A S A T E C . NASA TM X-52775

X I M E FUEL LOSS RATE AND WEIGHT ESTIMATES OF AN OPEN- CYCLE GAS-CORE NUCLEAR ROCKET ENGlNE

by Robert 6. Ragsdale Lewis Research Center Cleveland, Ohio

TECHNICAL PAPER proposed for presentation at Sixth Propulsion Joint Specialists Conference sponsored by the American Institute of Aeronautics and Astronautics SanDiego, California, June 15-19, 1970

I

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SOME FUEL LOSS RATE AND WEIGHT ESTIMATES O F AN

OPEN-CYCLE GAS-CORE NUCLEAR RQCKET ENGINE

by Robert Go Ragsdale

Lewis Research Center Cleveland, Ohio

TECHNICAL PAPER proposed for presentation at

Sixth Propulsion Joint Specialists Conference sponsored by the American Institute of Aeronautics and Astronautics

San Diego, California, June 15-19, 19'70

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

SOME FUEL LOSS RATE AND WEIGHT ESTIMATES OF AN OPEN-CYCLE GAS-CORE NUCLEAR ROCKET ENGINE

by Robert G. Ragsdale Lewis Research Center

National Aeronautics and Space Administration Cleveland, Ohio

An analysis is carried out to estimate engine weight and to SBow the effect on engine weight of engine thrust,

iments on two-

characteristic s

Tbe engine welght it3 dete ed by mre than just the uranium bee' rate. In the present study these other variable6 were either eesigned fixed values, or else tbey were treated a6 parameters in the oalculatbas. Tbs total englne weight is composed of the individual weights of the modbrutor, the preesure shell, the irbprmp, and the mzzle. This system is illustrated in Flgure 1. In this study, the cavity diameter and

moderator thickness were held constant. Thus mod- erator weight is a constant. Engine weight variations are caused by variations in the weighte of the pump, nozzle, or the pressure shell.

The three independent variables of the calculations are engine thrust, specific impulse, and the hydrogen- to-uranium flow rate ra tb . treated as a parameter thro Thus curves of engine weight versus the various in- dependent variables are given for three values of critic mass-25, 50, and 100 kg. Recent c

50 kg is the best curr the configuration used

critical mass is e calculatbns.

engine operating conditions. &tion was determined by sele thrustt, specific impulse, and

the sum of the individusl weights of hydrogen turbopump, the pressure

We = w, + wp + w, + w, These components are shown in a conceptual engine drawing in Figure 1.

1 TM X-52775

basic engine configuration that is described in the fol- loring subsection of Analysis. In order to calculate the weights Qf the other three engine components, it was necessary to determine the reactor pressure required for criticality. The pressure calculation was done us@ the fobwing expression presented in Reference 2:

3.3 0.7

(2) Dc Mf = 0.14

Equation (2) glves the fuel mass % in kilograms in the ep%ne as a function of the cavity diameter Dc in feet, the reactor pressure P in atmospheres, the engine thrust F in pounds, the specific impulse Isp in sec- onda, and the hydrogen-to-uranium flow rate ratio

study, Equatbn (2) becomes:

For the 12 ft diameter cavity used in this

EQustion (3) was used 60 obtain the reactor pressure neceseary to have a critical mass ]M4 in the engine for the various thrusts, specific im@ses, and hydmgen- to-nrmiuna flow rate ratios investigated.

Bu ic Engin e Configuration

The spherical engine geometry used as a basis €or the crlcol.tbne is ahown in Figure 1. The central rsrcbr cavity contains the fissioning uranium prSema ball sufioanded by fbwing hydrogen propellant. Thie t.rftp is ancbeed by concentric spherical regbns of nmcbrabr materials. The moderator is in turn con- tained by an outer pressure vessel that is alm spherical. Tbe presrure dell is pierced by a supermnic exhaust muis at the downstream end of the reactor cavity. A tprboprmp systttm is umd to pressurize the hydrogen h m a t m l pressure of 1 or 2 atmospheres up 00 the reacb~ caw pressure level of approximately 1000 rtmoakrrss.

TBe preeent calculatione were based QII a cavity dimnder af 12 R. This is wmuuded by successive layers of (1) bot heavy water, 6 in. thick, (2) beryl- lium msbl, 4 in. thick with 25 percent voids, and (3) oold heavy water, 26 in. thick. The total moderator Ihbkneu I s 2.5 ft. The moderator weight ie 120,000 Ibr. Ths critical mass of this configuration is a little lew tbin 50 kgl, for U-233 fuel and with some of the m g e n *%y-passing*93 the main portion of the reactor C r r i t y .

Scheduie of Caicuiations

The three variables of the calculations were engine thrust, specific impulse, and hydrogen-to-uranium flow rate ratio.' Critical mass was treated a s a parameter in the calculations, with values of 25, 50, and 100 kg. Table I shows the numerical values used hr each of the variables.

A reference case was selected to repreaent a ftreasonablefl set of values. The reference engine has the following characteristics:

Thrust . . . . . . . . . . . . . . . . . 400,000 lb Specific impulse . . . . . . . . . . . . . 1800 sec Hydrogen-to-uranium f b w ratio . . . . . . . . 100 Critical mass. . . . . . . . . . . . . . . . . 50 kg

These values were chsen on the folbwbg basis. The thrust is high enough to be approximately equal to the engine weight. The specific impulse is far enough beyond a mlid-core level to be of interest. The uranium loss rate is b w enough m as to mt be pmhibitive. The critical mass represents the beat current estimate. These values result in an engine weight that is m t in- tolerably large, and in a reacbr pressure that is high, but not unbelievably m. Thus, the reference engine is a mrt of compmmioe engine that has attractive per- dormance witbout excessive weight o r pressure.

Presmre Swll

The presaure shell we&& was obtained by using the equatbn br mechanical stress in a thfn waLled sphere. This gives tBe thickness of the shell in terms of the allowable stress u, the radius of the w e r e RE, and theenginepreseure P 811:

t, = - 2u (4)

This equatbn can be rewrittan to obtain the weight of the shell material with a density ps as:

For the fixed engine configuratbn of thisl study Rs

to density ratio (u/ps) wno takp b be 0.7~106 h.d a conetcmt value of 8.5 ft. The shell material

in. For a &el density of 0.29 lbs/in. , this ratio correeponds to a strength of 200,000 poi. Values higher than this are available in b a a metals, and weldment strengths above 150,000 psi have been re- ported. engine pressure vessel, complicated facbrs wch a8 thermal stress, radiation rctivatbn and dunage, and shell penetrafbns wuld have to be goutsidered. More detailed ~ tudies~-~ bawd on filament wound fiberglass designs (u/p, = 2. 5x106 in.), pmduced ahell weights comparable to the ones obwned in this study.

Certainly in an actual design of a nuclear

For the numerical values used here, Equation (5) becomes:

2

4

W, = 140 P (6 )

This equation gives the pressure shell weight W, in pounds in terms of the engine pressure P in atmos- pheres. This equation is shown plotted in Figure 2. A reactor pressure of 1000 atmospheres requires a pres- sure shell weighing 140,000 lbs.

prdvide the driving force to Uant from its storage tank

vely cooled regions of the engine reactor cavity. Turbopump in this study from an equation

/3 = 0.815 w

conditions gives

JeJoZZh P

zzle was obtained

The nozzle weight Wn is in pounds, the thrust F is in pounde, and the reactor pressure P is in atmospheres. Tbe area ratio E waB taken to be 300. Reference 10

gives C values ranging from 0.05 to 0.25: 0.25 was used in the present calculations. These values give:

w n = 5 - F P

For a thrust of 400,000 lbs and a reactor pressure of 1000 atmospheres, the mzzle weight is 2000 lbs. Equation (11) is shown plotted in Figure 4.

A reactor shield was not included as a component in this analysis because it appears possible that little, if any, additional weight of material would be required beyond that already present as moderator and pressure shell. To really prove that this is 80 would, of couree, require shield design calculations of detail and com-

NERVA mlid-aore nuclear engine were used b estimate gas-core engine shielding requirements.

It is currently estimated that a 157 engine would require an internal shield 3300 pbs, and perhaps an additional disk shield that

alue of 8300 be. l1 The

rce strength. Thus lding ranging from d pressure shell of

required in the crew direction, an additional 4000 lbe of lead distributed over 1/16 of the pressure vessel sur- face would provide it. Of course, in an actual engine, the shielding, criticality, and pressure vessel require- ments would all be considered together in an integrated deem. In this regard, it is worthwhile to note the

2 178 g/cm of moderator and pressure shell completely surrounds the reactor cavity, except for the mzzle. The point here is not to design a gas-core shield, but simply to shcw that incorporation of shielding require- mente into an engine design ie not likely to significantly change the weight estimates of this study.

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III. Discussion of Results

Reference Engine

The reference engine was selected to have the fol-

Thrust. . . . . . . . . . . . . . . . . .400,000 lbs *cific impulse. . . . . . . . . . . . . . 1800 sec Hydrogen-to-uranium flow ratio . . . . . . . . 100 Critical mass . . . . . . . . . . . . . . . . . 50 kg

The moderator weight for this engine is 120,000 lbs, a s it is for all the cases of this.study since the cavity and moderator dimensions were held constant. Equation (3) gives a reactor pressure of 1000 atmospheres required for the 50 kg critical mass.

lowing characteristics:

The weig?ht breakdown of the reference engine is given.in Table 2. The total engine weight is 281,000 lbs. This gives a thrust-to-engine-weight ratio of 1.4. The moderabr and pressure ahell comprise over 90 percent of the total engine weight. They are about equal con- tribubrs .

There is a trade-off available between themoder- ator weight and the pressure shell weight. The moder- 'aior weight could be reduced by decreasing the moder- a b r thickness. This would cause an increase in the

8, which would require a higher enginepres- "hie would cause an increase in the pressure eight. Thns there is

cavity diameter sbn 60 this engine weight optimization. The effects of

moderator thickness and cavity diameter were mt included in the present study.

eas that would minimize the total engine

The engine Weight itir d m affected by specific impulse, engine thrust level, and the hydmgen-to- uranium f b w rate ratio. These effects wil l be dis- cussed in the aOlbwing subsectbns.

For &e specific impulse variatbn, the enginethrust gen-to-uranium flow rate ratio were held at

their reference engine values of 400 , 000 lbs and 100 , pe&pe&ively. Engine weights for specific impulses in the 1000 b 2000 sec range are shown in Figure 5. Curves are h w n for critical masses of 25, 50, and 100 kg.

There is little effect of specific impulse. Engine weight does increase with increasing specific impulse, but the reIationship is a weak one. The reason for this iS $8 follows.

An increase in specific impulse at constant thrust is achieved by increasing the reactor power and de- creasing the hydrogen Bow rate. In order io radiate is higher power, the fuel temperature increases.

Then, in order to maintain a constant, critical mass of uranium in the engine, the reactor pressure must be increased. The increase in reactor pressure results in a heavier pressure shell. The combined effect of higher

pressure but lower hydrogen flow rate results in a lighter turbopump. The nozzle weight decreases slightly. The overall effect on engine weight of in- creasing specific impulse is that shown in Figure 5.

Figure 5 shows that there is no significant engine weight penalty caused by operating at a higher specific impulse. There is of course a considerable advantage of higher specific impulse because that would mean either less hydrogen propellant would be required on a given mission, or that the trip time could be reduced. Therefore, one would tend to operate at the highest possible specific impulse. Figure 5 simply says that the upper limit on specific impulse would not be placed by engine weight considerations. It would be placed by mmething else, such as mzzle heat transferlimitations, for example.

Figure 5 also shows that critical mass is more important in determining engine weight than is specific impulse. For example, if the critical mass of the ref- erence engine could be reduced by a factor of 2, the engine weight could be reduced by about 90,000 lbs. If the specific impulse is reduced by nearly a factor of 2 (1800 to 1000 sec), the engine weight would be reduced by about 15,000 lbs.

The reference engine condition is sbown in Figure5. The reference engine pressure is 1000 atmospheres. A w e r pressure is required if either specific impulse or critical mass values exceed k s e of the reference engine. The curveson Figure 5 are shown as mlid lines for pressures less than 1000 atmospheres and as dashed lines for pressures greater than 1000 atnaos- pheres. There is M particular significance to the choice of 1000 atmospheres as the change-over value. The curves are shown this way in Figure 5, and in succeeding figures as a reminder that engine pressure is varying from point to pcint along the curves. For the entire range of all the calculations of this study, engine pressure varied from 190 to 3700 atmospheres.

Engine thrust was varied over the range from 100,000 to 1,000,000 lbs. Specific impdm and hydrogen-to-uranium f i w rate ratio were held constant at their reference engine values of 1800 sec and 100, respectively. The results are shown in Figure 6.

An increase in thrust causes an increase in the required engine weight. The effect of thrust is a little stronger than that of specific impulse. The reason is that an increase in thrust at constant specific impulse requires an increase in both the reactor power and the hydrogen flow rate. The higher reactor power results in a higher uranium temperature. The reactor pres- sure must then be increaeed to maintain a constant, critical mass in the engine. The increase in hoth reac- tor pressure and hydrogen flow rate causes weight in- creases in the pressure shell, turbopump and nozzle. The overall effect of thrust level on engine weight is shown in Figure 6.

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The engine weight doe? not increase as rapidly as the thrust does. The reference engine, at a thrust level of 400,000 lbs, has a thrust-to-engine-weight ratio of 1.4. If the thrust is increased to 1,000,000 lbs, the thrust-to-engine-weight ratio increases to about 2.5. Figure 6 also shows the importance of critical mass, at

rust levels. For example, a decrease in critical from 50 to 25 kg would allow an increase in thrust

by b u t a factor of 4, at oonstant engine weight. Con- versely, an increase of critical mass from 50 to 100 kg would require a decrease of thrust by about a factor of 7 at constant engine weight.. The actual numbers here are not as important as the point they illustrate. There

e more potentialperformance gains available from improvements in reactor design than from varying engine operating characteristics like specific impulse and engine thrust level.

Uranium Loss Rate

as rate is obviously an undesirable engine characterietic. It can be reduced, but mt without changing mme other engine characteristic. For example, if the uranium loss rate is reduced while holding thrust and specific impulse constant, then the engine pressure and weight increases. This effect is ehown in Figure 7.

8ons underlying the exchange be- s rate and engine weight can be ex-

ing sequence of events. AEI a der an engine of fixed physical y operating with fixed values of

hydrogen flow rate, reactor power, specific impulse, reactor pressure, critical mass of uranium, and ura- dum flow rate. Througfiout the following sequence of changes, the hydrogen f b w rate, reactor power, and epecific impulse Q not change.

At this initial steady-state operating point, the u W u m flow rate into the engine is the same as the f b w rate out of the engine. A t time zero, the uranium flow rate into the engine is decreased to mme new, bwer value. The folbwing events and conditions then transpire:

1. Since the hydmgen flow rate is still the same, the uranium flow rate out of the engine does not changa,

is therefore now greater than the uranium flow rate the engine.

2. This then causes the fuel volume inside the en- to shrink Qwn toward mme new smaller size.

s would tend to decrease the total mass of ufanium inside the engine below the constant, required critical mass.

4. Therefore, the fuel density would have to'be in- creased in proportion to the decreasing fuel volume in order to maintain a constant, critical mass in the engine.

5. This would be accomplished by increasing the engine pressure.

6. Thus, at the final, new steady-state operating condition, the fuel volume is smaller, the reactor pres- sure is higher, the engine contains the same mass of uranium in it, and the uranium flow rate into and out of the engine is lower.

7 . The final, higher reactor pressure results in a heavier pressure shell and a heavier turbopump.

Figure 7 illustrates two points. First, i f the ura- nium loss rate is decreased by a factor of 8, the engine weight increases by a factor of 2 or less, depending on critical mass. Second, the amount of uranium required in the engine more strongly influences the engine weight than does the uranium flow rate through the engine. These results indicate that the amount of uranium to be lost on a given space mission could be varied by a factor of 2 to 4 witbout significantly changing the engine weight. The results also indicate that it is more important to know the critical mass pretty accurately, and to h w what factors influence its value, than it is to set a goal or a "desired" value for the ratio of hydrogen-to- uranium flow rate.

N. Conclusions

An analysis was carried out to estimate the engine weight and uranium loss rate of an open-cycle gas-core nuclear rocket engine. Results were obtained for engine therts ranging from 100,000 to 1,000,000 lbs and specific impulses ranging from 1000 to 1800 sec. All calculations are based on a reactor cavity diameter of 12 ft, surrounded by 120,000 lbs of moderator-reflector. Critical mass is treated as a parameter in the calcula- tions. Values of 25, 50, which is the current eetimate for this configuration, and 100 kg are used.

The results of this study indicate the following con- clusions for the thrust and specific impulse ranges given ahove .

1. An open-cycle, gas-core nuclear rocket engine will weigh between 250,000 and 500,000 lbs fiar a thrup rangeof 100,000 to ~,OOO,OOO lbs.

2. The moderator and the pressure shell account for WE& of the engine weight.

3. Engine weight is insensitive to the uranium bss rate. Therefore, the uranium loss rate for a given mission would be determined on some other basis.

4. Engine weight is more strongly influenced by the critical mass requirement than by specific impulse, thrust level, or the hydrogen-to-uranium flow rate ratio.

5. A reference engine with a thrust of 400,000 Ibs, a specific impulsc of 1800 sec, 3 hydrogen-to-uranium flow rate ratio of 100, and a critical mass of 50 kg is estimated to weigh 281,000 lba

5

f

V. Rclcrences

1. Wand, R. E . , "Evaluation of Critical Mass for Open-Cycle, G a s C o r e Rocket iicactor, to be Presented at the American Nuclear Society lGth Annual Meeting, June 1970.

adale, R. G. "Relatlonshlp between Engine Parameters and the Fuel Mas8 Contained in an Q p n - C y c l e G a s C o r e Reactor, ' 8 presented a t the NASA and University of Florida Symposium on Research o n Uranium Plasmas and Thei r Tech- nological Applicatfons, Gaineavillc, Fla., Jan. 7-9, 1970.

3. KaeCak, A. F., l"Rte Radiant Heat F l u Limit of By-Pass Flow in a Uranium PLaama Rocket,

and University of Florida Symposium on Reaearch on Urmlum Plaamae and Their Techaological Applications, Calaeeville,

pre-

Fh.; J s ~ . 7-9, 1970.

4. ICsmmer, P. A. and Martin, D. C . , "Welding Hlgh- Stre@ Steels, I * DMIC Rep. 229, July 1966. Battelle Memorial Inst., Columbus. O b .

5. MeLafferty, 6. H., "Arulytlcal Study of the Per- brraance Charac ter i s t ics of Vortex-S&abUJted G8mons N u c l e v Rocket Engbee, Is D-910093-20, BePC. 1965, United Aircraf t Carp. East Hartbrd, conn.

TABLE 1 EHEDULE OF C A U W L A T D N I

wH2'ukf, bydmgar- --- 25 w ~to-urmium I b w

200 rate r.tb looo

"22,000 MW reference engine

7 . McLafferty, G. H. and Bauer , H. E., fY3udies of Specific Nuclear Light Bulb and O p e n C y c l e Vortex-Stabilized Gaseous Nuclear Rocket Engine, ' 1 CR-1030, 1968, NASA, Washingbn, D.C.

8 . Bussard, R . W. and DeLauer, R . D . , Fundamentals of Suclcar Flight, McGraw-Hill, New York, 1965, p. 74.

9. Jennings. C . N . , l l P I D c e d ~ r e for the Design and Optimization of Liquid Rocket Propulsion Systems. Vol. IIA," SX-837FR-1, Vol. Ua, NASA CR- 78672, Apr. 1966, space General Corp. El ca l i f .

10. Bussard, R. W. andDeLnuer , R. D., Nuclear Rocket Pmpllebn, McGraw-Hill, New York, 1958, p. 60.

11. Warman, E. A . . Rogere, D. R . . andcour tney , Y. C . , 'Vperat lng Radfatbn Environment of Nuclear Rocket Systems, '* American Nuclear Society TransPctbns. Vol. 12, No. 2, Nov. 1969, pp 416-417. -

TABLE 2 REFERENCE ENGINE WEIGHT BREAKDOWN

F = 400,000 Ib

Crlt lcal m a s s = 50 kg

Xsp 1800 WC

CompDnat weteta, Ib

bbdcrabr . . . . . . . . . . . . . . . . 120.000 Resure shrll . . . . . . . . . . . . . 140,000 Turbopump . . . . . . . . . . . . . . . 19.000 Noorrlr. . . . . . . . . . . . . . . . . . , 2 0 0 0 -

Engine. . . . . . . . . . . . . . . . . 281,000

150 000- $3ERYLLIUM OXIDE MODERATOR m

j, 3 +-

2

g 100000-

9 - 2 2 W

I Ln

2 50000- 3 Ln

Ln w oc P

Figure I. - Conceptual gas-core nuclear rocket engine.

I I I

F, 5 0 N r THRUST. c 40 000

m 2

100 ooo I I I I

"4 '//

0 I I I I

200 400 600 800 loo0 ENGINE PRESSURE, P, ATM

Figure 3. - Hydrogen turbo mp weight for Isp = 1800 sec- onds; Wp=(3w / 1 P!!

H2 pH2

Figure 2. - Pressure shell weight; t = PRs/20; V = 47rR$tS; w, = psVs = 140 P; alp, = 0.69~106~inch; R, = 8.5 feet.

REACTOR PRESSURE, P, ATM

Figure 4. - Nozzle weight; Wn = 0.25d114.7 P; E = 300.

CHAMBER PRESSURE

- <IOOOATM - -- - >I000 ATM CRITICAL 0 REFERENCE ENGINE MASS,

kg

I

- ---- 50 25

I

Figure 5. - Effect of specific impulse o n engine weight. F = 400 OOO pounds; (!k~p$ = 100.

1oooo00

m

e- I W

2

500ooo E W z W

2

0

CHAMBER - PRESSURE,

ATM CRITICAL P <lo00 MASS, -e-- >1OOO kg

-

0 REFERENCE ENGINE

/ 0'

/ 0

00'

, / / /

I I I 500 000 1OOOOOO

THRUST, F, LB

Figure 6. -Effect of t h r u s t level o n engine weight; t W H p f ) = 100; Isp = 1800 seconds.

CHAMBER PRESSURE,

ATM

<lo00 > loo0

CRITICAL MASS,

kg ----

0 REFERENCE ENGINE

0 100 m H2-to-u FLOW RATE RATIO, W IW

H2 Figure 7. -Effect of u r a n i u m loss rate o n engine weight;

F = 400 OOO pounds; ISp = 1800 seconds.

NASA-Lew is-Com'I