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burning slurry drops by additives
dcta Astronautica Vol. 15, No. 5, pp. 253-258, 1987 Printed in Great Britain. All rights reserved
0094-5767/87 $3.00+0.00 © 1987 Pergamon Journals Lid
BREAKUP OF E V A P O R A T I N G / B U R N I N G SLURRY DROPS BY ADDITIVES P. RoY CHOUDHURY and M. GERSTEIN Mechanical Engineering Department, University of Southern California, Los Angeles, CA 90089-1453, U.S.A. (Received 12 June 1986; revised version received 26 January 1987)
A~traet--Single drops of silicon carbide-cumene slurry were suspended from a quartz fiber and ignited. An inert material such as silicon carbide was chosen so that the droplets can be burned until all the fuel is consumed and only the inert residue is left on the quartz fiber. Benzoyl peroxide was added to cumene and the time to disruption of the liquid drop was measured. In the case of benzoyl peroxide, the breaking up of the drop resulting from its thermal decomposition produced CO 2. Both the drop disruption time and the burning of the slurry to dryness were predicted theoretically. Radiation absorption was found to be an important factor in the case of the slurry. Benzoyl peroxide and carbamide peroxide were investigated as additives to a boron slurry to determine if effective drop break-up could be achieved. Both additives produced drop shattering. The carbamide peroxide was particularly effective due to the production of 02. The green flame associated with boron burning was clearly evident.
i. INTRODUCTION
The evaporation and/or burning rate of a liquid fuel is a function of drop size and other parameters of the flow. It is desirable to produce sprays containing relatively small drops for rapid evaporation and burning. However, it is not always possible to accomplish this especially for viscous liquids and slurries. Fuel slurries usually consist of a large number of micron or sub-micron high energy solid particles suspended in a liquid carrier. Unfortunately, as the liquid carrier evaporates, the solid particles are forced closer together as the solid loading increases and usually agglomeration of the small particles into one or more large particles results. If the fuel or additives decompose to high molecular weight residues as the burning proceeds, these residues may further bind the particles into a large difficult to burn agglomerate. The occurrence of liquid phase decomposition to produce non-volatile, slow burning residues has been reported by the authors in previous works[l, 2]. In order to enhance the combustion of the solid phase it would be desirable to break up the agglomerate early in the history of the slurry drop evaporation or to prevent its formation completely by time controlled shattering of the drop. Even for the case of nonslurry liquid fuels it is desirable to fragment larger droplets into smaller ones so that as a result of early droplet evaporation a more homogeneous combustible mixture can be produced. Three general methods of drop shattering have been reported in the literature. They are (a) Pulsed irradiation of slurry droplets at discrete frequencies; (b) Internal evaporation in a multicomponent fuel; and (c) Controlled evaporation/explosion of a stable additive in the fuel. Reference[3] describes a novel method of slurry ^.^. ~/s--B
droplet breakup by short duration (ns) infrared pulses. The liquid is transparent while the solid particles completely absorb the radiant energy in the selected frequency range and cause the droplet to shatter due to intense local boiling. Both boron and carbon slurries were studied in[3]. Disruptive burning of multicomponent and emulsified fuel droplets has been reported in[4]. The authors have observed the growth of vapor bubble of the more volatile component of the fuel. The final bursting of the bubble was deemed responsible for the fragmentation of a multicomponent droplet. Similarly, for a water/fuel emulsion superheating of the water vapor was assumed to cause droplet fragmentation. Thus, the authors suggest the use of water fuel emulsion or multicomponent fuels as a possible method of droplet breakup. Controlled explosion of additives in liquid sprays have been studied both analytically[5] and experimentally[6]. Among the materials investigated theoretically in[5] were azides which rapidly (explosively) release nitrogen when heated to a critical reaction temperature. These materials are stable when stored as liquid solutions at ambient temperature. Experimentally determined evaporation constants for selected burning azides have been reported in[6]. While[5] deals with azides,[7] has shown that certain peroxides are more advantageous especially when they release oxygen during their decomposition. It considers commercially available benzoyl and carbamide peroxides as additives in both the slurry and pure fuels. Benzoyl peroxide produces CO2 during decomposition whereas 02 is released during the decomposition of carbamide peroxide. Therefore, carbamide peroxide is preferable as an ignition promotor. 253
254
P. RoY CHOUDHURYand M. GERSTElN
The present work extends the analysis ot~7] to include slurry fuels. Additional experiments are reported which validate the analytical model and show the feasibility of using additives for fragmenting droplets of both the slurry and pure fuels. 2. ANALYTICALMODEL Solid particles in a slurry can absorb thermal radiation both from the flame and the walls of the combustor thereby experiencing a more rapid temperature rise than the liquid. Liquid hydrocarbons, on the other hand, are nearly transparent to the thermal radiation from the above sources. A boron slurry, for example, absorbs thermal radiation nearly as a black body over a large bandwidth. On the other hand, cetane, the liquid part of the slurry, transmits practically all the incident energy within that range of wavelengths except over two narrow bandwidths. Although cetane can absorb energy within these bandwidths (3.4-3.5 and 6.8-6.9 microns) the total energy radiated from the sources of interest within those bandwidths are very small. Cumene (isopropyl benzene), the fuel studied in this paper as an example, is also capable of absorbing energies over a number of bandwidths (e.g. 3.2-3.5, 6.7-7, 9.2 9.8 microns etc.,[8]. The total incident energy within 3.2 and 3.5 microns is small and it is insignificant within the other bandwidths. Thus, cumene can be considered as being transparent to thermal radiation from the flame and the walls of the combustor. A cumene based slurry, however, behaves as a black body and absorbs thermal energy. Since the particle loading in a typical slurry is rather high (60-80%) an exact analysis of the heating process in an absorbing, scattering and reflecting medium becomes rather complicated. A simplified analytical model of a slurry fuel droplet undergoing simultaneous heat and mass transfer in a one dimensional flowing medium has been developed here. Only a fraction of the particles near the surface of the slurry fuel droplet absorbs thermal radiation and gets heated up. This group, in turn, heats the liquid fuel and the other solid particles (which are not exposed to radiation) by convection. Thus, the slurry fuel is allowed to have two distinct temperatures, one for the irradiated solid particles and the other for the liquid and the remainder of the particles which do not receive any radiation. The number of solid particles receiving radiation is assumed to correspond to the ratio of the surface area of the droplet and the surface area of individual solid particles. As the heating process progresses the liquid reaches its boiling point and remains at that temperature while the temperature of the particles are allowed to increase. Assuming a spherically symmetric, one dimensional flowing system with constant ambient properties the following equations describe the physical model:t ?Nomenclature is given in Appendix at end of paper.
Particle energy dTp Ap 4 m s c s ~ - =¢rE-~(Ta-- T 4 ) - - h p A p ( T p - T,)
(1)
Liquid energy dT~ m~ cl ~ = hcAs(Ta - Tl) + N, hpAp(Tp - T~) + rhhfs (2) where rh = - h
m
At Xv for maximum evaporation rate
Droplet momentum du Pf (u_ - u)ZA m - ~ = C D-~
(3)
Diameter reduction rate dD dt
2rh zcpl D 2
(4)
=
(5)
Droplet location dx dt
--
u
These five equations have five unknowns, Tp, T I , u, D and x. With the following initial conditions these are solved by a fourth order Runge-Kutta method Tp(0) = T0, T~(0) = T0, u(0) = 0, D(0) = D0 and
x(0)=0
(6)
Equation (1) describes the heating process of a single particle which receives heat by radiation on 1 of its surface area and transfers heat to the liquid by convection. The liquid in the slurry is heated both by convection from the irradiated particles and by ambient gas. A part of the incident energy on the droplet increases its internal energy and the remainder is utilized for evaporating the liquid [eqn. (2)]. Both the heat and mass transfer coefficients are evaluated using the Ranz-Marshall correlation equation. Flow properties of the mixture such as the Reynolds number, Prandtl number etc. are evaluated at the film temperature using the one-third rule. The value of Co is a function of Re and three different correlation equations spanning the range of Re from less than 0.01 to 1500 have been used[9]. In view of the many simplifying assumptions in the analytical model, correction factors for the mass and heat transfer similar to those suggested in[10] were not used. In fact, the maximum possible mass evaporation rate is chosen for obtaining a more conservative estimate of the temperature rise and hence the onset of rapid decomposition of the additive. Transport properties of pure hydrocarbon vapors were obtained from[l l] and the transport properties of binary mixtures (assumed to consist of N 2 and hydrocarbon vapor) were calculated using the method ot"[121 outlined in[13].
Breakup of evaporating/burning slurry drops by additives 3. EXPERIMENTAL
In the present work, single drops of liquid and slurry fuel were suspended on a quartz fiber and burned. The drops were ignited by a flame and the burning process was observed by means of T.V. photography. A continuous time record to 1/100 s was also recorded on the T.V. tape. Figure 117] shows the comparison of the predicted time to disruption of a solution of 9.5% benzoyl peroxide in cumene (approximately a saturated solution) with earlier experimental data. Except for the correction factors of[10] and stagnant condition of a single phase fuel the analytical model of[7] is identical to that of this paper. In the case of fuels containing a gas producing additive, the time to drop disruption was measured as a function of initial drop size. In the case of evaporation to dryness of an inert solid (silicon carbide) in a flammable liquid (cumene) the time to dryness was measured as a function of initial drop size corrected for the size of the fiber. Spherical symmetry was assumed and a diameter was obtained by measuring a horizontal and vertical diameters and using the average. The mean diameter of the silicon carbide particles was approximately 8 micron. Typical photographs of drop disruption are shown in Fig. 2. Figure 2a shows the effect of adding a solution of carbamide peroxide and glycerine to a sample of boron slurry consisting of 33%JP10,2% stabilizer and 1 micron diameter boron particles. The mass loading of boron in the 2.5 mm droplet was 65%. Shortly after ignition the slurry droplet is shown to undergo an explosive disruption. The streaks in the picture represent condensing glycerine which has been ejected from the drop. The green flame associated with burning boron particles is clearly visible as green streaks in the color photographs. Their location is shown by an arrow in the black and white photograph of Fig. 2a. Figure 2b shows the violent disruption process at the onset of rapid decomposition of the additive in a 2.5 mm cumene droplet with 9.5% benzoyl peroxide. These
255
sample pictures clearly demonstrate the effectiveness of both of these peroxides in fragmenting droplets. Results of Fig. l have shown that for small times before any appreciable reaction can take place the analytical model of[7] predicts the correct trend. In order to validate the present analytical model of a slurry fuel for larger times, droplets of silicon carbide-cumene slurry were suspended from a quartz fiber and burned. The average size of silicon carbide particles was 8 micron and the mass loading for most of the experiments was 53%. With the addition of benzoyl peroxide to the slurry the decomposition temperature of 353 K is reached very quickly, much sooner than in the case of pure cumene. 4. RESULTS AND DISCUSSION
For the stagnant case corresponding to the laboratory experiments, eqns (1), (2) and (4) are solved simultaneously with applicable initial conditions of eqn (6). The ambient temperature Ta was assumed to be the adiabatic flame temperature of a stoichiometric mixture of cumene and air with only CO2/CO dissociation. As the droplet heats up the adiabatic flame temperature also increases and its new value is computed for every time step. Both the heat and mass transfer coefficients were calculated using the limiting value of 2 for the Nusselt numbers, which are valid only for spherically symmetric cases. Unfortunately, the flame envelopes of suspended droplets are not spherically symmetric and this will tend to increase the value of the Nusselt numbers. Also the actual ambient temperature will be somewhat lower than the calculated adiabatic flame temperature. These two opposing effects are assumed to reduce the overall error. In order to study theoretically the effect of additives such as benzoyl peroxide on a slurry fuel a fuel blend consisting of cumene and boron particles is considered as an example. The boron slurry has a mass loading of 65% and the solid particles are assumed to have a uniform diameter of 1 micron. Single slurry droplets with diameters from 50 to 200 microns are allowed to evaporate in 61 m/s high temperature (1 l l 0 and 833 K) air stream at 1 atm T o . 2 9 8 K Tcri,'353K (80=C} pressure. The droplets are assumned to have a zero initial velocity and an initial standard temperature of A 4 • 9.5% Benzoyt peroxide / E 298 K. E / • 4.75% Benzoyt peroxide The results of the experiments with silicon carbidecumene slurry droplets suspended from quartz fibers 5 are shown in Fig. 3. Predicted times for a range of -62 bead diameters of the quartz fibers along with the "E experimental data are shown. The scatter of the ( Ref. [71 } experimental data is partly due to the difficulty of measuring the diameters accurately from the CRT, In spite of the scatter, the agreement with theoretical 0 I J i I I I I iJ I I I I I I I I prediction is good and on the whole the experiments 0.1 I 10 validate the analytical model for both small[7] and Time to disruption {s) Fig. 1. Droplet shattering by decomposing additive. Fuel: large times. Cumene; Additive: Benzoyl Peroxide. Stagnant case.[7] Figure 4 shows the predicted time to disruption
256
P. RoY CHOUDI-IURY and M. GERSTEIN
Fig. 2a. Droplet disruption of a boron slurry containing carbamide peroxide additive.
Fig. 2b. Drop disruption of a Cumene-benzoyl peroxide mixture.
6: 5
Bead size,mm [] 1.9 2.0
250
A
Cumene
o 2.13
d b : 2,3 mm \ ,,
x 2.25 • 1.8to 2.3
//-"
/
\db=O
~3
.o
0 .I ¢::
BORON c u m e n e
-ol
//
i2®.
~/I/
E 4
- - -
~
833K ,<°rr~ ,,~/,~,;\ ,~j,, ,"
ooK 2
-~ ~
0
~
d
b
=l.8mm,
3//,i/
,-'.///
no radiation
db -1.8rn~/"
/"
=
orate oft Liquid in the sl.urry
J O j
0.1 i III
0.5
t
1
t
I
I
5
I I I11
10
I
I
I
50
Time to consume all. fuet (s)
Fig. 3. Comparison of theory and experiments. Cumenesilicon carbide slurry, 53% mass loading, 8 micron particles.
I
I
I
L
I
I I IJ
I
1
I
I
I
1 I
I I
10
Time to disruption ( m s )
Fig. 4. Predicted time to disruption with benzoyl peroxide of cumene and boron-cumene slurry. 1 micron boron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm, air stream.
Breakup of evaporating/burning slurry drops by additives
257
1.5
~-.~Bomn porlictea .-~ Boron porticLes r ~-/Liquid 1.4k //'- -- - / " - - " ~ /" "--(--- f ~ ' B o i t i n g 159micront / / / temperature of
I
LfLiq uid
/'-Cure.,. /
/
/
|, /
/
1.2k/ / / / / F-T-----7--7"TRopid
I,/
//.,,,"
t.I [--
/
/
/0umen.
O.6
{~o 0.4
d.c..sit.
,era.rotor,
/
0.2
\ 1 5 0 micron slurry,
0.0
0.1
1 Time offer injection (ms)
10
Fig. 5. Liquid and particle temperature histories of cumene and boron-cumene slurry, l micron boron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm. air stream.
I
25O 853 K -----
~rTn;turry
//
/ / /
/" / /
.~ 45O
833 K /
/./
/
.E t 0 0 "o
5O o
O01
..l J/I
I
1" ~ I Illlll
I (~1
"~//~ap°0nre~l:°Lt Liquid in the stuffy 11 =lllll I I I Ill== 1 10
Distance to disruption (cm)
Fig. 6. Distance to disruption with benzoyl peroxide as an additive. 1 micron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm. air stream.
I
I
I I IILI
0.1
\
150
I
I
I
I I I II
I Time ( ms )
10
Fig. 7. Diameter histories of cumene and boron-cumene slurry. 1 micron boron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm. air stream. 1.O,
when benzoyl perixide is expected to undergo a fast decomposition process and thereby shatter the droplets. Calculations show that the times to disruption are much smaller in a slurry fuel compared to those in a pure fuel and are considerably smaller than the total evaporation times. Also the importance of radiant heat transfer in slurry fuels is shown in the figure. The temperature time histories of both the slurry and pure fuels shown in Fig. 5 explain the reason for the smaller times to disruption. Because of the presence of particles the liquid temperature in a slurry increases at a faster rate than the liquid temperature of a pure fuel undergoing evaporation process in a given environment. Therefore, the decomposition temperature of benzoyl peroxide is reached sooner in a slurry. A case without radiation shows that the temperature rise is considerably smaller when radiation is ignored. Figure 6 compares the distance to disruption from the injection point for both the slurry and pure fuels. Since the decomposition temperature of benzoyl peroxide is rather low (353 K), the droplets shatter before any appreciable evaporation can take place. Typically this point is reached near D/Do of 0.99. Diameter histories of selected droplets of boron-cumene and pure cumene without the additive are shown in Fig. 7. It also shows the points where all the liquid in the slurry
,~_ 200 E
Cumene ~ Boron slurry \ Point of ¢omptete \ eva .po.ratlon. no additive ,50
---n
e,o Rapid decomposition of benzoyt peroxide
0.8
=--tureen. 0 6 J. . . .
:~
/ 50 micron
[] co,,pL.t, avo~-=ion of / Iqula m me slurry /
/
/
t0o
/
/
15o
/
Boron slurry
O.4
~o
~...--
0,0
I
0.1
~ I
-
I
e.t
I I I I li
I
1 Time ( ms )
I
I
I I I II
10
Fig. 8. Velocity histories of cumene and boron-cumene slurry. 1 micron boron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm. air stream.
evaporates completely leaving only the solid residue. Since benzoyl peroxide tends to decompose soon after injection, the droplets are not accelerated to any significant velocity before they are shattered (Fig. 8). This is particularly true for the slurry fuel. Results of this study and[7] show that the technique of drop shattering by means of additives which can decompose rapidly is rather attractive particularly when 0 2 is evolved during decomposition, Therefore, carbamide peroxide, in many fuels is a better additive than either benzoyl peroxide or the azides[5, 6]. There are many other additives which can be used for the purpose of droplet shattering. Perhaps some are better than either benzoyl peroxide or carbamide peroxide. Selection of an optimum additive is beyond the scope of this paper which deals only with the feasibility of drop shattering by means of additives. 5. CONCLUDING REMARKS
It is shown that the use of gas generating additives which decompose at a temperature below the boiling temperature of the liquid drop enhances atomization
258
P. Roy CHouDnuav and M. GERSTEIN
( d r o p d i s r u p t i o n s ) a n d burning. T h e s e additives are p a r t i c u l a r l y effective w h e n i n c o r p o r a t e d into slurry fuels. A well-stirred m o d e l was d e v e l o p e d to p r e d i c t the time to d r o p d i s r u p t i o n a n d to liquid e v a p o r a t i o n o f a slurry. B o t h p r e d i c t i o n s agreed well with the experim e n t a l data. R a d i a t i o n was f o u n d to be i m p o r t a n t in the b u r n i n g o f the liquid in slurry fuels. O x y g e n releasing additives such as c a r b a m i d e peroxide are f o u n d to be effective in p r o m o t i n g the c o m b u s t i o n o f b o r o n slurry d r o p s . APPENDIX
A
Nomenclature cross sectional area of a droplet surface area of a solid particle in the slurry surface area o f a droplet drag coefficient, f ( R e ) specific heat of liquid specific heat of the solid material in the slurry droplet diameter initial diameter of the droplet bead diameter on quartz fiber particle diameter, 1 micron for boron slurry heat transfer coefficient between the droplet and the environment h,, = mass transfer coefficient hp = heat transfer coefficient between the particles and the liquid h:g = enthalpy of evaporation m = total droplet mass, m I + (Nlt/6)d3ops • " -3 3 ml mass of hquld = (rcpl/6) (D-~ - Ndp - db) m o = initial mass fraction of solid material m~ = mass of a solid particle N = t o t a l number of particles mopl(D]-d3)/(1-mo+ mop,/p~)pfl3 N, = number of particles exposed to radiation P = mixture pressure, I atm p v = v a p o r pressure of liquid p v / P = e x p ( l l . 8 1 2 5024.87/Ti ) Re = Reynolds number based upon drop diameter and the relative velocity. Ta = ambient temperature T:= film temperature T 1+ (T:T~)/3 by the 1/3 rule To = standard temperature, 298 K T~ = temperature of liquid Tp = temperature of solid particles t = time u = droplet velocity ug = gas velocity x = droplet location Xv = concentration of fuel vapor at the surface, calculated by using Clapeyron equation and ideal gas relationship.
A = Ap = As = Co = ct = cs = D = Do = db = dp= h C=
Greek symbols E= p: = p~ = p, = a =
emissivity, assumed to be unity gas density at the film temperature density of liquid density of solid material Stefan Boltzmann constant
REFERENCES
1. P. R. Choudhury and M. Gerstein, The effect of liquid phase decomposition on the fuel droplet distribution function. AIAA J. 23, 271 275 (1985). Also AIAA paper no. 83-0069, 21st Aerospace Sciences Meeting, Reno, Jan. 10-13, 1983. 2. P. R. Choudhury and M. Gerstein, Liquid phase decomposition: a possible problem with fuels in high pressure systems. Proceedings o f the 1980Heat Transfer and Fluid Mechanics Institute Meeting, Stanford University Press, pp. 7%91, June (1980). 3. P. R. Choudhury, M. Gerstein et al., Slurry fuel droplet breakup by irradiation at discrete frequencies. AIAA paper no. 83-1142, A I A A / S A E / A S M E 19th Joint Propulsion Meeting, Seattle, June 2 ~ 2 9 (1983). 4. Loop T. Yap, I. M. Kennedy and F. L. Dryer, Disruptive and micro-explosive combustion of free droplets in highly convective environments. Combustion Sci. Technol. 41, 291 313 (1984). 5. M. Gerstein and P. R. Choudhury, Timed ignition of explosives and flammables from desensitized solutions. Dynamics of Flames and Reactive S.vstems, AIAA Progress in Aeronautics and Astronautics, Vol. 95, pp. 455-463 (1984). Also 9th International Coll. on the Dynamics o f Explosions and Reactive Systems, Poitiers, France, July 1983. 9. C. K. Law, Organic azides as jet fuel additives: combustion and micro-explosion characteristics. O N R /NA VAIR Compact Ramjet Combustion Instabilities, Monterey, Calif., October 24-25 (1984). 7. M. Gerstein and P. R. Choudhury, The use of additives to promote the atomization and combustion of slurry fuels. 22nd J A N N A F Combustion Meeting, Pasadena, Calif., October 7-10 (1985). To appear in a CPIA Publication. 8. Sadtler Standard Spectra. Midget Edition Sadtler Research Laboratories, Philadelphia (1980). 9. R. Cliff, J. R. Grace and M. E. Weber, Bubbles, Drops and Particles, p. 112, Academic Press, New York (1978). 10. R. B• Bird et al., Transport Phenomena. Wiley (1960)• 1 I. G. Beal, The Science o f Petroleum, Vol. II. Oxford University Press (1938). 12• C. R. Wilke, A viscosity equation for gas mixtures. J. Chem. Phys. 18, 517-519 (1950). 13. W. Rosenow and H. Y. Choi, Heat, Mass and Momentum Transfer, p• 498, Prentice-Hall, Inc., New York (1961).
0094-5767/87 $3.00+0.00 © 1987 Pergamon Journals Lid
BREAKUP OF E V A P O R A T I N G / B U R N I N G SLURRY DROPS BY ADDITIVES P. RoY CHOUDHURY and M. GERSTEIN Mechanical Engineering Department, University of Southern California, Los Angeles, CA 90089-1453, U.S.A. (Received 12 June 1986; revised version received 26 January 1987)
A~traet--Single drops of silicon carbide-cumene slurry were suspended from a quartz fiber and ignited. An inert material such as silicon carbide was chosen so that the droplets can be burned until all the fuel is consumed and only the inert residue is left on the quartz fiber. Benzoyl peroxide was added to cumene and the time to disruption of the liquid drop was measured. In the case of benzoyl peroxide, the breaking up of the drop resulting from its thermal decomposition produced CO 2. Both the drop disruption time and the burning of the slurry to dryness were predicted theoretically. Radiation absorption was found to be an important factor in the case of the slurry. Benzoyl peroxide and carbamide peroxide were investigated as additives to a boron slurry to determine if effective drop break-up could be achieved. Both additives produced drop shattering. The carbamide peroxide was particularly effective due to the production of 02. The green flame associated with boron burning was clearly evident.
i. INTRODUCTION
The evaporation and/or burning rate of a liquid fuel is a function of drop size and other parameters of the flow. It is desirable to produce sprays containing relatively small drops for rapid evaporation and burning. However, it is not always possible to accomplish this especially for viscous liquids and slurries. Fuel slurries usually consist of a large number of micron or sub-micron high energy solid particles suspended in a liquid carrier. Unfortunately, as the liquid carrier evaporates, the solid particles are forced closer together as the solid loading increases and usually agglomeration of the small particles into one or more large particles results. If the fuel or additives decompose to high molecular weight residues as the burning proceeds, these residues may further bind the particles into a large difficult to burn agglomerate. The occurrence of liquid phase decomposition to produce non-volatile, slow burning residues has been reported by the authors in previous works[l, 2]. In order to enhance the combustion of the solid phase it would be desirable to break up the agglomerate early in the history of the slurry drop evaporation or to prevent its formation completely by time controlled shattering of the drop. Even for the case of nonslurry liquid fuels it is desirable to fragment larger droplets into smaller ones so that as a result of early droplet evaporation a more homogeneous combustible mixture can be produced. Three general methods of drop shattering have been reported in the literature. They are (a) Pulsed irradiation of slurry droplets at discrete frequencies; (b) Internal evaporation in a multicomponent fuel; and (c) Controlled evaporation/explosion of a stable additive in the fuel. Reference[3] describes a novel method of slurry ^.^. ~/s--B
droplet breakup by short duration (ns) infrared pulses. The liquid is transparent while the solid particles completely absorb the radiant energy in the selected frequency range and cause the droplet to shatter due to intense local boiling. Both boron and carbon slurries were studied in[3]. Disruptive burning of multicomponent and emulsified fuel droplets has been reported in[4]. The authors have observed the growth of vapor bubble of the more volatile component of the fuel. The final bursting of the bubble was deemed responsible for the fragmentation of a multicomponent droplet. Similarly, for a water/fuel emulsion superheating of the water vapor was assumed to cause droplet fragmentation. Thus, the authors suggest the use of water fuel emulsion or multicomponent fuels as a possible method of droplet breakup. Controlled explosion of additives in liquid sprays have been studied both analytically[5] and experimentally[6]. Among the materials investigated theoretically in[5] were azides which rapidly (explosively) release nitrogen when heated to a critical reaction temperature. These materials are stable when stored as liquid solutions at ambient temperature. Experimentally determined evaporation constants for selected burning azides have been reported in[6]. While[5] deals with azides,[7] has shown that certain peroxides are more advantageous especially when they release oxygen during their decomposition. It considers commercially available benzoyl and carbamide peroxides as additives in both the slurry and pure fuels. Benzoyl peroxide produces CO2 during decomposition whereas 02 is released during the decomposition of carbamide peroxide. Therefore, carbamide peroxide is preferable as an ignition promotor. 253
254
P. RoY CHOUDHURYand M. GERSTElN
The present work extends the analysis ot~7] to include slurry fuels. Additional experiments are reported which validate the analytical model and show the feasibility of using additives for fragmenting droplets of both the slurry and pure fuels. 2. ANALYTICALMODEL Solid particles in a slurry can absorb thermal radiation both from the flame and the walls of the combustor thereby experiencing a more rapid temperature rise than the liquid. Liquid hydrocarbons, on the other hand, are nearly transparent to the thermal radiation from the above sources. A boron slurry, for example, absorbs thermal radiation nearly as a black body over a large bandwidth. On the other hand, cetane, the liquid part of the slurry, transmits practically all the incident energy within that range of wavelengths except over two narrow bandwidths. Although cetane can absorb energy within these bandwidths (3.4-3.5 and 6.8-6.9 microns) the total energy radiated from the sources of interest within those bandwidths are very small. Cumene (isopropyl benzene), the fuel studied in this paper as an example, is also capable of absorbing energies over a number of bandwidths (e.g. 3.2-3.5, 6.7-7, 9.2 9.8 microns etc.,[8]. The total incident energy within 3.2 and 3.5 microns is small and it is insignificant within the other bandwidths. Thus, cumene can be considered as being transparent to thermal radiation from the flame and the walls of the combustor. A cumene based slurry, however, behaves as a black body and absorbs thermal energy. Since the particle loading in a typical slurry is rather high (60-80%) an exact analysis of the heating process in an absorbing, scattering and reflecting medium becomes rather complicated. A simplified analytical model of a slurry fuel droplet undergoing simultaneous heat and mass transfer in a one dimensional flowing medium has been developed here. Only a fraction of the particles near the surface of the slurry fuel droplet absorbs thermal radiation and gets heated up. This group, in turn, heats the liquid fuel and the other solid particles (which are not exposed to radiation) by convection. Thus, the slurry fuel is allowed to have two distinct temperatures, one for the irradiated solid particles and the other for the liquid and the remainder of the particles which do not receive any radiation. The number of solid particles receiving radiation is assumed to correspond to the ratio of the surface area of the droplet and the surface area of individual solid particles. As the heating process progresses the liquid reaches its boiling point and remains at that temperature while the temperature of the particles are allowed to increase. Assuming a spherically symmetric, one dimensional flowing system with constant ambient properties the following equations describe the physical model:t ?Nomenclature is given in Appendix at end of paper.
Particle energy dTp Ap 4 m s c s ~ - =¢rE-~(Ta-- T 4 ) - - h p A p ( T p - T,)
(1)
Liquid energy dT~ m~ cl ~ = hcAs(Ta - Tl) + N, hpAp(Tp - T~) + rhhfs (2) where rh = - h
m
At Xv for maximum evaporation rate
Droplet momentum du Pf (u_ - u)ZA m - ~ = C D-~
(3)
Diameter reduction rate dD dt
2rh zcpl D 2
(4)
=
(5)
Droplet location dx dt
--
u
These five equations have five unknowns, Tp, T I , u, D and x. With the following initial conditions these are solved by a fourth order Runge-Kutta method Tp(0) = T0, T~(0) = T0, u(0) = 0, D(0) = D0 and
x(0)=0
(6)
Equation (1) describes the heating process of a single particle which receives heat by radiation on 1 of its surface area and transfers heat to the liquid by convection. The liquid in the slurry is heated both by convection from the irradiated particles and by ambient gas. A part of the incident energy on the droplet increases its internal energy and the remainder is utilized for evaporating the liquid [eqn. (2)]. Both the heat and mass transfer coefficients are evaluated using the Ranz-Marshall correlation equation. Flow properties of the mixture such as the Reynolds number, Prandtl number etc. are evaluated at the film temperature using the one-third rule. The value of Co is a function of Re and three different correlation equations spanning the range of Re from less than 0.01 to 1500 have been used[9]. In view of the many simplifying assumptions in the analytical model, correction factors for the mass and heat transfer similar to those suggested in[10] were not used. In fact, the maximum possible mass evaporation rate is chosen for obtaining a more conservative estimate of the temperature rise and hence the onset of rapid decomposition of the additive. Transport properties of pure hydrocarbon vapors were obtained from[l l] and the transport properties of binary mixtures (assumed to consist of N 2 and hydrocarbon vapor) were calculated using the method ot"[121 outlined in[13].
Breakup of evaporating/burning slurry drops by additives 3. EXPERIMENTAL
In the present work, single drops of liquid and slurry fuel were suspended on a quartz fiber and burned. The drops were ignited by a flame and the burning process was observed by means of T.V. photography. A continuous time record to 1/100 s was also recorded on the T.V. tape. Figure 117] shows the comparison of the predicted time to disruption of a solution of 9.5% benzoyl peroxide in cumene (approximately a saturated solution) with earlier experimental data. Except for the correction factors of[10] and stagnant condition of a single phase fuel the analytical model of[7] is identical to that of this paper. In the case of fuels containing a gas producing additive, the time to drop disruption was measured as a function of initial drop size. In the case of evaporation to dryness of an inert solid (silicon carbide) in a flammable liquid (cumene) the time to dryness was measured as a function of initial drop size corrected for the size of the fiber. Spherical symmetry was assumed and a diameter was obtained by measuring a horizontal and vertical diameters and using the average. The mean diameter of the silicon carbide particles was approximately 8 micron. Typical photographs of drop disruption are shown in Fig. 2. Figure 2a shows the effect of adding a solution of carbamide peroxide and glycerine to a sample of boron slurry consisting of 33%JP10,2% stabilizer and 1 micron diameter boron particles. The mass loading of boron in the 2.5 mm droplet was 65%. Shortly after ignition the slurry droplet is shown to undergo an explosive disruption. The streaks in the picture represent condensing glycerine which has been ejected from the drop. The green flame associated with burning boron particles is clearly visible as green streaks in the color photographs. Their location is shown by an arrow in the black and white photograph of Fig. 2a. Figure 2b shows the violent disruption process at the onset of rapid decomposition of the additive in a 2.5 mm cumene droplet with 9.5% benzoyl peroxide. These
255
sample pictures clearly demonstrate the effectiveness of both of these peroxides in fragmenting droplets. Results of Fig. l have shown that for small times before any appreciable reaction can take place the analytical model of[7] predicts the correct trend. In order to validate the present analytical model of a slurry fuel for larger times, droplets of silicon carbide-cumene slurry were suspended from a quartz fiber and burned. The average size of silicon carbide particles was 8 micron and the mass loading for most of the experiments was 53%. With the addition of benzoyl peroxide to the slurry the decomposition temperature of 353 K is reached very quickly, much sooner than in the case of pure cumene. 4. RESULTS AND DISCUSSION
For the stagnant case corresponding to the laboratory experiments, eqns (1), (2) and (4) are solved simultaneously with applicable initial conditions of eqn (6). The ambient temperature Ta was assumed to be the adiabatic flame temperature of a stoichiometric mixture of cumene and air with only CO2/CO dissociation. As the droplet heats up the adiabatic flame temperature also increases and its new value is computed for every time step. Both the heat and mass transfer coefficients were calculated using the limiting value of 2 for the Nusselt numbers, which are valid only for spherically symmetric cases. Unfortunately, the flame envelopes of suspended droplets are not spherically symmetric and this will tend to increase the value of the Nusselt numbers. Also the actual ambient temperature will be somewhat lower than the calculated adiabatic flame temperature. These two opposing effects are assumed to reduce the overall error. In order to study theoretically the effect of additives such as benzoyl peroxide on a slurry fuel a fuel blend consisting of cumene and boron particles is considered as an example. The boron slurry has a mass loading of 65% and the solid particles are assumed to have a uniform diameter of 1 micron. Single slurry droplets with diameters from 50 to 200 microns are allowed to evaporate in 61 m/s high temperature (1 l l 0 and 833 K) air stream at 1 atm T o . 2 9 8 K Tcri,'353K (80=C} pressure. The droplets are assumned to have a zero initial velocity and an initial standard temperature of A 4 • 9.5% Benzoyt peroxide / E 298 K. E / • 4.75% Benzoyt peroxide The results of the experiments with silicon carbidecumene slurry droplets suspended from quartz fibers 5 are shown in Fig. 3. Predicted times for a range of -62 bead diameters of the quartz fibers along with the "E experimental data are shown. The scatter of the ( Ref. [71 } experimental data is partly due to the difficulty of measuring the diameters accurately from the CRT, In spite of the scatter, the agreement with theoretical 0 I J i I I I I iJ I I I I I I I I prediction is good and on the whole the experiments 0.1 I 10 validate the analytical model for both small[7] and Time to disruption {s) Fig. 1. Droplet shattering by decomposing additive. Fuel: large times. Cumene; Additive: Benzoyl Peroxide. Stagnant case.[7] Figure 4 shows the predicted time to disruption
256
P. RoY CHOUDI-IURY and M. GERSTEIN
Fig. 2a. Droplet disruption of a boron slurry containing carbamide peroxide additive.
Fig. 2b. Drop disruption of a Cumene-benzoyl peroxide mixture.
6: 5
Bead size,mm [] 1.9 2.0
250
A
Cumene
o 2.13
d b : 2,3 mm \ ,,
x 2.25 • 1.8to 2.3
//-"
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-ol
//
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0.5
t
1
t
I
I
5
I I I11
10
I
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I
50
Time to consume all. fuet (s)
Fig. 3. Comparison of theory and experiments. Cumenesilicon carbide slurry, 53% mass loading, 8 micron particles.
I
I
I
L
I
I I IJ
I
1
I
I
I
1 I
I I
10
Time to disruption ( m s )
Fig. 4. Predicted time to disruption with benzoyl peroxide of cumene and boron-cumene slurry. 1 micron boron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm, air stream.
Breakup of evaporating/burning slurry drops by additives
257
1.5
~-.~Bomn porlictea .-~ Boron porticLes r ~-/Liquid 1.4k //'- -- - / " - - " ~ /" "--(--- f ~ ' B o i t i n g 159micront / / / temperature of
I
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/
/
|, /
/
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//.,,,"
t.I [--
/
/
/0umen.
O.6
{~o 0.4
d.c..sit.
,era.rotor,
/
0.2
\ 1 5 0 micron slurry,
0.0
0.1
1 Time offer injection (ms)
10
Fig. 5. Liquid and particle temperature histories of cumene and boron-cumene slurry, l micron boron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm. air stream.
I
25O 853 K -----
~rTn;turry
//
/ / /
/" / /
.~ 45O
833 K /
/./
/
.E t 0 0 "o
5O o
O01
..l J/I
I
1" ~ I Illlll
I (~1
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Distance to disruption (cm)
Fig. 6. Distance to disruption with benzoyl peroxide as an additive. 1 micron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm. air stream.
I
I
I I IILI
0.1
\
150
I
I
I
I I I II
I Time ( ms )
10
Fig. 7. Diameter histories of cumene and boron-cumene slurry. 1 micron boron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm. air stream. 1.O,
when benzoyl perixide is expected to undergo a fast decomposition process and thereby shatter the droplets. Calculations show that the times to disruption are much smaller in a slurry fuel compared to those in a pure fuel and are considerably smaller than the total evaporation times. Also the importance of radiant heat transfer in slurry fuels is shown in the figure. The temperature time histories of both the slurry and pure fuels shown in Fig. 5 explain the reason for the smaller times to disruption. Because of the presence of particles the liquid temperature in a slurry increases at a faster rate than the liquid temperature of a pure fuel undergoing evaporation process in a given environment. Therefore, the decomposition temperature of benzoyl peroxide is reached sooner in a slurry. A case without radiation shows that the temperature rise is considerably smaller when radiation is ignored. Figure 6 compares the distance to disruption from the injection point for both the slurry and pure fuels. Since the decomposition temperature of benzoyl peroxide is rather low (353 K), the droplets shatter before any appreciable evaporation can take place. Typically this point is reached near D/Do of 0.99. Diameter histories of selected droplets of boron-cumene and pure cumene without the additive are shown in Fig. 7. It also shows the points where all the liquid in the slurry
,~_ 200 E
Cumene ~ Boron slurry \ Point of ¢omptete \ eva .po.ratlon. no additive ,50
---n
e,o Rapid decomposition of benzoyt peroxide
0.8
=--tureen. 0 6 J. . . .
:~
/ 50 micron
[] co,,pL.t, avo~-=ion of / Iqula m me slurry /
/
/
t0o
/
/
15o
/
Boron slurry
O.4
~o
~...--
0,0
I
0.1
~ I
-
I
e.t
I I I I li
I
1 Time ( ms )
I
I
I I I II
10
Fig. 8. Velocity histories of cumene and boron-cumene slurry. 1 micron boron particles, 65% mass loading, 1110 K, 61 m/s, 1 atm. air stream.
evaporates completely leaving only the solid residue. Since benzoyl peroxide tends to decompose soon after injection, the droplets are not accelerated to any significant velocity before they are shattered (Fig. 8). This is particularly true for the slurry fuel. Results of this study and[7] show that the technique of drop shattering by means of additives which can decompose rapidly is rather attractive particularly when 0 2 is evolved during decomposition, Therefore, carbamide peroxide, in many fuels is a better additive than either benzoyl peroxide or the azides[5, 6]. There are many other additives which can be used for the purpose of droplet shattering. Perhaps some are better than either benzoyl peroxide or carbamide peroxide. Selection of an optimum additive is beyond the scope of this paper which deals only with the feasibility of drop shattering by means of additives. 5. CONCLUDING REMARKS
It is shown that the use of gas generating additives which decompose at a temperature below the boiling temperature of the liquid drop enhances atomization
258
P. Roy CHouDnuav and M. GERSTEIN
( d r o p d i s r u p t i o n s ) a n d burning. T h e s e additives are p a r t i c u l a r l y effective w h e n i n c o r p o r a t e d into slurry fuels. A well-stirred m o d e l was d e v e l o p e d to p r e d i c t the time to d r o p d i s r u p t i o n a n d to liquid e v a p o r a t i o n o f a slurry. B o t h p r e d i c t i o n s agreed well with the experim e n t a l data. R a d i a t i o n was f o u n d to be i m p o r t a n t in the b u r n i n g o f the liquid in slurry fuels. O x y g e n releasing additives such as c a r b a m i d e peroxide are f o u n d to be effective in p r o m o t i n g the c o m b u s t i o n o f b o r o n slurry d r o p s . APPENDIX
A
Nomenclature cross sectional area of a droplet surface area of a solid particle in the slurry surface area o f a droplet drag coefficient, f ( R e ) specific heat of liquid specific heat of the solid material in the slurry droplet diameter initial diameter of the droplet bead diameter on quartz fiber particle diameter, 1 micron for boron slurry heat transfer coefficient between the droplet and the environment h,, = mass transfer coefficient hp = heat transfer coefficient between the particles and the liquid h:g = enthalpy of evaporation m = total droplet mass, m I + (Nlt/6)d3ops • " -3 3 ml mass of hquld = (rcpl/6) (D-~ - Ndp - db) m o = initial mass fraction of solid material m~ = mass of a solid particle N = t o t a l number of particles mopl(D]-d3)/(1-mo+ mop,/p~)pfl3 N, = number of particles exposed to radiation P = mixture pressure, I atm p v = v a p o r pressure of liquid p v / P = e x p ( l l . 8 1 2 5024.87/Ti ) Re = Reynolds number based upon drop diameter and the relative velocity. Ta = ambient temperature T:= film temperature T 1+ (T:T~)/3 by the 1/3 rule To = standard temperature, 298 K T~ = temperature of liquid Tp = temperature of solid particles t = time u = droplet velocity ug = gas velocity x = droplet location Xv = concentration of fuel vapor at the surface, calculated by using Clapeyron equation and ideal gas relationship.
A = Ap = As = Co = ct = cs = D = Do = db = dp= h C=
Greek symbols E= p: = p~ = p, = a =
emissivity, assumed to be unity gas density at the film temperature density of liquid density of solid material Stefan Boltzmann constant
REFERENCES
1. P. R. Choudhury and M. Gerstein, The effect of liquid phase decomposition on the fuel droplet distribution function. AIAA J. 23, 271 275 (1985). Also AIAA paper no. 83-0069, 21st Aerospace Sciences Meeting, Reno, Jan. 10-13, 1983. 2. P. R. Choudhury and M. Gerstein, Liquid phase decomposition: a possible problem with fuels in high pressure systems. Proceedings o f the 1980Heat Transfer and Fluid Mechanics Institute Meeting, Stanford University Press, pp. 7%91, June (1980). 3. P. R. Choudhury, M. Gerstein et al., Slurry fuel droplet breakup by irradiation at discrete frequencies. AIAA paper no. 83-1142, A I A A / S A E / A S M E 19th Joint Propulsion Meeting, Seattle, June 2 ~ 2 9 (1983). 4. Loop T. Yap, I. M. Kennedy and F. L. Dryer, Disruptive and micro-explosive combustion of free droplets in highly convective environments. Combustion Sci. Technol. 41, 291 313 (1984). 5. M. Gerstein and P. R. Choudhury, Timed ignition of explosives and flammables from desensitized solutions. Dynamics of Flames and Reactive S.vstems, AIAA Progress in Aeronautics and Astronautics, Vol. 95, pp. 455-463 (1984). Also 9th International Coll. on the Dynamics o f Explosions and Reactive Systems, Poitiers, France, July 1983. 9. C. K. Law, Organic azides as jet fuel additives: combustion and micro-explosion characteristics. O N R /NA VAIR Compact Ramjet Combustion Instabilities, Monterey, Calif., October 24-25 (1984). 7. M. Gerstein and P. R. Choudhury, The use of additives to promote the atomization and combustion of slurry fuels. 22nd J A N N A F Combustion Meeting, Pasadena, Calif., October 7-10 (1985). To appear in a CPIA Publication. 8. Sadtler Standard Spectra. Midget Edition Sadtler Research Laboratories, Philadelphia (1980). 9. R. Cliff, J. R. Grace and M. E. Weber, Bubbles, Drops and Particles, p. 112, Academic Press, New York (1978). 10. R. B• Bird et al., Transport Phenomena. Wiley (1960)• 1 I. G. Beal, The Science o f Petroleum, Vol. II. Oxford University Press (1938). 12• C. R. Wilke, A viscosity equation for gas mixtures. J. Chem. Phys. 18, 517-519 (1950). 13. W. Rosenow and H. Y. Choi, Heat, Mass and Momentum Transfer, p• 498, Prentice-Hall, Inc., New York (1961).