**1. Introduction**

The dream of one day expanding humanity's presence into the solar system will require advanced propulsion systems that provide high levels of thrust and efficient use of fuels. Thrust will be needed to leave Earth's gravitation field and to establish stable orbits when approaching other planets and returning home. Many of the missions that will one day be of interest to human explorers will require travel to locations that are far away from the sun, so dependence on solar power will not be an option, and prepositioning enough chemical propellant to allow freedom of movement and the ability to return to Earth will be too expensive.

A wide range of studies, including the National Aeronautics and Space Administration's (NASA) recent Design Reference Architecture (DRA) 5.0 Study [1], have shown that nuclear power can enable exploration of the solar system. Nuclear thermal propulsion (NTP) and nuclear electric propulsion (NEP) are technologies that can provide the necessary thrust and power densities to enter and leave gravity wells of planets, moons, and large asteroids, and they do not need external sources of power to generate propulsion. Heat produced through fission is all that is needed to add energy to a propellant and produce thrust.

Space nuclear reactors rely on nuclear fuels that include a range of fissionable compounds. Uranium oxide (UO2), uranium nitride (UN), uranium carbide (UC and UC2), and uranium oxycarbide (UCO) are ceramic materials that have been studied by various space reactor technology development activities. Each of these materials has advantages and disadvantages related to use in space reactors, but they are all capable of achieving the extremely high temperatures that will be needed to move humans and equipment from Earth to other parts of the solar system.

### **1.1 Fundamentals of rocket propulsion**

The function of a rocket engine is to provide a force *F* ! over a time *t* to a body of mass *m* in order to change velocity *v* ! of the body by an amount Δ*v* �!. The rocket expends a mass Δ*m* of fuel in order to complete a velocity change maneuver. The force on the engine is produced by heating a propellant and expelling it through an expansion nozzle at a velocity *ve* with respect to the engine. The force produced is given by *<sup>F</sup>* <sup>¼</sup> *dm dt ve*, where *dm dt* is the propellant mass flow rate.

The efficiency of an engine is determined by the force produced by a unit of mass flow rate, which is frequently defined in terms of "specific impulse." Specific impulse is given by *Isp* <sup>¼</sup> *ve <sup>g</sup>* , where *g* is the acceleration of gravity (note that *Isp* has units given by *velocity* ÷ *acceleration* ¼ *seconds*). During a maneuver, the initial mass of the engine *mo* changes to a final value of *m* in order to produce a change in velocity Δ*v* �!, so that the mass ratio *<sup>m</sup> mo* is a measure of maneuver efficiency. In free space, with no other forces acting on the engine, conservation of momentum leads to the "rocket equation" given by:

$$\frac{m}{m\_0} = e^{-\frac{\Delta v}{\nu\_e}} = e^{-\frac{\Delta v}{\mathcal{E}^{lp}}} \tag{1}$$

This equation illustrates how *Isp* is tied to engine efficiency.

Another important aspect of rocket engine operations is that propellant exhaust velocity *ve* is given by:

$$\left|\upsilon\_{\varepsilon}\right|^{2} = \frac{k\frac{R}{M}T\_{\varepsilon}\left[\mathbf{1} - \left(\frac{p\_{\varepsilon}}{p\_{\varepsilon}}\right)^{\left(\frac{k-1}{k}\right)}\right]}{(k-1)}\tag{2}$$

where *k* is a constant given by the ratio of propellant liquid and vapor phase specific heats, *R* is the universal gas constant, *M* is the propellant molecular weight, *Tc* is the combustion chamber temperature, *pe* is the nozzle exit pressure; and *pc* is the combustion chamber pressure.

As a result, *ve* <sup>2</sup> ∝ *Tc <sup>M</sup>*, and therefore *Isp* ∝ ffiffiffiffi *Tc M* q , so that engine efficiency increases in systems that produce high temperatures and use low molecular weight propellants. In chemical rockets, the highest available *Isp* is produced by burning H2 and O2 to produce H2O with a molecular weight of approximately 18 g/mol. Nuclear rockets, on the other hand, use H2 as a propellant, so they produce specific impulses that are approximately ffiffiffi 18 2 q ¼ 3 times higher than the impulses produced by chemical rockets, for a given chamber temperature. **Figure 1** shows a comparison of theoretical specific impulses and mass ratios (i.e., ratio of take-off mass to final mass for Earth escape) for various propulsion systems [2].

### *Nuclear Thermal Propulsion Reactor Materials DOI: http://dx.doi.org/10.5772/intechopen.91016*

Nuclear thermal propulsion systems can use a range of fluids for thrust and reactor cooling. Examples include hydrogen, ammonia, methane, octane, carbon dioxide, water, and nitrogen [3]. Specific impulse is lower for higher molecular weight fluids, but the heavier fluids require less storage capacity, and they could be mined, or synthesized, on interplanetary trips.

Nuclear engine design requires iterative consideration of reactor neutronic thermal hydraulic and structural characteristics combined with engine system-level performance analysis [4]. Effective design and analysis sequences involve establishing a preliminary core design that meets the fundamental neutronic performance requirements of start-up criticality and reactor control. Fuel element designs using fixed fuel compositions and uranium enrichments are developed early in the design process, and then the preliminary design is used to determine neutron and gamma energy deposition characteristics that feed an integrated thermal hydraulic/structural analysis of the core's internal components. Once acceptable neutronic and thermal/structural performance is achieved, overall engine performance is evaluated to determine how well the design satisfies mission requirements. The analysis sequence is then revised as necessary to optimize engine performance characteristics to support specific mission profiles.

Engine performance can be improved by various methods of controlling propellant flow through the reactor core and varying fuel compositions. For example, enrichment zoning within the fuel elements, with lower enrichments in high-power regions of the core, can be effective at flattening reactor power profiles and producing more uniform propellant exit temperatures. The cost of these design complications is often slightly reduced core reactivity that can have an impact on engine performance (i.e., specific impulse), but compensation for the reactivity loss is

#### **Figure 1.**

*Comparison of rocket propulsion system characteristics.*

often possible through careful consideration of performance enhancements outside of the reactor fuel (e.g., propellant orificing, reductions in reactor mass, and the use of materials with low neutron absorption characteristics).

A wide variety of fast spectrum and thermal spectrum reactor designs have been developed for use in space propulsion systems. Fast spectrum reactors rely on highenergy (i.e., "fast") neutrons having average energies greater than 0.5 MeV to produce heat using materials that can fission after fast neutron absorption, while thermal spectrum reactors require the use of moderator materials to slow neutrons down to lower energies that are more readily absorbed. Fast reactors require fuel that is relatively rich in fissile material, while thermal reactors can operate with low-enriched uranium fuels.

Both fast and thermal spectrum reactors are typically designed with reflectors made from materials such as beryllium that prevent neutron leakage from the reactor core without producing a significant amount of neutron absorption. In space reactors, axial reflectors are often placed above and below the reactor core and radial reflectors are often placed around the core to reflect neutrons that would otherwise escape from the core back into the reactor's fuel. Control drums that are rotated to add enough reactivity to start up the reactor and make minor adjustments to its power profile are typically placed inside the radial reflector. A material with a high neutron absorption cross section (e.g., boron carbide, B4C) is placed on one side of the control drums to remove neutrons while the reactor is shut down. The drums are rotated to move the neutron absorption material farther away from the core in order to start up the reactor.

Fuel depletion and fission product buildup during reactor operation are typically areas of concern for reactor design, but space reactor operating times are typically very short, so fuel burnup and fission product buildup are usually of little importance to NTP reactor designs.
