Environment

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At certain conditions the combustion of emulsion drops is accompanied with a phenomenon of microexplosion. Microexplosion represents rapid disintegration of an emulsion droplet caused by explosive boiling of embedded liquid sub-droplets with a lower boiling point.25-30 Due to the secondary atomization one could significantly increase the efficiency of fuel spraying as well as the intensity of its combustion in diesel engines.31 At the same time it should be noted that there are certain limitations imposed on the composition of emulsion fuel due to the fact that water represents inhibitor of oils combustion. In number of cases a problem arises related with the direct burning of water-oil blend containing large amount of water without preliminary refining of components.32 For example, such issues arise when solving problems ecology associated with oil products spill on the water surface. Blend of water and oil gathered from the water surface could contain a sufficient amount of water fraction that makes it difficult to utilize it by combustion. However if this blend is subjected to foaming then it will keep combustibility even at 90 wt. % of water content.5 This feature of foamed emulsion as a combustible system extends significantly the range of its potential utilization. Besides, when using the foamed emulsion as a fuel one should not elaborate complex systems of its spraying that is especially actual for development of microscale power devices.33 Another important problem related with microscale power devices elaboration concerns the issue of combustor walls cooling. The foamed emulsion combustion is accompanied with formation of water drops that would favor combustor walls cooling due to the interaction with these drops. Such features of foamed emulsion make it a prospective type of fuel for microscale power devices even in spite of low heating value intrinsic to the foams due to high water contain. A significant disadvantage of foamed emulsion as a fuel is its ability to shrinkage. Therefore the combustible foamed emulsion should be utilized as a fuel immediately after its preparation. A potential field of foamed emulsion application is its utilization in the continuously operating burners connected with foam generator. Principle of such device operation could be the following. The emulsion is prepared inside the reactor by stirring oil with water and stabilizer. After it the emulsion is foaming inside a foam generator by dispersing of air or oxygen in it. Prepared foam fed to the continuously operating burner where the burning takes place. To create such a device it is important to solve the problem of matching between foam burning rate and foam preparation rate. Bubbly gas-liquid media formally can be divided into two classes: bubbly liquids (with volumetric content of gas < 10%) and foams. The main attention here is focused on the combustion of foams with volumetric content of liquid phase in the foam not greater than 12.5%. According to this the considered class of foams is intermediate between “wet foams” and “dry foams”. We analyze the combustion of foamed emulsion of the following type: gas bubbles contain oxygen, and liquid matrix of the foam represents a water solution of surfactant with oil drops dispersed in it. In our


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previous work devoted to the study of foamed emulsion combustion we focused our attention mainly on the analysis of oscillatory and accelerated regimes of combustion.5 This paper analyses the irregular regime of foam combustion accompanied with sequential quenching and re-ignition of combustible foam. Here this regime is called “quenching/reignition” regime. The interest to study exactly this combustion regime is due to its intrinsic character for foams with large water content. Experimental study is mainly focused on the analysis of magnesium oxide solid microparticles, fuel concentration and tube diameter on the possibility of realization of one or another regime of foam combustion (including “quenching/re-ignition” regime) and on the velocity of flame propagation. When using the foamed emulsion as a fuel an important question of its stability arises,34,35 therefore the paper also pays attention to this issue.

2.

EXPERIMENTAL

2.1. Materials: Surfactant, Oil, Gas, Particles. In this paper when preparing the combustible foamed emulsion the following hydrocarbons were used: heptane, o-xylene and isooctane (> 99 % purity). Their boiling temperatures at atmospheric pressure are correspondingly 98.4, 144.4 and 99.3℃. To stabilize the foam a commercial detergent was used. It is a stabilizer of mixed type consisting of anionic and nonionic components. To measure surface and interfacial tension the duNouy ring tensiometer Kruss K20 (Germany) was utilized with error 0.1 mN/m. The results of measurements are presented in Table 1.

Table 1. Surface and interfacial tension at 23°C Surface tension /

Water + stabilizer Water + detergent

29.9 Pure hydrocarbon surface tension

O-xylene Heptane

27.7 19.5 Water + stabilizer / hydrocarbon interfacial tension

Water + detergent /heptane

3.4

Water + detergent /o-xylene

1.9

It is known that oil drops are able to cause destabilization of the foamed emulsion.1 Foam stability depends on entry and bridging coefficients. Although the antifoam activity is only indirectly related to these coefficients,1 they are quite indicative when estimating the antifoam potential of the oils. The entry coefficient E is related to the ability of the oil dispersed in water to penetrate into the air/water interface. In case of its positive value the emulsion acts as an


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antifoam as a whole. The bridging coefficient B is related to the ability of oil globules to bridge the foam films. If > 0, then oil is potentially a fast antifoam. These coefficients are defined as follows: = + − ,

= + − .

Estimate of these values for the foam containing heptane provides following values: = 13.1 and = 0.5 . According to this it can be concluded that heptane is potential antifoam. To obtain oxygen bubbles in the foam a hydrogen peroxide (50 % purity) was used. Its decomposition was catalyzed with the use of ammonia solution of copper sulfate (1.05 mol/L). The powder of magnesium oxide with characteristic particles size from 100 nm to 2 was used as a fraction of solid microparticles. 2.2. Emulsion preparation. Emulsion was prepared via stirring of distilled water, oil and surfactant inside the vessel of 300 mL volume. The stirring was performed using a Teflon two-bladed stirrer during 10 min (stirring intensity, 200 rpm). Characteristic size of heptane drops in the emulsion was controlled by means of microphotography and belonged to the range from 7 to 85 .

2.3. Foamulsion Generation. Foamed emulsion was prepared on the base of preliminary prepared emulsion by means of chemical foaming. This was achieved by mixing of emulsion with hydrogen peroxide directly inside the tube where the combustion was studied. An ammonia solution of copper sulfate was used as a catalyst. In the process of hydrogen peroxide decay the oxygen was released 2" # = 2" # + # ↑. To obtain combustible foam the prepared emulsion together with hydrogen peroxide and catalyst were fed into the tube in which subsequently the flame speed was measured. Uncertainty in dosing of initial components was not greater than ±1.5 %. As the oxygen was releasing the foam was forming. Gaseous bubbles moved up in the water solution of stabilizer under the action of Archimedes force. The bubbles which were formed later pushed up those formed earlier while the space between the bubbles were filled with emulsion. Stabilizer molecules were adsorbed on the bubbles surface that prevented bubbles collapse after they enter on the liquid/air surface. Foam growth was realized during 2..4 s, therefore one can neglect the process of liquid flowing from the foam under the action of gravity. A typical microphotography of foamed emulsion is shown in Figure 1. This photography of the foam outer surface was obtained with the use of optical microscope Bresser Biolux NV (Bresser GmbH, Germany). To estimate the size of gaseous bubbles the foam was photographed immediately after preparation. Characteristic size of oxygen bubbles in the foam immediately after foam preparation was in the range from 50 to 190 . It is known that the smaller is the


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gaseous bubbles diameter the more stable is the foam. Therefore to obtain smaller bubbles a chemical method of foaming was used. It is not the only method allowing obtain microbubbles.36 Foam expansion ratio was determined as a ratio of the foam volume to the volume of the liquid phase of the foam.

Figure 1. Microphotograph of combustible heptane-based foamed emulsion, 127 s after foam preparation. 2.4. Monitoring Foamed Emulsion Ageing. Stability of the foamed emulsion was estimated on the base of foam shrinkage rate. Foam decays due to gravitational foam drainage or emulsion creaming, as well as through coarsening (or Ostwald ripening), i.e. gas or oil transfer between bubbles/drops due to capillary pressure differences. Value of “foam height fraction” was determined as a ratio of the current height of foam column (at given time instant) to the height of foam column at initial time instant.

2.5. Flame Speed Measurements. Measurement of the flame propagation speed in the foam was carried out inside a semi-opened tube where the foamed emulsion was prepared. The tube was installed vertically with open-end directed to the top (Figure 2a). Geometrical parameters of the tubes used in the experiments are presented in Figure 2b. Foam ignition was performed by pilot flame on the open end of the tube at the time instant when the expansion ratio of the foam achieved its maximum. Further the flame propagated from top to bottom. To measure the flame speed we used the high speed color camera RedLake MotionPro X3 with the frame rate equal to 1000 fps, and 995

& shutter. The

measurements were repeated using the high speed monochrome camera Phantom V2012 with the frame rate 10000 fps, and 10 & shutter. All the photographs of the combustion zone presented in the paper were obtained using the color camera RedLake. Term “flame speed” was used to determine the propagation speed of the fastest point of the flame front. The choice of such a definition of flame speed is related with the concept of the flame leading point.37 According to this concept the flame speed in the laboratory reference frame is defined by the propagation speed of the fastest point on the


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flame surface from which the ignition impulse spreads over the whole channel width. Herewith the flame speed depends not only on the burning rate of the mixture inside the flame front but also on the velocity of reacting mixture which could arise due to the action of gasdynamical processes. Term “total burning rate” was used to determine a flame speed averaged over the whole length of the tube. Flame speed at certain time instant was estimated from the measured distance ' travelled by the leading point of the flame during 1 & (Figure 3). At images processing the error in flame speed determination was ±1.7 %. When determining the total burning rate of the foam the tests were repeated at least 5 times. Dispersion of the experimentally obtained values is shown in the graphs with the use of error bars.

Figure 2. (а) Scheme of experimental apparatus: 1 - pilot flame; 2 - tube; 3 - highspeed camera. (b) Geometrical parameters of the tubes.

Figure 3. Scheme of flame speed determination.

3.

RESULTS AND DISCUSSION


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3.1. Fundamentals. In the process of flame propagation in the foam the slow and the fast regimes of combustion can be realized. The slow regime of foam combustion is usually characterized by the flame speed comparable with laminar burning velocity of the gaseous mixture which as a rule is not greater than 1 m/s.5 In this combustion regime the foam decays in a “smooth” manner with formation of water drops, oil drops and/or emulsion drops. Notion of “smooth” foam decay incorporates foam decay due to the evaporation of liquid films between bubbles and due to the fluctuations of capillary pressure.38 In this regime of foam combustion the flame speed is lower than that in case of premixed gaseous combustion. With the increase of water content in the combustible foam the flame speed decreases and upon reaching a certain critical value the foam becomes noncombustible. At this, the decrease in the flame speed is determined by the heat losses from the flame front on the drops evaporation.5 At fast regime of foam combustion the flame speed can achieve several tens of meters per second. Flame acceleration in the foamed emulsion is connected with a very specific process - an explosive boiling of liquid phase of the foam.5 The mechanism of this process is as follows. In the process of flame propagation the heat flux is transferred from the flame front to the cold layers of the foam. At certain conditions the heating of liquid phase of the foam leads to its explosive boiling. The formed flow of vapor and drops carries the reacting mixture to the cold layers of the foam. Burning kernels arise in the combustible foam from which the ignition impulse propagates over the entire tube cross section. In the considered case the combustion wave speed is determined not by the thermal conduction or diffusion of active centers but by the intensity of explosive boiling of liquid phase of the foam.5 When considering combustion of foamed emulsion with high water content or combustion in the narrow tube one can observe the irregular process of flame propagation in which the sequential change in events of flame quenching and re-ignition takes place. It is precisely this regime of combustion which is analyzed below.

3.2. Basic Stages of Combustion. Flame propagation in foams can proceed in the quenching/re-ignition regime. This regime of foam combustion is essentially as follows. If the acceleration of flame allows its front velocity to reach the limiting value, the flame quenching takes place as a result of the incomplete evaporation of fuel drops in the convectivediffusion zone of flame. These fuel drops are evaporated in the zone of combustion products and, in certain time (after ignition delay), initiate repeated ignition of the fuel mixture. This gives rise to the new combustion wave and the process is repeated. This regime of flame propagation is illustrated in Figure 4, where the flame is quenching after acceleration up to 22 m/s (Figure 4b, shot at 5 &) and exhibits repeated ignition with 2 & delay and acceleration up to 12 m/s. In this


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regime of foam combustion the flame speed changes in the irregular manner. Nevertheless all the combustible foam burns down and one does not observe a global quenching of the flame in the foam.

Figure 4. (а) Plots of the flame speed and distance traveled vs. time in a tube of ) = 20 ; foam is prepared from isooctane (1 mL), water (2 mL), SDS solution (1.6 mL, 0.5 mol/L), hydrogen peroxide (1 mL), and ammonia solution of copper sulfate (0.8 mL, 1.05 mol/L); foam expansion ratio, 22.5; total burning rate, 8.83 m/s. (b) Structure of combustion zone; time is measured from the moment of foam ignition.

In the considered combustion regime one can distinguish two basic stages: flame acceleration and quenching. 3.3. Combustion Mechanism. While the flame propagates in the combustible foam the foam decays with formation of water drops, fuel drops and/or emulsion drops. The most important requirement for foam combustibility is the smallness of fuel drops compare with water drops forming in the process of foam decay. In such conditions fuel drops are evaporated mainly in the convective-diffusion zone of flame, the fuel vapors mix with oxygen and burn down in the flame front (Figure 5a). At this the water drops (which are sufficiently larger than fuel drops) are evaporated mainly in the region of combustion products. That is why the combustible foam which for example contains 90 *+. % of water maintains its combustibility. The flame acceleration becomes possible while the flame propagates in the semi-opened tube. The mechanism determining this process is briefly described above. At the same time flame acceleration in the foamed emulsion is accompanied a set of attendant phenomena. Thus the process of flame acceleration itself determines a mechanism of its inhibition.


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Figure 5. Schematic representation of the process of flame propagation in the foamed emulsion: I – combustible foam; II - convective-diffusion zone of flame; III – flame front; IV – region of combustion products. 1 – fuel drops; 2 – water drops. (а) Stage of flame propagation in the foam. (b) Stage of flame quenching.

The time during which fuel drops are inside the convective-diffusion zone of flame decreases with the increase in flame speed (~-. ). At the same time the characteristic time of drop evaporation depends on its diameter as ~/0 . At significant rise in the flame speed one can observe the vapor flame quenching, as concentration limit is achieved due to incomplete evaporation of drops in the preheating zone. Assume that diameter distribution function for fuel drops is uniform in the range from 0 to /123 . Under the condition 6789:; -. > -4. ~5 B ,

(1)

0?@A CD EF

part of fuel drops belonging to the range from /0̅ to /123 has not enough time to be evaporated in the convectivediffusion zone of flame. Total volume of evaporated fuel drops equals to I

L

0 0 M HI ~ JN K K = //0 .

(2)

0?@A

The total volume of fuel is expressed via the equation: O HN ~/123 P .

(3)


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The concentration of fuel which enters the flame front in the form of vapor can be determined from the equation: Q

QR

=

T S

SR

.

(4) On the basis of Eqs. (1)-(4) with account of energy conservation law с∆W. = XY one can estimate a critical

value for flame speed corresponding to flame quenching: -.̅ = Z

[QR

E∆\]∗

_

⁄`

-4. .

(5)

As a result of flame acceleration the flame speed can increase only up to certain limit value Eq. (5). Further the flame quenching takes place due to incomplete evaporation of fuel drops in the convective-diffusion zone of flame. Nonevaporated fuel drops are evaporated in the region of combustion products that causes secondary ignition of the combustible mixture after a certain time period corresponding to the ignition delay39 bc90 d

e\ B fg@

g

hij Z @ _.

(6)

e\

In such a way combustion wave propagation is re-initiated and further the process is repeated again. Flame acceleration is accompanied with reacting mixture ejecting. So the time of water drop path through the foam can be taken as a characteristic time of reacting mixture ejection. The equation of drop motion through the foam has the form: O / k

l

mn

~o/

P .

(7)

Drag force for the droplet in Eq. (7) is written in the form of Stokes law and depends on effective viscosity of the foam.40 Equation (7) provides an estimation for characteristic time of reacting mixture ejection: bp ~

BC 0q q

r=

.

(8)

Schematic character of flame speed evolution in “quenching/re-ignition” regime of foam combustion is presented in Figure 6.

Figure 6. Plot of the flame speed vs. time.


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Consider one of the limit cases when the inequality bp ≪ bc90 takes place. Taking into account Eqs. (6) and (8) it can be written as: B C fg 0q q @

r= e\ B

hij Z−

g@

e\

_ ≪ 1.

(9)

In this limit case the total burning rate of the foam is expressed by the following relation: -. ~

8

mtuK

.

(10) Characteristic distance at which the reacting mixture is ejected equals v d -.̅ bp . Therefore in account of Eqs.

(6) and (8) the relation (10) takes the form: -. ~

B fg ̅ 0q w] @

r= e\ B

hij Z−

g@

e\

_.

(11)

According to Eq. (11) one can draw the following conclusions: 1) increase in effective viscosity of the foam favors decrease in total burning rate of the foam; 2) total burning rate of the foam depends exponentially on the temperature of the flame front, i.e. the change in the mixture composition or tube diameter (that determines heat losses from the flame front) would influence significantly on the flame speed in the considered limit case. Consider the opposite limit case bp ≫ bc90 when the ignition delay of the combustible mixture is significantly shorter than characteristic time of reacting mixture ejection. In this limit case the total burning rate of the foam is proportional to the limit flame speed: -. ~-.̅ .

(12) Almost simultaneously after flame quenching the combustion wave is re-initiated and starts to propagate. Total

burning rate of the foam in this case would be determined in many ways by the conditions of flame quenching.

3.4. Influence of Solid Microparticles. Nowadays a research interest increases towards the influence of solid particles on the combustion processes.41 Here we analyzed the influence of magnesium oxide microparticles on the process of foamed emulsion combustion. The dependence of total burning rate of the heptane-based foam on the fraction of magnesium oxide particles is presented in Figure 7. Note that with the increase in particles fraction the foam expansion ratio remains almost the same (Figure 7) and the foam stability increases insignificantly (Figure 8). Stabilization of the foamed emulsion with the use of solid microparticles is determined by the formation of incompressible armor around the bubbles and as a result by the decelerating of liquid flowing from the foam.


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Figure 7. Dependencies of total burning rate and foam expansion ratio on the fraction of magnesium oxide particles. Geometrical sizes of the tube corresponds to case A in Figure 2b. Foam is prepared from heptane (0.2 mL), water (3.3 mL), detergent (1.7 mL), hydrogen peroxide (3 mL), and ammonia solution of copper sulfate (1.3 mL, 1.05 mol/L).

To substantiate the dependence of total burning rate of the foam on the particles concentration it is useful to analyze the histories of instantaneous flame speed (Figure 9). At the increase of MgO particles content in the initial emulsion up to the value of 10.5 g/L the flame propagates in the “quenching/re-ignition” regime (Figures 9a, 9b). The negative value of flame speed (the reverse flame front motion) evidences that the quenching take place. Analysis of the photographs of combustion zone structure (Figure 10a) shows that in absence of MgO particles the luminosity of the combustion zone fluctuates in time that evidences a local flame quenching (photograph at time instant 41&, Figure 10a). With the increase in MgO particles content a reverse motion of the flame front degenerates, however the flame speed itself continues to change in oscillating manner (Figure 9c). Note that in this case the luminosity of the flame is changing in time insignificantly (Figure 10b) that evidences the absence of local flame quenching. In details the mechanism of flame speed oscillations appearance was considered in recent work.5 Note only that oscillations in the flame speed are also determined by the incomplete evaporation of fuel drops in the convective-diffusion zone of flame at its acceleration.


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Figure 8. Foamed emulsion height as a function of time. Foam is prepared from heptane (0.2 mL), water (3.3 mL), detergent (1.7 mL), hydrogen peroxide (3 mL), and ammonia solution of copper sulfate (1.3 mL, 1.05 mol/L). (А) Content of MgO particles in the initial emulsion, 0 g/L, foam expansion ratio, 16.8; (B) 10.5 g/L, 17.4; (С) 21.1 g/L, 17.9. To substantiate a phenomenon of change in the combustion regimes it is necessary to consider a question about the influence of magnesium oxide particles on the limit flame speed value Eq. (5). With account of Eq. (1) equation (5) yields that limit flame speed depends on the fuel drops diameter in the aerosol as -.̅ ~/123 .

In the superheated liquid MgO particles serve as centers of nucleation of vapor bubbles. This is due to the fact that heterogeneous work of critical bubble formation is smaller than homogeneous one so vapor nuclei are predominantly formed at the heterogeneous centers of nucleation.42 According to this it is reasonable to assume that characteristic size of fuel drops which are formed in the foam decay would depend on the volumetric fraction of the ⁄

⁄

O O particles in the emulsion as /123 ~yz{ . Note that if yz{ | /123 then characteristic fuel drops size in the aerosol

after foam decay will be smaller than their initial size in the foam. On the base of Eq. (5) with account of this model of fuel drops fragmentation one can obtain an estimate for limit flame speed: -.̅ ~ Z

[Q}

E∆\]∗

_

⁄` 6789:;< > ⁄ =

~

CD EF

⁄

O yz{ .

(13)


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Figure 9. Plots of the flame speed and distance traveled vs. time at different content of MgO particles. Geometrical sizes of the tube corresponds to case A in Figure 2b. (а) Parameters of the foam corresponds to the case А (Figure 8); (b) parameters of the foam corresponds to the case B (Figure 8); (c) parameters of the foam corresponds to the case C (Figure 8).


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Figure 10. Structure of combustion zone. (а) Parameters of the foam corresponds to Figure 9а; (b) parameters of the foam corresponds to Figure 9с. Time is measured from the moment of foam ignition. Instantaneous values of flame speed are presented for each time instant.


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Limit value of flame speed increases with particles fraction. This is due to finer fragmentation of fuel drops at explosive boiling of liquid phase of the foam. Smaller fuel droplets are evaporated in convective-diffusion zone more intensively and therefore concentration limits of the vapor flame are not achieved. As a result the increase in magnesium oxide particles fraction in the emulsion favors transition from the “quenching/re-ignition” regime of foam combustion to the oscillatory one (compare Figures 9a and 9c). In absence of magnesium oxide particles in the emulsion (Figure 9a) or at low fraction of particles (Figure 9b) the foam combusts in the “quenching/re-ignition” regime. Analysis of the experimental data shows that in considered case one of the limit cases for “quenching/re-ignition” regime is realized with bp ≫ bc90 . In this limit case according to ⁄

O Eq. (11) with account of Eq. (13) the total burning rate depends on MgO particles fraction as -. ~yz{ . This conclusion

corresponds to the experimental data represented in Figure 7. The leading role in the flame speed increase when using the MgO particles belongs to the explosive boiling of liquid phase of the foam. However this process cannot be directly observed using the high-speed filming due to the opacity of the foam. Nevertheless the sensitivity of the total burning rate towards the change in concentration of nucleation centers in liquid phase of the foam by itself attests the hypothesis of explosive boiling role in flame acceleration. As a result it can be concluded that the use of magnesium oxide particles favors the increase in flame speed and the stabilization of the foam at least in the considered range of particles fraction.

3.5. Combustion of the Isooctane-Based Foam. In the previous section one of the limiting case of foam combustion in the quenching/re-ignition regime with bp ≫ bc90 is analyzed on the example of the foam containing heptane as a fuel. The example of the foam for which a reverse limit case of “quenching/re-ignition” regime is realized with bp ≪ bc90 is the foam on the base of isooctane. In this case the ignition delay significantly increases (Figure 11). This is due to the less reactivity of isooctane compare with heptane.43,44 In this regime a short stage of flame propagation gives way to the long period of flame quenching after which re-ignition of the combustible mixture takes place.


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Figure 11. Plot of the flame speed vs. time in a tube (B Fig. 2b); foam is prepared from isooctane (1 mL), water (2 mL), detergent (1 mL), hydrogen peroxide (1 mL), and ammonia solution of copper sulfate (0.8 mL, 1.05 mol/L); foam expansion ratio, 9.4; total burning rate, 0.8 m/s.

3.6. Influence of Tube Diameter and Fuel Concentration. This section of the paper analyzes the influence of tube diameter and fuel concentration on the conditions of realization of “quenching/re-ignition” regime of foam combustion. The necessary condition for this regime to be established is the reaching of quenching conditions. The use of narrower tubes as well as leaner foams promotes flame quenching, therefore it is reasonable to expect that the probability of quenching/re-ignition regime should increase for narrower tubes and leaner mixtures. Figure 12 represents data on flame evolution depending on tube diameter and fuel content in the foamed emulsion. One can observe the transition to reverse propagation of the flame front with the decrease in tube diameter (compare Figures 12a and 12b). At that in case of lean foam the reverse flame propagation is observed in both narrow and wide tubes (Figures 12c and 12d). Reverse flame propagation (or flame propagation in the reverse direction) indicates flame quenching. The analysis of experimental data allows concluding that with tube diameter decrease as well as with the use of leaner foam the transition from the oscillating combustion regime to the regime of quenching/re-ignition takes place. Figure 13 represents the total burning rate dependence on the o-xylene volume content for two tube diameters. For case of 10 mm tube the regime of quenching/re-ignition is realized in the whole range of foamed emulsion composition. It is interesting to note that in such a case the fuel content influences the total burning speed weakly.


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Figure 12. Plots of the flame speed and distance traveled vs. time in foamed emulsion burning in tubes of diameters (a), (c) D = 20 mm and (b), (d) D = 10 mm. Foam is prepared from (a), (b) o-xylene (1.5 mL) or (c), (d) o-xylene (0.5 mL), detergent (0.8 m L), water (2 mL), hydrogen peroxide (1 mL), and ammonia solution of copper sulfate (0.8 mL, 1.05 mol/L). Foam expansion ratio, (a), (b) 21.6; (c), (d) 27.4.


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Figure 13. Plots of the total burning rate vs. volume content of o-xylene in emulsion in tubes with diameters D = 10 and 20 mm. 4. CONCLUSION

This paper considers the issues related with combustion of foamed emulsion. At that the main attention is focused on foam combustion in the “quenching/re-ignition” regime. On the basis of obtained results the following conclusions can be formulated: •

Foamed emulsion is an example of combustible system which can be used to burn water-saturated oils.

•

When propagating in the foam the flame can evolve in a “quenching/re-ignition” regime. The essence of this combustion regime is the following. In the process of flame acceleration its speed increases up to critical value corresponding to the flame quenching. The existence of such a limit is determined by incomplete evaporation of fuel drops in the convective-diffusion zone of flame. Non-evaporated fuel drops are evaporated in the region of combustion products and a secondary initiation of the combustion wave becomes possible at realization of certain conditions of self-ignition.

•

⁄

O ) and The use of magnesium oxide particles favors increase in total burning rate of the foam (-. ~yz{

stabilization of the foamed emulsion. The basic mechanism determining the flame acceleration in the foam is the explosive boiling of liquid phase of the foam. Magnesium oxide particles represent centers of nucleation of vapor bubbles in superheated liquid. The use of particles leads to finer fragmentation of the fuel drops at the foam decay. •

Reduce in the tube diameter and the use of leaner foam favor the realization of “quenching/re-ignition” regime.

∎ ACKNOWLEDGMENTS This work was funded by the Russian Science Foundation (Project Number 14-50-00124). ∎ AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. ∎ NOMENCLATURE


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= coefficient (K) = bridging coefficient (N2/m2) P = transfer number l = heat capacity of fuel vapor (J/(kg K)) = heat capacity of gas-drop mixture (J/(kg K)) /0 = diameter of fuel drops (m) /0̅ = maximal diameter of fuel drops evaporated in the convective-diffusion zone of flame (m) ) = diameter of tube (m) /123 = maximal diameter of fuel drops (m) / = diameter of water drops (m) = entry coefficient (N/m) 2 = effective activation energy (J/(kg K)) v = characteristic distance of reacting mixture ejecting (m) yz{ = number density of magnesium oxide particles in the emulsion (1/m3) Y = chemical energy release (J/kg) = universal gas constant (J/(kg K)) -. = total burning rate (m/s) -4. = maximum total burning rate of foam corresponding to complete evaporation of fuel drops (m/s) -.̅ = limit value of flame speed corresponding to flame quenching (m/s) W= temperature (K)

W. = difference between temperature of the flame front and initial foam temperature (K) W.∗ = difference between temperature of the flame front and initial foam temperature at flame quenching (K) HI = total volume of evaporated fuel drops per unit volume HN = total volume of fuel drops per unit volume o = velocity of the drop (m/s) X = fuel concentration in the vapor flame front


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XN = fuel concentration in the vapor flame front assuming evaporation of all the fuel drops = thermal conductivity coefficient of the gas (W/(m K)) P = effective

viscosity of the foam (Pa s)

k8 = liquid fuel density (kg/m3) k = water density (kg/m3) = surface tension of the oil phase (N/m) = oil/water interfacial tension (N/m) = surface tension of the aqueous phase (N/m) bp = time of reacting mixture ejection (s) bc90 = characteristic induction time (s) = thermal diffusivity of gas (m2/s)

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Reignition Regime

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