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UCRL-ID-125531

Effect of Parameter Variations onPulse Rocket Performance, withHydrogen PropellantJ. W. adley

JAN 3 t 1997o s r l

September 13,1963

3 is an informal report intended primarily for internal or l i i t e d externalribution. The opinion s and conclusio ns stated are those o f the author and maynay not be those of the Laboratory.rk perormed under the auspices of the US. epartment of Energy by thelrence Livermore National Laboratory under ContractW-7405-ENG-48.

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DISCLAIMERThis report was prepared as an account of work sponsored by an agency of the UnitedStates Government. Neither the United States Government nor any agency thereof, norany of their employees, make anywarranty, exprrssor implied,or assumes any legal liabili-ty or responsibility for the accuracy,completeness,or usefulness of any information, appa-ratus,product, or process disclosed, or represents that its use would not infringe privatelyowned rights. Reference herein toany specific commercial product, process, or service bytrade name, trademark, manufacturer, or otherwise does not necessarily constitute orimply its endorsement,recommendation, or favoring by the United States Governmentorany agency thereof. The views and opinions of authors expressed herein do not necessar-ily state or reflect thoseof the United States Governmentor any agency thereof.

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DISCLAIMERPortions of this document may be illegiblein electronic image products. Images areproduced from the best avaiiable originaldocument.

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. . . . . . . ._. .__.. . . . . . . . . . .

... CQPP63-34 . . . . . . . .. . . -- ............. ~ . - . ~.-_ADVANCED DEvELopp4ENT NOTE NO. 39 - September 13 , 1963To: Distr ibut ion . . I

.. ., ~.

The pulse rocket performance equations- given in ADN No. 37 &bebeen used t o construct 8 computer program from which a va.riety of numerica3.results have been obtained.figure form.

These are presented here in t abula r andmdrogen was used as a propellant.

One modification has been made, t o include the e f fec t of aquantity of material ejected from the rocket a t essentia l ly zero relativeve lo cit y ( fo r instance, chamber or nozzle coolant f l u i d used between pulsesor leakage of propellant Awn he nozzle before firing of the nucleardevice).total propellant plus nuclear device mass. The rocket equation becomes

z = 0.98 I

x P

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7

M s = W Y

Mf +*o = W ' y x p

. D = % M o + d 2 p J

(7)

. .,.... ...t J5 ,

The basic system considered was described by the &e parruaetersas the system calcuhted in the final section 'of ADN No. 37.values chosen a re listed below:

The numerical

. .- .

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Speci f ic impulse recoverycoeff ic ient (Mct ion ofi d e a l I for i n i t i a l chamberMss of nuclear devicePressure vessel mass t onuclear yield ratio

SP- condlt ons)

Propellant tahb ge f ract ionWaste mass fract ionPropellast mixtureen ta lw/ene rgy ra t ioCost of placing Mo i n o r bi tCost of each nuclear deviceSpecific enthalpy of propellantSpecific enthalpy of nuc1ea.rdevice residueEff ective atomic we i g h t ofnuclear device residue

Cr - 0.70E - 0.025 tons (50 lb)w - 21.3 tons/ton eq.B - 0.05d - 0.0

M .. 12

here.t o g e a e r w i ~series of diffe ren t d u e s 0% 1bottom, it will be seen that as Idecreases, the energy yi el d per charge decreases, th e total number ofcharges increases, and the weight i n orb i t and total cost go throughminim(this table repeats and extends one given i n ADN No. 37).

Wble 1 i s t s calculated results based on the values given aboveReqding f r o m top todecreases, the fract ion of hyeogenSP,SP

A number of siniilar cases-were c&uted, i n each of which oneormore of the basic parameters xias varied,resul ts of each calculation, showing f i r s t the whole s e t of systemch ar ac te ri st ic s copresponding t o the minimum cost for each set; and thenN, Mo, and I) f o r minimum total mass.

Table 2 l i s t s the essent ia l

Figure 1is taken from the tabulated data of fcable 1, and showshow the total mass in orbit varies w i t h the number of charges fired. AB

* the figure eugegsta,-~there s a mlmimm valw of Ei for 64Loh set of

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parameters, and i t i s approached as the propellant mixture approaches purehydrogen.t h i s condition.must be introduced i n disc re te packages, each bearing a mass E of non-hydrogeneous materia l.hydrogen, the amount of hydrogen per charge must become very large.the necessary energy yield per charge t o reach the desired temperaturemust also became very large, in di re ct proportion, and so must th e massof th e pressure vessel, The l a t t er becomes ess en ti al ly the en ti re s y s t e m .weight after burnout, and becawe of the fixed mass ra t to (pure hydrogena t fixed T, p), the i n i t i a l mass Mo and the total propellant mass tncreasei n proportion t o th e vessel mass, the yield, and th e mass of p r o p l l a n tper charge.per charge, IT nust be constant in t h i s limit.

The t o t a l system mass unfortunately approaches in fi ni ty forThe physical reasons can eas i ly be seen: The energy

In order for the m i x t u r e t o approach pureThen

The t o ta l propellant mass being proportional to the mss

An analytic approach w i l l help t o indicate the effects of thevarious system parameters on the number of charges:

From equations 5 and 6,

and from 8, 9, and 10,

-..

Combining these with equation 7 leads to

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M = p0

which upon rearrangement of tenus can be written

_BoT c= -"Mf + u.37 2% (p-1)Mo g1 cr2 ( l +d )l+& Y

which indica tes the general form of the relationship between Mo and Nwithout involving the qpantity 1-x, which renders equation 12 uselesswhen the propellant m i x t u r e approaches pure hydrogen.the q u a n t i t i e s z p y and 2 approach fi n i t e limits, and equation 13 takesthe form

In this case,

showing that N does approach a fixed l i m i t as Mo becomes very large. Letus epa lwte ' this l imit: . . ...I

Mo-+ 0 IX j . 1

and from equation 3 we have

Then from t h i s and equation 4,

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Combining 13 with 14 and 13 gives

As a numerical -le, this is equal to 2500 for the basic system ofm b l e 1.

By examinirsg equations 16 and 17 one can see which prametersmlght offer means of reducing the value of N:

The pressure sh ell mass/yield, a, i s cleesly of the firsttmpmtance&s.-ww3 Avzm *the pbcpsiical.,~scusmade eazlier). 5 s s confirmed by the results of problem13, Table 2.A n increase in chamber temperature w i l l increase h anddecrease p.exponential, so that higher temperatures permit somewhatlower values of N, See problems 1, 4, 5 , and 6.

PThe latter effect predominates, being

. - .Tfie value of ~-rincreases asd.increases, the net effectbeing to bring an increase i n N, as seen in problem 10,The tankage fract ion f3, being already small, has a weakeffect on N. See problem 14,Increases in the velocity recovery factor Cr act strongly,through p, t o decrease N. See problem 8.

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I n the region of minimum Mo, a l l of the derived system parameterstend t o change simultaneously i n a complicated way with the a l te ra t ion ofnearlyany one independent variable, so t h a t no useful simplication suchas equation 17 i s available t o study influences on M .i n Table 2 w i l l serve this purpose however, together with Figures 2through 15, i n which Mo -s N i s plotted f o r the mrious problems run, withthe curve for the base problem No. 1 hown dashed on each. Cautfon shouldbe used i n making inferences fram small differences among the l i s t edvalues of Table 2, since these may result only from the selection of valuesa t fixed I intervals.SP

Some in te res t ing features are seen i n the results represented

The resul ts l i s t e d0

by the figures:a) Reduction of the chamber pressure, as by using Large chamber

mdius, appears t o give improved performance. This resultsfrom increased hydrogen dissociation, which permits a given

d u e o be achieved, a t a given temperature, with a m I e ~ & ~ *;eixectIs*

will be at least part ly cancelled by an effect not takenin to account i n these calculations, namely the effect ofthis increased dissociation i n rais ing the effec tive valueof w and the pressure vessel mass.Increasing the temperature up t o about 7000' gives a marked .improvement i n performance.values produces improvement a t a much slower r a t e (in thepressure range considered he&) sin ce di sso ciat ion is nearlycomplete a t that point.carrying higher payloads requires roughly proportionalincreases in Mnumber of ctaanges I?.higher energy yields can be used, so that each nuclear

b)Going t o higher temperature

c )bu t only a very slow increase i n the0' This has t o do with the fac t that

efgiclently applid.

s .

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f)

Improved exit velocity recovery CN and Mo.The effective atomic weight (hence s pe ci fi c enthalpy) of thedevice residue i s of l i t t l e importance, since it tends t omake up a relatively small fraction of the propellant mixture.

a c t s strongly to reduce bothr

Ten percent .waste propellant (d) auses more than a t e npercent increase i n mfssion cost.Although increases i n the nuclear device mass E tend t o increaseoveral l system mass fairly rapidly when the propellant hydrogenf rac t ion is low, they have relative* slight effec t i n theregion of m i n i m cost. Note that a W $ increase i n E producedonly a ?$ increase i n t o t a l cos t D.The vessel mass/yield r a t i o w affects N very strongly, but hasl i t t l e e f fe ct on MooN and Mo are rel ativ ely insen sitive t o changes i n th e hydrogen

JWR: d

1. E. Goldberg3.. H. Reynolds4 H. Reynolds/File54 H. Reyndlds/File6. S, Ke-7. J. Foster8. J. Radcliffe9. T. Merkle10. W. B. Myers

20 J* Hadley

l l o A. Rot-

12. G. St. Leger-Earter13 . T. Stubbs14. R. Duff15. T. Wainwright .16. C. L&th . .17, R. levee18. J. Kane19. W. Wells20. M. Mintz21. G. Pierce23. To B. !Taylor - General Atomics22. W. B o C m ~ l e y

Series A -23/ASeries -G,2s+ Series - 6/6C4% Series 2 - 6/6D

Series E - 8/83-

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Table 1Performance with standard parameters f ixed as listed in text,

and varying specific impulse.

x

0.970.880.79

-0.700.610.520.430.34

Notation:

c1-3 .8k 75. 56.58.010.3

14.4

4.2

Y27.1-. 6.3

3 .11.81.20.80.50 .3

N Mc-6991121163226324490800

MP2000646445374348346364405

SM-578135673925173 . l7

D-12625695285%)72395513582 n 9

IJ, - Initiaf/fiaal mass r a t i oY - Energy yield per charge, tons TIJT equivalentN - Number of chargesM - Total mass of nuclear devices, tonsM - Total hydrogen propellant mass, tonsCPM - ~ S Sf pressure Shell, t a sSM - Total initial system mass, tonsD -. Cos t , millions ofdollars0 -

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M i n i m u m DrObNO

567891033,12131 416

Table2Effects of k e t e r Variations

Baee case 1200 0.79 4.7' 3.1 4800 1 2 1 445 67 717 528l?ressure 100 1x0 0.76 4.2 3.3 4620 115 367 70 63 4 484Pressure 1000 11% . 0.85 5.1 4.2 4370 109 640 90 933 592Temp. 5ooo 1000 0.83 6.5 2.8 5730 143 722 60 lQ.a4!! 696'pemp. 8OOo 14% 0.72 3.6 3.5 4420 in 287 75 549 441Hxed mass 100 1300 0.88 4.2 6.3 4330 io8 768 135 11% 677cr 0.8 1400 0.81 3.8 3 .7 3340 83 364 80 608 410lo$ waste-mass 1200 0.79 5.7 3.1 5430 136 90 67 853 613T0,OOO ft/sec Av 1200 0.78 3.6 3.1 3270 82 301 67 527 374

Temp. 7000 1350 0.74 4.0 3.3 4580 114 331 70 594 467

W e e at. wt . 5 1200 0.75 4.7 2.6 5240 131 383 56 651 522

M c e mass 6 75 lb. 1200 0.79 4.7 4.7 4b50 152 560 100 90 2 !%4vessel mass/yield 13 1200 . 0.79 4.7 3.1 4100 102 377 47 607 448Tankage fraction i$ 1.200 0.79 4.7. 3.1 $190 130 478 67 770 568T8000, p 1000 atm 1400 0.75 3.8 3.7 43% 109 330 78 596 4%

See Table 1 for notation

Minimum MoM DI N 0

_I_ - 76%0 658 5905840 583 5256390 770 6279550 960 8617120 546 574.6330 495 5158930 900 8075480 511 4787190 608 6027440 797 6906890 776 6555780 583 5227050 710 6366%0 526 538

5810 468 478

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_. _ __.,_. .-. I...

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,_-_ ____..-..

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- .- . . ... __ . . .

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04c

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,-;-