4.2 Nuclear Thermal Rocket
Adam Irvine
Nomenclature
Ae = exit area of nozzle
At = area of the throat
Isp = specific impulse, seconds
mprop = propellant mass, mT
mpay = payload mass, mT
ε = area ratio = Ae/At
λ = inert mass fraction
4.2.1 Introduction
The mission of the upper stage propulsion system is to first perform an inclination change in low earth orbit (LEO) and then inject into an interplanetary trajectory to Mars. The propulsion system must be ready to launch by 2011, when the first ERV launch will take place.
4.2.2 System Selection
We will consider using either chemical or nuclear propulsion systems for the upper stage. While there are better propulsion systems in development these two feasibly can be ready by the first launch date. There are two major factors that determine the payload capability of the system, and these are the specific impulse, Isp, and the inert mass fraction, λ. Chemical systems have superior values for λ (i.e. close to zero) while nuclear systems are superior in Isp (capable of over 1000). A simple calculation of the payload capability of both systems can be done to determine which system is better. Assuming an 80 Tonne payload and using typical values for Isp and λ for both systems we get the results shown in Table 3.2.1 by using eq. 1 and 2:
(eq. 1) (eq. 2)
Table 4.2.1 Comparison of Chemical vs. Nuclear
Propellant / Inert / SystemIsp (sec) / λ / mass (mT) / mass (mT) / mass (mT)
Chemical / 400 / 0.1 / 196.99 / 21.89 / 218.88
Nuclear / 1000 / 0.3 / 56.71 / 24.30 / 81.02
It is obvious that the nuclear system performs far better than a chemical system despite the larger inert mass fraction. Cost to develop the nuclear system it be greater; however, will cost less than the cost of building an enormous launch vehicle to lift the nearly 300 Tonne chemical upper stage to LEO. A benefit of using the nuclear system is that technology gained from development would benefit space missions outside the scope of this mission.
4.2.3 Nuclear Thermal Rocketry
A nuclear thermal rocket (NTR) is not a new system; the first program to develop these engines started in 1955, and ended in 1972 due to budget cuts. The Nuclear Engine for Rocket Vehicle Applications (NERVA) was developed for this program at the Los Alamos National Laboratory where twenty full-scale engines were built and tested. These engines prove that Isp values of up to 890 sec., 930kN of thrust, and 109 minutes of burn time are possible.1 These engines produce thrust by pumping hydrogen gas through coolant channels in a specially designed nuclear reactor core, and once heated to high a temperature the gas is expelled through a nozzle producing thrust. The performance of these engines is limited not by the temperature attainable by nuclear fission, but by the melting point of the materials containing the nuclear material. Graphite was used in the NERVA program, which limits the operating temperature of the reactor to around 2500K. A reactor can be made using carbide with current materials technology, which could push the reactor operating temperature up to 3250K. Higher reactor temperatures are desirable because as the reactor temperature increases so will the temperature of the exiting gases, and this increases the Isp so it also increases the payload.
The NERVA engines have the same basic configuration as the system we will use for this mission. So the research has already been done and the technology simply must be recovered and then updated using current materials. There are other NTR concepts that offer better theoretical performance over the NERVA derived reactor, but they would require more development and so they would not be ready to launch by 2011. Westinghouse estimates that the development of a NERVA derived reactor could be completed in eight years for 2.5 billion dollars.2
4.2.4 Configuration of Flight System
A basic configuration must be established before specifics of the system can be calculated. Hydrogen is used as the working fluid in NTR because of hydrogen’s low molecular weight, which will maximize the Isp. For a given increase in enthalpy a fluid with a lower molecular weight will increase in temperature more thus resulting in a higher performance. For the reactor depicted in Figure 4.2.1 hydrogen first flows through the nozzle, which is not shown, towards the core in order to cool it. The flow is then split between cooling the radiation shielding and the tie tubes; the tie tubes serve to structurally support the fuel elements in the core and moderate the reaction. Finally the flow is directed through the tubes made into the fuel elements of the core and then ejected through the nozzle with a small amount being redirected to power the turbopump.
Fig. 4.2.1 Cut away view of NERVA reactor.5
The heaviest part of the reactor is the shielding required to limit the radiation exposure of the crew as well as equipment that could be damaged by radiation. The shielding is comprised of beryllium, tungsten, and lithium hydride layers in that order. The beryllium is used because it is an excellent neutron reflector, and so it will not only help to sustain nuclear fission, but will shield the crew in the process. Tungsten helps to limit gamma radiation exposure not sufficiently reduced by the other materials and will absorb some neutrons as well. Finally lithium hydride first slows any stray neutrons with the hydrogen component and then absorbs them with the lithium component. This shielding will only be on top of the NTR to provide a shadow shield for the spacecraft because it is unnecessary to shield space from radiation, which would add weight.
The nuclear core is comprised of several long hexagonal fuel elements made of a uranium zirconium carbide matrix. We are using this combination due to its high melting temperature and lack of reactivity with hydrogen at high temperatures. Reactivity with hydrogen was a problem with the early graphite uranium core NERVA reactors, and an extra coating had to be added to the fuel rods to avoid this. Each fuel rod has several axial holes that allow for fluid flow through the core and down to the nozzle; a picture of the fuel rods is in Figure 4.2.2. The fuel rods themselves and the tie tubes absorb neutrons thereby moderating the reaction, and the control drums are used to throttle the reaction. The control drums throttle the reaction by rotating to expose either neutron reflective or absorbent material. By reflecting neutrons back into the fuel the reaction will increase in rate, and the opposite will happen for the absorbent material. When the reactor is shut down fission is still taking place in the core because not all the neutrons can be absorbed before they react with the fuel. The amount of fuel lost during the operation of the reactor is small, and the amount of fuel leftover is enough to produce heat that can be used to power an electrical system for the spacecraft in transit to mars. This power system is explained in detail in section 8.2.
Fig. 4.2.2 Diagram of fuel rod, and assembled configuration.6
Propellant feed systems need to be sized as well as a disposal system. When the spacecraft comes close to mars the NTR core will have to be placed on a disposal trajectory that will not intersect any planetary bodies, especially Earth. Firing the NTR engines a final time by using a supplementary propellant tank can accomplish this. Propellant will be fed to each of the engines using a separate turbopump and tanks will be pressurized with an inert gas, nitrogen.
4.2.5 NTR design
With the basic configuration chosen the specifics of the design can now be found. First three engines are chosen for safety reasons as well as simplifying development as it is easier to develop a lower thrust engine than a large one. These engines will have a thrust of 74kN for a total thrust of 222kN, which is sufficient to limit the burn time to 60 minutes in the case that one engine fails. This burn time has been demonstrated and exceeded by the NERVA program, and once these engines complete their development much longer burn times will be demonstrated. The operating temperature of the core will be 3250K heating the hydrogen to over 3100K1 and the chamber will be held at 3.5MPa. Knowing the chamber pressure and temperature an Isp of 1033 seconds is calculated. If the massflow of the hydrogen, 7.32kg/s, is known the required reactor power can be found to be 367.8MW by finding the power needed to heat this flow of hydrogen. By using an historical value for core power density, 1570MW/m3, the volume and mass of the core can be found to be 0.2343m3 and 538.8kg respectively. The length and diameter of the core is based on a historical L/D.3
The mass of the shield can be found now from knowing that the thickness of the Be is 18cm, W is 5cm, and LiH2 is 5cm resulting in a density of 3500kg/m3. If the radiation is found to be too high the neutron and gamma ray flux can be attenuated by varying the thickness of each component of the shield. For example if the gamma ray flux is too high it can be decreased by a factor of 10 by increasing the tungsten thickness by 1.9cm.3 The mass of the containment vessel, its cooling, and shielding can also be found with the known chamber pressure and core power.
Now sizing will become more complex as the sizing process needs to be iterated in order to find the optimal solution for the area ratio (ε, area of the exit divided by the throat area), λ, and the payload mass needed to take full advantage of the 179 Tones that can be delivered to low earth orbit. Iteration of these parameters is necessary because there are several masses of the system that are dependent on these parameters. The inert mass fraction will be iterated by first assuming a value for λ. Now knowing that what the changes in velocity for the inclination change, 417m/s, and the trans-Mars injection, 3.65km/s, are we can find a propellant mass.
Now the specifics of the propellant tank can be found, and then the pressurant mass and associated tank masses. The propellant tank will be made of aluminum and kept at a pressure of 393KPa. There is an additional 3% of volume taken into account for ullage. There are four pressurant tanks containing nitrogen that are kept at 21MPa. Turbopump mass takes some effort to find because the pressure drops across the system must be found. Historical trends are used to estimate the pressure drops of the system and the turbopump mass is then found. Disposal propellant requirements are somewhat tricky in that not only must there be enough propellant to dispose of the NTR at mars but there should be enough to dispose of it if the free return trajectory is implemented. This is a problem because the propellant boil-off, 0.043(kg/m2day)7 over such a long trip time, 793 days is significant. Nozzle mass is found by using the area of the throat and exit. Once all these masses are found they are added up to find the inert mass so a new λ is found, and if this λ coincides with the one guessed earlier the iteration is completed, and if not λ is increased or decreased accordingly.
The next level of iteration is finding the correct payload to maximize usage of the payload deliverable by the launch vehicle. This is done by simply changing the payload mass until the payload added onto the propulsion system mass is 179 Tonnes. The final iteration is to find the correct ε, and to do this everything above must be iterated because everything is influenced by it.
4.2.6 Resulting Design
Using the procedure above gives us the system detailed in Tables 4.2.2, 4.2.3, and 4.2.4. Table 4.2.2 shows an overview of the system while Tables 4.2.3 and 4.2.4 show some specifics of the engines and tanks respectively.
Table 4.2.2 System Parameters / Table 4.2.3 Engine SizingNumber of engines / 3 / Per Engine
Total Thrust (kN) / 222.4 / Thrust (kN) / 74.1
Total Delta V (km/s) / 4.067 / Core Mass (mT) / 0.539
Burn Time (min) / 41 / Core Length (m) / 0.9655
Ae/At (E) / 250 / Core Diameter (m) / 0.5558
Propellant (mT) / 56.13 / Containment Vessel Mass (mT) / 0.544
Pressurant (mT) / 1.745 / Turbopump Mass (kg) / 14.7
0.3005 / Nozzle Mass (mT) / 0.192
Inert Mass (mT) / 31.96 / Nozzle Length (m) / 3.535
Structure (mT) / 7.002
Disposal Prop. (mT) / 0.157 / Table 4.2.4 Tank Sizing
Prop. Boiled Off (mT) / 1.149 / Propellant Tank Mass (mT) / 8.3
Total System Mass (mT) / 91.15 / Propellant Tank Volume (m@@@@) / 814
Payload (mT) / 87.86 / Propellant Tank Length (m) / 15.05
Total Mass to LEO (mT) / 179.0 / Pressurant Tank Mass (mT) / 2.52
System Diameter (m) / 8.3 / Pressurant Tank Volume (M@@@) / 47.1
System Length (m) / Pressurant Tank Radius (m) / 1.411
Disposal Tank Mass / 193.2
Disposal Tank Volume (m@@@) / 18.95
Disposal Tank Radius (m) / 1.654
The system is arranged so that the engines are on the bottom with the pressurant and disposal propellant tanks arranged to take full advantage of the space. The main propellant tank is placed above the other tanks with the payload mounted on top of the main tank. We chose this configuration because it is easy to jettison the main propellant and pressurant tanks when the NTR is ready for disposal. This is desirable because decreasing the amount of mass that needs to be propelled for disposal will decrease the propellant needed significantly. A picture of the system is shown in Figure 4.2.3: