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Aviation History
1951
1951 - 2340.PDF
PLIGHT, 23 November 1951 657 NUCLEAR-ENERGY PROPULSION . . . and an expansion pressure ratio of approximately 20:1). Inserting the above values in equation (7):— Qn_ 186,000x5,280x^2 xo-3 x 0-000731 _ _- ——^——————^^-^^_ — Qc 7>2OO This result shows that, for two motors, one atomic and one chemical and both developing the same thrust, the atomic motor would give off almost 3,000 times the waste energy given off by the chemical motor. The use of nuclear fuels other than uranium would not alter the order of magni- tude. As the waste energy per unit thrust of existing chemical motors such as the above is already about the maximum which can be accepted, it would therefore appear impossible to construct atomic rocket-motors using pure nuclear fuel. This result is due to the extremely energetic nature of atomic fuels. At the beginning of this analysis, it was assumed for mathematical purposes that pure nuclear fuel could be used in a motor. However, even were this prac- ticable, the energy of the fuel could still only be trans- latable into kinetic energy by the normal rocket-motor procedure of expansion in a nozzle down from a high initial temperature T\. If the very high jet velocities predictable by equation (2a) were to be attainable in practice, therefore, it would inevitably be necessary to have fantastically high values of Ti, thus leading to the impossible cooling conditions predicted by equation (7). From a consideration of equations (4), (5) and (6), noting that('?n"?/\F~j corresP°nds to (Xj(^J, it will be ap- preciated that the factor Q is proportional primarily to the square root of the heat potential of the propellant used, be it either chemical or nuclear. Therefore, as the previous results show, this heat potential must be reduced to a reas- onably low figure if atomic motors are to be at all feasible in practice. This brings us naturally to a consideration of method 2, in which the pure nuclear fuel is "diluted" very considerably by the introduction of an inert working fluid or reaction mass. Method 2: Use of Nuclear Fuel with an Intermediate Working Fluid.—An atomic motor working on this principle can be pictured as a conventional chemical motor with a solid-type reactor installed in the combustion chamber. The inert propellant is pumped into the reactor, heated and then expanded in the nozzle in the normal fashion. The turbo- nuclear engines of the NEPA Project will presumably embody this form of construction. In such a motor, energy is trans- ferred to the gas complex from an external source, as opposed to an internal source with chemical motors and pure nuclear motors. The solid reactor must therefore of necessity be at a higher temperature than the gas complex if positive heat- transfer is to occur. This necessity constitutes a major con- structional obstacle. I Proceeding analytically as for method 1, except that a mass trip of inert propellant is now associated with the mass m, of nuclear fuel:— VnVomc2=impV2in (8) (neglecting the mass deficit and nit, as the ratio me/mp is later shown to be very small at the chamber temperatures permissible) •'• Vjn=c\/2r)nrj0 Vm,/wp (8a) (compare with equation 2a) , FJn and Vm,/mp=—7==- (8b) cy 2r)nr]0 The jet velocity Fjn attainable will be limited by the per- missible chamber temperature T\ and the expansion ratio P1IP2, and may be calculated, for conditions of optimum expansion ratio, from the equation:— H^.TJi-ftY^lY (9) To compare with the chemical motor as before, for a given working fluid, it will be necessary to take corresponding values of >?,, r)0, T\ and P\jPi and calculate Vm from equation (9). Knowing Vjn, -y/mdntp may then be calculated from equation (8b). To determine the Q ratio, we have as before:— And nuclear fuel used per unit mass of propellant=— trip •'• £>»=(i-vi)^"j7~;^;y heat""^ (") Substituting in (11) from (8a) — -J r\ 0 j (compare with equation 4a). Then from (5a) and (na):— ' Qn CV2Mo [me fT,\ (compare with equation 7). Table I gives the result of calculations based on the above for two working fluids, hydrogen and water (as superheated steam). It has been assumed in these calculations that 7\ =3,500 deg K, Pi =300 lb/sq in A and P2 = i5 lb/sq in A, and that dissociation effects cancel out losses and imperfect flow effects in the nozzle. TABLE I Working Fluid H2 H2O ft/sec 25.180 8,660 V m*> 1-224x10'3 0-421 x10~3 Qn Oc 3495 1-201 Table I shows that power-dissipation problems for Method 2 rockets would be very much less than for those of Method 1. This, of course, is because of the greatly reduced heat potential of the inert propellants. The table also shows, however, that the magnitude of the power- dissipation problem would depend on the particular working fluid used. For example, the problem is worse when using a lighter working fluid (hydrogen) than when using a heavier one (water). This result is due to the higher specific heat of the hydrogen allowing it to absorb more heat for a given chamber temperature 7i than the water. This effect corresponds to the hydrogen having a higher heat-potential than the water, hence the cooling problem is worse. It would therefore appear that atomic motors using an intermediate working fluid would be feasible on grounds of cooling problems, and that the use of a heavier working fluid would definitely be preferable in such motors. How this latter requirement would affect the overall performance of the rocket will now be considered. The fundamental equation governing rocket perform- ance is:— Vf^VilofrR (13) (neglecting gravitational and air-resistance effects). The effective mass ratio R of a single-step rocket may be written in the form:— ntf f Substituting in (i3)~from (14):— Vt=ViVogt i+xP) (13a) Equation (13a) enables the effect of the density of the working fluid on the rocket performance to be calculated, the parameter Vf being, of course, the one on which interest is primarily focused for practical purposes. The results of some such calculations are given in Table II for various types of rocket-drive. Table II shows that, judged on a basis of attainable velocity V[y an atomic motor employing water as a working fluid has a performance superior to that of all others con- sidered. The ethyl-alcohol motor comes second, being better than either of the hydrogen motors, each of which has roughly the same performance. It is shown that it is difficult to obtain high mass-ratios when using propellants of low density, and this disadvantage may more than cancel, in regard to attainable velocities, the
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