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The influence of droplet evaporation on fuel-air mixing rate in a burner
T H E I N F L U E N C E O F D R O P L E T EVAPORATION ON F U E L - A I R MIXING RATE IN A B U R N E R K. KOMIYAMA
Komatsu Ltd., Tok~to, Japan R. C. FLAGAN
California Institute of Technology, Pasadena, California U.S.A. AND
j. B. HEYWOOD
Massachusetts Institute of Technology, Cambridge, Massachusetts U.S.A. 02139 The importance of droplet evaporation in the overall fuel-air mixing process in liquid fnel spray flames is examined with a series of experiments in a simple atmospheric pressure burner burning a range of hydrocarbon fuels. Two types of fuel atomizers were studied--airassist and pressure jet--which have substantially different operating characteristics. Fuel-air mixing rates were determined from time-average oxygen concentrations measured with overall burner operation stoichiometric. It is shown that with air-assist atomizers, the kinetic energy of the atomizer jet determines the mixing rate intensity for both liquid and gaseous fuels. Since the droplet evaporation time is much less than the mixing time, the details of the evaporation process are not important and the jet length scale and kinetic energy govern the mixing process. With pressure jet atomizers, the characteristic evaporation and mixing times are comparable. The evaporating fuel drops create fuel vapor concentration nonuniformities on a scale much smaller than the fuel jet scale. Mixing rate intensities comparable to those obtained with air-assist atomizers can, therefore, be achieved with much lower turbulent kinetic energy dissipation rates. With pressure jet atomizers, both the kinetic energy of the fuel jet and the evaporation characteristics of the fuel droplets control the initial fuel-air mixing rate. 1. Introduction In most practical liquid-fuel continuousflow combustion systems, the liquid fuel is injected directly into the p r i m a r y c o m b u s t i o n region. The injected l i q u i d shatters into droplets; the droplets move relative to and exchange m o m e n t u m with the combustion air and already burnt gases. T h e droplets heat up, vaporize and decelerate. Since the fuel and air enter the combustor separately, the fuel vapor and air must mix to w i t h i n c o m b u s t i b l e limits through a t u r b u l e n t mixing process before the fuel will burn. W h i l e fuel atomization, trajectories of fuel droplets and fuel vaporization all p l a y a part in this overall process, the role of the l i q u i d fuel droplets in the c o m b u s t i o n of distillate fuel oil sprays in 549
different types of burners is still a sul~ject of m u c h speculation. E v i d e n c e as to the influence of droplets on the detailed structure of a spray flame is a p p a r e n t l y contradictory. It has been suggested that under certain conditions droplets b u r n with i n d i v i d u a l envelope flames. A large n u m b e r of droplet b u r n i n g studies have been c o n d u c t e d with single droplets under well defined flow conditions. These have been useful in d e f i n i n g the d y n a m i c s of i n d i v i d u a l droplet processes, but the a p p l i c a t i o n of these results to spray flames is c o m p l i c a t e d b y the large n u m b e r of droplets a n d the t u r b u l e n c e and nonuniformities in the flow. Numerous studies have suggested that droplets of distillate fuel sprays do not b u r n with e n v e l o p i n g flames. For example, Chigier 1 has p r o v i d e d
550
SPRAY AND DROPLET COMBUSTION
photographic e v i d e n c e that flame envelopes do not exist around individual droplets in spray flames produced b y certain types of pressure jet and air blast atomizers in an u n c o n f i n e d environment. O n u m a and Ogasawara 2 have shown that the character of a confined spray flame from an air assist atomizer is very similar in structure to a comparable gaseous fuel flame. On the other hand, Mellor a has p r o v i d e d indirect evidence that, with a relatively ineffid e n t simplex pressure atomizer, droplets p l a y a role in the details of the combustion process. He was able to correlate gas turbine c o m b u s t o r nitric oxide emissions with a parameter w h i c h is proportional to the combustor residence time divided by the d r o p l e t evaporation time. These observations are not necessarily in conflict; the conditions in many of these spray flames are not closely comparable. However, the role of the droplets in fuel spray flames is still unclear. It is the goal of our study to examine the influence of droplet evaporation on the process b y w h i c h fuel and air mix and burn in a spray flame. The rate of m i x i n g of fuel and air was measured in a burner with two types of atomizers. It is shown that, in some cases, droplets do not play a significant role whereas droplets significantly alter the fuel-air mixing rate under other conditions. Evidence is p r o v i d e d for the hypothesis that, even where droplets are important, it is not necessary to assume the existence of d r o p l e t envelope flames to describe the influence of the evaporation process on the fuel-air m i x i n g rate. The work d e s c r i b e d here builds on previously reported work with turbulent jet flames using both l i q u i d and gaseous fuels. This
Gas Sampling Probe
previous work had shown that single phase turbulent mixing models 4 when coupled with suitable kinetic schemes can be used to predict the pollutant emissions of simple burners with air-assist atomizers with liquid and gaseous fuels. 5,6,7 With gaseous fuels, those characteristics of the atomizer w h i c h determine the rates of fuel-air m i x i n g have been identified, and simple sealing laws have been developed. 7 The question we now address is: Under what conditions do the presence of liquid fuel droplets in the flow influence the rate of fuel-air mixing in a steady flow combustor? 2. E x p e r i m e n t a l Set-Up Experiments were carried out in an atmospheric pressure burner. A schematic of the burner is shown in Figure 1. A cylindrical geometry with refractory lined walls to reduce heat losses was used to simplify the flow pattern. For these experiments the b u r n e r dimensions were 4 in internal diameter a n d 24 in. in length. C o m b u s t i o n air was s u p p l i e d through 45 ~ b l a d e angle swirl vanes at 1 atmosphere pressure a n d room temperature. L i q u i d fuel (kerosene except where otherwise noted) or propane was s u p p l i e d through a nozzle on the burner axis. Both air-assist and pressure type atomizers were studied; Figure 2 shows cross-sectional d r a w i n g s on the particular atomizers used. W i t h the air-assist atomizer, up to 5 percent of the total air-flow went t h r o u g h the atomizer; the amount d e p e n d e d on atomizer air pressure w h i c h was controlled with a regulator. T h e fuel flow was controlled i n d e p e n d e n t l y w i t h a microvalve when l i q u i d
Refractory Igniters
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DROPLET EVAPORATION ON FUEL-AIR ATOMIZER . . . . .
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FUEL ATOMIZER
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FIc. 2. Cross sections of standard Delevan atomizers used in this study: I. Air-assist atomizer SNA 1.00, nominal capacity 1 gph., II. Air-assist atomizer AIRO 30615-1, nominal capacity 5 gph., III. Pressure atomizer, oil burner nozzle type B, nominal capacities used 1 and 0.6 gph.
fuel was used, and with a regulator w h e n propane fuel was used. With the pressure atomizer, the fuel flow rate was held constant as fuel pressure was varied, by using atomizers of appropriate capacity with similar geometries. Ignition was accomplished with a pair of standard oil b u r n e r electrodes which operated continuously. Shadowgraph techniques were used with each atomizer over the range of experimental conditions covered to determine the approximate droplet sauter m e a n diameter. High speed (5000 frames per second) color movies were taken of the flame with the pressure atomizer, with the cylindrical 4 i n ID duct of the b u r n e r removed, to examine the flame structure. The axial m o m e n t u m of each atomizer jet, over the range of operating conditions, was measured by i m p i n g i n g the jet on a plate normal to the flow on a spring balance. Carbon dioxide was used to simulate propane in the air-assfst atomizer; water was used to simulate kerosene in both atomizer types. These jet m o m e n t u m measurements were used to obtain
the jet kinetic energy. For the air-assist atomizer with gaseous fuel, the velocities of fuel and air at atomizer exit were assumed equal. For the air-assist atomizer with liquid fuel, the liquid velocity was assumed to be m u c h less than the air velocity. I n estimating the jet kinetic energy, allowance was made for jet swirl. Theoretical estimates of jet energy based on mass flow rates a n d the geometry of the atomizers were in good agreement with values derived from the m o m e n t u m measurements.7 Table I summarizes the b u r n e r operating conditions under w h i c h experiments were carried out. I n the experiments where the rate of fuel-air mixing was b e i n g examined, the burner was operated with the overall fuel-air ratio stoichiometric. T h e product gases were sampled u s i n g a fully traversable water-cooled stainless-steel s a m p l i n g probe, and passed through a standard gas analyzer system (condenser, filter, drying agent, nondispersive infra-red CO and CO 2 analyzers, chemiluminescent N O analyzer, paramagnetic O z analyzer and flame ionization total HC ana-
552
SPRAY AND DROPLET COMBUSTION TABLE I Burner fuel and air flow rates for stoichiometric operation
Atomizer
Fuel
Atomizing or fuel pressure psig
Air-assist I Air-assist II Air-assist I Pressure* Pressure Pressure
propane propane kerosene kerosene pentane isooctane
10-40 27-41 10-40 100-300 100r 100t
Primary airflow lb~,/hr
Atomizer airflow lbm/hr
Fuel flow lb m/hr
116-111 116-113 116-111 98 98 92
3.7-9.3 4.5-7.5 3.8-9.3 ----
7.7 7.7 8.0 6.6 6.8 6.1
*A different, but geometrically similar atomizer was used for each fuel pressure. tApproximate pressure level. lyzer). The local time-average oxygen concentration was used to evaluate the degree of fuel fraction n o n u n i f o r m i t y in the product gases. 5.6 For close to stoichiometric operation, the time-average oxygen concentration in the product gases increases with increasing mixture nonuniformity. Radial and axial concentration distributions within the burner were measured. Beyond about half a b u r n e r diameter downstream of the injection plan ( x / D >~ 0.5) the radial variations in oxygen concentration were small (~<20%) so cross-sectional average values were used; i.e., =
f
l
(r/R) [02] d(r/R)
(1)
20
Concentrations are presented throughout on a "wet" basis. Hydrocarbon concentrations decayed rapidly in the first b u r n e r diameter downstream of the injector, and were always less than 1000 ppm for x / D >~ 1.
3. I n j e c t o r Characterization Figure 3 shows shadowgraphs of the fuel jet issuing from the air-assist atomizer and the pressure atomizer u n d e r typical operating conditions. The differences in the two jets shown can be summarized as follows. I n the air-assist atomizer, a high velocity air stream (approximately sonic, d e p e n d i n g on atomizing air pressure) i m p i n g e s on and shatters a relatively low velocity liquid fuel stream, producing small droplets ( - 10-20p.m) with a high relative velocity (-~ 400-900 ft/s) between the drop and its immediate enviromnent.
For the liquid pressure atomizer,' the l i q u i d break-up mechanism is different, as shown in Fig. 3b. The pressure atomizer produces larger drops ( - 40-60~m) with lower relative velocity (= 20 ft/s), and has m u c h lower atomizer jet m o m e n t u m and energy (several orders of magnitude below the air-assist atomizer values).
4. Results and Analysis 4.1 Air-Assist A t o m i z e r
Figure 4 shows cross-section average 0 2 concentrations, on a wet basis, as a f u n c t i o n of distance along the b u r n e r for stoichiometric overall operation for propane and kerosene fuel. Two curves for each fuel are shown at two different fuel jet power levels. It is apparent that the kinetic energy i n p u t to the fuel jet affects the rate of fuel-air mixing,8 and that for the same kinetic energy input, whether the fuel is in gaseous or liquid form makes little difference to the rate of mixing. For higher jet energy inputs, the oxygen concentration decays more rapidly in the first two b u r n e r diameters than in the downstream region of the burner. A stochastic model of t u r b u l e n t mixing 6 was used to estimate the rate of fuel-air m i x i n g in the region of the b u r n e r where mixing is dominated by the atomizer jet. An e n s e m b l e of equal mass fluid elements is chosen to represent the i n c o m i n g fluid composition of the burner. Each element is assumed to be of uniform composition. A fraction of these elements is taken to represent the flow through the fuel atomizer a n d to have a composition determined by the equivalence ratio of the
DROPLET EVAPORATION ON FUEL-AIR
a
553
b
Fro. 3. Shadowgraph photographs of fuel jet from two types of atomizers: (a) air-assist atomizer I, atomizing air pressure i5 psig; (b) pressure atomizer, fuel pressure 100 psig.
atomizer jet. The r e m a i n i n g elements represent the primary c o m b u s t i o n air (qb = 0). Randomly selected pairs of elements are allowed to mix completely, separate and react. A mixing rate intensity, [3(s -1) the average frequency of mixing interactions, is specified. At any time d u r i n g the mixing process, the mean composition and other mean properties of the fluid in the b u r n e r can be evaluated by taking an ensemble average over all fluid elements. I n practice, c o m b u s t i o n can only occur after the fuel and air have mixed to some degree, a n d the range of equivalence ratio w i t h i n which c o m b u s t i o n is likely to occur is not well defined. However, based on the estimated flammability limits for propane and kerosene, c o m b u s t i o n is assumed to occur if 0.5 <~ r ~< 2.5. By comparing the values of mean oxygen concentrations calculated for the case of stoichiometric c o m b u s t i o n with measured mean oxygen concentrations, as a function of position within the burner, the value of 13 can be determined. With this model, oxygen profiles were
calculated a s s u m i n g a constant mixing rate intensity, 13(s-1), to match the measured profile for each experiment. Figure 5 shows an example of this m a t c h i n g process; a value of [3 = 400 s ~ gives good agreement with the measured data in the initial region of the burner. Studies of the air-assist atomizer with gaseous fuels reported elsewhere ~ show that f5 = C ( P j / M D 2 )
'/a
(2)
where Pi is the i n p u t flow power, M is the mass of fluid in which this power is dissipated, D is the b u r n e r diameter, and C is a constant of order u n i t y which is a f u n c t i o n of the b u r n e r geometry and the swirl n u m b e r of the flow. Given the similarity b e t w e e n Oe profiles with propane and kerosene fuel in Fig. 4, Eq. (2) was used with kerosene data a n d compared with previous propane data 7 as s h o w n in Fig. 6. E q u a t i o n (2) satisfactorily correlates both the propane and kerosene data suggesting that whether the fuel in the air-assist atomizer jet
554
SPRAY AND DROPLET COMBUSTION I
I
I
I
I
30
201L A
pj= 2 5 i b f f t / s
{ m PROPANE KEROSENE
Pj=125 Ibfft/s
{ e ~ PROPANE KEROSENE
-
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d
[3
z 0
9
9
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0
1.0
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@
o
9
0.2
I 0
I
I
I
I
9149 o
I
f
2 3 4 5 DISTANCE ALONG BURNER (x/D)
6
FIG. 4. Cross-section average oxygen concentrations for air-assist atomizer operation as a function of axial distance at two different input jet power levels, for kerosene and propane fuel, for stoichiometric overall operation. is a gas (relatively uniformly d i s t r i b u t e d through the jet), or is initially in the form of liquid drops, is immaterial under the conditions tested. I
I
I
I
I
2G
F u r t h e r support for this hypothesis comes from a comparison of nitric oxide concentrations measured at burner exit, for p r o p a n e a n d kerosene, as a function of overall fuel-air equivalence ratio, cb, a n d jet input power, Pj. A previous study in this burner 5,8 has s h o w n that when fuel-air m i x i n g rates are low (and the fuel and air flows are far from u n i f o r m l y mixed together) exhaust NO concentrations from the burner vary little as the overall mixture is leaned out from stoichiometric. In contrast, for m u c h higher fuel-air mixing rates (when the fuel a n d air flows are much more uniformly mixed) the exhaust NO concentrations decrease substantially as the overall mixture is leaned out. F i g u r e 7 shows exhaust NO concentrations for the two fuels, as functions of ~b and P~. T h e total air flow was h e l d constant at 125 l b m / h r for all these experiments as the fuel flow was changed. T h e similarity b e t w e e n the two sets of curves is obvious. Overlaying the two graphs shows the propane NO concentrations are very close to one-half the kerosene values at any given cb and Pj. It was previously demonstrated 5,8 that calculations of NO concentrations along the burner length, based on the Z e l d o v i c h mechanism (allowing for the fuel fraction n o n u n i formities in the p r o d u c t gases, and a s s u m i n g oxygen atoms are in e q u i l i b r i u m at the local nonuniform gas temperature), matched the magnitude and variation in these exhaust N O concentrations for kerosene. Estimates have been made of N O formation rate: d[NO]/dt
= 2 k f [ O ] ~ [N2]
(3)
where kf is the forward rate constant of the reaction o_
N 2+O~-NO+N
u z o
>-
:,s[o 0.~
o
o 0
B ,400
02
I I
I 2
0
I
I
I
3
4
5
0
DISTANCE ALONG BURNER ( ~ / D )
FIG. 5. Predicted mean oxygen concentrations from stochastic mixing model for different values of mixing rate intensity, compared with data.
(4)
which is the rate-controlling step in the Zeldovich mechanism, with [NO] < < [NO] eqin., for adiabatic c o m b u s t i o n products of kerosene and propane-air mixtures. The values of d [NO] / d t calculated for p r o p a n e are about a factor of two lower than the values calculated for kerosene for 0.6 ~ cb ~ 1.2. F o r n o n u n i f o r m mixtures, with an a s s u m e d gaussian distribution in fuel fraction of standard deviation half the mean fuel fraction, the factor of two difference in calculated NO formation rate persists. It is therefore c o n c l u d e d that the observed difference in Fig. 7 is p r i m a r i l y d u e to the difference in flame temperatures of the two fuels. Estimates of the characteristic times for
DROPLET EVAPORATION ON FUEL-AIR 3.0
I
I
I
I
I
I
I
I I
I
555 I
I
I
OATOMIZER I PROPANE X ATOMIZER ]I PROPANE OATOMIZER T KEROSENE
-.-. 2.0 ,N r',
o_1.0-----0.9
- x -
-
o.-O- 0%_0 _ o _
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O
0.8 0.7
I
I
I,
20
30
40
I
I
I 111
I
I
1
50 60 80 I00 200 :500 COMBUSTOR POWER INPUT ( I b f - f t / s e c )
400
I 500
FIG. 6. Correlation of nondimensional mixing rate intensity, fS/(Pj/MD 2)a/3 as function of atomizer jet power, Pj, for air-assist atomizers. I
1
t
Q; Z 0
~- I 0 0
-
I )C
Q
tr Iz ,,J u
z
0 t~
50
~C
X 0 IJ F--
PR
KEROSENE
N
o
~0
~:o.e
c
o ;-os x
d ~=0.9 0 ~=1.0
5
1 0
50
5
I tO0 COMBUSTOR
I i50 POWER
l 0
INPUT
SO (Ibf -ftl$oc)
I
9
IO0
ISO
FIc. 7. Burner exhaust nitric oxide concentration (ppm wet basis) as function of mean fuel-air equivalence ratio, ~b, and atomizer jet power for air-assist atomizers for kerosene and propane. droplet velocity e q u i l i b r a t i o n with the flow field, droplet evaporation, and the d y n a m i c response of droplets to the turbulent flow field, under conditions a p p r o p r i a t e to the range of operation of the air-assist atomizer, were m a d e and compared with the fuel-air mixing time. The basis of these computations is the mass transfer correlation of Ranz and Marshall ~ a n d the drag coefficient correlation of E i s e n k l a m et al? ~ Calculations were made for single
droplets in a series of assumed environments for the drops (constant temperature at various levels between the inlet air and adiabatic flame values; as well as linearly increasing environment temperature with distance, reaching the adiabatic flame temperature in two to four burner diameters). The droplet velocity relative to its-environment was also c o m p a r e d with the critical relative velocity above w h i c h a fully envelop-
556
SPRAY AND DROPLET COMBUSTION
ing flame is unstable, u The initial d r o p l e t mean relative velocity (300-900 f t / s ) is a b o u t two orders of m a g n i t u d e greater than the critical velocity above w h i c h an envelope flame is unstable (1.5-5 f t / s ) . Furthermore, the characteristic time of turbulent velocity fluctuations, -rp in the atomizer jet 9rf ~-- D j / V j
=
0.4 ms
I E]
I
I
PENTANE
I 0 0 psig
KEROSENE
IO0 psig
9
I
3 0 0 p$ig ISOOCTANE
I 0 0 psig
- - - - EQUIVALENT GAS PHASE MIXING B = 500
s-=
0
0
z 0 }-
(5)
rr
where Dj is the jet diameter and V. the m e a n jet velocity, is m u c h shorter than tfae time for the drop to a c c o m m o d a t e to these velocity fluctuations (=2 ms). T h e magnitude of the fluctuations (--- V , / 1 0 ) also exceeds the critical velocity for a stal~le envelope flame, so d r o p l e t combustion can never occur. Values for the average fuel-air mixing time, droplet velocity e q u i l i b r a t i o n time, vd, a n d evaporation time, re, for sauter mean diameter drops are given in T a b l e II for kerosene, for two i n p u t jet powers, P2 w h i c h span the range of interest for the air assist atomizer. T h e characteristic m i x i n g time, r,,, is 13-1 determ i n e d from Fig. 6. T h e ranges in r d a n d v e come from the range of assumed a m b i e n t environments for the drops in the burner. It is seen that "gm > > "re > Td
Z I0 bJ 0 Z 0 (J Z 51 bJ ~9 0
I
0
0
0
I
I
I
I
l
2
3
4
DISTANCE
A L O N G BURNER
(x/D)
FIG. 8. Measured cross-section average oxygen concentrations as function of burner length for pressure atomizer, with kerosene at 100 and 300 psig injection pressure, and with pentane and isooctane at 100 psig injection pressure. Fuel flow rate is held constant; stoichiometric overall operation.
(6)
Thus, droplet evaporation w o u l d not b e expected to influence significantly the fuel-air mixing process; u n d e r these conditions with air-assist atomizers w i t h liquid fuels such as kerosene, it is the kinetic energy of the fuel jet and the jet length scale (the integral scale) w h i c h controls the rate of fuel-air mixing a n d flame structure. 4.2 P r e s s u r e A t o m i z e r F i g u r e 8 shows the oxygen concentration profiles measured w i t h the pressure atomizer. Kerosene data for two different fuel pressures and different c a p a c i t y geometrically similar injectors (but the same fuel flow rate) are shown; the difference is small. To assist in
identifying the role of droplet vaporization, experiments were also carried out with single h y d r o c a r b o n fuels w i t h different physical p r o p e r t i e s - - p e n t a n e , and isooctane. The fuel injection pressure a n d injector were the same for pentane, isooctane, and kerosene at 100 p s i g injection pressure. T h e pentane and iooctane oxygen concentration results are also shown. T h e oxygen concentration profiles in Fig. 8 suggest two distinct regions; an initial region of more r a p i d fuel-air mixing (within the first burner diameter) followed b y m u c h slower mixing. T h e total m i x i n g achieved in the initial r a p i d mixing regime appears to d e p e n d on the fuel, with more volatile fuels mixing least. In the first burner diameter, the decay in oxygen
TABLE II Characteristic times for kerosene with air-assist atomizer Input power Pj, lbfft/s
Sauter mean diam, ~m
10 100
25 I0
mixing, ~'rn 6 2.5
Characteristic times in ms deceleration, ~a evaporation, % O.1-0.3 0.04-0.2
0.3-1 0.1-0.3
DROPLET EVAPORATION ON FUEL-AIR concentration is c o m p a r a b l e to the initial decay rates in Fig. 4 at higher jet input powers. A calculated oxygen concentration profile for 13 = 500 s -1, m a d e with the stochastic mixing model is indicated. For kerosene a n d isooctane, mixing rate intensities of the order of or greater than this value are achieved. T h e p o w e r i n p u t with the l i q u i d fuel jet is of order 10 -2 l b e f t / s . U s i n g the correlation of Eq. (2) d e v e l o p e d for gaseous fuel jets, this w o u l d give a mixing rate intensity J3 of about 20 s - l ; the stochastic mixing m o d e l then calculates an oxygen concentration profile indicated b y the d a s h e d line. T h e observed rate of m i x i n g m u s t be p r o d u c e d b y a different p h e n o m e n o n . Note that the mixing rates d i d not change significantly for kerosene w i t h a factor of three increase in a t o m i z i n g pressure. Such a change in pressure is estimated to decrease the sauter mean droplet diameter from 60 to 35 p.m, a n d increase the initial d r o p l e t velocity from 15 to 30 f t / s . To examine whether the structure of the flame with the pressure atomizer was different from the gaseous jet-type diffusion flame prod u c e d with the air-assist atomizer, high speed color movies of the pressure atomizer flame were taken. A print from one frame, with an explanatory schematic, is shown in Fig. 9. T h e structure is not significantly different from a gaseous jet flame. T h e scale on w h i c h motion of i n d i v i d u a l b u r n i n g eddies occurs is of the order of one-fifth the jet scale. No i n d i v i d u a l droplet c o m b u s t i o n is observed. T h e mixing rate intensity is a function of b o t h the rate of energy dissipation in the t u r b u l e n t mixing process, and of the length SCale l m of the concentration nonuniformities w h i c h are b e i n g mixed out. W i t h i n the equil i b r i u m range of t u r b u l e n c e xI < l m < I
557
/
FUEL NOZZLE ~LER
OUS :ULATION
(7)
where I is the integral scale of turbulence, a n d ~q = ( v / e ) 1/4 is the Kolmogorov microscale of turbulence, the m i x i n g rate intensity 13 is given approximately b y 13 ~- u' / l., ~- (~ / l ~ ) ~/3
(8)
where u ' is the m e a n t u r b u l e n t velocity fluctuation. It is significant that the mixing rate intensity increases w i t h decreasing length scale. W h e n the pressure jet atomizer is used, the Kolmogorov microscale ts approximately n ~ (u'l/v)
3/41
(9)
F o r the turbulent air flow into the burner, the
FIG. 9. Photograph from high-speed color movie of flame with pressure atomizer with kerosene fuel, indicating length scale of burning eddies, with explanatory schematic. Exposure time ~10-4s.
SPRAY AND DROPLET COMBUSTION
558
Reynold's n u m b e r is about 4000, u ' is a b o u t 0.6 f t / s ; thus, -q is about 100 txm w h i c h is comparable to the initial droplet diameter d o which is about 60 txm. Since 13 ~> 500 s -1, it follows from Eq. (8) that l,, ~< 400 p,m, i.e., of order or less t h a n about 7d o. The average distance b e t w e e n the drops in the fuel spray, l~, increases linearly with distance from the injector to about 30d o at a distance of x / D = 0.5 from the injector. Thus within the evaporation region, the following ranking of length scales exists: d o --= aq < < l m = l, < < 1
(10)
The local energy dissipation rate in the fuel-air mixing region, ~, can also be estimated. It follows from Eq. (8), for 13 ~> 500 s - l , that e ~> 300 ft 2 s -3. If the kinetic energy i n p u t with the liquid fuel jet is dissipated in t u r b u lent mixing w i t h i n the first burner diameter, then e -~ P ~ / M w h e r e M is the mass of fluid within the first diameter. Substitution of appropriate values gives e --= 103 ft 2 s-3. H o w e v er, not all of the fuel input kinetic energy is dissipated in this manner. The initial droplet velocity and the a m b i e n t velocity are comparable in magnitude; thus, though the drops are injected at least in part into a recirculation zone as indicated in Fig. 9, their velocity does not decrease to zero. From this analysis, it is reasonable to conclude that the length scale on w h i c h m i x i n g occurs is c o m p a r a b l e in magnitude to the droplet separation scale, and that the fuel jet provides the energy for the turbulent m i x i n g process. The e v a p o r a t i n g droplets can b e thought of as m o v i n g point sources of fuel vapor dispersed t h r o u g h o u t the flow field, as long as the droplets persist. Very high fuel vapor concentration gradients will exist a r o u n d the droplets; these high concentration gradients are r a p i d l y d i s s i p a t e d b y the combination of turbulent a n d laminar diffusion. Until the droplets have fully evaporated, their presence in the flow promotes enhanced m i x i n g of fuel vapor and air. Thus, if droplets evapo-
rate rapidly relative to the fuel-air m i x i n g process (as was the case with the air-assist atomizer), droplet evaporation w o u l d be expected to have only a small effect on the overall fuel-air m i x i n g process, whereas if the droplets evaporate slowly, mixing w o u l d be enhanced. The results s h o w n in Fig. 8 with the pressure jet atomizer with different injection pressures and different fuels were used to test this hypothesis. Estimates of characteristic droplet evaporation times, and droplet penetration distances prior to evaporation, were made for the two injection pressures for kerosene u s i n g the correlations of Ranz and Marshall 9 a n d Eisenklam et al. 1~ as outlined in Section 4.1. Table I I I gives the ranges of results for different assumed d r o p l e t environments. If we assume that the energy dissipation rate, e, is proportional to the initial kinetic energy of the fuel drops, and that the mixing length is proportional to the droplet separation distance (which is proportional to the initial d r o p l e t size), then from Eq. (8) 13 for the 300 p s i g injection pressure is twice that for the 100 psig injection pressure. However, the penetration distance is halved. The total amount of mixing, which is the integral of 13 along the flow path until the drops have evaporated, will be roughly proportional to the product of 13 and penetration distance and will, therefore, be constant. Furthermore, the calculated p e n etration distance is of the same order as the distance over w h i c h the rapid fuel-air m i x i n g occurs. The c o i n c i d e n c e of the oxygen concentrations for these two cases with kerosene can p l a u s i b l y be explained. To interpret the oxygen profiles from the different fuels, pentane, kerosene and isooctane, all at the same injection pressure, estimates were made of the steady-state evaporation constant, ko, h o = (8k/ptc.)
In (1 + B)
(11)
where k and c~, are the gaseous thermal conductivity and specific heat, and Pl is the l i q u i d
TABLE III Characteristic times and lengths for kerosene with pressure atomizer Injection pressure psig
Sauter mean diam. txm
Initial drop velocity m/s
Evaporation time, ms
Drop penetration
100 300
60 35
5.3 8.8
3-9 1-4
0.2-0.5 0.1-0.2
x/D
DROPLET EVAPORATION ON FUEL-AIR density; B (the transfer number) is given by
t~a,(T - T t ) / L where L is the latent heat at liquid boiling temperature T t. For the values of Reynolds and Prandtl numbers appropriate to these experiments, the evaporation time is approximately proportional to d~/k o" Table IV gives values of h 0 at T = 1000 and 2000~ with k a n d c evaluated at the film temperature ( T - TI)/]'n(T/TI). The values for kerosene are approximate since it is not a single hydrocarbon and its properties are not accurately defined. It is seen that the evaporation constant for p e n t a n e is larger than that for isooctane, and evaporation constants for kerosene and isooctane are comparable. Also, the surface tension of liquid hydrocarbon fuels generally decreases with decreasing specific gravity, and decreases as the l i q u i d temperaturre approaches the b o i l i n g point. Thus; even though the fuel injection pressure is the same for pentane as for the other fuels, the mean drop size is likely to be smaller. Thus, the characteristic evaporation time for pentane will be smaller than for isooctane and kerosene (which should have comparable evaporation characteristics). The total m i x i n g while droplets persist for pentane should therefore be significantly less, as the measured oxygen concentrations indicate.
5. C o n c l u s i o n s We have concluded that the influence of droplet evaporation on the fuel-air mixing process in liquid fuel sprays can be summarized as follows. While the droplets persist, and move through the a m b i e n t environment, they act as point sources of fuel vapor. The characteristic scale of the fuel vapor concentration n o n u n i f o r m i t i e s set up b y the motion and evaporation of the droplets in the spray is the droplet separation distance. Once the droplets have evaporated, the characteristic scale of fuel vapor concentration n o n u n i -
559
formities becomes the fuel jet length scale. Since mixing rate intensities vary as (e/1 ~)l/a, where e is the kinetic energy dissipation rate and l,, is the sclae of the nonuniformities, given mixing rate intensities are achieved in the droplet regime with m u c h lower energy dissipation rates than are required i n the jet mixing regime. The experimental results described in this paper with two types of fuel atomizer--air-assist and pressure j e t - - s u p p o r t this hypothesis. With the air-assist atomizers, the characteristic droplet evaporation times are small compared with the times characteristic of the fuel-air mixing process. The jet i n p u t power determines the mixing rate as in a gaseous fueled jet flame. With the pressure jet atomizer, the characteristic evaporation and mixing times are comparable. The mixing rate intensities achieved are comparable to those obtained with air-assist atomizers; the m u c h lower fuel jet i n p u t power is offset b y the m u c h smaller characteristic scale of fuel-air nonuniformities with the pressure jet atomizer. The evaporation characteristics of the l i q u i d fuel drops determine the total a m o u n t of mixing achieved while the droplets persist, with the more volatile fuels mixing the least.
Acknowledgment This work has been supported in part by the Environmental Protection Agency under Grant No. R-800729-02-0, by the Energy Research and Development Administration under Grant No. E (11-1)2680, and by the National Aeronautics and Space Administration under Grant No. NGR 22-009-378. The assistance of Monima Briggs and David Bigio is gratefully acknowledged.
REFERENCES 1. CHIGIER,N. AND MCCREATH,C. G., Acta Astronautica 1, 687-710, (1974).
TABLE IV Properties and steady state evaporation constants of different fuels
Fuel n-pentane isooctane kerosene
Boiling point ~
Specific gravity
556 670 760-940
0.631 0.707 0.84
ho T = 1000~ ft 2/ s 2 x 10 -6 1.3 x 10 -6 1.1 x 10 -6
ho T = 2000~ ft 2/s 4.8 x 10 -6 4.2 x 10 -6 4.2 x 10 -8
560
SPRAY AND D R O P L E T C O M B U S T I O N
2. ONUMA,Y. ANDOGASAWARA,M., Fifteenth Symposium (International) on Combustion, pp. 453466, The Combustion Institute, (1974). 3. MELLOR, A. M., Comb. Sci. Tech., 8, 101-109 (1973). 4. ComasiN, S., AICHEJ. 3, 329-331 (1957). 5. POMPEI, F. AND HEYWOOD, J. S., Comb. Flame, 19, 407-418 (1972). 6. FLAGAN,R. C. ANDAPPLETON,J. P., Comb. Flame, 23, 249-267, (1974). 7. KOMIVAMA, K. " T h e Effects of Fuel Injector Characteristics on Fuel-Air Mixing in a Burner,"
8.
9. 10.
11.
Ph.D. thesis, Mechanical Engineering Department, M.I.T., (1975). APPLETON, J. P. AND HEYWOOD, J. B., Fourteenth Symposium (International) on Combustion, pp. 777-786, The Combustion Institute, (1972). RANZ, W. E., AND MARSHALL, W. R., Chemical Engineering Progress, 48, (1952). EISENKLAM,P., ARUNACHALAM,S. A., ANDWESTON, J. A., Eleventh Symposium (International) on Combustion, the Combustion Institute, (1967). OGnsAw~, M., AND SAMI, H., Jap. Soc. Mech. Engr. Bull. 13, 407-426, (1970).
COMMENTS F. V. Braceo, Princeton University, USA. How do you reconcile the presence of recirculation with the assumption of one-dimensionality? Would you have a stable flame without recirculation in your configuration? Please check the paper by Onuma, Ogasawara, and Inoue for indication of strong radial variations of most relevant parameters. Authors" Reply. The radial concentration profiles in our burner were measured; variations were less than -+20% from the mean. Hence, we feel that cross-section average concentrations reasonably reflect the local conditions in the flow. The one dimensional model used in our paper is intended to describe the gross features of the fuel-air mixing process. The model is not expected to be able to predict local conditions with a high degree of accuracy; it was developed a n d used to help us interpret the experimental data and explain the relative importance of the processes occurring in the evaporating fuel spray. We were not attempting to predict flame stability, nor the details of the recirculating flow. Our experimental configuration cannot be readily compared with that used by Onuma, Ogasawara and Inoue; ours is a high Reynolds n u m b e r jet flow, theirs is a m u c h lower Reynolds n u m b e r jet flow, and the geometrical configurations of our two burners are quite different.
R. E. Pavia, Aeronautical Research Laboratories, Australia. Reference was made in the answer to the previous question of a 20 percent variation for the pressure jet flames in the radial distribution of oxygen concentration. It would appear to me that this could provide a physical explanation of the different fuel oxygen concentrations, for the pressure jet spray flames of isooctane, kerosene and pentane.
If, in fact, the latter fuel produces finer drop sizes and evaporates more rapidly, combustion may be completed before the spray reaches the combustion walls, allowing a significant part of the air to by-pass the flame. In this case the effective diameter of the flame may not be the combustor diameter D used in the turbulent mixing parameter. Would this discrepancy have a significant effect on the time turbulent mixing in the combustor?
Authors" Reply. We do not believe the explanation offered by Dr. Pavia could fit our experimental data. For the pressure jet spray flame, the characteristic lengthscale of the fuel-air nonuniformities b e i n g mixed out has to be orders of magnitude less than the jet scale because the energy dissipation rate is orders of magnitude lower than in the air blast atomizer spray flame, yet equivalent mixing rate intensities our achieved. Our estimates show the characteristic scale of these nonuniformities in the pressure jet spray flame is comparable to the droplet separation distance within the spray, while in the air blast atomizer spray flames, the characteristic length scale is the jet scale. Even if the pressure jet spray flame does not quite fill the burner, the change in jet length scale does not approach the magnitude of the change required to explain our data.
A. M. Mellor, Purdue University, USA. Our results and conclusions reported elsewhere in these proceedings are in essential agreement with those of Prof. Heywood and coworkers. Later work in our laboratory also shows the importance of fuel distribution, more explicitly than in the preliminary correlation we reported upon.
Komatsu Ltd., Tok~to, Japan R. C. FLAGAN
California Institute of Technology, Pasadena, California U.S.A. AND
j. B. HEYWOOD
Massachusetts Institute of Technology, Cambridge, Massachusetts U.S.A. 02139 The importance of droplet evaporation in the overall fuel-air mixing process in liquid fnel spray flames is examined with a series of experiments in a simple atmospheric pressure burner burning a range of hydrocarbon fuels. Two types of fuel atomizers were studied--airassist and pressure jet--which have substantially different operating characteristics. Fuel-air mixing rates were determined from time-average oxygen concentrations measured with overall burner operation stoichiometric. It is shown that with air-assist atomizers, the kinetic energy of the atomizer jet determines the mixing rate intensity for both liquid and gaseous fuels. Since the droplet evaporation time is much less than the mixing time, the details of the evaporation process are not important and the jet length scale and kinetic energy govern the mixing process. With pressure jet atomizers, the characteristic evaporation and mixing times are comparable. The evaporating fuel drops create fuel vapor concentration nonuniformities on a scale much smaller than the fuel jet scale. Mixing rate intensities comparable to those obtained with air-assist atomizers can, therefore, be achieved with much lower turbulent kinetic energy dissipation rates. With pressure jet atomizers, both the kinetic energy of the fuel jet and the evaporation characteristics of the fuel droplets control the initial fuel-air mixing rate. 1. Introduction In most practical liquid-fuel continuousflow combustion systems, the liquid fuel is injected directly into the p r i m a r y c o m b u s t i o n region. The injected l i q u i d shatters into droplets; the droplets move relative to and exchange m o m e n t u m with the combustion air and already burnt gases. T h e droplets heat up, vaporize and decelerate. Since the fuel and air enter the combustor separately, the fuel vapor and air must mix to w i t h i n c o m b u s t i b l e limits through a t u r b u l e n t mixing process before the fuel will burn. W h i l e fuel atomization, trajectories of fuel droplets and fuel vaporization all p l a y a part in this overall process, the role of the l i q u i d fuel droplets in the c o m b u s t i o n of distillate fuel oil sprays in 549
different types of burners is still a sul~ject of m u c h speculation. E v i d e n c e as to the influence of droplets on the detailed structure of a spray flame is a p p a r e n t l y contradictory. It has been suggested that under certain conditions droplets b u r n with i n d i v i d u a l envelope flames. A large n u m b e r of droplet b u r n i n g studies have been c o n d u c t e d with single droplets under well defined flow conditions. These have been useful in d e f i n i n g the d y n a m i c s of i n d i v i d u a l droplet processes, but the a p p l i c a t i o n of these results to spray flames is c o m p l i c a t e d b y the large n u m b e r of droplets a n d the t u r b u l e n c e and nonuniformities in the flow. Numerous studies have suggested that droplets of distillate fuel sprays do not b u r n with e n v e l o p i n g flames. For example, Chigier 1 has p r o v i d e d
550
SPRAY AND DROPLET COMBUSTION
photographic e v i d e n c e that flame envelopes do not exist around individual droplets in spray flames produced b y certain types of pressure jet and air blast atomizers in an u n c o n f i n e d environment. O n u m a and Ogasawara 2 have shown that the character of a confined spray flame from an air assist atomizer is very similar in structure to a comparable gaseous fuel flame. On the other hand, Mellor a has p r o v i d e d indirect evidence that, with a relatively ineffid e n t simplex pressure atomizer, droplets p l a y a role in the details of the combustion process. He was able to correlate gas turbine c o m b u s t o r nitric oxide emissions with a parameter w h i c h is proportional to the combustor residence time divided by the d r o p l e t evaporation time. These observations are not necessarily in conflict; the conditions in many of these spray flames are not closely comparable. However, the role of the droplets in fuel spray flames is still unclear. It is the goal of our study to examine the influence of droplet evaporation on the process b y w h i c h fuel and air mix and burn in a spray flame. The rate of m i x i n g of fuel and air was measured in a burner with two types of atomizers. It is shown that, in some cases, droplets do not play a significant role whereas droplets significantly alter the fuel-air mixing rate under other conditions. Evidence is p r o v i d e d for the hypothesis that, even where droplets are important, it is not necessary to assume the existence of d r o p l e t envelope flames to describe the influence of the evaporation process on the fuel-air m i x i n g rate. The work d e s c r i b e d here builds on previously reported work with turbulent jet flames using both l i q u i d and gaseous fuels. This
Gas Sampling Probe
previous work had shown that single phase turbulent mixing models 4 when coupled with suitable kinetic schemes can be used to predict the pollutant emissions of simple burners with air-assist atomizers with liquid and gaseous fuels. 5,6,7 With gaseous fuels, those characteristics of the atomizer w h i c h determine the rates of fuel-air m i x i n g have been identified, and simple sealing laws have been developed. 7 The question we now address is: Under what conditions do the presence of liquid fuel droplets in the flow influence the rate of fuel-air mixing in a steady flow combustor? 2. E x p e r i m e n t a l Set-Up Experiments were carried out in an atmospheric pressure burner. A schematic of the burner is shown in Figure 1. A cylindrical geometry with refractory lined walls to reduce heat losses was used to simplify the flow pattern. For these experiments the b u r n e r dimensions were 4 in internal diameter a n d 24 in. in length. C o m b u s t i o n air was s u p p l i e d through 45 ~ b l a d e angle swirl vanes at 1 atmosphere pressure a n d room temperature. L i q u i d fuel (kerosene except where otherwise noted) or propane was s u p p l i e d through a nozzle on the burner axis. Both air-assist and pressure type atomizers were studied; Figure 2 shows cross-sectional d r a w i n g s on the particular atomizers used. W i t h the air-assist atomizer, up to 5 percent of the total air-flow went t h r o u g h the atomizer; the amount d e p e n d e d on atomizer air pressure w h i c h was controlled with a regulator. T h e fuel flow was controlled i n d e p e n d e n t l y w i t h a microvalve when l i q u i d
Refractory Igniters
Lining\
/~
L\\I\\\\\\\\\\\\~.-~
~9 1 ~
,x~-',,N\\\\\~NN,~\'~'-,\\\'~I
4
,~N~%,\\\\\\\\\\\\\\\\'~
,%.~\\\\\\\\\\\\\\\\\\\NII
:-=
8
Atomizing
~ /
/,.-
/Nozzle
~ -~--
~ . _
f
4f --4 /
Swirler
Atmospheric Pressure Burner F[c. 1. Schematic of atmospheric pressure burner.
-
r-uel, ~-]
\
Air
\ PrimaryA r
DROPLET EVAPORATION ON FUEL-AIR ATOMIZER . . . . .
I
. . . . . . . . .
-.T"~t " [111
551
i~///1"
f T"T'l--/7;"';
I*////
IIIIII
tFUEL ATOMIZER
I[
FUEL ATOMIZER
I
Fu E L --,-
_-1+
lit
.
FIc. 2. Cross sections of standard Delevan atomizers used in this study: I. Air-assist atomizer SNA 1.00, nominal capacity 1 gph., II. Air-assist atomizer AIRO 30615-1, nominal capacity 5 gph., III. Pressure atomizer, oil burner nozzle type B, nominal capacities used 1 and 0.6 gph.
fuel was used, and with a regulator w h e n propane fuel was used. With the pressure atomizer, the fuel flow rate was held constant as fuel pressure was varied, by using atomizers of appropriate capacity with similar geometries. Ignition was accomplished with a pair of standard oil b u r n e r electrodes which operated continuously. Shadowgraph techniques were used with each atomizer over the range of experimental conditions covered to determine the approximate droplet sauter m e a n diameter. High speed (5000 frames per second) color movies were taken of the flame with the pressure atomizer, with the cylindrical 4 i n ID duct of the b u r n e r removed, to examine the flame structure. The axial m o m e n t u m of each atomizer jet, over the range of operating conditions, was measured by i m p i n g i n g the jet on a plate normal to the flow on a spring balance. Carbon dioxide was used to simulate propane in the air-assfst atomizer; water was used to simulate kerosene in both atomizer types. These jet m o m e n t u m measurements were used to obtain
the jet kinetic energy. For the air-assist atomizer with gaseous fuel, the velocities of fuel and air at atomizer exit were assumed equal. For the air-assist atomizer with liquid fuel, the liquid velocity was assumed to be m u c h less than the air velocity. I n estimating the jet kinetic energy, allowance was made for jet swirl. Theoretical estimates of jet energy based on mass flow rates a n d the geometry of the atomizers were in good agreement with values derived from the m o m e n t u m measurements.7 Table I summarizes the b u r n e r operating conditions under w h i c h experiments were carried out. I n the experiments where the rate of fuel-air mixing was b e i n g examined, the burner was operated with the overall fuel-air ratio stoichiometric. T h e product gases were sampled u s i n g a fully traversable water-cooled stainless-steel s a m p l i n g probe, and passed through a standard gas analyzer system (condenser, filter, drying agent, nondispersive infra-red CO and CO 2 analyzers, chemiluminescent N O analyzer, paramagnetic O z analyzer and flame ionization total HC ana-
552
SPRAY AND DROPLET COMBUSTION TABLE I Burner fuel and air flow rates for stoichiometric operation
Atomizer
Fuel
Atomizing or fuel pressure psig
Air-assist I Air-assist II Air-assist I Pressure* Pressure Pressure
propane propane kerosene kerosene pentane isooctane
10-40 27-41 10-40 100-300 100r 100t
Primary airflow lb~,/hr
Atomizer airflow lbm/hr
Fuel flow lb m/hr
116-111 116-113 116-111 98 98 92
3.7-9.3 4.5-7.5 3.8-9.3 ----
7.7 7.7 8.0 6.6 6.8 6.1
*A different, but geometrically similar atomizer was used for each fuel pressure. tApproximate pressure level. lyzer). The local time-average oxygen concentration was used to evaluate the degree of fuel fraction n o n u n i f o r m i t y in the product gases. 5.6 For close to stoichiometric operation, the time-average oxygen concentration in the product gases increases with increasing mixture nonuniformity. Radial and axial concentration distributions within the burner were measured. Beyond about half a b u r n e r diameter downstream of the injection plan ( x / D >~ 0.5) the radial variations in oxygen concentration were small (~<20%) so cross-sectional average values were used; i.e., =
f
l
(r/R) [02] d(r/R)
(1)
20
Concentrations are presented throughout on a "wet" basis. Hydrocarbon concentrations decayed rapidly in the first b u r n e r diameter downstream of the injector, and were always less than 1000 ppm for x / D >~ 1.
3. I n j e c t o r Characterization Figure 3 shows shadowgraphs of the fuel jet issuing from the air-assist atomizer and the pressure atomizer u n d e r typical operating conditions. The differences in the two jets shown can be summarized as follows. I n the air-assist atomizer, a high velocity air stream (approximately sonic, d e p e n d i n g on atomizing air pressure) i m p i n g e s on and shatters a relatively low velocity liquid fuel stream, producing small droplets ( - 10-20p.m) with a high relative velocity (-~ 400-900 ft/s) between the drop and its immediate enviromnent.
For the liquid pressure atomizer,' the l i q u i d break-up mechanism is different, as shown in Fig. 3b. The pressure atomizer produces larger drops ( - 40-60~m) with lower relative velocity (= 20 ft/s), and has m u c h lower atomizer jet m o m e n t u m and energy (several orders of magnitude below the air-assist atomizer values).
4. Results and Analysis 4.1 Air-Assist A t o m i z e r
Figure 4 shows cross-section average 0 2 concentrations, on a wet basis, as a f u n c t i o n of distance along the b u r n e r for stoichiometric overall operation for propane and kerosene fuel. Two curves for each fuel are shown at two different fuel jet power levels. It is apparent that the kinetic energy i n p u t to the fuel jet affects the rate of fuel-air mixing,8 and that for the same kinetic energy input, whether the fuel is in gaseous or liquid form makes little difference to the rate of mixing. For higher jet energy inputs, the oxygen concentration decays more rapidly in the first two b u r n e r diameters than in the downstream region of the burner. A stochastic model of t u r b u l e n t mixing 6 was used to estimate the rate of fuel-air m i x i n g in the region of the b u r n e r where mixing is dominated by the atomizer jet. An e n s e m b l e of equal mass fluid elements is chosen to represent the i n c o m i n g fluid composition of the burner. Each element is assumed to be of uniform composition. A fraction of these elements is taken to represent the flow through the fuel atomizer a n d to have a composition determined by the equivalence ratio of the
DROPLET EVAPORATION ON FUEL-AIR
a
553
b
Fro. 3. Shadowgraph photographs of fuel jet from two types of atomizers: (a) air-assist atomizer I, atomizing air pressure i5 psig; (b) pressure atomizer, fuel pressure 100 psig.
atomizer jet. The r e m a i n i n g elements represent the primary c o m b u s t i o n air (qb = 0). Randomly selected pairs of elements are allowed to mix completely, separate and react. A mixing rate intensity, [3(s -1) the average frequency of mixing interactions, is specified. At any time d u r i n g the mixing process, the mean composition and other mean properties of the fluid in the b u r n e r can be evaluated by taking an ensemble average over all fluid elements. I n practice, c o m b u s t i o n can only occur after the fuel and air have mixed to some degree, a n d the range of equivalence ratio w i t h i n which c o m b u s t i o n is likely to occur is not well defined. However, based on the estimated flammability limits for propane and kerosene, c o m b u s t i o n is assumed to occur if 0.5 <~ r ~< 2.5. By comparing the values of mean oxygen concentrations calculated for the case of stoichiometric c o m b u s t i o n with measured mean oxygen concentrations, as a function of position within the burner, the value of 13 can be determined. With this model, oxygen profiles were
calculated a s s u m i n g a constant mixing rate intensity, 13(s-1), to match the measured profile for each experiment. Figure 5 shows an example of this m a t c h i n g process; a value of [3 = 400 s ~ gives good agreement with the measured data in the initial region of the burner. Studies of the air-assist atomizer with gaseous fuels reported elsewhere ~ show that f5 = C ( P j / M D 2 )
'/a
(2)
where Pi is the i n p u t flow power, M is the mass of fluid in which this power is dissipated, D is the b u r n e r diameter, and C is a constant of order u n i t y which is a f u n c t i o n of the b u r n e r geometry and the swirl n u m b e r of the flow. Given the similarity b e t w e e n Oe profiles with propane and kerosene fuel in Fig. 4, Eq. (2) was used with kerosene data a n d compared with previous propane data 7 as s h o w n in Fig. 6. E q u a t i o n (2) satisfactorily correlates both the propane and kerosene data suggesting that whether the fuel in the air-assist atomizer jet
554
SPRAY AND DROPLET COMBUSTION I
I
I
I
I
30
201L A
pj= 2 5 i b f f t / s
{ m PROPANE KEROSENE
Pj=125 Ibfft/s
{ e ~ PROPANE KEROSENE
-
mH -
d
[3
z 0
9
9
[]
9
o
nr" IZ hJ 0 Z 0 0 Z
[]
9
9
9
[3 o
9
0
1.0
0
0
x o
0
0
o
@
o
9
0.2
I 0
I
I
I
I
9149 o
I
f
2 3 4 5 DISTANCE ALONG BURNER (x/D)
6
FIG. 4. Cross-section average oxygen concentrations for air-assist atomizer operation as a function of axial distance at two different input jet power levels, for kerosene and propane fuel, for stoichiometric overall operation. is a gas (relatively uniformly d i s t r i b u t e d through the jet), or is initially in the form of liquid drops, is immaterial under the conditions tested. I
I
I
I
I
2G
F u r t h e r support for this hypothesis comes from a comparison of nitric oxide concentrations measured at burner exit, for p r o p a n e a n d kerosene, as a function of overall fuel-air equivalence ratio, cb, a n d jet input power, Pj. A previous study in this burner 5,8 has s h o w n that when fuel-air m i x i n g rates are low (and the fuel and air flows are far from u n i f o r m l y mixed together) exhaust NO concentrations from the burner vary little as the overall mixture is leaned out from stoichiometric. In contrast, for m u c h higher fuel-air mixing rates (when the fuel a n d air flows are much more uniformly mixed) the exhaust NO concentrations decrease substantially as the overall mixture is leaned out. F i g u r e 7 shows exhaust NO concentrations for the two fuels, as functions of ~b and P~. T h e total air flow was h e l d constant at 125 l b m / h r for all these experiments as the fuel flow was changed. T h e similarity b e t w e e n the two sets of curves is obvious. Overlaying the two graphs shows the propane NO concentrations are very close to one-half the kerosene values at any given cb and Pj. It was previously demonstrated 5,8 that calculations of NO concentrations along the burner length, based on the Z e l d o v i c h mechanism (allowing for the fuel fraction n o n u n i formities in the p r o d u c t gases, and a s s u m i n g oxygen atoms are in e q u i l i b r i u m at the local nonuniform gas temperature), matched the magnitude and variation in these exhaust N O concentrations for kerosene. Estimates have been made of N O formation rate: d[NO]/dt
= 2 k f [ O ] ~ [N2]
(3)
where kf is the forward rate constant of the reaction o_
N 2+O~-NO+N
u z o
>-
:,s[o 0.~
o
o 0
B ,400
02
I I
I 2
0
I
I
I
3
4
5
0
DISTANCE ALONG BURNER ( ~ / D )
FIG. 5. Predicted mean oxygen concentrations from stochastic mixing model for different values of mixing rate intensity, compared with data.
(4)
which is the rate-controlling step in the Zeldovich mechanism, with [NO] < < [NO] eqin., for adiabatic c o m b u s t i o n products of kerosene and propane-air mixtures. The values of d [NO] / d t calculated for p r o p a n e are about a factor of two lower than the values calculated for kerosene for 0.6 ~ cb ~ 1.2. F o r n o n u n i f o r m mixtures, with an a s s u m e d gaussian distribution in fuel fraction of standard deviation half the mean fuel fraction, the factor of two difference in calculated NO formation rate persists. It is therefore c o n c l u d e d that the observed difference in Fig. 7 is p r i m a r i l y d u e to the difference in flame temperatures of the two fuels. Estimates of the characteristic times for
DROPLET EVAPORATION ON FUEL-AIR 3.0
I
I
I
I
I
I
I
I I
I
555 I
I
I
OATOMIZER I PROPANE X ATOMIZER ]I PROPANE OATOMIZER T KEROSENE
-.-. 2.0 ,N r',
o_1.0-----0.9
- x -
-
o.-O- 0%_0 _ o _
~) 0
O
0.8 0.7
I
I
I,
20
30
40
I
I
I 111
I
I
1
50 60 80 I00 200 :500 COMBUSTOR POWER INPUT ( I b f - f t / s e c )
400
I 500
FIG. 6. Correlation of nondimensional mixing rate intensity, fS/(Pj/MD 2)a/3 as function of atomizer jet power, Pj, for air-assist atomizers. I
1
t
Q; Z 0
~- I 0 0
-
I )C
Q
tr Iz ,,J u
z
0 t~
50
~C
X 0 IJ F--
PR
KEROSENE
N
o
~0
~:o.e
c
o ;-os x
d ~=0.9 0 ~=1.0
5
1 0
50
5
I tO0 COMBUSTOR
I i50 POWER
l 0
INPUT
SO (Ibf -ftl$oc)
I
9
IO0
ISO
FIc. 7. Burner exhaust nitric oxide concentration (ppm wet basis) as function of mean fuel-air equivalence ratio, ~b, and atomizer jet power for air-assist atomizers for kerosene and propane. droplet velocity e q u i l i b r a t i o n with the flow field, droplet evaporation, and the d y n a m i c response of droplets to the turbulent flow field, under conditions a p p r o p r i a t e to the range of operation of the air-assist atomizer, were m a d e and compared with the fuel-air mixing time. The basis of these computations is the mass transfer correlation of Ranz and Marshall ~ a n d the drag coefficient correlation of E i s e n k l a m et al? ~ Calculations were made for single
droplets in a series of assumed environments for the drops (constant temperature at various levels between the inlet air and adiabatic flame values; as well as linearly increasing environment temperature with distance, reaching the adiabatic flame temperature in two to four burner diameters). The droplet velocity relative to its-environment was also c o m p a r e d with the critical relative velocity above w h i c h a fully envelop-
556
SPRAY AND DROPLET COMBUSTION
ing flame is unstable, u The initial d r o p l e t mean relative velocity (300-900 f t / s ) is a b o u t two orders of m a g n i t u d e greater than the critical velocity above w h i c h an envelope flame is unstable (1.5-5 f t / s ) . Furthermore, the characteristic time of turbulent velocity fluctuations, -rp in the atomizer jet 9rf ~-- D j / V j
=
0.4 ms
I E]
I
I
PENTANE
I 0 0 psig
KEROSENE
IO0 psig
9
I
3 0 0 p$ig ISOOCTANE
I 0 0 psig
- - - - EQUIVALENT GAS PHASE MIXING B = 500
s-=
0
0
z 0 }-
(5)
rr
where Dj is the jet diameter and V. the m e a n jet velocity, is m u c h shorter than tfae time for the drop to a c c o m m o d a t e to these velocity fluctuations (=2 ms). T h e magnitude of the fluctuations (--- V , / 1 0 ) also exceeds the critical velocity for a stal~le envelope flame, so d r o p l e t combustion can never occur. Values for the average fuel-air mixing time, droplet velocity e q u i l i b r a t i o n time, vd, a n d evaporation time, re, for sauter mean diameter drops are given in T a b l e II for kerosene, for two i n p u t jet powers, P2 w h i c h span the range of interest for the air assist atomizer. T h e characteristic m i x i n g time, r,,, is 13-1 determ i n e d from Fig. 6. T h e ranges in r d a n d v e come from the range of assumed a m b i e n t environments for the drops in the burner. It is seen that "gm > > "re > Td
Z I0 bJ 0 Z 0 (J Z 51 bJ ~9 0
I
0
0
0
I
I
I
I
l
2
3
4
DISTANCE
A L O N G BURNER
(x/D)
FIG. 8. Measured cross-section average oxygen concentrations as function of burner length for pressure atomizer, with kerosene at 100 and 300 psig injection pressure, and with pentane and isooctane at 100 psig injection pressure. Fuel flow rate is held constant; stoichiometric overall operation.
(6)
Thus, droplet evaporation w o u l d not b e expected to influence significantly the fuel-air mixing process; u n d e r these conditions with air-assist atomizers w i t h liquid fuels such as kerosene, it is the kinetic energy of the fuel jet and the jet length scale (the integral scale) w h i c h controls the rate of fuel-air mixing a n d flame structure. 4.2 P r e s s u r e A t o m i z e r F i g u r e 8 shows the oxygen concentration profiles measured w i t h the pressure atomizer. Kerosene data for two different fuel pressures and different c a p a c i t y geometrically similar injectors (but the same fuel flow rate) are shown; the difference is small. To assist in
identifying the role of droplet vaporization, experiments were also carried out with single h y d r o c a r b o n fuels w i t h different physical p r o p e r t i e s - - p e n t a n e , and isooctane. The fuel injection pressure a n d injector were the same for pentane, isooctane, and kerosene at 100 p s i g injection pressure. T h e pentane and iooctane oxygen concentration results are also shown. T h e oxygen concentration profiles in Fig. 8 suggest two distinct regions; an initial region of more r a p i d fuel-air mixing (within the first burner diameter) followed b y m u c h slower mixing. T h e total m i x i n g achieved in the initial r a p i d mixing regime appears to d e p e n d on the fuel, with more volatile fuels mixing least. In the first burner diameter, the decay in oxygen
TABLE II Characteristic times for kerosene with air-assist atomizer Input power Pj, lbfft/s
Sauter mean diam, ~m
10 100
25 I0
mixing, ~'rn 6 2.5
Characteristic times in ms deceleration, ~a evaporation, % O.1-0.3 0.04-0.2
0.3-1 0.1-0.3
DROPLET EVAPORATION ON FUEL-AIR concentration is c o m p a r a b l e to the initial decay rates in Fig. 4 at higher jet input powers. A calculated oxygen concentration profile for 13 = 500 s -1, m a d e with the stochastic mixing model is indicated. For kerosene a n d isooctane, mixing rate intensities of the order of or greater than this value are achieved. T h e p o w e r i n p u t with the l i q u i d fuel jet is of order 10 -2 l b e f t / s . U s i n g the correlation of Eq. (2) d e v e l o p e d for gaseous fuel jets, this w o u l d give a mixing rate intensity J3 of about 20 s - l ; the stochastic mixing m o d e l then calculates an oxygen concentration profile indicated b y the d a s h e d line. T h e observed rate of m i x i n g m u s t be p r o d u c e d b y a different p h e n o m e n o n . Note that the mixing rates d i d not change significantly for kerosene w i t h a factor of three increase in a t o m i z i n g pressure. Such a change in pressure is estimated to decrease the sauter mean droplet diameter from 60 to 35 p.m, a n d increase the initial d r o p l e t velocity from 15 to 30 f t / s . To examine whether the structure of the flame with the pressure atomizer was different from the gaseous jet-type diffusion flame prod u c e d with the air-assist atomizer, high speed color movies of the pressure atomizer flame were taken. A print from one frame, with an explanatory schematic, is shown in Fig. 9. T h e structure is not significantly different from a gaseous jet flame. T h e scale on w h i c h motion of i n d i v i d u a l b u r n i n g eddies occurs is of the order of one-fifth the jet scale. No i n d i v i d u a l droplet c o m b u s t i o n is observed. T h e mixing rate intensity is a function of b o t h the rate of energy dissipation in the t u r b u l e n t mixing process, and of the length SCale l m of the concentration nonuniformities w h i c h are b e i n g mixed out. W i t h i n the equil i b r i u m range of t u r b u l e n c e xI < l m < I
557
/
FUEL NOZZLE ~LER
OUS :ULATION
(7)
where I is the integral scale of turbulence, a n d ~q = ( v / e ) 1/4 is the Kolmogorov microscale of turbulence, the m i x i n g rate intensity 13 is given approximately b y 13 ~- u' / l., ~- (~ / l ~ ) ~/3
(8)
where u ' is the m e a n t u r b u l e n t velocity fluctuation. It is significant that the mixing rate intensity increases w i t h decreasing length scale. W h e n the pressure jet atomizer is used, the Kolmogorov microscale ts approximately n ~ (u'l/v)
3/41
(9)
F o r the turbulent air flow into the burner, the
FIG. 9. Photograph from high-speed color movie of flame with pressure atomizer with kerosene fuel, indicating length scale of burning eddies, with explanatory schematic. Exposure time ~10-4s.
SPRAY AND DROPLET COMBUSTION
558
Reynold's n u m b e r is about 4000, u ' is a b o u t 0.6 f t / s ; thus, -q is about 100 txm w h i c h is comparable to the initial droplet diameter d o which is about 60 txm. Since 13 ~> 500 s -1, it follows from Eq. (8) that l,, ~< 400 p,m, i.e., of order or less t h a n about 7d o. The average distance b e t w e e n the drops in the fuel spray, l~, increases linearly with distance from the injector to about 30d o at a distance of x / D = 0.5 from the injector. Thus within the evaporation region, the following ranking of length scales exists: d o --= aq < < l m = l, < < 1
(10)
The local energy dissipation rate in the fuel-air mixing region, ~, can also be estimated. It follows from Eq. (8), for 13 ~> 500 s - l , that e ~> 300 ft 2 s -3. If the kinetic energy i n p u t with the liquid fuel jet is dissipated in t u r b u lent mixing w i t h i n the first burner diameter, then e -~ P ~ / M w h e r e M is the mass of fluid within the first diameter. Substitution of appropriate values gives e --= 103 ft 2 s-3. H o w e v er, not all of the fuel input kinetic energy is dissipated in this manner. The initial droplet velocity and the a m b i e n t velocity are comparable in magnitude; thus, though the drops are injected at least in part into a recirculation zone as indicated in Fig. 9, their velocity does not decrease to zero. From this analysis, it is reasonable to conclude that the length scale on w h i c h m i x i n g occurs is c o m p a r a b l e in magnitude to the droplet separation scale, and that the fuel jet provides the energy for the turbulent m i x i n g process. The e v a p o r a t i n g droplets can b e thought of as m o v i n g point sources of fuel vapor dispersed t h r o u g h o u t the flow field, as long as the droplets persist. Very high fuel vapor concentration gradients will exist a r o u n d the droplets; these high concentration gradients are r a p i d l y d i s s i p a t e d b y the combination of turbulent a n d laminar diffusion. Until the droplets have fully evaporated, their presence in the flow promotes enhanced m i x i n g of fuel vapor and air. Thus, if droplets evapo-
rate rapidly relative to the fuel-air m i x i n g process (as was the case with the air-assist atomizer), droplet evaporation w o u l d be expected to have only a small effect on the overall fuel-air m i x i n g process, whereas if the droplets evaporate slowly, mixing w o u l d be enhanced. The results s h o w n in Fig. 8 with the pressure jet atomizer with different injection pressures and different fuels were used to test this hypothesis. Estimates of characteristic droplet evaporation times, and droplet penetration distances prior to evaporation, were made for the two injection pressures for kerosene u s i n g the correlations of Ranz and Marshall 9 a n d Eisenklam et al. 1~ as outlined in Section 4.1. Table I I I gives the ranges of results for different assumed d r o p l e t environments. If we assume that the energy dissipation rate, e, is proportional to the initial kinetic energy of the fuel drops, and that the mixing length is proportional to the droplet separation distance (which is proportional to the initial d r o p l e t size), then from Eq. (8) 13 for the 300 p s i g injection pressure is twice that for the 100 psig injection pressure. However, the penetration distance is halved. The total amount of mixing, which is the integral of 13 along the flow path until the drops have evaporated, will be roughly proportional to the product of 13 and penetration distance and will, therefore, be constant. Furthermore, the calculated p e n etration distance is of the same order as the distance over w h i c h the rapid fuel-air m i x i n g occurs. The c o i n c i d e n c e of the oxygen concentrations for these two cases with kerosene can p l a u s i b l y be explained. To interpret the oxygen profiles from the different fuels, pentane, kerosene and isooctane, all at the same injection pressure, estimates were made of the steady-state evaporation constant, ko, h o = (8k/ptc.)
In (1 + B)
(11)
where k and c~, are the gaseous thermal conductivity and specific heat, and Pl is the l i q u i d
TABLE III Characteristic times and lengths for kerosene with pressure atomizer Injection pressure psig
Sauter mean diam. txm
Initial drop velocity m/s
Evaporation time, ms
Drop penetration
100 300
60 35
5.3 8.8
3-9 1-4
0.2-0.5 0.1-0.2
x/D
DROPLET EVAPORATION ON FUEL-AIR density; B (the transfer number) is given by
t~a,(T - T t ) / L where L is the latent heat at liquid boiling temperature T t. For the values of Reynolds and Prandtl numbers appropriate to these experiments, the evaporation time is approximately proportional to d~/k o" Table IV gives values of h 0 at T = 1000 and 2000~ with k a n d c evaluated at the film temperature ( T - TI)/]'n(T/TI). The values for kerosene are approximate since it is not a single hydrocarbon and its properties are not accurately defined. It is seen that the evaporation constant for p e n t a n e is larger than that for isooctane, and evaporation constants for kerosene and isooctane are comparable. Also, the surface tension of liquid hydrocarbon fuels generally decreases with decreasing specific gravity, and decreases as the l i q u i d temperaturre approaches the b o i l i n g point. Thus; even though the fuel injection pressure is the same for pentane as for the other fuels, the mean drop size is likely to be smaller. Thus, the characteristic evaporation time for pentane will be smaller than for isooctane and kerosene (which should have comparable evaporation characteristics). The total m i x i n g while droplets persist for pentane should therefore be significantly less, as the measured oxygen concentrations indicate.
5. C o n c l u s i o n s We have concluded that the influence of droplet evaporation on the fuel-air mixing process in liquid fuel sprays can be summarized as follows. While the droplets persist, and move through the a m b i e n t environment, they act as point sources of fuel vapor. The characteristic scale of the fuel vapor concentration n o n u n i f o r m i t i e s set up b y the motion and evaporation of the droplets in the spray is the droplet separation distance. Once the droplets have evaporated, the characteristic scale of fuel vapor concentration n o n u n i -
559
formities becomes the fuel jet length scale. Since mixing rate intensities vary as (e/1 ~)l/a, where e is the kinetic energy dissipation rate and l,, is the sclae of the nonuniformities, given mixing rate intensities are achieved in the droplet regime with m u c h lower energy dissipation rates than are required i n the jet mixing regime. The experimental results described in this paper with two types of fuel atomizer--air-assist and pressure j e t - - s u p p o r t this hypothesis. With the air-assist atomizers, the characteristic droplet evaporation times are small compared with the times characteristic of the fuel-air mixing process. The jet i n p u t power determines the mixing rate as in a gaseous fueled jet flame. With the pressure jet atomizer, the characteristic evaporation and mixing times are comparable. The mixing rate intensities achieved are comparable to those obtained with air-assist atomizers; the m u c h lower fuel jet i n p u t power is offset b y the m u c h smaller characteristic scale of fuel-air nonuniformities with the pressure jet atomizer. The evaporation characteristics of the l i q u i d fuel drops determine the total a m o u n t of mixing achieved while the droplets persist, with the more volatile fuels mixing the least.
Acknowledgment This work has been supported in part by the Environmental Protection Agency under Grant No. R-800729-02-0, by the Energy Research and Development Administration under Grant No. E (11-1)2680, and by the National Aeronautics and Space Administration under Grant No. NGR 22-009-378. The assistance of Monima Briggs and David Bigio is gratefully acknowledged.
REFERENCES 1. CHIGIER,N. AND MCCREATH,C. G., Acta Astronautica 1, 687-710, (1974).
TABLE IV Properties and steady state evaporation constants of different fuels
Fuel n-pentane isooctane kerosene
Boiling point ~
Specific gravity
556 670 760-940
0.631 0.707 0.84
ho T = 1000~ ft 2/ s 2 x 10 -6 1.3 x 10 -6 1.1 x 10 -6
ho T = 2000~ ft 2/s 4.8 x 10 -6 4.2 x 10 -6 4.2 x 10 -8
560
SPRAY AND D R O P L E T C O M B U S T I O N
2. ONUMA,Y. ANDOGASAWARA,M., Fifteenth Symposium (International) on Combustion, pp. 453466, The Combustion Institute, (1974). 3. MELLOR, A. M., Comb. Sci. Tech., 8, 101-109 (1973). 4. ComasiN, S., AICHEJ. 3, 329-331 (1957). 5. POMPEI, F. AND HEYWOOD, J. S., Comb. Flame, 19, 407-418 (1972). 6. FLAGAN,R. C. ANDAPPLETON,J. P., Comb. Flame, 23, 249-267, (1974). 7. KOMIVAMA, K. " T h e Effects of Fuel Injector Characteristics on Fuel-Air Mixing in a Burner,"
8.
9. 10.
11.
Ph.D. thesis, Mechanical Engineering Department, M.I.T., (1975). APPLETON, J. P. AND HEYWOOD, J. B., Fourteenth Symposium (International) on Combustion, pp. 777-786, The Combustion Institute, (1972). RANZ, W. E., AND MARSHALL, W. R., Chemical Engineering Progress, 48, (1952). EISENKLAM,P., ARUNACHALAM,S. A., ANDWESTON, J. A., Eleventh Symposium (International) on Combustion, the Combustion Institute, (1967). OGnsAw~, M., AND SAMI, H., Jap. Soc. Mech. Engr. Bull. 13, 407-426, (1970).
COMMENTS F. V. Braceo, Princeton University, USA. How do you reconcile the presence of recirculation with the assumption of one-dimensionality? Would you have a stable flame without recirculation in your configuration? Please check the paper by Onuma, Ogasawara, and Inoue for indication of strong radial variations of most relevant parameters. Authors" Reply. The radial concentration profiles in our burner were measured; variations were less than -+20% from the mean. Hence, we feel that cross-section average concentrations reasonably reflect the local conditions in the flow. The one dimensional model used in our paper is intended to describe the gross features of the fuel-air mixing process. The model is not expected to be able to predict local conditions with a high degree of accuracy; it was developed a n d used to help us interpret the experimental data and explain the relative importance of the processes occurring in the evaporating fuel spray. We were not attempting to predict flame stability, nor the details of the recirculating flow. Our experimental configuration cannot be readily compared with that used by Onuma, Ogasawara and Inoue; ours is a high Reynolds n u m b e r jet flow, theirs is a m u c h lower Reynolds n u m b e r jet flow, and the geometrical configurations of our two burners are quite different.
R. E. Pavia, Aeronautical Research Laboratories, Australia. Reference was made in the answer to the previous question of a 20 percent variation for the pressure jet flames in the radial distribution of oxygen concentration. It would appear to me that this could provide a physical explanation of the different fuel oxygen concentrations, for the pressure jet spray flames of isooctane, kerosene and pentane.
If, in fact, the latter fuel produces finer drop sizes and evaporates more rapidly, combustion may be completed before the spray reaches the combustion walls, allowing a significant part of the air to by-pass the flame. In this case the effective diameter of the flame may not be the combustor diameter D used in the turbulent mixing parameter. Would this discrepancy have a significant effect on the time turbulent mixing in the combustor?
Authors" Reply. We do not believe the explanation offered by Dr. Pavia could fit our experimental data. For the pressure jet spray flame, the characteristic lengthscale of the fuel-air nonuniformities b e i n g mixed out has to be orders of magnitude less than the jet scale because the energy dissipation rate is orders of magnitude lower than in the air blast atomizer spray flame, yet equivalent mixing rate intensities our achieved. Our estimates show the characteristic scale of these nonuniformities in the pressure jet spray flame is comparable to the droplet separation distance within the spray, while in the air blast atomizer spray flames, the characteristic length scale is the jet scale. Even if the pressure jet spray flame does not quite fill the burner, the change in jet length scale does not approach the magnitude of the change required to explain our data.
A. M. Mellor, Purdue University, USA. Our results and conclusions reported elsewhere in these proceedings are in essential agreement with those of Prof. Heywood and coworkers. Later work in our laboratory also shows the importance of fuel distribution, more explicitly than in the preliminary correlation we reported upon.