FOR AERONAUTICS

TECHNICAL NOTE 3883

PROPELLANT VAPORIZATION AS A CRITERION FOR

ENGINE DESIGN; CALCULATIONS OF CHAMBER LENGTH TO

VAPORIZE VARIOUS PROPELLANTS

By Richard J. Priem

Lewis Flight Propulsion LaboratoryCleveland, Ohio

Washington

September 1958

AFW’C. i~—-,. . .

TECHLIBRARYKAFB,NM

NATIONAL ADVISORY C@MHTE13 M)R A3ROI?YWEK

TECEl%tCALNOTE 3883

PROP13LUNl VAPORMA!ITOliAS A CRITERION IXIRROCKEC-E’JGRW

0fJb7C174

DESIGNj

CAUXIUUTONS OF CIiM13ERIJNG’I’E!03VAPORE?X VAR1OUS PROPEIUNTS

By Richard J. Priem

Vaporization rates were calculated for drops of ~-heptane, ammonia,hydrazine, oxygen, and fluorine. The percent propellant vaporized is

s correlated with an effective chamber length for various spray conditions,r-l and various engine-alesign and operating parameters. The results show$ that the effective chamber length required to vaporize a given high per-* centage of propellant is the shortest with oxygen and incre~es for

fluorine, heptane, ammonia, and hydrazine in that order.

INTRODUCTION

Calculations were reported in references 1 and 2 for the rate offuel vaporization in the combustion chamber of a n-heptane - oxygen rocketengine. IIowthe vaporization-rate calculations c=uld be used to predictcombustion efficiencies and to design combustors was also indicated.The results of these calculations, based on ~ combustion model in whichvaporization of the fuel was rate controlling, showed how vsrious design-and operating-parameter changes would affect the vaporization rates of~-heptane drops burning in oxygen. Reference 2 also indicated that asmall nuuiberof large drops that do not vaporize completely may %e re-sponsible for much of the loss in rocket-engine performance. Experimentalresults obtained with an engine (ref. 3) using ~-heptane as the fuelagreed with the calculations for sprays having geometric standard devia-tions of 2.5 and mass median drop radii of 70 to 280 microns dependingon the type of injector.

This report covers the additional calculations made at the NACALewis laboratory to determine the vaporization rates of oxygen, fluorine,ammonia, and hydrazine in rocket engines. The results axe presented interms of an effective chamber length required to vaporize a given percentof the propellant. The analysis assumes that the vaporizing propellantis burned instantaneously at stoichiometric conditions. The analysisfurther assumes that there is one-dimensional steady-state flow and that

●

2 NACA TN 3883

all drops sre produced at the injector face and have equal velocities.The model and equations of reference 1 are used to determine the veloc-ity, mass, and temperature of the indiviilual-drops at various distancesdownstream.

METHOD

The calculation used the model, the iteration technique, and thefollowing equations from

Mass-transfer rate,

Heat-transfer rate,

Drop-heating rate,

Drop acceleration,

Gas velocity,

Drop-size distribution,

references 1 and 2:

w= AI@

qv = Ah(T - Tt)Z

dT% ~ - WA

%=-

dv ~ CD~~2—=-.de 8 pzr

L1-=1-.. z ‘imi ,0%in

$ exp [u]2in Q-

MM-i in ag

(1)

(2)

(4)

(5}

(6)

For calculation purposes the propellant was assumed to bezi~ five drop-size groups, which were arbitrarily chosen from equation (6) as thoseequal to 10, 30, 50, i’O,and W perce@ of the wss in ~OPS smallerthan the drop radius. With a median drop radius of 75 microns and astandard devtation of 2.3 the five drop radii selected by this method

.

0

* NACA TN 3883 3

. were 25, 48, 75, 120, and 225 microns. The number of drop in each groupwas so chosen that each group had 20 percent of the total mass. Thesymbols used in this report sre defined in appendix A.

The equations were solvedby an iterative procedure as describedin reference 4. The average physical properties in the mantle surround-ing the drop were also determinedly the method described in reference 4.

gTable I shows the design and operating conditions used in the calculations.Append& B shows equations used to describe the physical properties for

d heptane, smmonia, and hydrazine vaporizing in a gaseous-oxygen atrnos-pherej oxygen vaporizing in a gaseous-heptane atmosphere, and fluorinevaporizing in a gaseous-hydrogen atmosphere.

RESULTS AND DISCUSSION

The results of the calculations are droplet histories, examples ofwhich are shown in figure 1. Droplet temperature, droplet velocity,gas velocity, percentage of mass vaporized, and valorization rate meshown at various chsmber lengths for ~-heptane, ammonia, hydrazine,oxygen, and fluorine. The conditions used in the calculations shownin figure 1 are indicated in table I. The initial temperature of heptaneand hydrazine was taken at room temperature. Ammonia was arbitrarilytaken at its normal boiling point while the initial temperature forfluorine and o~gen corresponds to the normal boiling point of nitrogen.The effect of selecting other temperatures and conditions is indicatedin reference 1 and later in the Correlation of Results section.

Temperature Histories

The temperature histories of the small drops (25 microns), mediandrops (75 microns), and large drops (225 microns) in the spray areshown in figure l(a) for five propellants. The calculated temperaturesrise to a steady value corresponding to a wet-bulb temperature. Thewet-bulb temperature and corresponding vapor pressure are tabulated inthe following table for the various propellants. Also t&bulated is theratio of the distance required to attain the wet-bulb temperature tothe distance required to vaporize the drop.

—

Propellant Wet-bulb Vapor pressure Ilength to wet bulbtempera- at wet btib, Length to vaporizeture, lblsq in.

%

Heptane 845 133 1/6H@azine 860 165 @5Ammonia 555 205 1/15Oxygen 235 275 1/15Fluorine 220 255 1/15

~A3A ‘IN3883*

Gas-Velocity Eistories .- *

The average velocity of the vapori~ed and burned propellant atvarious positions down the chamber is shorn-in figure l(b). For allpropellants this gas velocity initialQ” increases rapidly and thenasymptotically approaches the final gas:velocity. The gas-velocitycurves for oxygen and fluorine sre about the same (liquid oxygen beingslightly higher than fluorine) and were’higher than the other threepropellants. The lowest gas velocityThe ranking order of propellants withit at a fixed chamber length was (1)(4Y ammonia, and (5) hydrazine.

Droplet-Velocity

curve was oltained with hyitrazine.respect to decreasing gas veloc- %oxygen, (2) fluorine, (3) ~-heptane~ 8

Histories *’

Droplet-velocity curves for the small-, median-, and large-diameter&rops are shown in figure l(c) for the five propellants. The velocity

“*

of the drop when it is 99 percent vaporized_is indicated by the solid.symbol. The lowest velocity at complete vaporization was obtained with -the high-density fluorine. The small drops-acceleratefaster than the_larger drops; thus, a mixing effect occ~s.~ecause of the relative mot_ion - ~of the drops.

Mass Histaries

Curves showing the percent mass vaporized of the small, median, andlarge drops in the spray as well as the average for the spray are shownin figure l(d) for the five different propellants. The order of thepropellants, based on vaporization rate; was (1) o~gen, (2) fluorine,(3) n-heptane, (4) ammonia, and(5) hydrazine. Theshapesofal-l thecurv~s were simiw with the exception.of n-heptane which crosses theatmnoniacurves. W curves show that in 2-inches the small drops ofall propellants are almost completely vaporized. However, in 2 inchesonly a small percentage of the large drops was vaporized.

Vaporization-Rate Histories

The total-vaporization-rateper unit-length curves (fig. l(e)) aresimilar to those shown in references 1 and 2. There are two peak pointsand a minimum for each propellant. Th highest peak vaporization rateis obtained with fluorine. Second highest peak is with oxygen, thirdwith ammonia, fourth with heptane, and the lowest peak occurs with hydra- , .zinc. The peak values occur at differetitpositions in the cham%er withthe various propellants. The peak occurs glosest to the injector facewith oxygen and fluorine. The peak is the farthest from the injector ,_ . _with heptane and hydrazine. Ammonia falls between the two extremes.

NACA TN 3883 5A

Correlation of Results

The calculated results obtained for the conditions listed in table Iwere correlated for each propellant. Percent mass vaporized and unvapor-ized curves for sprays having a standard deviation ag of 2.3 wereplotted against effective length in figure 2 for each propellant. Thisdeviation represents a spray in which 68.23 percent of the mass is inthe tiop-size range between %&g and a&g,M” The correlation of

3;U results was accomplished by modifying chamber length with

+ obtain an effective length.a factor to

L@” %~~:%. 9xlo-5Effective length =

(1 - q)o.404;~5v:. 75

This factor was obtained from crossplots of the lengths required touvaporize 90 percent of the mass. The correction factor is slightly dif-ferent from that determined in references 1 and 2. The critical tem-perature was used to obtain a reduced initial temperature Tr. The term

(1 - !l?r)was used to indicate that the model of va~rization does not

apply when the initial temperature is &eater than the critical.tempera-ture (in this situation Tr >1 and a negative effective length is ob-

tained]. In addition to these changes, it was found that the exponentson pressure and final gas velocity obtained for heptane in references1 and 2 did not fit all propellants; therefore, new exponents were de-termined for these parameters.

The spread in the effective length required to achieve a givenpercent vaporized was greatest in the 20- to 30-percent vaporized regionas was also found in references 1 and 2. W variation in the positionof the inflection point in the mass vaporized curve prduced most ofthe spread. The plot of percent-mass unvaporized as a function of ef-fective length gave almost a single curve for each propellant.

Correlated results for vsrious standard deviations of the fivepropellants are shown in figure 3. With all propellants, increasingthe standard deviation of the spray increased the effective length re-quired to vaporize a given high percentage of the propellant. The linesin figure 3 represent the log mean effecttve length for various operatingconditions. The results of cold-flow spray studies (ref. 5) indicatethat rocket-engine sprays have a standard deviation of about 2.3; there-fore, the results shown in figure 2 should be applicable to most rocket-engine systems. This was verified in the comparison of experimentaland calculated results of reference 2.

.

CONCLUDING REMARKS

NACA TN 3883 &

.

Calculations were made to determine the vaporization rates of liquiddrops for ~-heptane, ammonia, hydrazine, oxygen, and fluorine. The cal-culations were made for each propellant with vsrious spr~ conditions,and vsrious engine-design and operati~ psreuuetersto show how thesevsriables would affect the vaporfzatiotirtiteand chamber length requiredto vaporize the drops. The results are correlatedby an effective lengthfor each propellant. The calculations have shown that the effectivelength required to vaporize a given higjhpercentage of propellant is “!

the shortest with oxygen and increasesfo<jfluorine, Q-heptane, ammonia, 1[and hydrazine, in that order.

Lewis Flight Propulsion Laboratoryr

National Advisory Committee for AeronauticsCleveland, Ohio, June 2, 1958 &

NACA TN 3883.

7

.

A

a’

c!~

%u

D

.h

K

k

L

M

Mg,M

mf

mi,o

‘f

P

P

!l~

R

r

T

APPENDIX A

SYMBOLS

surface srea of drop, sq in.

constant for mass distribution>fil: ag

coefficient of drag for spheres, dimensionless

specific heat at constant

diffusion coefficient, sq

pressure, Btu/(lb)(OF)

in./see

heat-transfer coefficient, Btu/(sq in.)(sec)(°F)

coefficient of mass transfer, sec-1

thermsl conductivity, Btu/(in.)(see)(°F)

chamber length, in.,

molecular weight of propell.ant~

mass median drop “radius,in.

mass of ‘li[tdrop, lb

lb/mole

mass of “i” drop at beginning of time, lb

number of drops in group of “i” sized drops

chamber pressure, lb/sq in.

vapor pressure of liquid, lb/sq in.

heat-transfer rate of drop, Btu/sec

percent of mass in drops smaller than “r”

drop radius, in.

temperature of gas, %

8

Tc

TZ

Tr

T

u

u

‘fin

v

w

z

a

e

A

P

P

‘g

critical temperature of propella@, ‘R

temperature of liquid drop, ‘R

reduced temperature, Tt,o/Tc ,

mean gas temperature, OR

velocity difference between gas and drop, in./see

velocity of gas in chamher, in./see

final velocity of

droplet velocity,

vaporization rate

correction factor

correction factor

time, sec

gas, in.~sec .

/in. sec

of fuel, lb/see

for heat transfer, dimensionless

for mass transfer, dimensionless

latent heat of vaporization, Btu/lb

viscosity, lb/(in.)(sec)

density, lb/cu in.

r, at R = 84.13geometric standsrd deviation, ~at R = 50.0

Subscripts:

2 liquid fuel

m vapor mixture

o initial condition

P combustion products

v vapor mixture

NACATN 3883.

_-

-.

9NACA TN 3883.

APPENDIX B

PHYSICAL PROPERTIES

Heptane with Gaseous Oxygen

Density of liquid,

: pz = 3.1662x10-2 -

*Heat of vaporization,

4 h= 139.9 +

9.5355x10-6TZ - 6.945X10-8T~, lb/cu in.

0.181 Tz - 2.7875x10-4T~,Btu/lb

Specific heatu

; Specific heat

Specific heat

of liquid,

cp,2 = 0.231 +5.62XL04TZ, Btu/(lb)(°F)

of heptane vapor,

Cp,v= 0.5755 +L805x10-%, Btu/(lb)(°F)

of combustion products,

~,p = 0.2898 + 4.07Xl_0-%, Btu/(lb)(°F)

Thermal.conductivity of heptane vapor,

~ = 2.914x10-8 +5.847X10-u~, Btu/(in.)(sec)(°F)

Thermal conductivity of combustion products,

~ = 1.3349x10-7 + 3.411JXL0-l%?,Btu/(in.)(see}(“F)

Vapor pressure,

hp = 1.1.94763- 5255.89687/(Tz -

Viscosity of heptane vapor,

102.58), lb/sq in.

h= 2.106x10-7 -t-7.690XL0-%} 13/(in.)(sec)

Viscosity of combustion products,

%?=5.5615Xl.0-7+ 1.4214X10-%, lb/(in.)(sec)

10 NACA TN 3883 *

Diffusion coefficient

D = [-9.815X10-4 -t

of vapor mixture,

1.973xlo-6z+ 1.1319xlo-9(F)@gQ,

‘ Molecular weight.of combustion products,

Density of Liquid,

Pz = 0.023079

%=31, lb/mole

Oxygen with Gaseous Heptane

.

sq in./sec

i.2.7359x10-4Tl - 9.9465xl.0-7T~,lb/cu tn.

Heat of vaporization,

A = 61.332 +0.5916 Tz - 2i48x10-3T:,Btu/lb

Specific heat

Specific heat

Specific heat

of liquid,

~,z = 0.3726 + 2.0482x10-4T~, Btu/(lb)(°F)

of oxygen vapor,

~,v = 0.21333 + 2.2111X10-%, Btu/(lb)(°F)

of combustion products, ~ .-

Cp,p = 0.2898 + 4.07X10-5~, Btu/(lb)(%)

Thermal

Thermal

conductivity of oxygen vapor,

~ = 2.6611xl.0-7+ 3.4057x10-1.%,Btu/(in.)[see)(%)

conductivity of.combustion products,

~ = 1.3349x10-7 + 3.4111x10-~@, Btu/(in.)(see)(°F)

Vapor pressure,

in p = 11.9584 - 1476.49123.5680\)

lb/sq in.(T2 -

.

NACA TN 3883 11.

viscosity

Viscosity

Diffusion

of oxygen vapor,

b = 2.250CDU0-7 + 1.1702x10-%, lb~(in.)(sec)

of combustion products,

%=5.5615x10-7 +1.4214x10-~, l../(i)(sec)c)

coefficient of vapor mixture,.<G D =[-2.36396~0-3 + 5.7897Xl.0-%’+ 2.87685x10-g@)2]~, sq in./sec

Molecular weight of combustion products,

i%=31, lb/mole

a’ Ammonia with Gaseous O~genj

Density of liquid,

: Pz = 30~3955m0-2 - 6.0219fi0-6TZ - 2.23169ti0-8Tf,lb/cu in.

Heat of vaporization,

Specific

Specific

Specific

h

heat

heat

= 676.362 + 0.32247 Tz - 1.2UM.0-3T?, Btu/lb

of liquid,

Cp,z = 0.8314 + 5.7993x10-%3, Btu/(lb)(°F)

of aumonia vapor,

Cp,v = 0.60931 + t3.31.361X10-5~,Btu/(@ (OF)

heat of combustion products,

~,p = 0.403578 + 6.996x10-6~, Btu/(lb)(OF)

Thermal conductivity of ammonia vapor,

~ = 4.6853Xl.0-7+ 3.552XL0-l@, Btu/[in.)[see)(°F)

12

Thermal conductivity of combustion produgts,

~ = 5.1069&10-8 + 7.616145x10-?%,

Vapor pressure,

NACA TN 3883%

.

Btu/(in.)(see)(°F)

lnp= 13.1485 - 3899.209(T2 - 58.2354)) lb/sq in.

Viscosity of amnonia vapor, 2No

%= 1.07097x10-6 + 8.11607x10-1%, lb/(in,)(sec)

Viscosity of combustion products,P

‘P =1.64352x10-7 -I-2.45252x10-9~, lb/(in.)(sec)

Diffusion coefficient,“

D= (-4.87304x10-2+4.01198x10-%-8.358x10-1%2) ~, sqin./sec

Molecular weight of combustion products,

~. 24, lb/mole

Hydrazine with Gaseous Oxygen

Density of liquid,

P~ = 3.062318x10-2 +4.028897)U0-5TZ - 5.54321x10-8T.~,lb/cu in.

Heat of vaporization,

1= 730.747 - 0.3591305 TZ -t1.214X10-4Tf,Btu/lb

Specific heat of liquid} .

Cp, ~ = 0.589125 + 2.80708x10%2, Btu/(lb)(°F)

Specific heat of hydrazine vapor,

Cp,v = 0.3360 + 1.804x10-4~, Btu/(lb)(°F)—

.

-

NACA TN 3883.

Specific heat of combustion products,

%,P = 0.403578 + 6.996xI.0-6~,Btu/(@(°F)

‘I%rmsl conductivity of hydrazine vapor,

~=1.23753x10-8 +2.230358fi0-1~, Btu/(in.)(sec)(O.F)

g Thermal conductivity of combustion products,F+

~ = 5.10692xLO-8 + 7.616145x10-Z%, Btu/(in.)(sec)(°F)

Vspor pressure,

4

.Viscosity of

%

viscosity of

lnp= 14.328787 - 7363.22(TZ - 63.1713)>

lbjsq in.

hydrazine vapor,

= 4.19981x10-8 + 9.581164x3.0-1%, lb/(in.)(sec)

combustion products,

.

%= 1.64352x10-7 + 2.45252x10-g~, lb/(in.)(sec)

Diffusion coefficient of vapor mixture,

D= (-5.3537x10-4+3.1387w0-6~ +3.37045fi0-52) ~, sq in./sec

Molecular weight of combustion products,

‘P = 24, lb/mole

Fluorine with Gaseous Hydrogen

Density of liquid,

pz = 6.846x10-2 - 3.036xL0-5TZ - 3.9308XL0-7T~, 1%/cu in.

Heat of vaporization,

A= 48.8196 +0.4993xT3 - 2.2932x10-3T~,Btu/lb

13

.

-. --. —.— - —-. —L4

Specific heat

Specific heat

Specific heat

NACA TN 3883-

of liquid,

Cp>z = 0.349 -i-1.21mo-41! ~; Btu/(lb)(*F)

of fluorine vapor,

Cp,v= 0.223994 +1.667x10-6~, Btu/(lb)(°F)

of combustion products,

c~,p = 0.32332 + 2.068x10-5~, Btu/(lb)(°F)

Thermal conductivity of fluorine vapor,

~= 2.7606x10-7 +3.47122x10-1%, Btu/(in.)(sec)(°F)

Thermal conductivity of combustion products,

~ =1.0765x10-7 +4.31280%L0-?%!,Btu/(in.){sec)(OF)

Vapor pressure,

viscosity

viscosity

Diffusion

lnp= 12.3171

of fluorine vapor,

~ = 1.2591x10-6

1482.B545(Tt - 2.5645}> lb/sq in.

+ 1.584x10-%, lb/(in.)(sec)

of combustion products,

%?=2.60098x10-7 -t1.04178~0-g~, lb/(in.)(sec)

coefficient of vapor mixture,

D . [-4.573~0-3 + -1.078xl.0-%+ 5.421X0-’@)2] ~, sq in./sec

Molecular weight of combustion products,

~= 20, lb~mole

P

“

-.

NACA TN 3883 15.

INFERENCES

1. Wiem, Richard J.: Propellant Vaporization as a Criterion for Rocket-Engine I%ignj Calculations of Chamber Length to Vaporize a Single~-Heptane Drop. NACA TN 3985, 1957.

2. Priemj Richard J.: Wopellant Vaporization as a Criterion for Rocket-Engine Design; Calculations Using Various Log-Probability Distri-butions of Heptane Drops. NACA TN 4098, 1957.

3. Heidmann, M. F., and Auble, C. M.: Injection Principles from Couibus-tion Studies in a 200-Pound-ThrustRocket Engine Using Liquid Oxygenand Heptane. NACARME55C22, 1955.

i 4. E1.Wakil, M. M., ~ehera, O. A., and Myers, P. S.: A TheoreticalInvestigation of the H6ating-Up Period of Injected Fuel DropletsVaporizing in Air. NACATN 3179, 1954.

5. Ingebo, Robert D.: Drop-Size Distributions for Impinging-Jet Breakupin Airstreams Simulating the Velocity Conditions in Rocket Combustors.NACATN 4222, 1957.

TABLE I. - RAtWE OF CONDI’lTONS UW?iD FUR CALCUMTIONS

InitM drop tewrature, % M.a8s Geo- Initial lkhlal. Clmmber I

rHep -tane

I

400

%00

,,

7(X

!lnmo-

d.a

300

’400

v

5(XI

mmedian metric arop w pressure,

Jydra- Oxy - Flue- drop stand-’ velocity# velocity,zine gen rlne radius, - a.e-

%g,w viatlon, in~~ec ‘fin’l~l;~ In.

In.lsecmicrons %

I 1 I I I 1 1# I t

75 2.3 1200 9,600 w

%00 %40 %40 75 %.3 9200 %,600 %co

25 2.3 lzco 9,600 303b

7

.,#

3.6 lm 9,600 w

1 Y 225 2.3 1200 9,600 300

700 2m 220 75 2.3 1200 9,600 m

1.0 1200 9,600 300

1.34 MM) 9,600 300

2.3 600 9,600 3(XI

12(X) 2,400 3m

, I ,

9,6(X 150

1600

19,200 300

2400 9,603 500r

%onditions used for cal,culat Ions presented in figs. 1 to 5.

1 ,.

C;-3 ~ 47$ s ,

m

/ :. -

m Y

L {/

700{

I 1

m tI

4CQ

m.

-- -. _- ._. ._

Ih’OPlet initial rallllm,25 UJICIYJM

lwo .1 .2 .5

/---

/

L y/

[ ‘J7

I

hJp ——-.

t,)

7’

. -- —. -— —/ -/. -/ Dr0p19t IDltwi *U ,

75 l@A?MnS

.5 1.0 1.5 2.0Ckriberlength, ii

.——

(a) DrC@3t-tmpeAUre hbtories .

/

/ ‘/ /

// — Flu9rine

( —-- -m

/ /—-— Heptane

I—--— Amon?a

I — — EYdrazineI

/

1

- — — “ — -—

/ ‘///

F. - - -- —. .- -. .-

/

DrG’pintinitialmaius,225 dOlW?16

2 4 6 8 lo

F@re 1, - Ty@?al. droplnt MEtorien for V8ricm prO@UJmt B (sea table I for cmdi’ci.ma ).

10,W

0,030

6,0XI

4,CCXJ

1

2,CCX3

o

I ! I

- - +—

~ *

- - / -

8Fluorine

–-––- %vW—— Heptene

——— Anmnie——Hydra93.ne

5 20 24 28 32 s

Ckmba length, in.

(b) Qea-.elocity M.starles.

F1.gme 1. - Continued. ~ical droplet hidmries far ve.rioua ~ts (see table I for .@tiom).

w01

t f

Ir:-.1 .2 .5 1 2

j

i

.9,Oxl

~7,QM

f“ fi,am

5,CC0

4,m

3,fxlo

2,C03

l,CCO1 z 5 10 20

CY-~ back* 4720 8

5 lo Eo m mCi-t?aber length, in.

(c) Lkplet-velcdty histories.

Figure 1. - Ccmtimd. &pical droplet histories for wioua pmpdlmts (me tablm I for comiitiona ).

1

er length, ti.

(d) Droplet-mml hlstarlas.

F@re 1- - C4mtjmued. ~ica.1 droplet histcu’lm for varloua propdU@B (see tahb I f~ tit~s) -

I

El(Acoa)CN

t

1

0

(e) 92* vwmatio~ ~~es.

Flume 1. - Conchd@. Typical drcplet histories for various propehts (see table I for

&naitions ) .

I

lCQ

82

$: 60wPI

f

z8$40

i!

20

0.02 .04 .M .08 .1 .2 .4 .6 .8 1 2 4 6 8 10

m

1%

LP”%I$??$l.5XL0-5 ~ 0.66 ~w 0.35Effective length =

(1 - qo.’y;$’v:.’” ( ‘Jz.11 g

(a) I&m vapxrlzed for hept.ane.E

Figure 2. - Correlated results for pmpdlmt with stamtard deviation of 2.3.mco

8

● ✌.4 ,

CaL? , 41

i . 4’(20 # *

Kn

20

60

40

20

10

.9

6

4

2

1..1 .2 .4 .6 .8

I@%&f3. WO-5Effective length -

W(1 - Tr)oo~;#v:”75’ .

(b) MM!S unw.~ed for hqtaua.

Fi&?.Uw 2. - C0nt3nu.ed. ‘COrrd.ated remults for pr0pdL9nt with 6taMard dmiaticm of 2.S.

. “m

1-1.,

60

60

4.0

20

0.01

l?igure 2.

, ,

4 .’ 1 2 4 68

(C) k, ~WiZfj% fCiC ~h.

- Ccmtirwd. C~ted results for propellant with st4m5ard deviation d z .3.

* ,

CY-4●

47a3I

m

m —

60

40

m

10

B

6

4 .

1.1 .2. .4 .6 .8 1 2 4 6 ala 20 4060m

((l) b, Ulmporizd r. &m!Jmla.

F&U, 2. - W-. Correlation muul’cs for propellant with stauduml 6mi8tl.m of 2.5. Nol

-. -. .-

1

.04 .06 .08 .1 .2 .4 .6 .8 1 2 4 6 8 10~o .66#&l ,MO-5

(m 0.66(~ec 0,35Effect Ive length =

(1 - T! Jo”@$j%:”75’ (in.)z”~

(e) M96E vaporized for hydrazlne apre.y6.

Figure 2. - CwMnued. Correkted results for propel.laut w!.th standard deviation of 2.3.

4 .

.,1. , t+)w

~o.w 0.40

Effectiva length -~ Lllxlo-s (m)o.~(,ec)o. =

(1 . TJ*-%$y’ (ta. )z’u

(f) Mm@ Um’npOrizc.i ml- ilydrasbs e~a .

mglm i?. - c0ntim104. Cm.relatul results rer pl.qellalt vith 6b.m8ml dedation of 2.S. w+

.-

Nm

1

%

i

:’

m

I

1

0~0.66 0.401 ~o-5

Effective length = ‘fin ‘ (n)o.66(~w 0.35

(1 . Tr)0”%&:”75’ (bl. )2”~E

(d Mms Worizd for I.iquld-oxygm sprays. s

FQure 2. - Cmtiaued. Cm’related results for propdhat with &andard deviation W 2.3. G

g

29

.

. L10

8

6

2

1E.1

I

1

+

)

PO. 66 0.401 ~o-s

Effective length =‘fin . (1b)&66(~&.35

(1 - Tr)O+J#;:V:.75’ (ti.)z”~

(h) Mess unvaporiz~ for liquid-oxygen spr~s.

Figure 2. - Ccmtfnued. Correlated results for propellant with stendard deviation of 2.3.

.

. -.

o.02 .04 .06 .08 .1 .2 .4 .6 .8 1 2 4

, I

~o.66 0.40

Effective length .l+h 1.9xlo-5 &o.66(*ec 0.35 -

(1 - Tr)0”w~”45v0.75’g,M O (in. )2”M

(i) K9e13 vaporized for liquid-fluorine sprays.

FlgLme 2. - Continued. Correlated resolts for pmpeUk@ with SteJ&xa aevlatlon of 2.3.

6

31

.

10

8 E=

4

F

I

z

1EEf feet We

(J)

- Ccmclllaed.

length =L#”’yg%.smo-s ~lblo.66(*= 0.35

(1 - T.Jo.40&45vo.75’ (in.)z”~

g,M O

Mass unvaporlzed for I.iqtid-fluortie sprays.

CorrelAe3remits forpropellantwtth Etenderd deviation of 2.3.

)

t40

F1“r

““k---

E.1

● I

I.6

Effectivelength .

, .W

\

h! !! \. I\

\

\

\

\

(b) Ammnia.

MgmO s. - ccuathllJA. C-lated mmilts for SP~S with whw s%H deviatlcms .

. . -- -*O..% 0.401 ~-5

% -~ 0.66 0.35

Effective lmstll -(See)

(1 - T#”%g;fv:”75’ (ti.)z””

(a) Ey&4mn9.

M@U-8 3. - m-. cOrrddd lwult.sfa6sauYa uithmrima Eh?dard m-.

.

. ,

# 4

lCQI

Exl

mI I

,

40

20

lo

a

6

4

2

:1 ,2 ,4 .6 .8 1 2 4 6 B 10 20 a W&llm

SMcatlva length =““””’%”% W

(1 - ‘+) “ ~;Mvo” .

(d) Mqu2d CIXWFU.

!a

r~ 3. - Contimmd. cOr’nYIAed rmul.ts for ‘prayn titb Wrious sta@dma dav-iatian’ .

~o.66 0.40

Effectivelength=Uffi 1.9 XL0-5 lb)o.66(~ec)o.35

(1 - @“40&;fv:”75’ ( (in. )2”~

(e) Liquid fluorine.

Figure3. - concluded. cOl?3Xd.Bted ZY36UI%8 fur ~~yS with V@OIIS StEll~ deviations .

i t