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Design and Analysis of a Nuclear Thermal Propulsion Reactor for an 1

Altitude Compensating Nozzle 2 3

Abstract 4 5

The following research consists of the system design and analysis of a nuclear 6 thermal propulsion reactor system. The reactor system is of a design explicitly for 7 the use with an altitude compensating nozzle. The research consists of five 8 sections, which include the need for a new kind of propulsions system, the system 9 design and analysis, analysis through Computational Fluid Dynamics, and the 10 conclusion of the new design and analysis. The second section consists of a 11 system engineering design approach to the reactor. At a moderate resolution 12 level, the new reactor system consists of three primary systems, followed by five 13 sub-primary systems. The primary systems and their subsystems are the focus of 14 the design and systems engineering analysis. The Analysis through Computational 15 Fluid Dynamics, section three, mainly focuses on the performance of the 16 propellant interacting with the newly designed reactor core. The Computational 17 Fluid Dynamic results have allowed for a greater understanding of the behaviors 18 of the exhausting propellant that may occur when interacting with an altitude 19 compensating nozzle system. Thus, this current configuration provides an answer 20 to limiting factors of modern high thrust rocket engines, thereby further enabling 21 humankind to more readily explore their closest celestial neighbors and beyond. 22 23 Keywords: Space Systems Engineering, Nuclear Thermal Propulsion Reactor, 24 Gas-Cooled Nuclear Reactor, Computational Fluid Dynamics, and Rocket 25 Propulsion 26

27

28

Introduction 29 30

Modern high thrust rocket engines operate using the same fundamental 31

principles. The first of these principles is that the engines use combustion as a 32

means of adding energy into the fluids of the rocket engine. By adding energy, 33

the outward pressure of the fluid begins to increase rapidly. This allows the 34

fluid to expand and accelerate through an expanding de Laval nozzle resulting 35

in thrust. By the laws of physics and thermal dynamics, these fundamental 36

principles of current engines have largely reached their maximum potential. 37

The technological plateau is due to the critical parameter known as specific 38

impulse, which is the thrust per unit of the propellant flow weight. Therefore, 39

the ideal specific impulse is proportional to the combustion temperature 40

divided by the molecular weight of the fluid, leaving the engine. Therefore, to 41

produce higher ideal specific impulse values, the engine must have a high 42

operating temperature coupled with a low molecular weight of the exhausting 43

fluid. Modern rocket engines all have relatively the same combustion chamber 44

temperatures. The similarity is due to the limiting factor of the material used 45

for the combustion chamber, with the combustion chamber temperature 46

relatively fixed due to this material. Thus, to produce a higher ideal specific 47

impulse is to reduce the molecular weight of the exhausting fluid. The removal 48

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of combustion as a means of adding energy to a fluid is the logical way to 1

reduce the molecular weight while simultaneously retaining high temperatures. 2

The second fundamental principle is the use of the conservation of 3

momentum by exhausting the high-pressure fluid out through an expanding de 4

Laval nozzle. The de Laval nozzle operates under the principle of fluid 5

expansion through the throat to nozzle exit area ratio. The altitude at which the 6

engine is designed to produce optimum thrust will determine this expansion 7

ratio. Thus, an engine using a De Laval nozzle will only produce optimum 8

thrust at a single altitude, which will only occur for a moment in the use of the 9

engine. Therefore, most of the time in which the engine is in use, it will not be 10

performing optimally. The underperformance will lead to more significant 11

consumption of fuel, which results in a lower mass that can be lifted. For the 12

engine to produce optimum thrust consistently, the nozzle must be able to 13

adjust for the constantly changing atmospheric pressure. Therefore, with 14

specific impulse being directly related to the molecular weight of the 15

exhausting fluid and indirectly related to the thrust optimization, this confirms 16

that the two limiting factors in achieving high specific impulse and high thrust 17

within a rocket engine (Huang & Huzel, 1992; Mattingly, 2012). 18

The previously discussed limiting factors have become some of the core 19

reasons that humanity is limited to only increasing the size of rockets to lift 20

more and to go further into space. Understanding of these limiting factors and 21

the forces that drive them will pave the way for solutions. Thus, by solving the 22

problem of the molecular weight and thrust optimization, this stands to 23

dramatically influence what humanity can accomplish in space. 24

25

26

Literature Review 27 28

Theory of Nuclear Thermal Propulsion 29

30

The principles behind a nuclear thermal propulsion system are to put it 31

simply, to produce thermal energy in the nuclear reactor core, as the core 32

undergoes the prosses of nuclear fission. Fission is when an unstable atom is 33

split into two lower atomic mass atoms. Niels Bohr and John A. Wheeler 34

illustrated this prosses with a theoretical model known as the “Liquid-drop 35

model,” as seen in Figure 1 (Pethig, 2014). 36

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Figure 1. The “Liquid-drop Model” 1

2 3

The atoms with a heavier atomic mass are split into the two lighter mass 4

atoms. The fragmenting of the nuclei produces a tremendous amount of energy 5

along with subatomic particles. The subatomic particles known as neutrons are 6

the catalyst for the fission reaction. Thus, the abundance of neutrons from the 7

reaction causes a cascade effect of fission reactions, as shown in Figure 2. This 8

cascade provides the thermal energy that is used by the nuclear thermal rocket 9

engine to heat the outgoing propellant (Pethig, 2014). 10

11

Figure 2. The cascade effect of a fission reaction 12

13 14

The propellant fluid expands rapidly from the random thermal motion 15

generated from a large amount of kinetic energy being added. As a result, the 16

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fluid rapidly expands and is then allowed to expand through the nozzle. The 1

nozzle acts as a converter by transforming the random thermal energy of the 2

propellant fluid into a single direction of flow. Thus, creating a force acting in 3

the opposite direction of the propellant flow, thereby producing forward thrust. 4

(Huang & Huzel, 1992). 5

The parameter that is used to examine the performance of a rocket engine 6

is known as a specific impulse. Specific impulse is a measurement of the force 7

produced by the same per-unit amount of propellant mass consumed. Thus, the 8

universally recognized units of this parameter are seconds; sense specific 9

impulse is a measurement over a period of time. To equate specific impulse 10

back to the fundamental limitations of modern high thrust rocket engines, the 11

derivation of specific impulse needs to be understood. Through thermodynamics, 12

the specific impulse of a given engine is comparable to the chamber 13

temperature divided by the molecular weight of the exhausting fluid. This 14

relationship between chamber temperature and molecular weight driving the 15

specific impulse of an engine is shown in the following table and equations 16

(Huang & Huzel, 1992; Mattingly, 2012; Papadopoulos, 2019). 17

𝐼𝑆𝑃 =𝑉𝑒𝑔

𝑔0 (1)

𝑉𝑒𝑔 = 𝑉𝑒 +(𝑃𝑒 − 𝑃𝑎) ∙ 𝐴𝑒

�̇� (2)

𝑉𝑒 = √(2𝛾

𝛾 − 1∙

ℝ

𝑀𝑤∙ 𝑇𝑐 ∙ [1 ∙ (

𝑃𝑒

𝑃𝑐)

𝛾−1𝛾

]) (3)

�̇� =𝑃𝑐 ∙ 𝐴∗

√(ℝ

𝑀𝑤∙ 𝑇𝑐)

∙ √𝛾 ∙ (1 + 𝛾

2)

1+𝛾1−𝛾

(4)

𝑃𝑖 = 𝜌𝑖 ∙ℝ ∙ 𝑇𝑖

𝑀𝑤𝑖

(5)

Table 1. Symbol definitions for equations 1-5 18

𝑔0 = Acceleration of Gravity 𝑇𝑐 = Chamber Temperature

𝑃𝑒 = Exit Pressure ℝ = Gas Constant

𝑃𝑎 = Atmospheric Pressure 𝑀𝑤 = Molecular Weight

𝑃𝑐 = Chamber Pressure 𝐴∗ = Throat Area

𝛾 = Ratio of Specific Heat 𝐴𝑒 = Exit Area

19

In order to understand the relationship between chamber temperature and 20

molecular weight, the definition of specific impulse must be expanded by 21

substituting equations (2) into (1). Further expanding the equation, by 22

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substituting equations (3) and (4) into equation (2) the relationship between 1 𝑇𝑐

𝑀𝑤⁄ and specific impulse is more evident. The final substitution of equation 2

(5) into the expanded equation of (1) for the pressure terms. Thus, it makes the 3

majority of terms in the specific impulse equation to be in terms of 𝑇𝑐

𝑀𝑤⁄ . 4

Therefore, solidifying that the significant driving parameters of specific 5

impulse are chamber temperature and molecular weight. 6

7

Historical perspective of the U.S. nuclear thermal propulsion development 8

The notion of using nuclear thermal power as a means to produce thrust 9

for rockets was first suggested in 1945 by Theodore Von Karman. After about 10

a decade of campaigning by Von Karman, the advisory board gave the go-11

ahead to begin the development of nuclear thermal propulsion systems. Thus, 12

the establishment of the Rover Project in November 1955. The Los Alamos 13

Scientific Laboratory would conduct the project. The rapid development of 14

chemical ICBMs, resulted in the reduction in the urgency for a new kind of 15

engine, causing the first test of the nuclear thermal rocket engine to be in 1959. 16

The Reactor was named the Kiwi-A, for it was named after the flightless bird 17

from New Zealand because, like the bird, the Reactor was never intended to fly 18

[6,7]. Even though the reactor test was considered successful, the Kiwi-A did 19

sustain structural damage to the carbide fuel particles from the combination of 20

the fuel configuration and core temperature. A year later, the testing of the 21

second iteration of the Kiwi-A that had a newly improved fuel-elements in the 22

core, eliminating the damage from the core temperatures. With the second 23

successful test by the Rover Project program, NASA and the Atomic Energy 24

Commission formed the Space Nuclear Propulsion Office Later that year. With 25

the new backing, the Kiwi-A3 was able to be tested mere months after the 26

second Kiwi test. With three hugely successful tests of the Kiwi series, the 27

newly formed Space Nuclear Propulsion Office enlisted some of the biggest 28

names in space research and development. In 1961, the Office contracted 29

Aerojet-General, Westinghouse Electric Corporation, and The Lockheed 30

Corporation to develop the next phase of the Rover Program. The next phase of 31

reactors was named Kiwi-B series, the second engine of this series was the first 32

engine to run using liquid hydrogen. Where all the previous engines were using 33

gaseous hydrogen, this change was proven to be very advantageous, for the 34

Kiwi-B1B was able to run for a brief time at 900 Mega Watts. The next major 35

milestone came in the form of a project called Nuclear Engine for Rocket 36

Vehicle Application (NERVA). Under this project, the successful demonstration 37

in 1964 of the first throttle reactor known as NRX-A2, was able to be operated 38

at the half and full power all in the same run. The NRX-A2 also tested out at a 39

vacuum specific impulse of 760s, which far surpassed the leading chemical 40

rocket of the day, at only 308s. Between 1964 to 1972 saw significant 41

advancements in the program. At the zenith of the program, saw the production 42

of two nuclear engines that showcased the potential of this technology. The 43

first of these two is the Phoebus-2A engine. The Phoebus boasts the title of the 44

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most powerful nuclear rocket reactor ever constructed; at only 80% power, the 1

Reactor produced 4,000 Mega Watts of thermal power, with a thrust output of 2

1,123 kN. The second engine, the Pewee, was able to have the highest core 3

temperature of 2,750K, which also produced the highest specific impulse of 4

845s. This specific impulse made for the Pewee to be the most power-dense 5

nuclear engine ever built. Despite all these incredible achievements, in January 6

of 1973, the Rover Nuclear Rocket Program was terminated due to the 7

changing national priorities of the time. Thus, ending the United States nuclear 8

propulsion development (Koenig, n.d.; Robbins, Olmsted, Finger, & Robbins, 9

1991; Wade, 2019b). 10

11

Historical Perspective of the Development of Nuclear Fuels 12

13

Before being terminated in 1973, the Rover and NERVA programs 14

produced over 20 different prototype engines, as shown in Table 2. The most 15

significant changes that came from the two programs were the development 16

and refinement of the nuclear fuel elements for the reactor. The first kind of 17

nuclear fuel element was of a highly enriched uranium oxide in a graphite 18

matrix formed into a plate form. The fuel type gradually evolved into an all 19

carbide fuel matrix, consisting of enriched uranium, zirconium, and carbon. 20

The full carbide fuel was formed into hexagonal tubes of the would-be 21

arranged into clusters forming a cylindrical core, as seen in Figure 3 22

(Benensky, Westinghouse, & Ray, 2013; Gunn, n.d.; Koenig, n.d.). 23

24

Table 2. Various Types of Reactor Tests 25

26 27

The Nuclear Furness (NF-1) was the first engine to test the all carbide fuel 28

matrix. Thus, meaning both the Phoebus-2A and Pewee, the two-record 29

holding engines, use the less durable and lower operating temperature nuclear 30

fuel. The program’s goal was to raise the endurance at the operating 31

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temperature to obtain an ever higher thrust and specific impulse. Thus, both the 1

Pewee and Phoebus’s records would have been quickly surpassed due to the 2

new fuel type alone (Benensky et al., 2013; Dayah, 2017; Koenig, n.d.). 3

4

Figure 3. Hexagonal Fuel Elements 5

6 7

Figure 4. Fuel Endurance Levels for Various Temperatures 8

9 10

While the United States Rover Program was underway, the Soviet Union 11

was developing its own nuclear thermal propulsion program, but with the 12

approach of a modular style of a nuclear reactor. The modular nuclear reactor 13

used what is known as heterogeneous nuclear fuel, which did not use a 14

moderating material and a small amount of uranium. By doing so, the Soviet 15

nuclear reactor was able to have a single section of the reactor operating at high 16

temperatures. Between 1962-1963 the Soviet Union’s program completed 17

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testing on a modular reactor that could have an exit temperature of 3,000 K. 1

With the success of the reactor, the Soviet nuclear propulsion program much 2

like the U.S., focused on the reduction of the nuclear reactor size and 3

maximizing the exhaust temperature of the propellant. Therefore, the Soviets 4

needed a new fuel that would be optimized for heat transfer while maintaining 5

the operating temperature needed for an exit temperature of at least 3,000 K. 6

The Soviet program continued into the early 1990s, some 20 years more than 7

the United States. This extended time, along with the technology advancement, 8

allowed the Soviet program to test many configurations and permutations of 9

fuel geometries and compositions. With these critical advantages, the Soviet 10

program was able to achieve a new kind of fuel is known as Ternary Carbides 11

or Tri-carbides. The fuel compound is comprised of three main elements, 12

uranium, zirconium, and carbon, with later models adding tantalum for even 13

higher operating temperatures shown in Table 3 (Benensky et al., 2013; Dayah, 14

2017). 15

16

Table 3. Fuel Types and Corresponding Operating Temperature. 17 Type of Fuel Uranium

Density

Maximum Operating

Temperature(K)

Carbide

(U, Zr) C, C

(U, Zr) C

(U, Zr, Nb) C

(U, Zr, Ta) C

≤ 2.5

2,500

3,300

3,500

3,700

Carbonitride

(U, Zr) C, N

6-8

3,100

CERMET Carbonitride

(U, Zr) C, N-W

≤6.5

2,900

18

Table 4. Fuel Geometries for The Soviet Union and The United States. 19

Type of

Fuel

Element

General Form

Cross-section

Dimensions

(mm)

Fuel Arrangement

& Composition

Ribbon

Rod

Prismatic

Block

Plate

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Spherical

1

The Soviet program needed a way of maximizing the heat transfer between 2

the high operating temperatures of the Ternary Carbides fuel and propellant. 3

Thus, the development of the so-called “twisted-ribbon” geometry fuel, as seen 4

in Table 4. This configuration allowed for the best heat transfer while 5

maintaining the high operating temperatures. The Reactor would then consist 6

of dozens of the fuel rod assemblies, with each fuel rod containing the new fuel 7

ribbons bundled together. This new reactor configuration could produce the 8

desired exit temperatures while still upholding the original design of a modular 9

style of their original Reactor, as seen in Figure 6 (Benensky et al., 2013). 10

11

Figure 5. The Soviet Union’s modular “Twisted-Ribbon” reactor 12

13 14

The Soviet program incorporated the new “twisted-Ribbon” reactor onto 15

an engine assembly in 1985. The new nuclear engine was given the designation 16

RD-0410 and would become the most successful nuclear engine developed by 17

the Soviet Union. The RD-0410 operated at a core temperature of 3,500-18

3,700K for 1 hour. With such a high operating temperature, the RD-0410 had a 19

1.8 thrust to weight ratio while achieving a specific impulse of 910 s. 20

Following this, the Soviet program began to focus on the development of a 21

much larger engine, an engine that could produce 20 times the thrust of the 22

RD-0410. Unfortunately, the drive for further development of nuclear thermal 23

propulsion systems collapsed with the Soviet Union, with the program ultimately 24

being terminated in 1994 (Benensky et al., 2013; Wade, n.d., 2019a). 25

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Theory of Computational Fluid Dynamics 1

Computational fluid dynamics (CFD) is a field of fluid mechanics centered 2

around the understanding of the physical events that occur within fluid flows in 3

and around objects through numerical analysis. The related phenomena 4

resulting from these events encompass convection, diffusion, boundary layers, 5

slip surfaces, dissipation, turbulence, and shock waves, which are characterized 6

by the compressible Naiver-Stokes equations. The majority of these relations 7

are inherently nonlinear and often have no analytic solution. Consequently, this 8

motivates the acquisition of the associated partial differential equations. The 9

use of numerical methods to solve these partial differential equations 10

introduces approximations that can vary from the fundamental equations. The 11

theory associated with the numerical analysis of fluid mechanics was 12

developed mainly by scientists, interested in the physics of fluid flow and, 13

consequently, errors identified with a particular physical phenomenon on 14

which the flows mentioned above have a substantial effect, often occur. If the 15

effects of these errors are not thoroughly understood and controlled, they can 16

lead to severe difficulties that produce erroneous results. This effect, due to 17

errors, has motivated the studying and incorporation of concepts such as 18

stability, convergence, consistency, stiffness factorization, and algorithm 19

development. The aggregate of these concepts incorporated into a Naiver-20

Stokes numerical analysis software mainly represents modern CFD platforms 21

commercially available or otherwise (Lomax, Pulliam, & Zingg, 2001). 22

23

24

Methodology 25 26

Nuclear Propulsion 27

28

The reasoning for the use of a nuclear thermal propulsion system to solve 29

limiting factors of modern high thrust rocket engines are that the fundamental 30

principles of the engine are different. For the nuclear thermal engine, the 31

energy is added to the fluid in the plenum by forcing the fluid through the 32

fission reacting core. By doing so, there are no chemical reactions taking place. 33

Therefore, the molecular weight of the exhausting fluid remains the same. By 34

using a low molecular weight propellant, the resulting exhausting fluid will 35

have the same low molecular weight. Thus, increasing the Specific impulse of 36

the propulsion system while maintaining a high thrust output. By coupling the 37

nuclear thermal rocket engine with the toroidal aerospike nozzle will cause the 38

engine to be at optimum thrust throughout the engines use. Through doing so, a 39

significant amount of overall performance will increase along with further 40

increasing the specific impulse of the propulsion system. The verification of 41

this new potential design for a high thrust rocket engine will be first to 42

construct the central systems and the corresponding subsystems of the new 43

nuclear thermal propulsion system. With the construction of the systems 44

finished, the second phase of the methodology will begin. This phase will 45

consist of the verification process, of which the operation of the systems and 46

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the theoretical aspects of the new propulsion system will be tested. This 1

verification process will be conducted through the use of computational fluid 2

dynamics. When verified, this nuclear thermal propulsion system will be the 3

first engine to utilize the new hoop core design for the nuclear Reactor. This 4

design will also be the first nuclear thermal propulsion system to employ an 5

active cooling system for a toroidal aerospike nozzle (Wade, n.d.). 6

7

Annulus Reactor System 8

9

System Analysis and Design 10

The Reactor System is the proverbial heart of a Nuclear Thermal 11

Propulsion System, making this system key in the redesign process. The main 12

two changes between the new Nuclear Thermal Propulsion System and the 13

benchmark engine, the Phoebus-2A system, is the use of a new reactor fuel 14

compound and the reconfiguring of that fuel within the core. The new 15

configuration of the core is known as The Annulus Reactor. As the name 16

infers, the reactor system is fashioned into a hoop or ring shape. The primary 17

purpose of this configuration is to allow the inner coolant to pass directly 18

through the reactor to the nozzle spike. The inner coolant pass-through, along 19

with the nozzle support structure, provide full structural rigidity to the nozzle 20

spike. Both systems also provide the coolant return channels from the nozzle 21

system to a propellant feed system. The partially heated returning inner coolant 22

from the nozzle spike is then diverted into heating channels within the 23

moderator of the reactor, as illustrated in Figure 6. The inner moderator heating 24

channels allow the innermost section of the core to remain at an adequate 25

operating temperature by allowing the inner coolant to absorb a large volume 26

of the heat from the fuel. The heated inner coolant is consolidated into the 27

outer wall of the coolant pass-through in order to allow for the heated coolant 28

flow from the inner moderator section of the reactor to flow into a propellant 29

feed system. Simultaneously the partially heated coolant flowing from the 30

nozzle cowling is diverted into the outer heating channels of the moderator. 31

The outer heating channels function similarly to the inner channels, by 32

consolidating and directing the heated outer coolant to the propellant feed 33

system. In order to accommodate the inner coolant pass-through, the nuclear 34

reactor had to be reconfigured. The traditional hexagon-shaped fuel rods used 35

in the benchmark engine was not suitable for the reconfiguration of the reactor. 36

Thus, leading to the second redesigned aspect of the reactor system. The 37

Annulus Reactor System would replace the hexagon-shaped uranium carbide 38

fuel rods with Tri-Carbide fuel pucks. The Tri-Carbide fuel pucks are stacked 39

into rods containing six pucks in each rod. The rods allow for the arrangement 40

of nuclear fuel into a ring about the inner coolant pass-through, as illustrated in 41

Figure 7 (Benensky et al., 2013; R. R. Gouw, n.d.; Nam et al., 2015; Plancher, 42

2002). 43

44

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Figure 6. Annulus reactor fuel rod cut-a-way 1

2 3

Figure 7. The layout of the Annulus Reactor core 4

5

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The use of the new fuel type and configuration has allowed for some 1

critical advantages over the benchmark engine: the most significant being the 2

estimated amount of enriched uranium required to reach critical mass. The 3

Annulus Reactor would only need an estimated 97.4kg of 93% enriched 4

uranium for the entire Reactor. The Phoebus-2A core, in comparison, 5

contained around 300 kg of 93% enriched uranium. Thus, the Annulus Reactor 6

would have a 67.5% reduction in the needed uranium in over the Phoebus-2A. 7

The reduction in uranium is from the use of Tri-Carbide fuel pucks and the 8

configuration of the moderator and reflector. The nuclear fuel and moderator 9

that is being proposed for the Annulus Reactor is based on the Moderated 10

Square-Lattice honeycomb reactor design. The implementation of the fuel 11

pucks also allows for the Tri-Carbide compound to have the potential for a safe 12

operating temperature in excess of 3,000 K. Whereas the Phoebus-2A reactor 13

core could only safely operate at 2310 K. With the Annulus Reactor operating 14

at a core temperature of 3,000 K, it would be, on average, 30% hotter than the 15

benchmark engine. 16

Initially, the honeycomb reactor design was scaled up to match the same 17

cross-sectional flow area as that of the Phoebus-2A core. However, through 18

analysis and research, it was determined that the sizing of the flow channel of 19

the honeycomb reactor could not be equally scaled. The reason for the inability 20

to equally scale the honeycomb reactor is due to the fact that the Annulus 21

Reactor is operating at a higher chamber pressure and mass flow rate. Both the 22

chamber pressure and mass flow rate are driving factors in determining the 23

correct size of flow channels that are needed. Through several iterations, the 24

proper flow channel size was determined to be 2.2 mm square, as seen in 25

Figure 8. With this channel size, the total needed cross-sectional flow area was 26

significantly reduced, with only 5.06 % of each puck was removed. Thus, 27

newly scaled fuel pucks have a total cross-sectional flow area of 0.0632 m2, 28

with each fuel puck will contain, on average, 2.71 kg of uranium, as listed in 29

Table 5. By having the flow channel size and by establishing the thickness of 30

the Tri-Carbide around each channel, an approximation was needed for the 31

number of channels necessary to equal the total cross-sectional flow area of the 32

reactor. The approximation mirrors the “Square peg in a round hole” problem; 33

thus, equation 6 was used for the approximation of the number of needed 34

channels. Equation yelled that each puck would need 2,178 channels to match 35

the total cross-sectional flow area need. The size of each puck was kept to the 36

same size as the initial scaling, as seen in Figure 9. By doing so, the puck 37

should be able to handle much higher chamber pressure than the original 38

design. Thus, by coupling, the increase in the core temperature with added 39

strength from the puck design should enable the Annulus Reactor to be capable 40

of multiple restarts while producing higher thrust and Isp levels than that of the 41

Phoebus-2A (Benensky et al., 2013; R. Gouw & Plancher, 2004; R. R. Gouw, 42

n.d.; Hennessy & Patterson, 2007; Nam et al., 2015; Plancher, 2002; Sapir & 43

Orndoff, 1970). 44

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𝐷𝑃𝑊 =𝜋 ∙ (

𝑊𝐷

2 )2

𝐷𝐴−

𝜋 ∙ 𝑊𝐷

√2 ∙ 𝐷𝐴

(6)

Figure 8. Nuclear Fuel Puck 1

2 3

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Table 5. Annulus Reactor Design Data 1

Annulus Reactor Data

Fuel Rod

Diameter (m) Height (m)

Fuel

Puck

Diameter

(m) Height (m)

0.876 1.32 0.514 0.1

Total

Number

Tri-Carbide

Wafer Grid

in Present of

the Radius

Total

Number

Cross-

Sectional

Flow Area

(m2)

6 58.69% 36 0.0105

Graphite in

Present of the

Radius

Coolant

Channel in

Present of

the Radius

Total

Estimated

enriched

U235 Per-

Puck (kg)

Percent of

Removal for

Flow

Channels

11.74% 0.50% 2.71 5.06%

Zirconium

Tri-Oxide in

Present of the

Radius

Zirconium

Hydride in

Present of

the Radius

5.87% 23.21%

Annulus

Core

Cross-

Sectional

Flow Area

(m2)

Total

Estimated

enriched

U235 (kg)

Fuel

Puck

wafer

Grid

Flow

Channel

Width (m)

Flow

Channel

thickness (m)

0.0632 97.4 0.0095 0.0036

Inner Coolant

pass-through

Diamere with

Reflector (m)

Reflector

Thickness

(m)

Flow

Channel

Cutout

Width (m)

Total

Number of

Flow

Channels

Per-Puck

0.876 0.1 0.0022 2178

Core

Diameter

with

Reflector (m)

Core height

without top

Reflector

(m)

2.827 1.3

2

A decomposition is needed to have a better understanding of all the 3

systems and subsystems of the Annulus Reactor. The decomposition of the 4

Annulus Reactor System begins with the primary system under the central 5

system, which is shown in tier 0-1 of Figure 9. The Annulus reactor System is 6

further divided into two more subsystems. The further division is to obtain the 7

needed resolution level for an analysis of this grade of design. The fuel rod 8

system, as discussed previously, consists of a total of six fuel rods with each 9

rod containing six nuclear fuel pucks. The pucks are stacked vertically with the 10

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flow channels aligned to allow for the maximal heat transfer between the pucks 1

and the propellant. The moderator system is a subsystem within the fuel rod 2

system, which is the key to the reduction of the needed uranium within the 3

whole Annulus Reactor. The moderator is comprised of a zirconium hydride 4

matrix, which facilitates the thermalization of the neutron spectrum. Thus, 5

increasing the neutron interaction with each fuel puck. By increasing the 6

number of neutrons interacting with each fuel puck, the needed uranium to 7

maintain critical mass is reduced. The reflector system also aids in the 8

reduction of uranium by using beryllium to reflect escaping neutrons back into 9

the core to interact with the fuel pucks. The reflective beryllium is placed at the 10

top of the reactor core and axially around it. With no beryllium being placed at 11

the base of the core due to the exhausting propellant temperatures. The control 12

rod system is a cylindrical rotating control rod system, which is similar to the 13

system used in the Phoebus-2A Reactor. The control rods are comprised of two 14

different materials, a neutron reflective material long with absorption material. 15

The neutron reflective material is comprised of beryllium, which occupies the 16

vast majority of each rod. Thus, a fraction of the rod is comprised of the 17

neutron absorption material of boron carbide. By rotating the rod to expose 18

more or less of the boron carbide material, the rate of fission can be controlled. 19

Thus, controlling the temperature of the Annulus Reactor and giving the 20

Nuclear Thermal Propulsion System the ability to vary its thrust level 21

(Benensky et al., 2013; R. Gouw & Plancher, 2004; R. R. Gouw, n.d.; Koenig, 22

n.d.; Nam et al., 2015; Pethig, 2014; “Physics of Uranium and Nuclear Energy 23

- World Nuclear Association,” n.d.; Plancher, 2002; Sapir & Orndoff, 1970). 24

25 Figure 9. Decomposition of the Annulus Reactor system 26

27 28

An architecture analysis allows for a precise visualization and 29

understanding of how each system and subsystem interacts within the Annulus 30

Reactor System. The architecture analysis consists of two sections, the input, 31

and output analysis, shown in Figure 9, and the flow chart layout, shown in 32

Figure 10. The input and output analysis (N2 diagram) has a resolution level, 33

which is focusing on the three primary systems illustrated in tier 0-1 of Figure 34

10. The N2 analysis begins with the primary system of the fuel rods, from 35

which the other systems receive input from or output too. The other two 36

primary systems at this level of analysis will only interact with the fuel rod 37

system. The two significant outputs based on the N2 analysis are the high-38

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temperature and high-pressure propellant along with the desired fission rate of 1

the Reactor, the other interactions between each system of the N2 analysis are 2

listed in Table 6 (R. Gouw & Plancher, 2004; R. R. Gouw, n.d.; Nam et al., 3

2015; NASA Systems Engineering Handbook, 2007; Papadopoulos, 2018; 4

Plancher, 2002). 5

6

Figure 10. N2

Diagram for the Annulus Reactor System 7

8 9

Table 6. Inputs and Outputs of the Annulus Reactor System N2

Diagram 10 The Direction of Input & Output Performed Operation

In → 1.0 Preheated High-Pressure Propellant

1.0 → Out High-Pressure and High-Temperature

Propellant

1.0 → 2.0 Escaping Neutrons

1.0 → 3.0 Escaping Neutrons

2.0 → 1.0 Reflected Neutrons

3.0 → Out Desired Fission Rate

11

The second level of the architecture analysis consists of a flow chart layout 12

of the Annulus Reactor System. The flow chart layout conveys the interactions 13

between each of the primary systems. In Figure 11, the centrality of the fuel 14

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rod system becomes more prevalent, as the fuel rod system influences each of 1

the other primary systems. Thus, the fuel rod system’s principal function is the 2

transfer of thermal energy from the nuclear fuel pucks to the propellant. 3

Whereas, the other primary systems and subsystems principal functions are to 4

maintain or regulate the number of free neutrons that are interacting with the 5

nuclear fuel pucks. Thus, the combination of the three primary systems enables 6

the maintaining of the desired fission rate. Therefore, the Nuclear Thermal 7

Propulsion System would, in theory, be able to produce variable thrust levels 8

for different stages within a mission profile (R. Gouw & Plancher, 2004; R. R. 9

Gouw, n.d.; Nam et al., 2015; NASA Systems Engineering Handbook, 2007; 10

Papadopoulos, 2018; Plancher, 2002). 11

12

Figure 11. Flow Chart for the Annulus Reactor System 13

14 15

Computational Fluid Dynamics 16

17

An investigation into the characteristics of the flow and heat transfer 18

through the core channels of the six nuclear fuel puck assemblies was 19

performed with the use of the computational fluid dynamics program ANSYS 20

Fluent. The subsequent analysis was accomplished with a two-dimensional 21

symmetry model of the center core channels running the diameter of the puck 22

geometry. In order to comprehensively characterize the performance of the 23

core geometry, two versions of the simulation were constructed and tested at 24

varying conditions. The first model was that of a single puck with fore and aft 25

separation space, and the second model was an arrangement of all six pucks as 26

a non-separated solid length. In the case of the single puck model, the resultant 27

conditions of the initial run were set to the initial conditions of the subsequent 28

run. With the former, the conditions were static and ran individually for each 29

case. The following sections in this paper detail the process by which each of 30

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these simulations were created, geometry, grid generation, including topology, 1

and boundary conditions. (“Ansys Fluent,” 2006) 2

The 2D fuel puck geometry was constructed as the center 49 channels that 3

run the diameter of the puck circle. These 49 channels were then further 4

separated into a radius of 24.5 channels with asymmetry to reflect those across 5

the central axis. The channel reduction was made in order to increase the 6

fidelity of the mesh generation while reducing the computational requirements 7

associated with CFD. The channel geometry, along with the aft and fore 8

sections of the core separations, were created with the use of ANSYS 9

Spaceclaim and subsequently modified further to distinguish the solid and fluid 10

cell zones. In the case of the non-separated configuration, the same methods 11

were utilized for the extended length required in incorporating all six 12

individual pucks(“Ansys Fluent,” 2006). 13

14

Figure 12. Single Nuclear Fuel Puck Geometry 15

16 17

A 2D mesh was generated in ANSYS Fluent Meshing utilizing the 18

geometry discussed earlier. The mesh is a structured mesh in an H-mesh 19

configuration in which the center channels incorporate a higher cell count in 20

order to account for boundary layer formation across the geometry. In contrast, 21

the solid cell zones receive lower fidelity meshing as the constant values 22

attributed to them enable such a structure without sacrificing result accuracy 23

(“Ansys Fluent,” 2006). 24

Regarding the topology of the mesh, the fore and aft sections of the puck 25

separations were segmented with interior lines. This structured topological 26

configuration allows for the creation of a reasonably dense mesh around the 27

areas that experience boundary flow gradients. Similar to the geometry, this 28

process was repeated for the full-length fuel puck simulation as well. An 29

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overview of the topology discussed here can be seen in Figure 13 below 1

(“Ansys Fluent,” 2006). 2

3

Figure 13. H-meshing of Single Nuclear Fuel Puck Section 4

5 6

The physics conditions below were utilized in the creation of the CFD 7

model. The following conditions cover the general case, boundary conditions, 8

operating conditions, solution methods, and solution initialization. 9

10

Table 7. General Settings 11

General Settings

Conditions Settings

General Solver Pressure Based

Simulation State Steady State

Velocity Formulation Absolute

Geometric settings Symmetric about the X-axis

Energy equation On

Viscous Model K-epsilon Realizable

Fluid Model Hydrogen Gas (Ideal Gas)

Radiation Model P1 Radiation

12

The general settings of the model are utilizing a pressure-based, steady-13

state solver with a K-Epsilon Realizable model. The pressure-based solver uses 14

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a solution algorithm where the governing equations are solved sequentially due 1

to the nonlinear governing equations. This solver was chosen for its frequent 2

utilization in low-velocity flows. The K-Epsilon Realizable is an improved 3

version of one of the first complete turbulence models. It was utilized for its 4

robustness and accuracy for a wide range of turbulent flows. These qualities 5

make the solver popular for use in industrial flow and heat transfer simulations. 6

Ideal Hydrogen gas was used in the fluid model to reflect compressibility 7

within the system. The P1 radiation model was then implemented as it is the 8

simplest case of the more general P-N model. This model is oriented around 9

the expansion of the radiation intensity I into an orthogonal series of spherical 10

harmonics(“Ansys Fluent,” 2006). 11

12

Table 8. Set Boundary Conditions Table 13

Boundary Conditions

Settings Inlet

(Mass Flow)

Outlet

(Pressure)

Walls

(Mixed)

Gauge Pressure 6,890,000 Pa 6,890,000 Pa N/A

Operating Pressure 0 Pa 0 Pa 0 Pa

Total Temperature 300 K 300 K 3000 K

Mass Flow Rate 0.74 kg/s N/A N/A

Heat transfer coefficient N/A N/A 50 W/m^2K

Free Stream Temperature 300 K 300 K 300 K

Heat Generation Rate N/A N/A 3000 W/m^3

14

The boundary conditions were set to reflect the desired conditions in the 15

core assembly and approximated to the center 49 channels that comprise the 16

diameter of a fuel puck. The conditions of the inlet reflect the incoming 17

hydrogen from the pump system such that the pressure is 6.89 Mpa, the 18

temperature is 300K, and the total 129 kg/s mass flow rate was taken to be that 19

experienced by the 49 channels at 0.74 kg/s. The outlet conditions were set to 20

reflect the pressure and temperature conditions of the inlet and ensure the 21

correct flow direction. The wall conditions were set such that the cell zone 22

temperature was set to a constant 3000 K, and heat generation and heat transfer 23

coefficients were set as 3000 W/m^3 and 50W/m2 K(“Ansys Fluent,” 2006). 24

25

Table 9. Solution Methods Table 26

Solution Methods

Settings Type

Formulation Implicit Formulation

Flux type Roe-FDS

Gradient Least Squares Cell-Based

Flow Second-Order Upwind

27

In the case of the solution methods, the settings for the simulation can be 28

seen in table 9 above. Second-Order Upwind formulation was utilized as while 29

the first-order discretization generally yields better convergence than the 30

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second-order scheme, Second-Order will provide greater accuracy in our 1

results and given that a structured mesh was utilized the convergence 2

discrepancy is mostly offset. 3

4

Table 10. Solution Initialization Table 5 Solution Initialization

Settings Type

Initialization Method Standard Initialization

Computation Reference From Inlet

Reference Frame Relative to Cell Zone

Number of Iterations 2000

6

In order to ensure that results were accurate, a grid independence study 7

was undertaken to utilize generating several independent meshes in ANSYS 8

Fluent and testing the results from each against the primary case. Through this 9

process, it was found that there is a minimum of roughly 85000 nodes for the 10

simulation to exhibit the desired heat transfer and flow properties. As per 11

standard simulation accuracy requirements, the prime simulation case was 12

simulated until convergence of at least three orders of magnitude(“Ansys 13

Fluent,” 2006). 14

15

16

Results 17 18

By utilizing the simulation mentioned above, two simulation tests were 19

constructed in order to test the capabilities and limits of the fuel puck geometry 20

and configuration. The following contours and graphs of pressure, velocity, 21

and temperature represent the results of this testing process. The first test 22

established a baseline and ran at the standard boundary conditions and values 23

the setup and results of which can be seen below. 24

25

Table 11. Annulus core first configuration: Test 1 26 Baseline Core Run

Conditions Values

Wall Temperature (K) 3000

Propellant Temperature (K) 2865

Mass flow Rate (Kg/s) 129

Inlet Pressure (Mpa) 6.89

Core inlet Temperature (K) 300

Temperature after Puck 1 (K) 1245

Temperature after Puck 2 (K) 1785

Temperature after Puck 3 (K) 2325

Temperature after Puck 4 (K) 2460

Temperature after Puck 5 (K) 2595

Temperature after Puck 6 (K) - Exit 2865

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Exit Temperature of the Non-Separated

model (K) 2863

1

The first test was run at initial values meant to reflect the baseline 2

operating conditions of the engine. The hydrogen experienced and increase in 3

temperature on average, 427.5 K of increase as it passed through the heating 4

channels of each puck, culminating in a total temperature of 2865 at the exit of 5

the core assembly. This value was corroborated through the solid model run, 6

which produced a final temperature of 2863 K. Given the large cross-sectional 7

flow area provided by the numerous flow channels, the flow did not experience 8

a significant increase in velocity and accelerated only to a value of 5m/s though 9

each channel. This minimal change in velocity through the system resulted in 10

an average pressure drop experienced across each puck to be negligible, which 11

ensures minimal losses. Figures 14-16 represent the change in the values for 12

temperature, pressure, and velocity derived from test one across the center fuel 13

puck, puck three. Whereas Figures 17-18 represent an approximation of the 14

temperature gradient across all of the fuel pucks within a single fuel rod. 15

16

Figure 14. Total temperature profile across puck three from Test 1 17

18 19

Figure 15. Total pressure profile across puck three from Test 1 20

21 22

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Figure 16. Velocity Magnitude across puck three from Test 1 1

2 3

Figure 17. Temperature contours for all six pucks in sequence 4

5 6

Figure 18. Temperature contour for non-separated configuration 7

8 9 Table 12. Annulus core Phoebus-2A configuration: Test 2 10

Matching the Phoebus-2A run

Conditions Values

Wall Temperature (K) 2256

Propellant Temperature (K) 2158.2

Mass flow Rate (Kg/s) 119

Inlet Pressure (Mpa) 3.827

Core inlet Temperature (K) 77.6

Temperature after Puck 1 (K) 731.12

Temperature after Puck 2 (K) 1166.8

Temperature after Puck 3 (K) 1493.5601

Temperature after Puck 4 (K) 1711.4

Temperature after Puck 5 (K) 1820.3199

Temperature after Puck 6 (K) - Exit 1929.24

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Exit Temperature of the Non-

Separated Model (K) 2147

Historical Exit temperature 2283

1

The second test was run at initial values meant to reflect the actual 2

operating conditions produced by that of the Phoebus-2A engine in order to 3

benchmark the simulation and determine the accuracy of its results. The 4

temperature increase the hydrogen experienced due to the process was, on 5

average, 309.5 K of increase as it passed through the heating channels of each 6

puck, culminating in a total temperature of 1929K at the exit of the core 7

assembly, as seen in figure 21. Additionally, it was noted that the increase in 8

temperature attenuated as the flow passed through the channels of each puck, 9

experiencing lower increases up to the final puck. In the case of the non-10

separate model, the temperature value at the exit of the core, produced a final 11

temperature of 2147 K, was much closer to that of the benchmark case given 12

an 11 K difference in final temperature. Figure 19 shows details of the flow, 13

including boundary layer formation and heat transfer phenomena experienced 14

by the non-separated case for this test. 15

16

Figure 19. Heat transfer in channels within boundary layers 17

18 19

Figure 20. Comparison of exit temperatures between tests 1 & 2 20

21 22

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Discussion 1 2

System Analysis 3

4

With the resolution level of which the system analysis was conducted, 5

yielded similar elements to that of previous generations of nuclear thermal 6

propulsion systems. Simultaneously, the system analysis also revealed that a 7

nuclear thermal propulsion system is capable of reconfiguring for an aerospike 8

nozzle without sacrificing key elements. The reconfiguring of the core into a 9

separated fuel puck system produced evidence that the core has the possibility 10

of a wide range of configurations. A theoretical possibility is that the nuclear 11

core could be made smaller while maintaining equivalent performance levels to 12

that of the current configuration. 13

14

CFD Analysis 15

16

Simulations of the separated and non-separated core configurations yielded 17

similar results in regards to temperature and enthalpy increase of the hydrogen 18

fuel. However, it was observed that the separated puck configuration did not 19

yield higher values as predicted in the initial design phase. In actuality, the 20

non-separated configuration produced fluid temperatures closer to that of the 21

benchmark case. This discrepancy in performance is likely due to the laminar 22

flow-induced into the separated simulations with each puck requiring an 23

isolated simulation. The potential turbulence lost in this process would likely 24

result in more significant fluid interaction and heat transfer. Additionally, it 25

was noted that the temperature increase attenuated towards the end of all 26

simulations, indicating that more extended core designs may prove 27

superfluous, and a markedly smaller system than initially conceived may be 28

achievable 29

30

. 31

Conclusions 32 33

Based on the system analysis and CFD analysis, a nuclear thermal 34

propulsion system has the capability of being redesigned for use with an 35

aerospike nozzle. The CFD analysis also yielded that due to the 36

implementation of the fuel puck design, the core has the possibility of being 37

reconfigured into a more compact design. A design that would still have the 38

ability to produce the same or greater performance than that of the current 39

configuration. Thus, in conclusion, this current configuration provides an 40

answer to limiting factors of modern high thrust rocket engines. By providing a 41

solution to both molecular weight and thrust optimization, this configuration 42

would dramatically influence what humanity can accomplish in space. 43

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