1

Nuclear Thermal Propulsion using a Particle-Bed Reactor

Benjamin Bauldree1 Graduate Student in Aerospace Engineering, Auburn University, AL

Using nuclear energy as a means of propulsion with regards to space flight has long been a topic of discussion. Nuclear fission produces large amounts of energy, far greater than that produced by typical chemical propellants such as liquid oxygen and RP-1. The idea of a nuclear thermal propulsion system consists of transferring thermal energy from the nuclear material to a propellant of some flavor via a nuclear reactor, vaporizing the propellant into a high-pressure gas which is then expanded through a nozzle. The particle-bed reactor (PBR) offers the highest performance compared with other solid-core reactors. The PBR consists of fuel elements, typically spherical, that are surrounded by layers of moderator blocks. The propellant flows directly over the fuel elements before passing into a channel and exiting through the nozzle. The direct heat transfer from the fuel particles to the propellant increases the temperature of the gas entering the nozzle and ultimately the performance of the system. The PBR has undergone preliminary system design work with promising results, but due to lack of funding, no physical specimen has ever been assembled and tested.

Nomenclature A = atomic mass number c = speed of light (m/s2) cp = specific heat of propellant (J/kg-K) c* = characteristic exhaust velocity (m/s) dx = distance traveled by neutron Hcore = height of the reactore core (cm) hv = enthalpy of vaporization (J/kg) i = interaction type (scattering, fission, absorption) mcore = mass of the core (kg) mp = mass of the proton (kg) me = mass of the electron (kg) mn = mass of the neutron (kg) matom = actual mass of the atom (kg) mprop = mass flow rate of propellant through the reactor (kg/s) n = concentration of atoms in material (atoms/cm3) P = probability of interaction i Pcore = reactor power generated (W)

Pw = specific reactor power (W-s/kg) R = universal gas constant (m2 kg s-2 K-1 mol-1) Rcore = radius of the reactor core (cm) T = propellant temperature (K) T0 = chamber temperature (K) T1 = propellant temperature entering the reactor (K) T2 = propellant temperature exiting the reactor (K) Vcore = volume of reactor core (cm3) Z = atomic number Δ = mass defect (kg) γ = specific heat ratio ρcore = density of the reactor core (kg/m3) Σ = macroscopic cross-section for isotope j of interaction i (cm-1) σ = microscopic cross-section for isotope j of interaction i (cm2), as a function of energy (E, in eV)

I. Introduction HE age of rocketry dawned in the early twentieth century with Wernher Von Braun and his V-2

rocket, the first successful, long range ballistic missile. [1] With his success came the next footsteps in human exploaration and the technology to reach beyond the realm of Earth and into the heavens for which all of 1 Graduate Student, Aerospace Engineering, Davis Hall, Office 313.

human history had long dreamed of. Larger and more grand rockets followed the V-2, such as the Mercury Redstones and then the Saturn family. Despite putting men on the moon with the awe-inspiring Saturn V and its many ground-breaking achievements, the technology to extend human reach beyond that of the

T

2

moon and possibly outside of this solar system has remained elusive, even to this day. Nuclear energy, however, has provided a possible solution to this problem. In a nuclear rocket, the energy released from the controlled fission of a “fuel” such as uranium can be used to thermally excite a propellant; whereas in chemical propulsion, the propellant releases energy through combustion typically with some thermal source. The efficiencies of these two systems provides the nuclear system the key advantage. A comparison of each system (Fig. 1) can be made using specific impulse, where the higher the specific impulse of the system, the more efficient it typically is. To increase the specific impulse, the propellant must exit with either a higher exit temperature or a lower propellant molecular mass. The nuclear thermal system allows the use of propellants with extremely low molecular masses; in fact, the system can use the propellant of lowest molecular mass: hydrogen. Extremely high exit velocities can be achieved without the limitation of combustion properties of the propellant. The only requirement is that the temperature of the fuel (the radioactive material) does not reach its melting point. [2]

The nuclear thermal propulsion system consists of many different concepts, most of them revolving around the design of the reactor and its fuel. The most famous nuclear system by most regards is the Nuclear Engine for Rocket Vehicle Applications (NERVA). The NERVA program consisted of the most extensive nuclear rocket development and demonstration in

history, achieving twenty-eight succesfull full-power tests and even meeting certification requirements for a human mission to Mars before the end of the program in 1972. The NERVA reactor, called NRX (Nuclear Reactor Experimental) consisted of graphite fuel elements impregnated with pyrolyic graphite uranium carbine particles. [3] The fuel particles provided the heat source while the graphite matrix provided the structural support and stability, which can be seen in Fig. 2. Rotary drums made of boron plates were used to control the fission process by rotating in toward the core or out toward the perimeter to absorb neutron production. This reactor design suffered limitations, though, one being the temperature of the fuel rods. Because of the thermal gradient between the coolant channels and the fuel rods, increases in the coolant (propellant in this case) temperature would raise the core temperature beyond the allowable constraints. Overall, the NERVA design demonstrated a thrust-to-weight ratio of ~5:1 and a specific impulse of 825 seconds. [2]

In 1987, nearly a decade after the NERVA program ended, the Space Nuclear Thermal Propulsion (SNTP) program started with the goals to achieve a specific impulse of 1000 seconds, with a thrust-to-weight ratio of 25:1 to 35:1 for engines producing thrust between 20,000-80,000 pounds. The design concept focused on the particle bed reactor (PBR), conceived by Dr. James Powell of Brookhaven National Laboratory in the late 1970s. [4] The PBR core consisted of a number of small fuel particle spheres suspended along the inner diameter of a cylindrical assembly of hexagonal moderator blocks, shown in Fig. 3. The spheres consisted of a uranium-carbine fuel coated with layers of graphite with an outer layer of zirconium hydride, while the moderator block had a combination of beryllium and lithium hydride.[4]

Figure 1. Performance Comparison of Various Propulsion Systems. Solid-core fission rockets have greater specific impulse than chemical rockets while maintaining similar thrust-to-weight ratios. [2]

Figure 2. NERVA Fuel Element. The NRX fuel elements made with graphite uranium carbine particles embedded in a graphite matrix for support. [2]

3

The hydrogen propellant flowed through an inlet channel in the moderator before penetrating the outer edge of the cylindrical fuel element (called the cold frit). The propellant directly cooled the particulate fuel spheres before passing through the hot frit (the inner diameter surface separating the particle bed from the inner hollow region of the structure) where the propellant, now a hot gas, would exit towards the nozzle. By directly cooling the fuel elements, this reactor design was capable of achieving much higher temperatures, over 3000 K, as opposed to the NERVA which was limited to 2650 K. [2] This design also decreased overall system weight drastically from the NERVA design by using the small fuel particles as opposed to fuel rods. This made the PBR much more ideal for launch vehicle upper stages. The overall performance improvements compared to chemical propulsion systems were dramatic, with payload mass capabilities increased nearly two-to-four times what current configuartions allowed. [4]

II. Nuclear Physics

A. Nuclear Fission The subdivision of an atomic nucleus, such as that

of uranium or plutonium, is defined as nuclear fission. The splitting of an atom can be induced by exciting the nucleus to an energy equal to or greater than its fission barrier or through excitation of the nucleus by the bombardment of particle(s), typically nucleons (protons or neutrons). [5]

Before beginning the fission process, consider the forces that hold an atom together. The neutrons and protons are held together by the strong nuclear force. The electrons maintain their orbit around the nucleus due to Coulomb forces, the electromagnetic force that causes like charges to repel and opposite charges to attract. [2]

Fission begins once a nucleon, typically a neutron, breaks through the electron cloud and imparts energy

(between 0.25 eV to 10 MeV) upon the nucleus. The additional neutron exerts enough energy on the nucleus to cause it to split into two charged fragments. These fragments separate to a distrance greater than the range of the nuclear force, leaving Coulomb forces to be the dominant force. This causes the fragments to experience a large Coulomb repulsive force pushing them further apart. The fragements will experience velocity increases as they repel off other atoms, while also exerting kinetic energy onto neighboring atoms causing additional nuclei to split, eventually creating a chain reaction effect of nuclei splitting. [2]

The division of the nucleus of an atom results in the release of large amounts of energy. This energy comes from the mass defect within the original nucleus. The mass defect is the difference between the actual mass of the nucleus and the sum of the masses of the nucleons that make up the nucleus. In fact, the sum of the masses of the nucleons is always greater than the total mass for the nucleus for heavy atoms. The mass defect can be calculated using the equation below:

The mass defect is then converted into energy using Einstein’s equation:

where c is the speed of light. The energy conversion yields the total binding energy of the nucleus. The release of the binding energy through fission causes the average temperature of the radioactive material, or fuel, to increase due to the collision and iteractions of neutrons with other atoms and fragments. This increase in temperature is the cornerstone for many of the worlds nuclear devices and applications including nuclear plants, military vessels, and, of course, the nuclear thermal propulsion system. [2]

B. Reactor Control After the fission process has started, control

mechanisms regulate the fission reactions to insure criticality of the system. When the number of neutrons being produced is constant (the rate of change of neutron production is equal to zero), the reactor is said to be in a critical state. If the criticality is not controlled, radioactive fallout (beta and gamma rays along with fission products) can increase to dangerous levels and cause the fuel elements to melt. There are two primary methods used for fission control: moderators and control rods (drums). [2]

For a thermal nuclear reactive, fission is caused by neutrons with energies at or below 1 MeV. The typical

Δ = [Z(mp +me )+ (A − Z )mn ]−matom

E = Δc2

Figure 3. Cross Sectional Views of the Fuel Particle (left) and Fuel Element (right). The fuel particles consisted of a uranium carbide core surrounded by graphite with a zirconium carbine exterior surface for protection against high heat. [2]

4

fission process, however, produces neutrons with energies much higher than 1 MeV (up to ~10 MeV). In fact, for a uranium-235 atom, most neutrons produced from fission fall within 1-5 MeV, as shown in Fig. 4. Moderators help to slow down the neutrons to correct operating levels. The moderator is made of a low atomic mass material (beryllium, lithium

hydride, graphite) and envelops the radioactive fuel creating a control blanket. [2]

Control rods assist in slowing down the fission reaction by acting as “poisons”. Where moderators assist in decreasing the kinetic energy of the neutrons after the fission reaction, control rods can stop the reaction altogether. The control rods are usually made from boron, which has a high nuclear cross section, and are dispersed symmetrically around the core to insure that neutron absorbtion is adequate for fission control. By controlling the fission process in such a manner, the control rods can increase or decrease the power level of the reactor simply by either being removed or rotated outoff or away from the reactor for an increase in power or by being inserted or rotated into or towards the reactor for a decrease in power. For the rotation method, a single control road would have one side made of boron with the otherside my of a reflective material such as beryllium. [2]

1. Nuclear Cross Sections The nuclear cross section can be used to describe

the probability of a neutron interacting with the nucleus of some material. Neutrons can interact with a nucleus in one of three ways:

1) Scattering: the neutron impacts the nucleus,

transferring some or all of its kinetic energy, before rebounding off in a different direction.

2) Absorption: the neutron can be absorbed into the nucleus

3) Fission: the neutron has a sufficient kinetic energy to split the nucleus

The nuclear cross section of a material can help determine the probability of which interaction will happen. The interaction concept depicted in Fig. 4.

The probability of the interaction of a neutron with a nucleus can be described mathematically in terms of the energy of the nucleus, in the following manner:

The relations above show that a probability of interaction exists for all neutrons, with dependence related to the target nucleus size and the energy of the fissioned neutrons. A difference is made between microscopic area and macroscopic area due to the inability to precisely define the area of an atom. The microscopic cross-section simply defines an “effective area” that the neucleus will have the greatest possibility of being located, whereas the macroscopic is a relation to the probability of a neutron encountering the nucleus of a material after traveling some defined distance through it. [2]

C. Thermal Hydraulics As the fission process begins heating up the fuel

particles, propellant flows through the moderator and over the particles. The goal here is to transfer as much heat from the fuel particles to the propellant as possible. This achieves two goals:

1) As the cryogenic liquid hydrogen flows over

the particles, it extracts the heat from the particles, maintaining a safe level within the reactor to avoid melting the exterior shell as well as the radioactive material.

Pi = njσ i

j (E)dx = (E)i

j∑ dx

Figure 4. Neutron Energy from Fissioned U-235. Most fissioned neutrons have energy leves between 1 and 5 MeV. Moderators assist in slowing down the neutrons for usability in a thermal reactor. [2]

Figure 5. Neutron Cross Section. The neutron cross section analogy is best represented by imagining a slab of volume dAdx with some neutron bombardment impacting its surface. [2]

5

2) The heat transfer from the fuel to the propellant causes vaporization. The gas then expands rapidly upon entering the gas flow chamber and then exits the nozzle at a high exit velocity.

It should be noted from the above points that in order to insure the nuclear fuel particles do not reach their melting point, a minimum heat transfer must be achieved. Therefore, one key limiting factor in a nuclear thermal propulsion device is what amount of thermal energy can be transferred from the fuel particles to the propellant, which is largely dependent on the material used in the fuel element shell and the moderator material, the surface area available for the propellant to make contact with, and the flow rate of the propellant through the moderator.

III. Particle-bed Reactor System Design Designing a nuclear thermal rocket is simpler than

designing a liquid rocket in many aspects. Because there is no combustion occurring within a nuclear rocket, one does not need to concern themselves with the many factors that must be considered in a liquid propulsion system. The nuclear thermal rocket simply heats the propellant from storage temperature to the maximum chamber temperature, which ultimately depends on the maximum temperature allowable by the fuel and materials.

The key preliminary steps to designing a functional nuclear thermal propulsion system are as follows:

1) Determine the gaseous properties in order

to choose the appropriate propellant. 2) Choose the expansion ratio that will

provide the level of Isp required for the mission.

3) Calculate the propellant flow rate given the Isp and required thrust level

4) Determine the required reactor power needed to heat the propellant to the necessary temperature to achieve the required characteristic velocity.

5) Determine system pressure levels, specifically pressure drops through the core.

6) Calculate the reactor and core size. While the above steps are not all-inclusive, they touch on the major functional points of a nuclear thermal propulsive device. The following will provide more detail on particular steps. [2]

A. Gaseous Properties

The characteristic velocity for the system depends soley upon the propellant molecular weight and chamber temperature. The common choices for propellants are listed below:

1) Hydorgen (H2) – 2.016 grams/mole 2) Methane (CH4) – 16.043 grams/mole 3) Carbon dioxide (CO2) – 44.01 grams/mole 4) Water (H2O) – 18.015 grams/mole

The specific heat ratio can be determined from the molecular weight and specific heat of the propellant. Figure 6 shows the specific heat distrubtion for a temperature range of 300-3500K. [2]

The characteristic velocity for the various propellants can be calculated using the specific heat ratio for each with the equation below.

Taking the specific heat values as calculated before gives a characteristic velocity trend as shown in Fig. 7. The data for the four common gases shows why using a low molecular weight propellant offers the best possibility for an increased Isp for a nuclear thermal rocket. By having a reactor at a high thermal temperature with a low molecular weight propellant, the system can produce very high exit velocities and ultimately increase the specific impulse greatly above what is achieveable by chemical propulsion rockets. [2]

c*=γ RT0

γ 2γ +1

⎛⎝⎜

⎞⎠⎟

γ +12 γ −1( )

Figure 6. Cp as a Function of Temperature for Various Gases. The specific heat values for the common nuclear thermal propulsion system propellants. Hydrogen has a much greater specific heat compared to the others.

6

B. Required Reactor Power A simplified version of the first law of

thermodynamics can provide the required reactor power in order to increase the temperature of a fluid (in a liquid state) to some temperature given a specified mass flow rate. The equation to calculate core power is given below:

In Space Propulsion Analysis and Design, the authors provide a useful chart showing the correlation between desired temperature of the propellant and specific reactor power. This chart is provided in Fig. 8. It should be noted that hydrogen requires the most specific power to increase its thermal energy; however, because of the high specific impulse it generates, the mass flow rate is lower than compared to the other propellants, required less reactor power overall. [2]

C. Reactor Sizing Using all the information discussed so far, a

simplified assessment of the reactor size can be calculated. Typical reactor sizing depends on the type of reactor under analysis, but generally requires a detailed examination of thermal hydraulics, control rod effects, Doppler feedback, and many other factors. A lumped-parameter approach is typically used for simplification purposes by assuming the reactor to be homogenous (no variation in power distribution and performance through the core). However, for the particle-bed reactor, this generalization does not hold true due to the disperision of fuel particles within the system.

Instead, for this discussion, a parametrix analysis of Fig. 9 below can be done to determine reactor sizing. Figure 9 was developed by Ronald W. Humble and coauthors for Space Propulsion Analysis and Design and is based off a Los Alamos National Laboratory (LANL) code derived empirically from a Los Alamos particle-bed reactor. Using the calculated reactor power from previous discussions, one can simply use the graph to determine the radius and height required for the core. The curve equations for replication of the graph are provided in the appendix.

Pcore = !mprop hv + cp dTT1

T2∫( ) = !mpropP

Figure 7. Characteristic Velocity as a function of temperature. Hydrogen, having the lowest molecular weight and highest specific heat, has the highest characteristic velocity.

Figure 8. Reactor Power Required for a Given Propellant Temperature. Given a required propellant temperature, the required specific reactor power can be determined from which the necessary reactor power for a given mass flow rate can be calculated. [2]

7

In the case where two solutions are possible for a given reactor power, the best solution is typically the core with the smallest radius, which minimizes the required radiation shield size. [2] Once the reactor size has been determined, the mass of the core can be calculated. To calculate the mass of the core, the overall core density is multiplied by the core volume. Although this method is not precise, the results are generally close, within 90%. The reason for the inaccuracy is based on the nature of the particle-bed reactor. The PBR has very complex geometries such as fuel particle size, distance between the fuel particles, and the makeup of the material. [2] For calculation purposes, the core is considered to be cylindrical; in relation to PBR fuel particles, this is applicable for if the particles were packed into a cylindrical container (which is basically the overall design of the reactor itself). The volume of the core can be calculated using the equation below:

The mass of the core can then be calculated using the core density, which for a PBR is typically ~1,600 kg/m3. [2]

This mass calculation provides the total mass for the entire reactor, including plumbing, moderators, control rods, and other components, except for the propellant tank. Figure 10 shows a comparision of reactore core mass of a particle-bed reactor compared to two other nuclear thermal propulsion systems: NERVA and CERMET. The PBR is approximately five to six times less in mass then the NERVA. This is because the NERVA uses a fuel rod configuration. The power density is much less than the PBR which

requires more hardware to increase the temperature of the propellant. Comparably, the PBR is two to four times less in mass than the CERMET, except for powers below 1000 MW, where mass differences are below ~100 kg. The figure also shows the differences in the number of fuel elements chosen for the PBR system. The three element configurations (7, 19, and 37) are restrictive to a certain range of power output by the reactor. The 37 fuel element configuration can operate in the greatest range of powers, from ~600-2000 MW. [2]

IV. Analysis of the SNTP Program The Space Nuclear Thermal Propulsion Program,

started in 1987, was a follow-up to the NERVA program which ended over a decade before. The SNTP’s goals were to:

1) Verify the feasibility of a particle-bed

reactor as a propulsion source for an upper stage launch vehicle

2) Perform ground demonstration tests of the PBR design

3) Launch a PBR nuclear thermal stage using an Atlas IIas launch vehicle

The program partially completed the second phase of the program (ground demonstration) before being terminated in January 1994. [4] During the program, many significant advancments in terms of nuclear thermal propulsion were accomplished, including:

1) Identified missions that were enabled or enhanced based on SNTP performance

Vcore = πRcore2 Hcore

mcore = ρcoreVcore

Figure 9. Reactor Core Sizing. The radius and height of a core can be determined based on the required reactor power for the system, as well as the number of fuel elements required for the system, based on criticality constraints. [2]

Figure 10. Reactor Mass Comparison. The particle-bed reactor outperforms all other nuclear thermal propulsion systems except at low power outputs, where the CERMET has the lower mass. [2]

8

2) An engine was designed with a specific impulse of 930 seconds and a thrust-to-weight ratio of 20:1

The original performance goal for the program was to have an egine that could achieve a specific impulse of 1000 s with a thrust-to-weight ratio ranging from 25:1 to 35:1 (88-355 kN); however, additional safety criteria and a desire for a system that could be restarted multiple times caused the decrease in performance to just 20:1, which still outperformed the NERVA by four times. [4]

A. Sizing the SNTP System The SNTP program developed a preliminary

engine design by selecting the following initial properties: thrust of 178 kN (Isp = 930 s) with a reactor power of 1000 MW that used liquid hydrogen as the propellant. All engine designs also made us of a thirty-seven fuel element configuration to take advantage of the larger operating power range. An engine of this design would have the following properties:

Comparison of these calculations to the actual engine are within a few percent difference. The final iteration of the “LV03” engine had a total core assembly mass of 475 kg. Figure 11 provides a schematic of the side profile of the engine. [4]

The overall mass of the system came in to 910 kg, including reactivity controls, nozzle assembly, and instrumentation. The final thrust-to-weight ratio was 21:1. [4]

B. Reactor System The reactor system for the SNTP engine had the

following requirements:

A trade study was performed between a bleed cycle system and a partial-flow expander cycle system. This greatly affected the materials that would be used for the construction of the propulsion system as a whole. The trade study results are provided below. [4]

1. Fuel Particles and Elements

One of the major efforts of the SNTP program was to develop a fuel particle that woulc withstand the high temperatures produced in a particle-bed reactor system. The particle would need to operate in the range of 3100-3500 K in order to produce an exhaust gas temperature of ~3000 K. The program ended up zeroing on a mixed-carbide nuclear fuel particle that could withstand temperatures up to 3200 K. However, before the end of the program, it was discovered the

Table 1. Preliminary Design Configuration for SNTP Engine

Properties Design Mass flow rate 19.5 kg/s Radius of Core 40 cm Height of Core 62 cm

Volume of Core 311,646 cm3 Mass of Core 499 kg

Figure 11. SNTP Engine “LV03”. [4]

Table 2. SNTP Reactor Requirements Power 1000 MW Outlet Temperature 3000 K Outlet Pressure 6.89 MPa Firing Time 600 sec

Table 3. Design Characteristics based on the Type of Cycle.

Bleed Cycle

Partial Flow Expander

Cycle Reactor Power (MW) 1000 1000

Engine Thrust (kN) 184 185

Isp (s) 930 935 Reactor:

Reflector Beryllium Beryllium Moderator Be/Li-7H Be/Li-7H

Turbine:

Material Carbon-Carbon Titanium

Inlet Press (MPa) 5.8 15.7

Inlet Temp (K) 2750 375

Nozzle:

Material Filament Wound C-C

Filament Wound C-C

Exit Area Ratio 100 100

9

Soviet Union, under the Nuclear Rocket Engine (NRE) program had developed a mixed-carbide fuel capable of 3500 K. The SNTP team was unable to reproduce this before the program was terminated. [4]

The fuel elements consisted of hot and cold frits that contained the nuclear particles and controlled the flow of liquid hydrogen over the fuel bed. The moderator “moderated” the production of neutorns to maintain structural integrity of the reactor and to avoid overheating. The cold frits were made out of stainless steel while the hot frits were made of a combination of graphite and nurobium-carbide. During test, fractures were found in the hot frit, which under a post-test analysis, were found to be due to large temperature gradients within the moderator causing by a movement of fuel particles. The cold frit also suffered deformations to the maximum extent. [4]

C. Mission Applications The SNTP program performed mission design

analysis for a nuclear propulsion system using the particle-bed reactor and showed that the PBR offered great improvements over current capabilities for second stage, chemically propelled systems. Payload improvements varied from 1.5 to 4 times greater than conventional systems. The program also showed greater financial savings by utilizing the PBR design. The higher payload capabilities meant smaller first stages could be used to deliver payloads to orbits that would conventionally require much larger systems. [4]

The program looked at a multitude of launch systems and developed variations of each based on sub-orbital ignition and orbital ignition. The vehilces of primary focus were based the Atlas IIE for suborbital insertion, Titan for orbital ignitions, and Minutemen for intercontinental ballistic applications. Figure 12 shows an overview off all different

configurations along with payload capabilities for each. [4]

V. Conclusion Nuclear thermal propulsion has great advantages

over conventional, chemically based propulsion systems. Nuclear thermal designs allow for greater efficiencies in terms of specific impulse, as well as simpler overall vehicle configuartions. The nuclear propulsion system also have the ability of sustaining large thrust-to-weight ratios, ranging from 5:1 – 35:1, making them viable as full-stage propulsion systems and not just for orbital transfers. The high efficiencies and thrust-to-weight ratios attest that the system can satisfy most mission requirements, while also decreasing mission lengths substantially, sometimes by half.

The past half-century has proven the viability of a nuclear thermal propulsion system, from the NERVA program in the 60s and 70s, to the SNTP program at the end of the 20th century. And of the nuclear propulsion systems, the PBR has exhibited performance characteristics do not have to be sacrificed in order to achieve significant efficiency increases. The SNTP program is a testament to this, showing that the PBR system can increase the capabilities of human-space flight reliably, with higher performance than any other system, while still maintaining strict safety guidelines and cost effective methods.

In order for human exploration to move beyond the moon and into deeper areas of our solar system, and even possibliy beyond, nuclear thermal propulsion technology must be considered a critical component of the next phase of launch vehicle development.

Figure 12. SNTP Upper Stage Applications. [4]

10

Appendix Curve fits for replication of the particle-bed reactor dimension (specifically, the radius and height) based on the

number of fuel elements to be used in the reactor. These equations are curve first for the Los Alamos design code, as presented in Fig. 9. For 7 Elements:

For 19 Elements:

For 37 Elements:

Rcore = 9.0958(10)−10Pcore

4 −1.3261(10)−6Pcore3 + 7.1665(10)−4Pcore

2 − 0.1735Pcore + 47.625

Hcore = −0.000283Pcore2 + 0.5203Pcore + 26.06

Rcore = −2.655(10)−12Pcore5 + 8.846(10)−9Pcore

4 −1.1703(10)−5Pcore3 + 7.427(10)−3Pcore

2 − 2.2955Pcore + 313.34

Hcore = −4.027(10)−5Pcore2 + 0.1427Pcore +17.9883

Rcore = 4.905(10)−11Pcore

4 − 2.881(10)−7Pcore3 + 6.2522(10)−4Pcore

2 − 0.5992Pcore + 252.28

Hcore = −6.502(10)−6Pcore2 + 0.05009Pcore +18.335

11

References [1] K. Grinter, "A Brief History of Rocketry," [Online]. Available: http://www-pao.ksc.nasa.gov/history/rocket-

history.htm. [Accessed 1 May 2016]. [2] R. W. Humble, G. N. Henry and W. J. Larson, Space Propulsion Analysis and Design, McGraw-Hill, 1995. [3] W. H. Robbins and H. B. Finger, "An Historical Perspective of the NERVA Nuclear Rocket Engine

Technology Program," NASA, Cleveland, 1991. [4] R. A. Haslett, "Space Nuclear Thermal Propulsion Program," Grumman Aerospace Corporation, Bethpage,

1995. [5] E. P. Steinberg, "Nuclear Fission," Encyclopædia Britannica, [Online]. Available:

http://www.britannica.com/science/nuclear-fission. [Accessed 2 May 2016].