I
ROBERT
L. POTTER, GORDON E. GUFFNER, and THOMAS
F. REINHARDT
Bell Aircraft Corp., Buffalo 5, N. Y.
cket Working Fluids Hydrogen und Helium
This discussion explores the performance potentialites of hydrogen and helium as inert working fluids in a rocket using a separate heat source
B E C A U S E they do not require air for combustion, rocket engines are virtually the only propulsion devices that can be considered for extreme altitude or space flight. However, they require enormous quantities of propellants, and the range of a rocket-powered vehicle is seriously limited by the weight of propellant that can be carried. Therefore, much effort is devoted to finding propellants having high specific impulse or high thrust per unit of weight consumed per second. The specific impulse obtainable by chemical propellants that yield energy by rearrangement of chemical bonds is limited. The hydrogen-ozone system has the highest specific impulse of any chemical propellants, closely followed by the hydrogen-fluorine system. For these systems the maximum specific impulse, which is approximately proportional to ( T J ' M ) ~ ' ~where , T , is the flame temperature and M is the molecular weight, occurs a t a mixture ratio equivalent to roughly 100% excess hydrogen. This illustrates the remarkable effectiveness of hydrogen as a working fluid, and leads to the deduction that even higher performance could be obtained by using hydrogen alone as a working fluid, supplying the energy from an external source. The maximum performance obtainable with an inert working fluid is limited by the maximum temperature attainable by the working fluid and the available power. Presumably the power would have to be supplied by a nuclear reactor, or by recombination of free radicals. To explore the performance achievable with inert working fluid rockets, calculations for hydrogen and helium have been made. I n these calculations,
specific impulse, characteristic velocity (a measure of flow rate of working fluid through a nozzle throat of unit area), power consumption per unit of thrust, nozzle area ratio as a function of pressure, and the coefficient of heat transfer to the nozzle walls are of particular interest. Each of these quantities is required for rocket design considerations. The independent parameters are pressure (varied from 20.414 to 68.048 atm. in the chamber and from 1 to 0.0625 atm. in exhaust) and temperature (varied from 2000' to 3000' K. in the chamber). The computations required to arrive at rocket performance parameters are described by Altman and Carter (7). A general program for these calculations has been coded for an IBM 650 digital
computer at Bell Aircraft Corp., allowing for many gas species (8). At high temperatures hydrogen dissociates into monatomic hydrogen and calculation of the performance of hydrogen as a working fluid requires consideration of both atomic and molecular hydrogen. When the chamber conditions of temperature and pressure are fixed, the composition is fixed by minimizing the Gibbs free energy, if it is assumed that thermodynamic equilibrium exists in the chamber. Because the composition 'is fixed, so are all the thermodynamic properties. The working fluid is then presumed to expand isotropically to the exit pressure along a path composed of equilibrium points. Each point may be found by requiring that the specific entropy of the gas equal that at chamber conditions.
I
0.0I
01
1.0
NOZZLE EXIT PRESSURE (ATM.)
Figure 1.
-
I
1
IO
I
IC
I
Influence of chamber temperature on limiting specific impulse of hydro-
gen as exit pressure decreases Performance increases with increuring altitude VOL. 50, NO. 10
OCTOBER 1958
7557
.
sure divided by the maximum densityvelocity product in the isentropic expansion curve. This parameter supplies information necessary for the design of rocket nozzles and in particular gives the throat area required for a given chamber pressure and propellant weight flow. Thus (ft.hec.1 = P c / ( ~ V ) m a x
c*
where curve may be selected, and iterations made on the temperature until the resulting composition gives a specific entropy that matches the chamber specific entropy. On the basis of one-dimensional isentropic flow, the specific impulse is given, when the exit pressure equals the outside pressure, by
-
15)''~
P, is the chamber pressure and
is the maximum of the densityvelocity product on the expansion curve. Multiplying the right side of Equation 2 by A,g/A,g, where g is the gravitational Constant and A , is the throat area of the nozzle, and using the continuity equation, gives
To do this a pressure on the expansion
Zsp (sec.) = 9.3281 (h,
(2)
c*
(ft./sec.) = Po X Atg/tb
(3)
where tb is the total weight flow of propellants through the rocket. In the present calculations, the density-velocity product on the isentropic curve from chamber to exit condition was found a t several points near the throat and these products were fitted to a quartic in
(1)
where h, is the specific enthalpy in the chamber and h is the exit specific enthalpy, both in calories per gram. O n the same basis, the characteristic velocity, c*, is given by the chamber pres-
the pressure by least squares. The maximum in the density-velocity product was found by analytical methods and c* was calculated according to Equation 2. However, c* is used as given by Equation 3 to determine throat areas in rocket design calculations. The power required to produce 1 pound of thrust is given by
where hi is the specific enthalpy of the working fluid prior to heating. For liquid hydrogen a t equilibrium and at its normal boiling point, 20.39' K, ( g ) , h, takes on the value -55.66 ea!. per gram when referred to hydrogen gas a t equilibrium a t the absolute zero. The thermodynamic data used came from IVoolley, Scott, and Brickwedde (9) and the Bureau of Standards compilation (7). There is no completely satisfactory relation for the gas film coefficient; however, the Colburn correlation (5) has been used with success in other rocket design applications and is used here. I t is given as
20
t
5 E e 0
c
IO
w
9 v,
v,
w 5 %
k X W
O k !
N
N
s A/Ai
-
Figure 2. Gas film coefficient and exit pressure as a function of nozzle area ratio for hydrogen, T, = 3000' K., P, = 2 0 . 4 1 4 atrn. Maximum heat flux occurs in nozzle throat. performance increases
Table 1. T,, K. 3000
2500
2000
1558
Pc, ,4tm. 20.414 34.023 68.048 20.414 34.023 68.048 20.414 34,023 68.048
As exit pressure decreases, nozzle area ratio for optimum
Rocket Performance Parameters for Hydrogen Mole % Hz 96.572 97.334 98.107 99.446 99.571 99.696 99.964 99.972 99.980
Specific Enthalpy,
Cal./G. 12451 12237 12022 9501 9467 9433 7287 7285 7283
INDUSTRIAL AND ENGINEERING CHEMISTRY
I,,, Sec.
769.7 805.2 843.5 681.4 715.4 752.3 601.2 631.2 664.1
C*,
Ft./Sec. 17,808 17,719 17,632 15,888 15,853 15,842 14,016 14,013 14,012
Kw./Lb. Thrust 30.859 28.988 27.186 26.627 25.272 23.948 23,188 22.078 20.981
where h, is the gas film coefficient, d the diameter of the nozzle station, k the thermal conductivity of the gas, p the density, V the particle velocity, p the viscosity, and the specific heat a t constant pressure of the gas. All the gas properties are evaluated a t free stream conditions, and the units must be consistent. Most of the properties required for insertion into the correlation become available when the isentropic expansion curve is calculated. The specific heat was taken to be 2%X , C$/2 X,M,, where Xi,Cpi, and M , are the mole fraction, heat capacity per mole, and molecular weight of species z. Except at the highest temperatures, the difference between this and (dh/dT), is small, and was ignored for purposes of these calculations. The viscosity was calculated as outlined by Hirschfelder, Curtiss, and Bird ( 4 ) , using values of the collision diameter and ~ / kfor a Lennard-Jones potential as listed by him for molecular hydrogen and a value of G = 2.53 (2) and elk = 9.8 for monatomic hydrogen. The values of the potential constants used for monatomic hydrogen may be in error: but the amount of dissociation near the throat is small and little error is expected in the gas film coefficient because of the values estimated for potential parameters of atomic hydrogen, T o obtain values of the thermal conductivity, Eucken's assumption in its original form was employed ( 4 ) . Although the transport of chemical energy is thus excluded ( 3 ) , it is ex-
cp
ROCKET WORKING FLUIDS pected that the Prandtl number will be reasonably constant at and below 3000" K. The composition and specific enthalpy of the hydrogen working fluid at three different chamber pressures and temperatures are given in Table I, as well as values of c* and the specific impulse, when both exit and outside pressures are equal to 1 atm., and the power requirements necessary to produce 1 pound of thrust under the same conditions. Figure 1 shows the specific impulse as a function of exit pressure with chamber pressure and temperature as parameters. Figure 2 shows the gas film coefficient and exit pressure as a function of area ratio in the nozzle for one chamber condition. The calculations for helium were carried out to yield the same information as for hydrogen. Because helium is a monatomic gas and does not ionize at the modest temperatures involved, ideal gas laws could be used throughout. The standard state of helium was taken to be the ideal gas at the absolute zero and the initial state was considered to be liquid at its normal boiling point, 4.2' K. The viscosity was calculated as before, using values of 6 / k and for helium given by Hirschfelder, Curtiss, and Bird (4), and the thermql conductivity was obtained by use of Eucken's assumption. The thermodynamic data came from the Bureau of Standards compilation (7). For helium, values of c* are given in Table 11, with the specific impulse and power requirements per pound of thrust when both exit and exhaust pressures are 1 atm. In Figure 3 is plotted the specific impulse as a function of exit pressure with chamber pressure and temperature as parameters. In Figure 4 the gas film coefficient is shown, with the exit pressure as a function of area ratio in the nozzle. The highest temperature considered in these calculations, 3000" K., appears to be the limit, beyond which it is doubtful that a working fluid can be heated by direct heat transfer means. This temperature is exceeded by most bipropellant systems, and in some cases with energetic oxidizers flame temperatures may reach 4500' K. The maximum specific impulses of the systems hydrogen-ozone and hydrogen-fluorine are 373 and 365 seconds, respectively, when the chamber pressure is 20.414 atm. and the exhaust pressure is 1 atm. (6). For the same pressure ratio and a temperature of 3000' K., the specific impulse of helium is 476.3 seconds, and for hydrogen an impressive 769.7 seconds. While the high specific impulse of hydrogen is very attractive, inspection of the calculated performance param-
5801
y 420
Y
0
5;i
'
340.
VJ
.o I
0.I NOZZLE EXIT PRESSURE ( a t d
-
1.0
Figure 3. Influence of chamber temperature is shown on limiting specific impulse of helium as exit pressure decreases Performance increases with increasing altitude
Table
II.
Rocket Performance Parameters for Helium
To,OK.
P,,Atm.
IBp, Sec.
c,* Ft./Seo.
Kw./Lb. Thrust
3000
20.414 34.023 68.048
476.3 494.7 513.7
11,273 11,273 11,273
14.844 14.290 13.762
2500
20.414 34.023 68.048
434.8 451.6 468.9
10,291 10,290 10,290
13,550 13.045 12.564
2000
20.414 34.023 68.048
388.9 403.9 419.4
9,205 9,205 9,204
12,119 11,668 11.237
*O I5
-t E
c
0
v
k X W
1 0
4
-I
N P4
4
DIVERGENT
-
2
3
4 5 6
810
30 40
A/At- -----c
4.
Gas film coefficient and exit pressure as a function of nozzle area ratio urn, T, = 3000' K., P, = 20.414 atm.
Maximum heat flux occurs in nozzle throat. performance increases
As exit pressure decreases, nozzle area ratio for optimum
VOL. 50, NO. 10
OCTOBER 1958
1559
interest only. To put it another way, to achieve specific impulse of 476 seconds with hydrogen, the power consumption would be 18.2 kw. us. 15 kw. for helium, but the temperature would be only 1280’ K. I t would probably be much easier to engineer the reactor with the higher power output operating a t the lower temperature. The nuclear reactor could, however, be used as an indirect heat sourcethat is, it could generate electric power, which would then heat the working fluid by means of a confined arc discharge. In this case, the temperature of the working fluid would not be limited, but the output of the reactor power plant would be fixed. Hence, under these circumstances helium would be the better working fluid. Another possible source of power to heat the working fluid prior to expansion comes from the energy content of free radicals; in this case the best free radical would be atomic hydrogen. If a solution of about 38 mole % (23.5 weight a/c) of atomic hyrogen in liquid hydrogen could be formed, enough energy would be available to heat the entire mass to 3000” K. and 20.414 atm. with a corresponding I,, of 769.7 seconds. I t would require in the neighborhood of 27 mole yo (8.5 weight yc)of atomic hydrogen in liquid helium to produce the same chamber conditions, in this case yielding about 507 seconds for the specific impulse. For comparison. the same weight per cent solution of atomic hydrogen in liquid hydrogen will yield a temperature of 1260’ K. and a specific impulse of 474 seconds. Thus helium looks better than hydrogen in this case, and it may prove easier to stabilize free radicals in liquid helium than in liquid hydrogen. These figures are uncertain
eters reveals that the power required per pound of thrust with hydrogen is roughly double that for helium when the chamber temperature is 3000’ K.. mainly because of the higher specific heat capacity of hydrogen. The parameters of power per pound of thrust and the propellant consumption per pound of thrust for hydrogen and helium at the chamber pressure of 20.414 atm. are plotted in Figure 5 as a function of chamber temperature. If a maximum temperature of 3000’ K. is allowed, the specific impulse of hydrogen is much superior to helium and the flow of propellant per pound of thrust is 1.3 X pound per second of hydrogen and 2.1 X pound per second of helium. If a nuclear reactor is used as a direct heat source to heat the working fluid. the thrust per pound of working fluid at a given reactor power setting favors helium over hydrogen. Thus (Figure 5), if the power output were limited to 15 kw. per pound of thrust, the corresponding specific impulse for helium would be 476 seconds, and that for hvdrogen only 377 seconds. When it is noted, however, that the temperature of the hydrogen working fluid under these conditions is only 800’ K. us. 3000’ K. for the helium, the apparent advantage of helium may be of academic 30
/
28
/
/
/
3.0 2.8
26
t
c
Icn
3
(L
5
5
3.2
2.6
1 F w
24 22
2.4
20
2.2
18
2.0
16
1.8 1.6 ?g
14
I I-
5 6‘
-
41% Q
SL
12
1.4
IO
1.2
500
1000
1500
-
2000 T,
(OK)
2500
--I
3000
Figure 5. Power per pound of thrust and propellant flow, pounds per sec. per pound of thrast for hydrogen and helium as a function of chamber temperature for chamber pressure of 20.414 atm. Hydrogen is superior i f temperature is the limiting factor; helium, superior i f power is limiting
1560 INDUSTRIALAND ENOINEERINO CHEMISTRY
because of lack of information concerning the heats of condensation and solution of atomic hydrogen; however, they indicate what may be expected. I t is doubtful if regenerative cooling would be feasible with atomic hydrogen in the working fluid, because of the strong probability of recombination in the cooling jacket. If regenerative cooling is not possible, the duration of the rocket firing would be limited by the uncooled chamber life. The forced convection heat transfer coefficients encountered with either hot hydrogen or hot helium working fluids are several times as high as for conventional chemical propellants. Thus, even at relatively modest gas temperatures, heat rejection to the nozzle walls is substantial. Countering this is the fact that both hydrogen and helium are excellent coolants, and a regeneratively cooled nozzle design should be entirely practical. The heat transfer coefficient of helium is about 75y0 that of hydrogen; hence for a given gas temperature helium produces the lower heat rejection. For a given specific impulse, or for a given power setting, however, the lower temperature of the hydrogen more than compensates for the higher heat transfer coefficient, and hydrogen will have the lower heat rejection. The potential prrformance gain of the inert working fluid rocket over the chemical rocket is substantial. However, to realize this potential, energy sources of high output per unit of weight are needed. The primary effort in the development of inert working fluid rockets will, no doubt, have to be directed toward optimization of the power source. Literature Cited (1) Altman, D., Carter, J. M., “High Speed Aerodynamics and Jet Propulsion, Vol. 11, Combustion Processes,” Section B, Princeton University Press, Princeton, N. J., 1956. (2) Clingman, W. H., Brokaw, R. S., Pease, R. N., Fourth Symposium (International) on Combustion, p. 310, LVilliams & M‘ilkins Co., Baltimore, Md., 1953. (3) Hirschfelder, J. O., J . Chem. Phys. 26, 274 (1957). (4) Hirschfelder, J. O., Curtiss, C. F., Bird, R. B., “Molecular Theory of Gases and Liquids,” Wiley, New York, 1954. (5) McAdams, W. H., “Heat Transmission,” McGraw-Hill, New York, 1942. (6) Potter, R. L., Bell Aircraft Corp., unpublished calculations. (7) Rossini, F. D., Wagman, D. D., Evans, W. H., Levine, S., Jaffe, I., Natl. Bur. Standards, Circ. 500, Series 111 (1952). (8) Vanderkulk, W., Potter, R. L., Bell Aircraft Corp., unpuhlished work. (9) Woolley, H. W., Scott, R. B., Brickwedde, F. G., J . Research iVatl. Bur. Standards 41, 379 (1948).
RECEIVED for review January 2, 1958 ACCEPTEDJune 27, 1958
Firing Key
Gas Meter
Feed Gas
Rotameter
Transformer
Back Pressure Regulator
Feed Gas Inlet System Shut-off Valve e
Ignition Plug (Hot
Heat Exchanger IPA Feed Reservoir
Explosion Vessel
S. S . Cylinder I.D. 2” Length 4” Fitted with 2 stainless steel screens as spray
IPA Drain
baffles
Figure 1.
Ignition limits of the system were measured in a cylindrical, electrically heated steel
I
bomb
HARRY SELLOl
Shell Development Co., Emeryville, Calif.
Ignition Limits of the Gaseous System Isopropyl Alcohol-Oxygen-Nitrogen To minimize hazards in handling and processing isopropyl alcohol, operate outside ignition limits or reduce oxygen. Sources of ignition are always present. This report tells how to avoid explosion
A
COMBUSTIBLE gas or vapor may, under certain conditions, be ignited so that a rapid self-propagating combustion or deflagration occurs. For such a combustion, the combustible and the oxidant gas must be present in the proper concentrations, and a source of ignition or suitable energy input be available to initiate reaction. The regions of suitable concentrations for the combustion of a fuel and oxidant gas which delineate this region are known as the limits of flammability. T o minimize the hazard in handling and processing of a combustible, the flammability region must be scrupulously
1 Present address, Shockley Semiconductor Laboratory, Mountain View, Calif.
avoided and sources of ignition eliminated. The latter goal, however, is practically impossible, and ignition must be considered omnipresent. Thus, avoidance of hazard essentially is dependent upon a knowledge of the limits of flammability. Coward and Jones (7) describe “standardized” apparatus used to measure flammability limits of a number of fuels. It consists mainly of a glass cylinder 5 cm. in diameter and 150 cm. long, placed vertically and open at the bottom. The fuel and oxidant gas are mixed in the cylinder and ignited by an open flame or spark gap, If a flame travels the length of the tube, the mixture is self-propagating and is said to be flammable. This method is applicable only to measurements at atmos-
pheric pressure. I n the work reported here, the limits are more properly classified as ignition limits, as differentiated from true flammability limits, because the method of measurement precluded observation of the extent of flame propagation. Both types of limits are strongly dependent on the nature of the equipment and type of ignition ( 4 ) . This dependence is reflected, for example, by the variation in the values reported for the upper limit of flammability for isopropyl alcohol (IPA) in air (7, 6)-i.e., 11.8 and 7.99%. Many other methods have been used to study gaseous explosions, depending mainly on the nature of the source of ignition and the type of explosion chamber. The ignition sources commonly used are intense sparks, open flames, or VOL. 50, NO. 10
OCTOBER 1958
1561
