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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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