NASA Technical W-nomdum 86944 

, 1 

9 Liquid Fuel Spray Processes 

ii in High-pressure Gas Flow 

(NASA-TI-€6944) LIQUID FUEL SPRAY PBOCBSSZS 

?I HIGH-PIBSSURE CIS FLOW (11151) 22 p EC AOZ/HP AP1 CSCL 20D 

Robert D. lngebo 

Lewis Research Center 

Cleveland, Ohio 

Prepared for the 

Third International Conference on .& 

C 

$. Liquid Atomization and Spray Systems 

"t sponsored by ICLASS 

London, United Kingdom, July 8-10, 1985 

1 
LIQUID FUEL SPRAY PROCESSES IN HIGH-PRESSURE GAS FLOW 

Robert D. Ingebo* 

Atomization of single liquid jets injected downstream in high-pressure and high-velocity airflow 

was investigated to determine the effect of airstream pressure on mean drop size as measured 

with a scanning radiometer developed at NASA 

Lewis Research Center. For aerodynamic-wave 

br'?akup of liquid jets, it was found that mean 

drop diameter D32 varied with -3: 5s tream pressure Pa as follows: D32 s Pa . This 

result was compared with the effect of airstream 

pressure on drag and heat-transfer coefficient; 

of accelerating and vaporizing d~ops. 

INTRODUCTION 

The fluid mechanics of producing sprays and the aerothermodynamics 

of droplet acceleration and vaporization have been receiving considerable attention ir spray process research studies. Spray 

drying for food processing, spray painting of manufactured items, 

pesticide sprays for agricultural use, icing sprays in wind tunnels, and fuel sprays in gas turbine combustors are some of the 

major fields of application of spray process studies. In the 

field of combustion, Ingebo (1) determined that the fuel spray 

vaporization rate is very import2nt in determining burning 

characteristics such as ignition delay, flame stability, and 

completeness of burning. Fuel droplets formed by atomization 

simultaneously accelerate and evaporate in airstreams and thereby 

produce a combustible fuel-air mixture. Chemical reaction between 

fuel and air, or oxidznt vapor, produces a combustion gas stream 

of rel'ltively high velocity, temperature, and pressure, which 

accelerates the drops as the chemical reacti~n continues to accelerate the combustion gas flow in the combustor. Thus, a clear 

understanding of liquid f~el spray combustion requires knowledge 

of how aerothermodynamics and fluid mechanics may control the 

processes of atomization, vaporization, and acceleration, and how 

these processes are related t> chemical reaction in determining 

combustor perfornance and exhaust emissions. More specifically, 

in~tial drop size and velrcity as well as combustion gas conditions must be known to caiculate heat-transfer and drag coefficienis and thereby determine the lifetime histories of burning 

fuel drops. New data of this type are especially nneded to 

*National Aeronautics and Space Administration, Lewis Research 

Center, ?leveland, Ohio 44135 
determine rates of drop vaporization and combustion under highpressure gaz flow conditions. 

Empirical expressions are quite useful in the design of fuel 

injectors for combustor applications since fuel nozzles can be 

calibraLed with water, and mean drop diameters can then be calculated for the desired fuel, such as Jet-A, with the aid of such 

correlations. The product of the Weber and Reynolds numbers 

WeRe has been corre ated with atomrzation data, and, for the 

condition WeRe > LOi, atomization occurs in the regime of aerodynamic breakup. This condition was chosen for this investigation 

since the airstream velocity in turbojet combustors at idle, takeoff, and cruise operating conditions is usually quite high; i.e., 

combustor reference velocities are generally of the order of 20 to 

30 m/s. 

Since previous studies on atomization were limited to atmospheric pressure conditions, the present investigation was made to 

determine thz effect of airstream pressure on mean drop size. 

Water jets injected downstream were atomized in the airr'ow, and 

mean drop diameters were measured with an improved scanninq radiometer recently developed at NASA Lewis Research Center. Combustor 

inlet-air static pressure was varied £row 0.10 to 2.10 YPa over a 

range of airflow rates per unit area of 10 to 177 g/(cm-) is) at 

293 K. Two injector tubes with orifice diameters of 0.1016 and 

0.216 cm, respectively, were used with liquid flow rates of 27 to 

68 liters/hr. Mean drop diameter data were correlated with the 

Weber-Reynolds number WeRe an a pressure sensitive molecular -9 scale dimensionless group gl/c . The resulting empirical relations for liquid jet breakup were compared with ex~ressions 

obtained in previous experimental investigations. Also, the 

effect of airstream pressure on atomization is compared with airstream pressure effects on droplet acceleration and vaporization 

rates as reported in previous spray studies in order to bring 

together high-pressure airflow data for spray processes reported 

in the literature. 

APPARATUS AND PROCEDURE 

The high-pressure airflow apparatus and auxiliary equipment are 

shown in figure 1. The test section, water spray, and scanning 

radiometer optical path are shown in figure 2. Two 5.1-cmdiameter windows pass the laser beam through the spray 25.4 cm 

downstream of the fuel injector. Single jets of water were 

injected downstream at the duct centerline with the fuel tube 

shown in figure 2. Two different 0.635-cm-outside-diameter tubes 

were used to obtain drop size data with two orifice diameters of 

0.1016 and 0.216 cm, respectively. 

At 273 K, single water jets were injected downstream at flow 

rates of 27 and 68 liters/hr, respectively, as measured with a 

turbine flowmeter. After setting water and airflow rates, mean 

drop diameter data were obtained with the scanning radiometer 

shown in figure 2. The optical system consisted of a 1-mW heliumneon laser, a 0.003-cm-diameter aperture, a 7.5-cm-diameter collimating lens, a 10-cm-diameter converging lens, a 5-cm-diameter 
collecting lens, a scanning disk with a 0.05-cm-diameter hole, a 

timing light, and a photomultiplier detector. 

The spatial resolution of the scanning radiometer is 2.86 cm, 

which is also the laser beam diameter in the test section where a 

sufficient volume of spray was sampled to minimize spray pattern 

effects on mean drop diameter. ~lso, the effect of drop size 

distribution function on the scanning radiometer measurements is 

discussed in detail by Dobbins, et al. (2), who found that the 

irradiance distribution is only weakly related to the particle 

diameter distribution function. Thus, irradiance distribution 

was used in determining Sauter mean diameter, and changes in the 

drop size distribution function were assamed to have negligible 

effect on mean drop size correlations. Reproducibility tests 

showed that experimental measurements of mean drop diameter agreed 

within 25 percent. Three sets of monosized polystyrene spheres 

having diameters of 25, 50, and 100 pm, respectively, were used 

to calibrate the scanning radiometer. A more complete description 

of it and the method of determining mean particle size are 

discussed by Buchele (3,4) . 

EXPERIMENTAL RESULTS 

To determine the effect of airstream pressure on liquid jet atomization, an ir,:proved model of the scanning radiometer was developed 

at NASA Lewis Research Center. It was used to measure the mean 

diameter of droplets in sprays produced by liquid jets breaking up 

in high-pressure and high-velocity airflow. 

Liquid jet atomization 

In a previous study conducted with atmospheric pressure airstreams, drop size distribution data for the breakup of liquid 

jets were obtained with the high-speed droplet tracking camera 

shown in figure 3 and described by Ingebo and Foster (5). Photomicrographs of the droplets and a schematic of the liquid jet 

breakup process are shown in figure 4. Short wavelength disturbances near the injector orifice produce relatively small droplets 

and grow into longer wavelengths as the jet penetrates farther 

into the airstream and produces relatively large drops. Mean 

drop size measurements obtained with this imaging technique gave 

the data shown in figure 5 for five different liquids. The following correlation of the ratio of mean diameter to orifice diameter g30/Do with the W ber-Reynolds number WeRe was derived 

for values of WeRe < 10 %: - 

In deriving this relationship in reference (5), the spatial size 

distribution data obtained with the high-speed came-a were mass 

weighted using the liquid-concentration profile data obtained 

with a sampling probe. The temporal size distribution produced 

is more useful in combustion studies. 

In a later study, an early model of the scanning radiometer as 

described by Ingebo (6) was used to study liquid jet breakup. 

Here it was found that equation (1) was valid only in the regime 
of capillary-wave break p which occurs for values of WeRe < lo6. tl At values of WeRe > 10 , it was found in reference (6) that 

for liquid jet atomization in the regime of acceleration-wave 

breakup. Date from reference (6) for both capillary and 

acceleration-wave breakup are plotted in figure 6. 

In this investigation an attempt was made to extend the applicstion of equation (2) to the atomization of liquid jets in highpressure airflow. Single jets of water were injected axially 

downstream in airstreams having static pressures from 0.1 to 

2.7 MPa. Atomizatisn data obtained with the two different fuel 

injector tubes are shown in figure 7 where the reciprocal mean 

drop diameter D,-~ is plotted against airstream mass velocity 

p V,. As shown, the effect of paVr on D,'~ decreases marke81y as airstream pressure is increased from 0.1 to 2.7 MPa. To 

extend equation (2) and make it applicable to high airstream pressules, (Do&,) (WeRe)'Oa4 is plotted against the pressure sensitive 

grc.up g1/c2 (fig. 8). In this dimensionless group g is the 

accele-ation due to gravity, 1 the mean free molecular path, 

and E~ the root-mean-square velocity of the air molecules. 

The evaluation of this dimensionless group is as follows. The 

mean free molecblar patb 1 may be expressed as 

since the number of molecules per cubic centimeter n is 2.7x1019 

at a temperature of 0 OC and a pressure cf 1 atm and the diameter 

of an air molecule Dg is 3.7x10-* cm. 

- The root-mean-square molecular velocity E may be expressed as 

c = (~RT/M) Oo5, which yields 

Since g is 980 cm/s/s, 

From the data lotted in figure 8, it is evident that 

Dm-' (91/~ -2 o*'~. Thus, the following expression is obtained 

from the data plotted in figure 9: 

0.4 -2 0.15 D0/D32 = 1.2 (WeRe) (gl/c ) 

which agrees with the expression obtained by Ingebo (7) for the 

cross stream injection of liquid jets - i.e., 

-2 0.15 Do/D32 = 1.4 (WeRe) O* (gl/c ) 
for accel ration-wave breakup of liquid jets with values of % WeRe > 10 . Since the molecular-scale momentum-transfer group 

gl/c2 is inversely propor ional to airstream pressure, it is f evident that gl/c2 z Pa- . It was jyst shown that, at 273 K 

and 1 atm pressure, ?l/c2 = 2.55~18- I,lso, since WeRe z Pa, 

equation 13) shows that D32 z Pa - *25' Thus, the effect of 

airstream pressure on D32 is somewha; less than that which 

would be obtained by extrapolating an atmospheric pressure expression up to high airstream pres u es. For exampl?, equation (2) 

would indicate that D32 z Pa -8.5. 

A comgarison of the results obtained by several investigators 

of airstream effects on atomization is given in table I. Best 

agreement was obtained wi h Lorenzetto and Lefebvre (8j where it 

was found that D32 z Pa *5-3. This is in good agreement with 

equation (3) since it is assumed that Dm 7 D32 for the measurements of D made with the improved scanning radiometer in the 

present st&. Kim and Marshall (11) and Wolfe and Andersen (12) 

give values more in agr e nt with the theoretically predicted 

relationship D32 z Pa -'*" given by Adelberg (13). The atomization data presented in this study and in reference (8) were 

obtained over a much broader airstream pressure range than that 

used in references (11) a~d (12). This indicates a need to 

improve the theory proposed in reference (131, which does not 

account for molecular-scale forces such as those given in the 

group gl/c2. 

Droplet drag coefficients for accelerating sprays 

The high-speed droplet tracking camera used to obtain drop size 

data also gave drop velocity data. Thus, it was possible to 

determine drag coefficients of drops accelerating in gas streams. 

In the study described by Ingebo (14), it was found that the drag 

coefficient C:j couid be correlated with Reynolds Re .ased on 

drop diameter as follows: 

at atmospheric pressure. 

Studies of propellant atomization and droplet acceleration in 

the hiqh-pressure rocket combustor shown in figure 10 were made 

with the droplet tracking camera as described by Ingebo (15). It 

was found that the drag coefficient based on the mean drop diameter D20 could be correlated with the Reynolds number Re and 

the dimensionless group gl/c2 as follows: 

where Re is based on the area number mean drop diameter D20. 

A plot of the data used to derive this expression is shown in 

figure 11. From equation 4, the effect 8f irstream pressure on 

drag coefficient appears to be Cd z *6'. As in the study 

of atomization, the effect of airstream pressure is somewhat less 

than that predicted from atmospheric pressure studies. 
Heat-transfer coefficients for vaporizing drops 

In the study of vaporization rates of single drops in atmospheric pressure airstreams, Ingebo (16) found that the Nusselt 

number Nu could be correlated with the product of the Reynolds 

and Schmidt numbers ReSc as follows: Nu = 2 + 0.30(ReS~)~*~, 

where Nu = hD/kg, h is the heat-transfer coefficient, D the 

drop diameter, Sc = p/bpw,. k2 and p the gas thermal conductivity and viscosity, resp ctlv ly, and the vapor diffusivity. 

In a later study by Ingebo (17). at anb3?rstrean static pressure 

range of 0.6 to 2 atrr,, data for the Nusselt number were obtained as 

shown in figure 12 and the following expression was derived: 

where k is the thermal conductivity of the vapor. Thus, 

NU z pao: However, airstream pressure still influenced vaporization rate by its effect on temperature difference across the 

air-vapor film surrounding the drop. 

CONCLUSICNS 

As a result of this study and previous spray studies in highpressure airstreams, graphical or numerical integration methods 

of calculating spray vaporization rates will not be very useful 

until more atomization, drag coefficient, and heat-transfer 

coefficient data are available for very high-pressure airstreams. 

The effects of airstream pressure on mean drop diameter D32, 

drag coefficient Cd, and Nusselt number Nu are shown in 

table I1 for comparison. Probably the most critical need at present is for high-pressure airstream data on drop size distribution 

and on mean drop size for spray processes in high-temperature and 

highly turbulent gas streams. Also, a more fundamental picture 

of simultaneous heat, momentum, and mass transport properties is 

needed for a more comprehensive treatment of fuel spray processes 

and the overall combustion process. 

NOMENCLATURE 

b9,w = ~olecular mass diffusivity (g/(cm) (s) ) 

Cd = drag coefficient 

- 

c = root-mean-square molecular velocity (cm/s) 

D = diameter (cm) 

D32 = Sauter mean diameter, ln~~/ln~2 (cm) 

9 = acceleration due to gravity (980 cm/s2) 

h = heat-transfer coefficient (g-cal) / (sec) (cm2) (OC) 

k = thermal conductivity (g-cal) / (sec) (cm2) ( OC/'cm) 

1 = mean free molecular path (cm) 
M = molecular weight 

Nu = Nusselt nsmber for heat transfer, hD/k 

n = number of molecules per unit voluxe 

P = static pressure (atm) 

R = universal gas constant (8.31:-lo7 ergs/(K) (mole)) 

Re = Reynolds number based on orifice diameter, DoTI,/yl 

Sc = Schmidt number based on mass aiffusivity, g/bg,, 

V = velocity (cm/s) 

We = Weber number based on orifice diameter, D,~,v:/cJ 

T = kinematic -~iscosity (cm2/s) 

a = surface tension (dynes/cm) 

P = density (g/cm3) 

V = absolute viscosity (g/(cm) (s) ) 

Subscripts: 

a = airstream 

9 = gas molecule 

1 = liquid 

m = mean 

o = orifice 

r = relative 

v = vapor 

REFERENCES 

1 Ingebo R D , "Atomizing Characteristics of Swirl Can Combostor 

Modules with Swirl Blast Fuel Injectors,'' NASA TM-79297, 1980. 

2 Dobbins R A, Crocco L, and Glassman I, AIAA J., L (1963) 1882. 

3 Buchele D R, "Scanning Radiometer for Measurement of ForwardScattered Light to Determine Mean Diameter of Spray Particles," NASA 'I'M-X-3454, 1976. 

4 Buchele D R, "Particle Sizing by Measurement cf ForwardScattered Light at Two Angles," NASA TP-2156, 1983. 
5 Ingebo R D, and Foster H ii, "Drop-Size Distribution for CrossCurrent Breakup of Liquid Jets in Airstreams," NACA TN-4087, 

1957. 

6 Ingebo R D, "Capillary and Acceleration Wave Breakup of Liquid 

Jets in Axial-Flow Airstreams," NASA TP-1791, 1981. 

7 xngebo R D, "Aerodynamic Effect of Combustor Inlet-Air Pressure 

on Fuel Jet Atomization," NASA TM-83611, 1984. 

8 Lo.enzetto G E, and Lefebvre A H, AIAA J., (1977) 1006. 

9 Nukiyama S, and Tanasawa Y, Japan Society of Mechanical Engineers, Transacz, 2 (1939) 63. 

10 Weiss M A, and Worsham C H, ARS J., a (1959) 252. 

11 Kim K Y, and Marshall W R, AIChE J., 17 (1971) 575. 

12 Wolfe H E, and Andersen W H, in "Proceedings of the 5th International Shock Tube Symposium," Naval Ordnance Laboratory, 

White Oak, MD, 1965, pp. 1145-1169. 

13 Adelberg M, AIAA J., (1968) 1143. 

14 Ingebo R D, "Drag Coefficients for Droplets and Solid Spheres 

in Clouds Acceleratitlg in Airstreams," NACA TN-3762, 1956. 

15 Ingebo R D, "Vaporization Rates of Ethanol Sprays in a Combustor with Low Frequency Fluctuations of Combustion-gas 

Pressure," NASA TN-D-1408, 1962. 

16 Ingebo R D, "Vaporization Rates and Heat-Transfer Coefficients 

for Pure Liquid Drops," NACA TN-2368, 1951. 

17 Ingebo R u, "STudy of Pressure Effects on Vaporization Rate of 

Drops in Gas Streams," NACA TN-2850, 1953. 
TABLE I. - EXPERIMENTALLY DETERMINED E; 'GNENTS OF 

PROPERTIES PROPORTIONAL TO RECIPROCAL MEAN DROP 

DIAMETER D;' FOR AERODYNAMIC-WAVE BREAKUP 

OF LIQUID SHEETS AND JETS 

Airstream 

exponents 

MPa 

Experimental (eq. (3) ) 

Nukiyama and 

Tanasawa (9) 

Weiss and Worsham (10) 

Kim and Marshall (11) 

Wolfe and Andersen (12) 

Lorenzetto and 

Lefebvre (8) 

aUsed variable 1 + p,/pl. 

bJ3xponent for initial drop diameter instead of orifice 

diameter. 

TABLE 11. - COMPARISON OF EFFECT OF AIRSTREAM 

PRESSURE Pa ON SPRAY PROCESS PARAMETERS 

Dm and Cd AND NUSSELT NUMBER Nu 

Atomization -2 0.15 Do/D,,, = 1.2 (WeRe) Ow4 (gl/c ) 

-0.25 

Dm % 'a 

Vaporization 6 -2 0.6 Nu = 2 + 2.6~10 [(ReSc) (gl/c )I 
TOR 

1 .A 

Figure L - Apparatus and auxilliary quiprr~ent. 
AIR 

q-6 cm@l 

WATER -- r LIGHT SCATTERING 

\!+.- /' ANGLE, 0.05 rad / ,, 10 cm 

p- lOOcm -= 

Figure 2. - Highpressure test section and scanning radiometer optical path. 
FUEL-AIR MIXTURE INDICATOR-'I SPARK GAP 

Figure 3, - Diagram of test section equipment and camera unit 
. 

? 

1 

6 

ORdw~~ PAW 18 " QUA LIT^ 

Figure 4 - Schematic of a liquid jet breaking up into ligaments and drops with crossstream inidion. 

I I. 

j ; 

{ 

1 

1 

i 

Ir 
0 ISOOCTANE 

0 WATER 

V CARBON TnRACHLORlDE 

A JP-5 FUEL 

V BENZENE 

Figure 5. - Relation between mean to orifice diameter ratio 

and Weber-Reynolds number ratio. 

ORIFICE 

DIAMETER, 

Figure 6. - Relation between orifice to mean diameter ratio and Weber-Reynolds 

number. 
d 

5 

-;.; loo n 80 g :I 60 

2 - 40 

% (a) Orifice diameter. 0.216 cm. 

40 I 1 

10 20 40 60 80 100 200 

AIRSTREAM MASS 'JELOCIN, 

paVr, g~~m*-~ 

(b) Orifice diameter, 0.1016 cm. 

Figure 7. - Variation of reciprocal mean 

drop diameter with airstream mass 

velocity. 
INLET-AIR 

STATIC 

PRESSURE, 

MPa 

0 a10 

.m 

0 .30 

D .50 

- 

5 (a) Orifice diameter, Do, 0.216 cm. 

n 

0 

n 

(b) Orifice diameter, Do, 0.1016 cm. 

Figure 8. - Correlation of mean drop diameter Dm 

with air dream pressure sensitive group gllc-2 
ORIFICE 

DIAMER, 

0, 

cm 

Figure 9. - Correlation of mean drop diameter Dm with dimensionless groups 

gl ic2 and W eRe. 
INJECTOR INFRARED FILM (9 il2 in) 

PROJECTION \ / 

LENS I 

ROTATING 

MIRROR 

Figure 10. - Diagram of experimental apparatus. 
FUEL SPRAY NALUATION TEMPERATURE AT .- 

FINE COARSE EXPERIhEMAL EXPERIMENTAL TOTAL HEAT 

NUSSELT REYNOLDS REQUIREMENT 

NUMBER, NUMBER, PER UNIT OF 

N"20 Re20 MASS, 

H-rs 

g-call g 

0 0 f T = 1T9 + T,112 

0 0 Tstoic TIf = (TStoic + Tx)12 

f 

A 

T ' f 

Tstoic TIf = (TStoic + T,)/ 2 T'f 

(CDla = 0.13 ~e& M(gl/c)-a 

1.6 

Figure 11. - Correlation of drag coefficient 

with Reynolds number and gl~c-~ group. 
0 n -OCTANE AIR 29. 0 

a BENZENE AIR 28.0 

ACETONE AIR 28.0 

0 ACETONE AIR 93.0 

D METHANOL AIR no 

A METHANOL HELIUM 260 

V METHANOL ARGON 15.5 

A METHANOL CARBON 13.0 

DIOXIDE 

FR~~SSLING'S DATA 

b WATER AIR MO 

E~esc) (g~lc-~)]~-k~lk,,)~* 5, [(dcplbgn,) (gllc2)]~ ( kglk,,)o. 

Figure 12 - Correlation of Nusselt number with momentum-transfer groups 

and thermal-conductivity ratio. 

pn 

atm 

0.6-2 0 

.6-2 0 

.6-2 0 

.6-2 0 

.6-2 0 

.97 

.97 

.97