Design based on NASA TM X-2772 Reactor Moderator, Pressure Vessel, And Heat Rejection System of An Open-Cycle Gas-Core Nuclear Rocket Concept Link to PDF.
The study describes a preliminary design of a 6000 megawatt open-cycle gas-core nuclear thermal rocket engine purposed to provide for very fast round trip interplanetary missions.
NASA TM X-67823 Gas Core Rocket Reactors-A New Look Link to PDF describes fast manned Mars missions (called currier missions) with durations of 80, 100, 150, and 2OO days. Jupiter and Saturn missions are also considered.
I set out to simply model an open-cycle gas core rocket, everything starts out simple. However, one does not, simply, model an open cycle gas core nuclear thermal rocket.
A number of talented individuals added their expertise to this project, joining in on my G+ discussion threads, you will find them quoted in the text below and credited at the bottom of the page.
Of note, Dogmatic Pyrrhonist, talented creator of KSP mods, lent his design insight. Dogmatic Pyrrhonist’s eye for realism in engine detailing is impeccable, and I’ve learned a great deal from his design thought as we shared results in the process of modeling our respective engines.
The Open Cycle Gas Core Rocket
Like the solid-core nuclear rocket engine, the job of a gas-core engine is to heat hydrogen and then expand it through a nozzle to convert the thermal energy into thrust. In order to obtain a higher specific impulse than the 825 seconds of the solid core, a gas core has to produce hotter hydrogen. For a specific impulse of 825 seconds, the hydrogen temperature at the nozzle inlet is approximately 2500 K. A temperature of 22,000 K is required for a specific impulse of 5OOO seconds. The temperature levels required for specific impulses in the range 3000 t o 5OOO seconds cannot be obtained by simply running solid-core type fuel elements at a higher temperature because the uranium, must be hotter than the hydrogen, and at these elevated temperatures the fuel elements would simply melt and vaporize.
The gas-core concept is to use an incandescent, radiating ball of fissioning uranium plasma as the "fuel element." The nuclear heat released within the uranium plasma leaves its surface in the form of thermal radiation, or photons. This thermal energy is picked up by a surrounding stream of hydrogen propellant, which is then expanded through a nozzle to produce thrust.
Description and Specifications
The reactor is spherical: a titanium pressure shell with an internal 4.267-meter (14-ft) cavity surrounded by a 0.61-meter (2-ft) thick Beryllium oxide (BeO) reflector-moderator. The reactor is fueled with enriched uranium (98 percent U235) and generates about 6000 megawatts of thermal energy, with a hydrogen propellant flow rate of 4. 54 kilograms per second (10 Ib/sec).
Engine thrust: 196,600 newtons (44, 200 Lbs). Specific impulse: 4400 seconds.
The study notes these data are consistent with a mission analysis of a very fast 80-day manned Mars round trip (Mars courier mission) with an engine having a total weight of about 100,000 kilograms.
The edge or radiating temperature of the plasma is about 26,000 K (47,000 R). The hydrogen propellant is seeded with about 10 percent by weight of small particles (about the size of smoke particles) which absorb the thermal radiation from the plasma and then convectively heat the hydrogen. The seeded hydrogen enters the cavity through porous or slotted walls.
The study suggests seeding material of either graphite or tungsten.
Hydrogen, unfortunately is transparent to gamma radiation. Hence the seeding.
As example, Winchell describes the properties of the seeding material, per use in a Nuclear Lightbulb engine.
In the nuclear lightbulb: The tungsten dust that the propellant is seeded with has a particle diameter of 0.05 microns. The seed density is 1.32 x 10^-2 lb/ft^3, which is about 3.9 percent of the inlet propellant density. This can probably be reduced if tungsten dust was in the form of thin flat plates instead of spherical particles.
Physicist Luke Campbell
Graphite and tungsten are the two things that stay solid at higher temperatures than anything else. Seeding [the propellant] gives you a reasonable amount of black-body radiation, whereas the gas would be optically thin and not thermally radiate much. Then you could couple the heat from the reactor to the propellant via radiation.
As Winchell Chung observes, only in rare cases (like chemical propulsion) are propellant and fuel the same thing.
For the gas core rocket, the fuel is enriched uranium (98 percent U235 ) and hydrogen is the propellant. For a typical Mars mission the gas core rocket needs 3,350 kg of enriched 98 percent U235 .
Because it is enriched uranium criticality is a concern.
[The uranium] embedded in a waxy substance. For example wax, or LDPE. The wire-rod form could just be plastic-coated. The powder form could just be evenly distributed particles in bulk plastic.
To access it for propulsion, you simply easily melt away the plastic.
Plastic and wax would act to moderate the neutrons, increasing your criticality problems. You might get around this by heavily loading the wax/plastic with boron or lithium or gadolinium, which are good at absorbing thermal neutrons.
Reactor startup would be achieved by first establishing the hydrogen flow. Next uranium particles would be blown into the dead cavity region to achieve nuclear criticality. The power would then be increased to a level sufficient to vaporize the incoming uranium rod.
A possible fuel injection technique consists of pushing a very thin rod of solid uranium metal through a shielded pipe (perhaps made of cadmium oxide) that penetrates the moderator. As it enters the cavity, the uranium vaporizes and rises in temperature to about 55,000 K.
Criticality is maintained by adding uranium and increasing the hydrogen pressure till full power is achieved. Thereafter, only enough uranium is added to the plasma to make up for the fuel loss to the propellant. Based on flow experiments the uranium loss rate is expected to be of the order of l/100th of the hydrogen propellant flow rate. The reactor can be shut down by simply turning off the uranium fuel supply.
Radiative Cooling versus Regenerative Cooling
For the initial research an upper limit of 3000 seconds on specific impulse resulted from the use of only regenerative cooling to remove heat deposited in various parts of the engine structure. Higher specific impulses would require a space radiator.
Seven percent of reactor power is expected to be deposited into the reflector-moderator (as 420 megawatts of waste heat) by the attenuation of high-energy gamma and neutron radiation. The waste heat is rejected to space by an external high pressure helium gas, fin and tube type, radiator.
NASA TM X-2772 suggested rectangular radiator panels arrayed around the rocket nozzle and, what immediately struck me about this configuration, is the that radiator panels in this arrangement would reflect radiation foreword, irradiating vehicle and crew. So, a long truss was needed to carry much longer, radiator panels of a truncated triangular form, positioned forward of the engine – the truncated triangular panel conforms to the safe conical radiation shadow cast by a shadow shield.
This called for a 54.5 meter (178.9 ft) truss between gas core reactor and propellant tank to carry four radiator panels, in cruciform configuration.
Radiator panels are 51.4 meters (168.9 ft) long, with a forward elevation (above and below the truss) of 29.9 meters (98.1 ft) and an aft elevation of 3 meters (9.8 ft).
Radiation Shadow Shield
Note that fission neutrons and gammas will scatter off of anything they can reach, turning each unshielded strut and pipe and surface into another radiation source. The shadow shield will need to intercept all these scattered neutrons and gammas as well as those directly streaming from the reactor – you probably want it so that anything on the shielded side can't see anything on the unshielded side without going through the shadow shield.
Struts can pierce the shield if they zig-zag. That way, radiation can't take a straight path through – it might follow a strut part way, but then plow into the borated poly when the strut turns.
Shared NASA TM X-67927 Crew Radiation Dose From The Plume of A High Impulse Gas-Core Nuclear Rocket During A Mars Mission Link to PDF
The study is focused on that part of the total radiation problem that arises from the fission fragments in the gas core rocket plume volume, examining crew dose in two locations (100 and 200 meters from the plume source) for specific missions. The missions chosen are manned "courier" round-trip missions with durations of 80, 100, 150, and 2OO days. These fast trip times require a large number of megawatt hours of energy, and crew radiation dose is a function of the energy required for a mission.
As it turns out, I needed that length of truss.
Atomic Rockets Link Crew radiation dose from plume of Gas-Core rocket
In the open-cycle gas-core nuclear rocket concept the heat source is fissioning uranium gas. This released heat is radiated to and absorbed by the hydrogen propellant. The heated propellant is exhausted through a nozzle, producing thrust. The fission fragments that are formed and the unfissioned uranium fuel are also exhausted into the vacuum of space. As the plume is formed, the crew is exposed to gamma radiation from the fission fragments in the plume.
The radiation dose to the crew from the fission fragments in the plume can be separated into two components. Component one results from the fact that there is a microscopic amount of plume material that has sufficient kinetic energy to flow back towards the vehicle. Some of this material will strike and stick to the vehicle. Since this material will contain fission fragments, these gamma radiation sources will stay with the crew throughout the entire trip and this dose could represent a significant source of radiation. Masser(3) has estimated this dose and has concluded it would be less than 10-3 rem for a typical manned Mars mission.
Component two of the dose results from the fission fragment distribution throughout the entire plume volume and is potentially much larger than component one. Since the plume contains over 99 percent of the exhausted material, 99 percent of the fission fragments will be in the plume. It is the purpose of this paper to estimate the radiation dose rate and total dose to the crew from the fission fragments in the plume for four specific missions to the planet Mars.
Another source of radiation is caused by the delayed decay of the fission fragments that are passing through the nozzle. This includes delayed neutrons which can cause secondary fissioning and gamma's. This source, however, has not been included. There is another radiation source associated with the gas-core reactor, that of the reactor core. This radiation source, along with solar radiation, must be ultimately considered when total dose rates to the crew are evaluated. This study, however, is concerned only with that part of the total radiation problem that arises from the fission fragments in the plume volume.
For the most probable fission fragment retention, time of 100 seconds, and crew nozzle separation of 100 meters, the radiation dose varied from 170. to 36. rem for the 80 and 200 day round trip times respectively. Five centimeters of lead shielding would reduce the radiation dose by two orders of magnitude, thereby protecting the crew. The increase in vehicle weight would be insignificant. For example, a shield of five centimeters thickness and four meters in diameter would add 7120 kilograms to the vehicle gross weight of 0.94 million kilograms. Also additional attenuation is available In the form of liquid hydrogen propellant, spacecraft structure, nuclear fuel, equipment, and stores.
Lead would be good for shielding against the prompt fission gamma rays and the gamma rays from the radioactive decay of the fission products and actinides. It would be a poor choice for protecting against neutron radiation. For that, you will want several (or several tens) of cm of iron to slow down fast neutrons to less than an MeV via inelastic collisions with the nuclei (these are collisions that leave the nucleus in an excited state, whose energy comes from the kinetic energy of the neutron), then another several tens of centimeters of borated polyethylene to slow down and absorb the slower neutrons. Make sure to put the lead shield behind the neutron shield, so the neutrons encounter the iron and borated poly first (neutron reactions can also generate gamma rays, but not so much the other way around).
Running a few numbers, over the energy range typical of reactor neutrons, it will always be more mass effective to skip the iron part of the shield and just add more polyethylene. For the prompt fission neutrons you will be looking at something like a 1/e interaction length of about 10 cm. Each interaction will scatter the neutron and on average its energy will drop by half. The interaction length decreases with each scatter until you get to a broad plateau of a 1 cm scattering length for energies less than 100 keV - this will take about 3 to 4 scatters on average to reach from fission spectrum neutrons. Then you are looking at another seven scatters or so until the energy drops low enough that it will be sopped up by the boron. Since the interaction length keeps decreasing, and because it is a random walk type process (with the neutron going backwards as well as forwards), you can probably assume that any neutron will be absorbed within about 10 cm of where it first scatters. So if you want to decrease the neutron flux by a factor of 10,000, you will need a thickness of [ln(10,000) + 1] * 10 cm ~= 100 cm of borated polyethylene.
On Luke Campbell’s recommendation I elected to go with 5% borated polyethylene rather than the layered lead and polyethylene, and increased the shadow shield diameter from the report recommendation of a 4.26 meters (14 ft) diameter shield to a 100cm (3 ft) thick by 6.7 05 meter (22 ft) diameter shadow shield.
Data for 5% Borated Polyethylene Neutron Radiation Shielding, scroll down at the link, DEQ Tech
Hydrogen Atom Density/cm^3: 7.5 x 10^22
Natural Isotope Distribution: 99.98% 1H
Boron Atom Density/cm^3: 3.0 x 10^21
Total Density: 1.08 g/cm^3 (67 lb/ft^3)
Macroscopic Thermal Neutron Cross Section: 2.00 (cm^-1)
Gamma Resistance: 5 x 10^8 rad
Neutron Resistance: 2.5 x 10^17 n/cm^2
As noted above Dogmatic Pyrrhonist and I had been working out the design of our gas core rockets and sharing the results. On one of Dogmatic Pyrrhonist’s threads Ron Fischer offered the following insight:
You can use lighting and shadows in your CG rendering program to analyze your shadow shield, this is where the original math for lighting simulation came from: radiation studies on tanks in the 60s. This is (oddly enough) where computer graphics lighting began. I cannot find an exact reference but believe it was Lawrence Livermore Labs. Might as well go "Back to the Future" on that one!
I found this to be a compelling proposition, an opportunity to test out the validity of one’s design.
Dogmatic Pyrrhonist and I both set about individually setting up a radiation simulation by CG lighting; his results are to be found at links in this thread November 6, 2015
For more detail and my results see Radiation Design by CG Modeling.
Integrated Elements of The Open Cycle Gas Core Rocket
So, rather than a simple gas core rocket diagram, we have the integrated elements of the radiatively cooled gas core rocket, the gas core reactor, shadow shield, and entire propulsion bus, the radiator panels, and a hydrogen propellant tank (one of four) scaled for the proposed 80-day Mars courier mission.
The R.A. Heinlein
Open-Cycle Gas-Core Nuclear Thermal Rocket
Mars Courier Mission, Earth-Orbit Escape Burn With Radiator SFX
Mars Courier Mission, Earth-Orbit Escape Burn
Mars Courier Mission, Earth-Escape Tank Jettison
Radiation Design by CG Modeling
Gas Core Rocket New Radiation Simulation
A number of talented and knowledgeable individuals joined in on my G+ discussion threads lending their expertise to this project. I would like to express my thanks and appreciation to the following individuals for their contributions:
Winchell Chung of Atomic Rockets
Luke Cambell, Physicist
Dean Callahan, Smithsonian Institution
Dogmatic Pyrrhonist, talented creator of KSP mods
Ron Fischer, Virtual Production Engineer
this would mean less piping mass, less overall mass for tank plus shadow shield, less truss mass because the truss would no longer have to support the propellant mass.
Is there a reason for mounting the lh tank forward of the truss?
Yes. There are several reasons.
This is the basic propulsion bus diagram for a gas core rocket, it is not a complete mission-spacecraft.
Mission scenario's for the propulsion system involve clustered tanks, and tank jettison scenario's. So for different planetary missions you have a cluster of tanks, the number of tanks depends on the mission. The single tank shown is a representative tank, it is scaled for the volume of propellant required for the Mars-escape/Earth-capture leg of a manned Mars courier mission scenario.
The Mars mission scenario requires a cluster of four LH2 tanks, three of which are jettisoned. Dropping that mass of empty tankage is critical to the overall system performance. Moving the LH2 tanks in among the radiator panels makes for problematic (impossible, really) tank jettison scenarios.
Moving the tank cluster behind the radiator panels creates several additional problems, each of which increase the overall mass of the spacecraft.
It seems to me you could save considerable mass by mounting the tank just forwardof the reactor, integrating the shadow shield into the aft tank cover.
You cannot just shadow one tank, the entire tank cluster needs to be within the shadow region, you would need an even larger diameter (and thus more massive) shadow shield. This is not better, it is worse. This is what I meant when I said your suggestion creates a worse problem: It increases the total mass of the spacecraft.
Your suggestion increases the spacecraft mass in another way as well. As I've explained, you need to jettison empty tank mass over the course of a mission, so the LH2 tanks cannot be in among the radiator panels, these would still need to be forward of the tank cluster.
Your suggestion trades a single long LH2 line for at least two long high pressure helium lines, because you need to transfer helium coolant from the reactor to the radiator panels and return coolant to the reactor. So there is no magical mass savings with your suggestion.
You end up with more mass in terms of plumbing, not less.
You also get a free secondary shadow shield with the forward cover.
You get some radiation shielding benefit from structure, but in itself the tank end is insignificant in terms of radiation protection; you get more shielding from the hydrogen in the tank than from the structure of the tank itself. The shielding effect of the tank (and hydrogen it contains) is the same value regardless of where the tank is located in the propulsion bus stack.
this would mean less piping mass,
No it would mean more mass in terms of plumbing as explained above.
less overall mass for tank plus shadow shield,
No it would mean a larger and more massive shadow-shield, and more plumbing mass, as explained above.
less truss mass because the truss would no longer have to support the propellant mass.
You seem to be thinking that you can substitute a length of LH2 tank for a length of truss, but that really is not the case.
The spacecraft needs a crew/nozzle separation distance between 100 and 200 meters. The length of truss is a relevant design feature, not something to be eliminated. I've taken the necessary crew/nozzle separation distance into account in my design. See the reference in the caption text for NASA TM X-67927 “Crew Radiation Dose From The Plume of A High Impulse Gas-Core Nuclear Rocket During A Mars Mission” and the linked pdf.
The truss also supports the radiator panels. You could make the radiator panels shorter, but then they need to be wider, the area of the panels must remain the same, and making them wider effects the shadow shield geometry, the radiator panels must be within the radiation-shadow-cone cast by the shadow-shield, if they "poke" through the shadow-cone, radiation will travel along them and scatter forward onto vehicle and crew. Making the radiator panels shorter and wider still would not mean you could have a shorter truss due to the required separation distance between crew and nozzle.
It's not really a question of the truss "supporting the propellant mass" there is more than one dimension to it.
The structural truss only needs to be strong enough to bear the force of the engines thrust, and sustain structural integrity under any shear or torque forces generated by orienting the spacecraft for orbital plane changes and course correction burns, regardless of how you arrange vehicle components. Rearranging the spacecraft does not mean you get to use lighter/weaker structural elements. There is no magic way to shave mass here.
I suppose because of the energy content, you're less likely to use up Uranium 235 as quickly though. Then again, once you start a reaction, you'd better use the resulting energy effectively...
Real spacecraft are governed by Newton’s laws of motion and the Tsiolkovsky rocket equation. The tyranny of the equation dictates that every gram counts.
For a real spacecraft the course is plotted in advance, propellant and fuel load are calculated based directly on the mass of the vehicle, the efficiency of the engine, and the delta-v changes necessary to accomplish the mission.
If by some extremely foolish or unthinking act, you manage to run out of propellant you will not be “dead in space …” Newton’s first law of motion applies: “Every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force.”
So, without propellant you just keep going, in whatever direction you are traveling … forever. Or until you hit something. Or until the gravitational pull of a planet or asteroid alters your course. And then you hit something. You’ll likely, depending on your final velocity, wind up in a long elliptical orbit about the sun … for all of eternity. Unless you are traveling fast enough to slip the gravitational pull of the sun … then you can enjoy that long slow tour of the cosmos … until the sandwiches run out, or you roast alive or suffocate because your life support system stops working.
Fun video that drives this home Sir Isaac Newton is the deadliest son of a bitch in space
The only work-around is wilderness ISRU (in situ resource utilization) … If your spacecraft carries the necessary equipment for wilderness ISRU (highly unlikely), you better have propellant to get to the nearest rock where water-ice exists in abundance.
If you exhaust your nuclear fuel, you are probably dead, but certainly not “dead in space.” You’ll just be off an infinitely slow tour of the cosmos … see final options above.
By the way, notice the names mentioned in the video, Servicemen Burnside is Ken Burnside (google search Game designer. Purveyor of recreational mathematics. Writer.) author of The Hot Equations highly recommended essay on space combat and realistic propulsion systems found in this collection Riding The Red Horse, and, of course, Servicemen Chung is Winchell Chung of Atomic Rockets.
I should probably add that, this particular spacecraft, is interplanetary, suitable for missions only between bodies of our own solar system. Your suggestion of "Bussard collectors" (I assume) is a reference to the Bussard Interstellar Ramjet ("Bussard collectors" is STNG techno-babble, which doesn't actually describe any technology, existing or proposed). Bussard's ramjet concept has a velocity requirement absurdly higher than any velocity this vehicle would attain. You simply do not need to be moving at significant percentages of c to span distances between the planets of our solar system.
Thanks for explaining the difference to me! That is something I'll always keep with me.