.. ;

,,

● e* ●°0 :

● m ● ●a. ●

● **9 ● 9*

‘a9b

: ● 0 ●0::

● e :0 ● ::

● 00 : ●:6 :*C ● 0

,.

LAMS-2021

(’@●

—

I

LOS ALAMOS SCIENTIFIC

OF THE UNIVERSITY OF CALIFORNIAo LOS

LABORATORY

ALAMOS NEWMEXICO

POSSIBLE

IN A

PROPELLANTS FOR

NUCLEAR ROCKET

- , - .--. --. ----”’’ --7- 7’-’=—- —- —’------ -“-

USE

--.--..7- --. .—=.:,

_

~ ——. ..—

. . .. ..— -.~~

—. .

–.-.–e

~.~ -.. .A— — -r --— —- —

a.-. --- . . . -

-L— —.—-—. —-----

-==i= -y——== -— —--- . .. . .

.—. .—— —

------ .-L

.--=

,—. .— . .. —-- -. ...-.-=

s-’=a%-a- ae.”=ie. ”’’=i - - “ - - ‘_:__

- —-.—. —*— ~— .*— ——.*—~—e . . . —__

-—— .—— ..- .—— .:—. . . ● ,0 ●

9* ● ae, ee ● ● * ..

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
.

LAMS-2021

NUCLEAR PROPULSION

LOS ALAMOS SCIENTIFIC LABORATORY

OF THE UNIVERSITYOF CALIFORNIA LOS ALAMOS NEW MEXICO

REPORT WRITTEN March 1956

REPORT DISTRH3UTED: JUN 29 ]956

POSSIBLE

IN A

PROPELLANTS FOR USE

NUCLEAR ROCKET

by

Lawrence R. Sitney

.+

Contract W-7405 -ENG. 36 with the U. S. Atomic Energy Commission

AH Los Akmos reports present the opinions of the author or authors and

do not necessarily reflect the views of the Las Alamos Scientific Laboratory.

Furthermore, this LAMS report is an informal document which has been

prepared for a special purpose and is not considered suitable for general

distribution. It is accordhgly requested that no distribution be made without the permission of the Office of the Director of the Laboratory.

iGi - **e ● **

● 0 ● eme. e ● *

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
INCLASSIFIED

NUCLEAR PROPULSION

LAMS-2021

AEC Classified Technical Library (H. W. Skinner, DMA)

AEC Classified Technical Library (D. J. Keirn, DRD)

Aerojet General Corporation

Manager, Albuquerque Operations (Russell Ball)

Manager, San Francisco Operations

North American Aviation, Missile Development Division

North American Aviation, Rockel.dyne Division

University of California Radiation Laboratory, Livermore

Western Development Division (A.RDC)

Wright Air Development Center

Los Alamos Report Librsry

1-2

3-4

5

6

7

8

9

10

11

12

13-30

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
3

..:. ,;...-+

.-,A.

.. *..

.“.,

4.’ ,~=,~$:;:=’

‘.,,:. ,

. ...”

● * ●°0 ●

‘~% ● 00

● ** ●

b**

.- ., . ...**

.

< \**

9* .0

● ● ●’ jo

● :** . . . ::

● *mm ●:* ::

● ● 00 : ●:0 :00 ● 0

UNCLASSIFIED

ABSTRACT

A series of propellants which might be applicable to nuclearpowered rockets have been investigated thermodynamically. These

propellants include methane, ethane, propane, mixtures of hydrazine

and these hydrocarbons, mixtures of ammonia and these hydrocarbons,

hydrazine, ammonia, methanol, ethanol, and propanol. The dissociation

products of these compounds and their concentrations have been calculated for the temperature interval 1000 to 3000°K. The mean molecular weights of these various potential propellants were determined

from the concentrations of the dissociation products.

The pure hydrocarbons have the lowest mean molecular weights

of any of the propellants investigated but are of doubtful use due to

the fact that they deposit solid carbon onto the reactor over the entire temperature range studied. Some compositions of ammonia and

hydrocarbons and of hydrazine and hydrocarbons do not deposit graphite

at reactor operating temperatures but either deposit carbon at certain

lower temperatures or corrode the reactor at higher temperatures as

well as at temperatures in the range 1000 to 2000°K.

ACKNOWLEDGMENT

H. M. Peek materially assisted the author in the coding and

checking out of the first composition problem as well as by providing

a program to calculate the thermodynamic properties of polyatomic

gaseous molecules.

0000 -’0 ●****9.

● * ● ** b

● ☛

:0:

● @

● *

b

● 9

● s

::

9*

● *

●☛☛●

●

●

● O

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
---

‘Wlm●om ●

● * ● **

● 9* ●

.*. *

● ae

.. ,’.

● * -.6:0-:00 ●:0 :00 ● *

● ● 9

● 6 ● * ● moo

9* :0 ● : ::

● ●:0 : ●:0 :** ● 9

UNCLASSIFIE

CONTENTS

Abstract

Acknowledgment

1.

2.

3.

4.

5.

Introduction

Calculation of Thermodynamic Data

2.1 Rigid Rotator -Harmonic Oscillator Method

2,2 Hindered Internal Rotation

Equilibrium Calculations

Results

Discussion

● 9.* ● ● 99 ● *, ● *

● ● a

● :

:.4; :0 ● ● ::

● *O .* .98*

*“

● ** ● *

● ● : ●*e

● - L-b ...● ob ●

●Y-oa ● ● ** ●*000: ● e*

9* 9**,** ● D

Page

3

3

5

6

6

9

10

16

17

UNCLASSIFIE

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
.*. **so ● be

UNCLAS$lFIED

● 0 ●:- ● 00 ●:0 :00 ● e

● ● 9* ● O:. ● ***

● :0 ● m ● :** ● *

● ● 00 b ●:0 :** ● 0

1. INTRODUCTION

The nuclear-powered rocket offers a golden opportunity to one interested in obtaining the

most efficient propellants for rocket use since it frees him from the complications imposed

by the combustion of the propellant in a chemical rocket. Since the nuclear reactor provides

the heat source required to raise the propellant to the operating temperature, one can use a

monopropellant which dissociates tberm ally into” low-molecular-weight fragments at elevated

temperatures.

Liquid hydrogen, the most efficient propellant that we are in a technical position to use

at the present time, presents logistical and cryogenic problems to any large-scale rocket endeavor. To circumvent this situation, one would like to find other propellants which are not

too inferior to hydrogen in their performance. In addition, these propellants should be available in large supply, should not require cryogeny, and should not be so reactive chemically

as to require special materials for containers or special handling procedures for storage.

The maximum theoretical propellant gas exhaust velocity, Vm, is given by the relation

where g =

~=

R=

T=

.)/.

Cpi =

Cvi =

‘m=-

acceleration of gravity at sea level

mean molecular weight. of propellant gases

universal gas constant

gas temperature within rocket motor prior to expansion

specific-heat ratio of propellant gases = 2hiCPi/ZniCvi

heat capacity at constant pressure for itJ component

heat capacity at constant volume for itJ component

1.1

The over-all performance of a missile is primarily a function of the exhaust velocity attainable

with the propellant considered. It is obvious, therefore, that the mean molecular weight of the

propellant gas is the dominant factor in determining the theoretical exhaust velocity of a propellant, since, except for monatomic molecules, y is in the range 1.22 to 1.40. Although there

are no other propellants which have a mean molecular weight near that of hydrogen, there are

● ● *9 ● .09 ● ** ● -

b ● ● 0

● 0 :*5 -: :0

● O ::

● 9..* ● *

*

● *O ● *

● 0

● ● ●*@

● ● --9 ● O* ●

● ***** ● **

UNCLASSIFIED

●9**a0m8:* b**.* ● em

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● 9 ● ** ● 9* ●:0 :00 ● *

● ● ● *

● :000:000

● *O ●:0 ::

● ● ** : ●:0 :** ● -

many for which the square root of the ratio of molecular weights of the ]

is less than 2. Since all these propellants have densities in the range 0.

to 0.07 for liquid hydrogen, it is possible to build a rocket with a given (

ture which will be much smaller than the nuclear hydrogen rocket, althou

what heavier. This statement results from considerations of the impulse

are not treated here.

This report covers a study of potential propellants which would be :

rocket. Materials which have been investigated include methane, ethane,

ammonia, mixtures of hydrazine. and these hydrocarbons, mixtures of amI

hydrocarbons, methanol, ethanol, and propanol. Data for the first three 1

hydrocarbons were extrapolated to such hydroc~bons as hexane and gasol

easier to handle than the low-molecular-weight members of the series. ‘

culation used in this study will be discussed in the next two sections. T]

given in Section 4 and a discussion in Section 5.

2. CALCULATION OF THERMODYNAMIC DATA

2.1 Rigid Rotator-Harmonic Oscillator Method

Thermodynamic data were calculated by the rigid rotator-harmonic

for those molecules for which data in the temperature range above 1500°

literature. Molecules treated by this method include the hydrocarbons tlx

rated and unsaturated, ammonia, hydrazine, hydrogen cyanide, methanol, z

These calculations were carr~ed out originally on a desk calculator

against calculations made on an IBM 701 electronic computer. No large

served between the two methods, although there were small differences of

due to the different numbers of significant figures carried in the desk cd

and due to small arithmetical errors which arose in the manual calculatit

importance of these small differences is essentially zero, however, since

decrease the number of significant figures which should be considered in

culations.

The rigid rotator-harmonic oscillator treatment assumes that the m

are rigid rotators and harmonic oscillators, with no interaction between t

tion. Although none of these assumptions is strictly true, only the anhar]

ecules at high temperatures introduces any appreciable error into the the

tained. However,

the anharmonicity

even this error tends to cancel out in the equilibrium

always shifts the free-energy function in the same dire

● 9.* ● ● *9 ● 09 ● *

●

● ● -0“6:;!-: 9*9* ● *

● 00 :

“k

● *

b :** ● *

● *

● 6 9.*

● *–*— Q ● ● e* ●

● ****** ● * ●e**m*a ● *O 9* ● ** ● ***

ropellant to hydrogen

I to 0.8 as compared

xhaust-gas tempera-

;h it will be someof a rocket which

uitable for a nuclear

mopane, hydrazine,

Lonia and these

omologous aiiphatic

ke, which are much

‘he methods of cale results will be

oscillator treatment

: do not exist in the

ough C3, both satuld ethanol.

and later checked

differences were ob0.01 to 0.10 per cent

culator and in the 701

m. The practical

they serve only to

the equilibrium cal-

]lecules concerned

he rotation and vibranonicity of the molrmodynamic data obalculations, since

:tion; hence, for any

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● a ●:0 :00 ●:0 :90 ● 0

● ** ● 0:0 ● *eO

● :0 ● * ●:oc ● ● *

● ● ** ● ●:8 ● ** ● m

given equilibrium

energy functions.

approximately the same error is added to both the reactant and product

The thermodynamic behaticw of a molecule can be conveniently treated in terms of

partition function, which is defined as follows in terms of the energy, En, per molecule ix

n~ state and the a priori probability y, gn, of that state:

-e n/kT

Q= fgne

n=o --

Here k is the Boltzmann constant and T the absolute temperature in

The total energy of the molecule can then be broken down into

2

oK

a translation energy,

and an internal energy, ~ht. The internal energy, however, is composed of a rotational I

tion, erot , a vibr ationai portion, e , and an electronic portion, c el. vib For polyatomic mo

ecules considered in this study, the degeneracy of the ground electronic state is unity, an

contribution of higher electronic states is negligible; the electronic contribution to the tot;

partition function is, therefore, zero.

degrees of freedom in the molecule.

translational motion. Two degrees of

linear polyatomic molecules, whereas

If there are n atoms in a given molecule, there ar

Three of these degrees of freedom are assigned to

freedom are used by rotation in diatomic molecules

three degrees of freedom are necessary to describe

rotation in non-linear polyatomic molecules. This Qaves (3n-5) degrees of vibrational fr(

in diatomic and linear polyatomic molecules and (3n-6) degrees in non-linear polyatomic x

ecules. This number of vibrational frequencies will be designated as i (running index in 1

vibrational partition function).

In accordance with the above energy breakdown, one may now write the partition function

as:

Q = Qtr “ Qrot “ ~b 2.2

The translation~ rotational, and vibrational partition functions are derived in any good text

1

on statistical mechanics or chemical thermodynamics. Making use of these derivations, one

1. G. Herzberg, Molecular Spectra and Molecular Structure, Vol. II, Infrared and Raman

Spectra of Polyatomic Molecules, pp. 501-530, D. Van Nostrand Company, Inc., New York,

1945.

S. Glasstone, Theoretical Chemistry, pp. 347-422, D. Van Nostrand Company, Inc., New

York, 1945.

J. E. Mayer and M. G. Mayer, Statistical Mechanics, pp. 149-217, John Wiley & Sons,

Inc., New York, 1940.

9*9 ● ●:* ● ** ● * ●°0 :

. :- 7*::: i a-o:.:: m● 9

● ** ● 8

● 0

● ● ●*b

● boo ●

. ...9** ● e

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● eo moome ● 9

uHluiiu

● 0 9** ● 9O ● *9 ● 9* ● *

● *m*e

● *m* *o* ::

● 000 9* ●: ● ● 0

● ●:m ● ●:0 :** ● 0

obtains for the respective partition functions

where c =

h=

I=

‘A’ lB’ lC =

k=

M=

N=

P=

R=

T=

()%M 3/2(RT)5/2p-l Qtr = -ij--

hN

Q

_ &r21kT

rot

u h2

(linear molecules)

Qrot=J-q$)(kT)3’2(non-linear molecules)

( )

-1

%it) = ~ ~ - e-hcvi/kT i=o

2.3

2.4

2.4,

2.5

10 velocity of light = 2.99776 x 10 cm/sec

Planck’s constant = 6.62377 x 10-27 erg sec

moment of inertia of molecule

moment of inertia around X, Y, or Z axis

Boltzmann’s constant = 1.38026 x 10-16 erg/molecule/deg

molecular weight of the molecule

Avogadr&s number = 6.02544 x 1023

pressure in dynes/cm2 = 1.01332 x 106/atm

gas constant = 1.98718 cal/deg/mole

temperature in ‘K

symmetry number (number of equivalent orientations in space as the result of

simple rotation)

-1 vibrational frequent y in cm

Iy.

v.

Although all of the thermodynamic functions can be calculated with the partition function,

only the free-energy function is of use in making the equilibrium calculations. The transla-

()

Fo-E~ tional, rotational, and vibrational contributions to the free-energy function, - ~ , are

listed below.

-( )

FO-E:

Tti = 5/2R~T+3/2~~lnM+ R~[(%r’2$’2]-R~p

= 11.4392 log T + 6.86349 log M - 7.2795

●.0

●

●

●

8*

● ☛

✚✚

● ✘

● ☛

● ☛

● 9* ● ● ** .*m ● *

● ● 9*

● : :+.-::

9 ● m

● ☛ ● 9**

..{ Sam ●

:ao ● ● 0

2.6

2.6,

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
()Fo+j

-—

T

= R in Qrot

rot

=Rln

()

8n21’T

2

uh

. . m.. ● . . .*e .*9 . .

b 9*O

● :***** ::

99*9*9 ● :

● 41:0:

● 9 ●:0 :00 ● 0

[

= R in (8m31AIBIC)10@#21

(linear molecules)

(non-lineax molecules)

2.7

2.71

2.7”

-( )

F“-E~

T ‘Rh%ib vib 2.8

‘R~[~o(l-~hcvi’kT)-’l 2~8,

“( -hcvi/kT

. -R ~ In l-e )

2.8”

i=o

2.2 Hindered Internal Rotation

Some molecules, namely saturated hydrocarbons with more than two carbon atoms and

alcohols, have potential barriers which restrict the internal rotation of the different hydrocarbon grouns with respect to one another or to the hydroxyl group of the alcohol. Hydrazine has a barrier hindering the rotation of the two NH2 groups with respect to each other.

Although the exact nature of this potential barrier is not known, it is known that the barrier

(

I

is a threefold symmetry type for all these cases. That is,

v

v = f (1-COS 39) 2.9

I

where V = the maximum height of the barrier

o

@ = angle of rotation

j Pitzer and Gwinn2 have worked out a method of calculating the contributions to the

I various thermodynamic quantities of a molecule with one or more degrees of hindered internal

rot ation. For each degree of hindered internal rotation of threefold symmetry

>’”

2. K S. Pitzer and W. D. Gwinn, ~~Energy ~vels ad Thermodynamic Functions fOr Molecules with Internal Rotation, I. Rigid Fr~e with Attached Tops, ” J. Chem. Phys. 10,

428 (1942).

● 00 ● ● ** 9*9 ● e ●’0 ● ●

● **

i

● mm**iiliiii: ● 00 ●999*: ● 80

● **a**** ● *

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
and

● ☛ O*9 ● , ● . .

u!i:.wlimsl

● *o.. ● m. ● e. ● . . . .

● ● ***

9 ● * ● ● @ :: :*9* ●: ●

● *

● 9*

● 4):0● ●:O ● ** ● e

~hi,ro . R)l/2(2n/3jvO/2kT)(1-cOs 30)d,

()F;E~

[

. ~1 ~ %IkT 1’2 ‘O + in Jo(iVo/2RT)

h.i.r. h2 -m 1

where Jo(iVo/2RT) is a Bessel function of zero order. It can be evaluated

pansion as

2.10

2.11

by a series exX2 x’ x’ x2k

Jo(iVo/2RT) = Jo(ix) = 1 +— — — 22+4 ‘6 ‘“””+2k 2.12

2 (2!)2 2 (3!)2 2 (k!)2

For calculations involving a desk calculator, Pitzer and Gwinn have a two-entry table by which

()

F-E:

-—

T

can be evaluated as a function of Vo/RT and of l/Qf, where Qf, the partition

h.i.r.

function for free internal rotation, is defined as

1/2

()

Qf= + 2.13

h

For calculations on an IBM 701 computer, Jo(ix) is evaluated directly and the free-energy

function for hindered internal rot ation is then calculated by equation 2.11.

The total free-energy function for a molecule with hindered internal rotation is the sum

of the rigid rotator-harmonic oscillators translational, and hindered-rotation free-energy functions. Here the vibrational partition function has one vibrational mode removed for every

degree of internal rotation so that the total number of degrees of freedom of the molecule is

still 3n.

3. EQUILIBRIUM CALCULATIONS

The equilibrium

d+

can be written as

constant of the gas reaction

bB+”””~ mM+nN +... 3.1

●

● O ●:0 :00 ●:0 :00 ● 0

:“.

● 9***.*:aumi: ● *

● se*@ ● 00 ●*..*: 9*9

● 90m**0b ● 0

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛ 41,0 ● ** 90* ● 00 .0

● e**e

● ● b. ● * ::

● * :.*. ● :0 ● *

● O** : ●:O :00 ● 0

‘M ~PNn “““

Kp =

‘AapBb “ “ “

3.2

‘here ‘M, PN, “ “ “ Y PA, PB, “ 00 are the partial pressures of M, N, .” “ , A, B, 000 .

A well-known theorem of thermodynamics states that

‘R‘n‘p= ‘“”= ‘E’ Z(=)pr.du.t. ‘Xt+)rea.t~~s 303 ~

Here AF is the total standard free-energy change and AE~ is the total stand~d zero-point

energy chsnge for the reaction.

any possible reaction of interest

lated quite simply. The various

Since E: is known for all atoms and molecules involved in

in this propellant study, AE~ for the reaction can be caicu-

()

FO-E~ free-energy functions, - ~ , for substances participating

in the reactions can be calculated by the methods of sections 2.1 and 2.2. One is thus in a

position to calculate the equilibrium constants for any reaction and the equilibrium compositions of the several possible species existing in a multicomponent gaseous system.

Let one suppose that methane is passed through a nuclear reactor under such conditions

that the methane decomposes to the following products:

1) C solid 6) CH

2) C gas 7) C2H4

3) H2 8) C2H6

4) H 9) C3H8

5) C2H2

The following equilibria can be written:

1)c(s)= c(g)

2) 1/2 H2 ~ H

3) c(s) + 1/2 H2 ~ 1/2 C2H2

K1 = nc (RT/V)

(g)

‘2=— ‘H1,2 (RT/#2

‘H2

1/2

‘C2H2

K3=— 1/2

‘H2

● ● *O ● ● ** ● ** ● *

88

●

●

●

be

:’0

● m

● ✚

● ● ☛ ✍❉❉❉

● 0

● 00 ● 00 ●:0 :a. ilmR!Bl ●

● *999:

● ☛

✚✚

90

9*

●’*

●

3.4.1

3.4.2

3.4.3

● O*** i*e-

● 09 ●0: ● 00

● - ● ***m* ● 0

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
4,C(s) + 1/2 H2 ~ CH

5) c(s) + H2 ~ 1/2 C2H4

6, C(s) + 3/2 H2 ~ 1/2 C2H6

● ✎ B*8 ● . . .** ..* . .

b ● **

● :0. .oe ::

● eO **e ●: ● *

● ●:0 : ●:0 :00 ● 0

7) c(s, + 4/3 H2 $ 1/3 C3H8

K4 .

K5 =

K6 =

‘CH-@RT/V)l’2

‘H2

1/2

‘C2H4

—(RT/V)-1/2

‘H2

1/2

‘C2H6

3/2 (RT/V)-l

‘H2

1/3

‘C3H8

~4/3 (RT/WI-l

3.4.4

3.4.5

3.4.6

3.4.7

“H2

It is assumed that the partial pressure of any component can be replaced by the product of

the number of moles of that component and the total pressure. Let ni represent the number

of moles of component i per gram of total material. Assuming that the gas law

PV = nRT 3.5

nRT holds, one can substitute ~ for the pressure, P. If these substitutions are made in equation

3.3, it is transformed into equations of the type 3.4.

There are now seven equations in nine unknowns. One can obtain two more equations by

setting up mass balances for the carbon and hydrogen. These are

ZC=nc +nc

(s) (g)

+ ‘CH - 2nC2H2 + 2nC2H4 + 2nC2H6 + 3nC3H8

ZH = nH + nCH + 2n11 + 2n

2 C2H2 + 4nC2H4 + 6nC2H6 +

If one replaces each of the ni in the two mass-balance equations by

ni in terms of the equilibrium ccmstant, the hydrogen concentration,

900 ● .** .*. ● . ●** ● ● 0

● :

: l~e- : :

● : ● 0

3.6.1

8nC3H8 3.6.2

the corresponding value of

and (RT/V), he obtains

● ● 0

● 0 ●:0 :00 ●:0 :.* 9*

r:● *9ab9*mu ● ●“:m

● Oi - ● 00

● *

*9O

8**0*e ● *

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ✎ ✎ ✎ ✎ ✎ ✎✎ ● -o ● 00 ● .

● ● * ● O ● *

● ● **9*.. :000 ●:0 ● *

● e

● ,000 : ●:0 :00 ● 0

3.6.3

ZC = nC + K1(RT/V)-l [1 +K4n~:! (RT/V)-1/2 + 2 K3n~/2 2

(s) 2

[ 1[ :2(RT’v!2+3in~’ + 2 K5nH2(RT/V) 1’22+2 K6nH

1’2 (RT/V)-1’2 + K4n~’2 (RT/V)-1/2 + 2n [11/2 2

‘H = ‘2nH2 2 ‘2 + 2 ‘3*H2

[

+ 4 ‘5nH2 (RT/V) 1[ 1/2 2

+ 6 l~n~~ (RT/v)] 2 + 8[~n~f (RT/v)] 3 3.6.4

Let one now pick some definite quantity of methane to exist initially in the calculation;

for the sake of simplicity, 1 mole. Then,

ZH =

number of H atoms 4

molecular wt. of CH4 ‘m

Also, one can make two guesses as to the number of moles of hydrogen per gram which will

,

exist at the equilibrium conditions. Let one use here

1

‘H2 = 0.01

2

‘H2 = 0.1

H one now rewrites equation 3.6.4 as

G = (K2+K4)nH21/2 (RT/V) ‘1/2 + 2n (1+4) + 4~n~2 (RT/V)

‘2

+ 6K$; (RT/V)2 + 8#n~ (RT/V)3 - ZH 3.’7

2 2

he can evaluate a G1 with nH = 0.01 and a G2 with nH = 0.1, where G is simply the differ2 2

ence between the actual ZH and the ZH which is calculated by using the appropriate powers of

‘H2 in equation 3.7. He can then use a standard iteration formula to s61ve for a new nH

2

which will make G3 equal to zero. By repeating this iteration until Gn converges to within

a given criterion (10 -8 in all these calculations), one obtains a value for the number of moles

● ☛ ● O9 ● 00 ● ** 9*9 ● e

!“:

● 90- !@@m! ● ● mo .“:

● ee - ● ** 9*9

b* ● *9*** ● *

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛ ● O****

i.; Limd ● n ● a- ● .- ● 9. .** ● m

● 0000

● ● * : ● 0 :: :0 ●:00

● ● *

9*

● ● 00 ● ●:0 :00 ● 0

of hydrogen which is sufficiently exact to carry out the remainder of the computation.

One now substitutes the value of nH obtained from the iteration process above and the

2

various Ws derived from thermodynamic free-energy functions into equations of type 3.4 to

obtain values for the number of moles of the various components. The number of moles of

solid carbon is obtained by subtracting the sum of all the hydrocarbon and gaseous carbon

components from ZC in equation 3.6.1. Here

Zc =

number of C atoms 1

16.042 = lm

In setting up the conditions for the problem so that the 701 computer has sufficient information to complete the calculation, one must specify a volume, a pressure, and a total

number of moles per gram at an elevated temperature, T, to be used in the calculation. When

one adds up the total number of moles calculated by using the equilibrium constants and the

number of moles of hydrogen obtained from the iteration process, one undoubtedly will get a

different value for the total number of moles. By adding half the difference between the original number of moles stipulated iri the initial data input and the calculated number of moles

with the appropriate sign to the original number of moles, one can obtain a new guess for the

total number of moles.

One now calculates a new volume, using the pressure and temperature data-input for the

elevated temperatures, Thus,

RT “ Zni

v= ~ 3.8

A new (RT/V) is calculated and the evaluation of a new nH is made using the same two ini1 2

2

tia.1 guesses for ‘H2 andn. When the desired value for the number of moles of hydrogen

‘2

at equilibrium is obtained, the number of moles of each component is again computed and a

total number of moles calculated. Half the difference between this new number of moles and

the previous Zni is added with the correct sign to the previous Zni and a new (RT/V) is calculated. A new number of moles of hydrogen at equilibrium is obtained and the iteration of

‘H2 and Zni is continued until half the difference of the Zni used in that cycle and the Zni

computed at the end of that cycle is less than some specified value (usually about 1 to 5 x 10-5).

The mole fractions of the individual components are then evaluated in the standard way,

where

● 06-

41* ● ** ● 80 ●:0 :.. ● .

Y’:

● b*e*?mm:”; Soo

9*99.:* ● e

i 41 ● ***** ● *

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
‘Y* 8e0 ● 00 *O* 8** ● e

● ** ● e be

● ● ● . 99. *

*O :e

e: ::

● ●:0 : ●:0 :.0 00

‘,

‘i

Xi=q 3.9

Here

Xi is the mole fraction of component i

ni is the number of moles of component i per gram

Zni is the total number of moles per gram of the system

The mole fractions, as well as the total number of moles, the pressure, the temperature,

and the final volumes are then printed out by the 701 computer. The conditions of the problem

are changed such that the temperature is increased lOOoK and the volume is correspondingly

corrected. In all the problems studied in this series, the initial temperature was 1000°1$ to

correct the volume, therefore, one merely multiplies the final volume by 0.1 and retains this

number as a volume increment to be added for each 100°K temperature rise. The temperature and volume are increased by the appropriate amounts; the pressure and the total number

of moles are held to their values at the previous temperature. The machine goes through the

entire sequence of events described previously and arrives at a solution for the increased

temperature. This cycle is repeated until the temperature has risen to 3000°K and, in a few

instances, 4000°K At this point the problem has been completed.

The calculations become more complicated if oxygen or nitrogen is introduced into the

system either as the element or in the form of some chemical compound. Additional equilibria

considering all possible reactions of importance with oxygen or nitrogen as reactants are incorporated into the series of equilibria already existing for carbon and hydrogen. A massbalance equation for the oxygen or nitrogen is then put into the calculation so that one will

still have n simultaneous equations in n unknowns. This mass-balance equation, when expanded

in terms of equilibrium constants, hydrogen concentrations, and oxygen or nitrogen concentrations, has always turned out to be a quadratic equation in terms of the oxygen or nitrogen

molecular concentration; therefore, a solution is easily obtained.

One proceeds to solve the three-element equilibrium problem in the same manner as the

two-element problem. Two guesses are made for the equilibrium hydrogen concentration and

the corresponding oxygen or nitrogen concentrations are obtained by means of the quadratic

equation referred to in the preceding paragraph. One then substitutes the values of the oxygen

or nitrogen concentrations into the places where they occur in the hydrogen mass-balance equation and calculates two G’s as was done in the two-element calculation. The new n is next

‘2

fed back into the quadratic equation for the oxygen or nitrogen concentration and the iteration

is conttiued until G has converged as closely as desired to zero. A criterion of 10-8 has

● ● O9 ● 9** ● ** ● *°: : ● ● .

: :9

● * ● * 150- ● * ::

● ● 9

● * ●:. :.. ●:. :00 se

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● a ● . . 9** ● ** ● *s . .

‘1 ●

●

● ● *

::eooo ::

● 8000 ● :*O ●

/

● 0

u ● *O ● ●:0 **C ● *

been used for the three-element as well as for the two-element calculation. The molar concentrations per gram are then evaluated for all species and an iteration is performed on Zni

until the difference between the ‘Zni used in the cycle and the Zni calculated in that cycle is

as small. as desired. The mole fractions for all species are computed as before and printed

out and the temperature is raised 100°K.

4. RESULTS

The principal dissociation products formed in the thermal decomposition at 100 atmospheres of methane, ethane, and propane, as well as their mole fractions, are indicated in

Figures 1 through 3. Figure 4 shows how the mean molecular weight, fi, of the decomposi-

\ tion products of methane varies with temperature. The other hydrocarbons show a similar

behavior. The minimum in ~ at 2400°K is caused by a decrease in ~ from 1000 to 2400°K

due to the dissociation of the parent hydrocarbon primarily into hydrogen and solid carbon and

by an increase in ~ above 24000K due to the formation of acetylene from hydrogen and solid

carbon. Figure 5 is a plot of log ~ at 27730K against C/H for methane, ethane, and propane.

Values of ~ for other hydrocarbons through C~H18 (gasoline) are extrapolated.

The data for hydrazine and ammonia are not presented graphically, since the products

above 1000°K are the stoichiometric quantities of hydrogen and nitrogen. At 2773° the mole

fraction of hydrogen atoms in both cases becomes significant since it then amounts to 1 per

cent of the total hydrogen concentration; at 3000°K this fraction increases to 3 per cent of the

total hydrogen concentration.

The hydrazine-hydrocarbon and ammonia-hydrocarbon mixtures are considered together

since their behaviors are so similar. The similarity holds whether the hydrocarbon is methane,

ethane, or propane and whether it is mixed with hydrazine or ammonia. As would be expected,

the mean molecular weights of the decomposition products for these six systems increase as

one goes to higher hydrocarbons or if one replaces ammonia by hydrazine. For any given

system, ~ goes through a minimum at about 2200°K. Figure 6 indicates the major decomposition products and their mole fractions from 1000 to 3000°K at 100 atmospheres for the system

90 mole ~ NH3 - 10 mole % CH4, whereas Figure 7 gives a more accurate plot of the mole

per cent of solid carbon at varic,us temperatures in the temperature interval. An increase in

\ the percentage of ammonia (or hydrazine) decreases the mole fraction of solid carbon at any

given temperature, but a decrease in the percentage or a change from methane to ethane or

propane at the same percentage of hydrocarbon increases

any given temperature.

The results for ethanol and propanol are also quite

most completely as carbon monoxide over practical y the

the mole fraction of solid carbon at

similar. The oxygen is tied up alentire temperature range. Figure 8

● *O ● ● ** ● 00 ● 0 ●8. ● *

● : :-

● *** 1* +0 ::

● ● ● 0

9* ●:0 ● 00 ●:0 :00 ● *

Bumlm ● 9* ●:: ● ** 800

● * ● *m *mm* ●

—

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ☛☛ :“c ●

● * ●*. : :*: ●

● e**99 ● I

9* ● . . ● 00 ● ** ● *m .0

● ● * ● * ● *

● 99* ● 00.

● * :* 0: ● 9

●

●

● * ●:. ● ●:* :*. ● *

shows the variation in the mole fraction of the decomposition products of ethanol at 100 atmospheres as a function of temperature. At 2773°~ ~ for ethanol is 9.61

8.96.

Since methanol behaves quite differently from the higher alcohols,

products are shown in Figure 9. It is important to note that carbon is

only at temperatures below 1250°K, whereas it deposits over the entire

and ~ for propanol is

the decomposition

deprisited from methanol

temperature range for

the higher alcohols. Figure 10 shows the deposition and removal of carbon over the temperature interval 1000 to 3000°K

5. DISCUSSION

\

If one is interested in choosing the propellant with the lowest mean molecular weight, he

will choose hydrogen. However, since the density of hydrogen is so low, he can pick a more

dense propellant with a larger ~ and still have a missile that is smaller in over-all size than

the hydrogen rocket.

The pure aliphatic hydrocarbons have the lowest mean molecular weights after hydrogen,

ranging at 2779°K from 5.61 for methane to 7.2 for gasohne. Mixtures of hydrocarbons and

ammonia or hydrazine have @s between the M of the hydrocarbon and that of the ammonia or

hydrazine. At 27730K the ~ of ammonia is 8.48 and the R of hydrazihe is 10.64. Methanol

/

has an ~ of 10.66, whereas the @s of ethanol and propanol, respectively, are 9.61 and 8.96.

If one also is concerned about the chemical behavior. of these propellants in a graphite

reactor, then he is faced with another problem. All of them either corrode the graphite or

deposit additional carbon onto the reactor when they thermally decompose. It is possible to

make a blended propellant which will not attack the reactor chemically or deposit carbon onto

it over a limited temperature range but, so far, no mixtures have been investigated which do

not affect the reactor over a several hundred degree temperature interval.

Hydrogen, ammonia, hydrazine, and methanol attack graphite over 2000°K The hydro-

.

carbons, ethanol, and propanol deposit carbon at all temperatures of interest. Mixtures of

hydrocarbons and ammonia or hydrazine can be made which will not attack the reactor at

operating temperatures but which, unforhmatel y, corrode the reactor at lower and higher temperatures, as Figure 7 indicates.

An effort will be made to blend multicomponent systems containing carbon, oxygen, nitrogen, and hydrogen which will neither deposit carbon nor corrode the reactor over an appreciable

/

temperature tnterv~ around 2500°C. This work will be described in a future report.

● ☛☛ ● ● *O ● *O ● - ●*. ● ● *

● : : :0

.- 1?-:” ..

● *.* ::

● 0

● * ● *9 .00 ● em 9m. ● .

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● ne

:*. ● ●°0 :

a. *..

W!lli9@ ● e . . . ● e. ..*

● ** ●

● ****

● am ● :

● ●:6 : ●:0

● 9* .0

●

● 0 ::

● ● 0

● ● 0

● ** 90

I I I I I I

Ixlo-’

IXIO-2

IXIO-3

Ix IO-4

—

—

/ \/ 1

C3H4

I I

1000 14CI0 1800 2200 2600 3000

T“K

Fig. 1 Principal decomposition products of methane

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
8* ● m* .e. a’.:

● O**OO

z

o

lx 10-1

IXIO-2

I x 10-4

9* ● 0. ● 00 ● me

● ** ●

● O**

● 0 : ● :

● ●:0 : ●:0

● ☛ ✎✌

✚✎✚ ●

●

aoe ●

9***

. . .

— I I I I

b(s)

—

—

.\

\ /

C2H2

1000 1400 1800 2200 2600 3000

Fig. 2

T°K

Principal decomposition products of ethane

● ee ● ●:* 9** so ●*b

b : :-1%-:::

● 0*0*9 ●

b ● m ● 0 ●:0 :00 ●:* :00 ● *

● 9. Oa. . . .

00 600 -0– i - ● - -.*

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
● mb ●000°0: ● 0 ●°0 ●

● ***** ““mub ● *O

● ● 00 o

● ● *9*

.0 ● 9,8

Ixlo-1

Ixlo+

IX IO-3

IX IO-4

● e 9*O ● *9 ● ** ● 0. . .

● *O ● *

● *** 90 ::

●

● * :000

:

● ●:0 :

,0 ●:0 :Oa ● 0

—

r“

H:

‘~ C(

-

— \

— C2 H

—

—

x

C2‘6

1000 1400 1800 2200 2600 3000

T°K

Fig. 3 Principal decomposition products of propane

mm%;: ● e ● *9 ● ● ● 8*

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
10,0

9,0

8.0

7,0

6.0

5.0

● 0 ● *e ● ** ● *e ● ** .*

9** ● *

● **9 ● o ::

● 0 :0 ●:0 ::

● ● *9 : ●:0 :00 cc

1000 1400 1800 2200 2600 3000 3400 3800

To K

Fig. 4 Mean molecular weight of methane as a function of temperature

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
9

8

7

6

5

4

3

2

● a ● mm ● ** ● . . . . . . .

● 00 ● o

* ● ● e ● 0 ::

● * :0 ●:

● *

9*

● ●:0 : ●:0 :00 ● 0

I

I I I I I

cfJH,fJ

(GASOLy

C6 H14

C4H10A*-

--*- ~5H12 ~7~16

C2H6

CH4

L

I I

0.250 0.280 0.310

Fig. 5 Mean molecular

0.340 0.370 0.400

Cl H

weights of various hydrocarbons

● eb~ ●

~:

.;* :.. :s,

.m - 2p +. : :

● * ● O

● *6 9m9 ● *3 8e* ● m

0.430 0.460

at 2773°K

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
Ixlo-’ 1

IX IO-2

x I0-3

.,o-41_xldL_

1000 140CI 1800 2200

HCN

C2H2

H

C H4

CN

C2H4

NH3

C2N2

2600 3000

To K

Fig. 6 Principal decomposition products of 90 mole YO ammonia - 10 mole ‘%0 methane

● a* ● ●:* ● ** ● a ●°0 ●

:-43-::

● *O

i

● mm*O%liiiiK ●

● 00 ●0: ::0

● 0 ● *ee*s ● 0

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
0

2

-14

-16

-18

-20

-22

1-

a ● 90, 0000°0: 9** ●

aa ****O ● 0

~.:m~ “:; ● *● O* ● ** ● ** ● *O .*

O** ● *

● *** ● 9 ::

● ** :0 ● O

a8*

● eo :

● ,

9 ●:0 :00 ● 0

2

0

-2

-4

-6

-8

—

1200 1400 1600 1800 2000 2200 2400 2600 2800

ToK

Fig. 7 Mole per cent of solid carbon from the 90-10 NH3 - CH4 system

99* ● ● 9, ● *9 9* ●’0 ●

● : :

● : ● 0

●

.++

● e ●:0 :00 ●:* ● O9 ● 0

3000

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
Ixlo-’

IX IO-2

!5

o

z

I XIO-4

1( )U 1400 1800 2200 2600 3000

T°K

Fig. 8 Principal decomposition products of ethanol

●

!3aiiiE;:- ● 9 ● m.=-.–– . . . .

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
Ixlo-’

IX IO-2

IXIO-3

IX IO-4

.’ //,

● 9 9** ● 0

9.****: ●’* ●

9****** ● *

‘“::diiiam“m:

.

.

“(s)

I

1400

Fig. 9

H2

co

C2H2

H

C H4

C2H4

H20

1800 2200 2600 3000

T“K

Principal decomposition products of

:“mllm?: ● **

● 68’***

● 0 ?“**”***

_,. ---

--------

F..,

,

.

APPROVED FOR PULBIC RELEASE

APPROVED FOR PUBLIC RELEASE
o

—

a) N o ml

1

NOEIW9 % 31OW

● ● ☛

Oc ●:0 :00 ●:0 :00 ~o

ml

0

o

‘*

x

APPROVED FOR PUBLIC RELEASE