Sunday, October 4, 2015

Nuclear powered VASIMR and plasma propulsion doable now, Page 2.

Copyright 2015 Robert Clark

 In the blog post "Nuclear powered VASIMR and plasma propulsion doable now", I argued that nuclear space reactors already have the capability to do fast transit times to Mars using plasma propulsion systems such as VASIMR or Hall effect thrusters.

Low Power Operation for Long Life.
 However, there was a key fact left out of that analysis: when space nuclear reactors are run at full power they only have limited lifetimes, measured in hours:

Bimodal NTR.
Engine (Thrust Mode)
Thrust per engine 67,000 N
Total Thrust 200,000 N
T/Wengine 3.06
Exhaust Velocity 9,370 m/s
Specific Impulse 955 s
Mass Flow 7.24 kg/s
Full Power
Engine Lifetime 4.5 hours
Reactor Power 335 MWthermal

 This is alright for the applications usually thought of the nuclear rocket engines where they are used only for a few minutes for takeoff and landing.
 But for plasma propulsion as with other types of electric propulsion they achieve high speeds by running them continually for days. Note though that in examples such as the Bimodal nuclear thermal rocket (NTR), they have two modes of operation, a propulsive mode at full power, and an electricity generator mode at greatly reduced power.
 It is in the low power, electricity generator mode that they can run for months to years. Then one idea to deal with the short lifetime at full power is to run the engines at an intermediate power level that will allow them to run for just the few days needed for plasma propulsion.
 We'll use this report to estimate the possible run-times when operated at lower power:

A One-year, Short-Stay Crewed Mars Mission Using Bimodal Nuclear Thermal Electric Propulsion (BNTEP) - A Preliminary Assessment.

 This report is interesting in that it uses the nuclear thermal engines for high thrust maneuvers such as Earth departure and slowdown at Mars arrival, and electric propulsion for the long interplanetary traverse to Mars. I envision as well low thrust electrical propulsion would be best utilized if they spacecraft is sent far outside Earth's deep gravity well by either chemical or nuclear thermal propulsion before the electrical propulsion system is turned on.
 The full power level for the engines used in the report is 545 megawatts thermal for each of the three nuclear engines, at a weight of ca. 2,200 kg each. They would only be run at full power for less than two hours however. Most of the trip the engines would be run in low power mode:

 For the 1-year round trip BNTEP mission, the total operational time for the BNTR engines is 324 megawatt - days (MWD) which includes 1.75 hours of high thrust / high power mode operation totaling 40 MWD and 284 MWD of reduce power EP mode operation. Assuming 1.2 grams of U-235 consumed per MWD, the total U-235 fuel loss in each engine is 389 grams. Since each cermet fuel BNTR has in excess 200 kg, the burn-up is less than 0.2% which is quite acceptable.

A One-year, Short-Stay Crewed Mars Mission..., P. 7.

 Then to get a maximum of 324 megawatt-days while using it only in the long life, low power mode for say a 39 day flight time, that would correspond to a power level of 8.3 megawatts for each engine. At a weight per engine of 2,200 kg, that corresponds to a specific power of 3,800 watts thermal per kilo.

Long Life by Multiple Nuclear Fuel Canisters.
 The above method would be to run the engine just at much reduced power to get the long life. Another method would be to run the engine at full power but just have multiple nuclear fuel canisters that can be used when one gets depleted. The mass of the fuel as given in that passage above from "A One-year, Short-Stay Crewed Mars Mission", page 7 is 200 kg. The run time for the engine at full power is given in that report as 2 hours. Then for a 39 day run time you would need (24/2) * 39 days = 468 fuel canisters, for 468 * 200 kg = 93,600 kg. Plus the 2,200 kg for the engine this would be 95,800 kg for the nuclear power system. Since in this case the engine is always running at full power this would be 545,000,000 W/95,800 kg = 5,700 watts thermal per kilo specific power. You could improve the average specific power perhaps by a factor of 2 by jettisoning the depleted fuel canisters.

Short Flight Time Actually Gives Smaller Mission Size.
 Actually in a follow up post I'll discuss the specific power is actually higher in both these methods because the engines will not have to be run the entire 39 days to get the high delta-v needed for the short flight times. The main reason is you can use a much smaller habitat perhaps only 6 metric tons when the flight time is only about a month compared to the 25 metric tons or higher usually estimated for a 6 to 8 month flight time. I discuss this in the blog post, "Propellant depots for interplanetary flight." This then would translate into a smaller fuel load and shorter burn time.

 In fact, the surprising conclusion you get is the short flight time requiring high delta-v results in a smaller mission size.

Efficiency of Conversion to Electrical Power.
 Remember to get VASIMR or Hall effect thrusters at the 39 day flight time, we only need 1,000 watts per kilo as discussed in "Nuclear powered VASIMR and plasma propulsion doable now". But this has to be electrical power, not the thermal power of the NTR's. To get the conversion of the thermal to electrical power, I suggest turbines modeled on the Space Shuttle SSME's hydrogen turbopumps. These have a remarkable power to weight ratio of 150,000 watts per kilo, and efficiency of 80%:

Space Shuttle Main Engine Orientation.

 The "turbine efficiency" in the table is the isentropic efficiency. This is the percentage of the ideal efficiency possible with no loss of heat or friction losses. But what we really need to know is the thermal efficiency, the percentage of the thermal energy converted to mechanical power by the turbines.
 Note that the thermal efficiency is limited by the Carnot limit, dependent on the temperature of the thermal source compared to the temperature of the outlet. For the SSME turbopumps the temperature drop is not very large, necessitated by requiring high pressure for injection into the combustion chamber:

 However, by being a space reactor we can have the pressure of the outlet be near vacuum and therefore get a much larger temperature drop. Then the Carnot limit can be above 90% and the 80% isentropic efficiency can put the thermal efficiency above 70%.
 Once you have the conversion to mechanical power the conversion then to electrical can be 95% efficient.
 Ground based power plants including nuclear ones may only get thermal conversion efficiency of ca. 30%. But this is limited by the Carnot limits of the temperatures of thermal source compared to that of the outlet, typically a cold water reservoir.
 For the nuclear powered electrical propulsion, we want to have high efficiency to avoid needing large, and heavy, radiators, to reject the waste heat. If the efficiency were only 30% or below, most of the energy produced is simply thrown away and at great mass penalty.

Can We Improve the Burn Lifetime of Space Nuclear Reactors?
 Space nuclear reactors have full-power lifetimes of just a few hours. This is compared to the fuel burn time of a few years for ground-based nuclear reactors before they need to be refueled. This is due to high temperature and high power level for their size for the space reactors. Indeed the temperature might be 3 times as high at full power for the space reactors compared to the ground ones.
 Most disconcerting is the very small amount of nuclear fuel that actually gets burned because of the short runtime for the space reactors. From that passage in "A One-year, Short-Stay Crewed Mars Mission" cited above, only 0.2% of the nuclear fuel may get burned during the engine lifetime.
 Compare this to the burn-up in ground-based reactors that might be in the range of 6.5%:

The Nuclear Fuel Cycle.

 The reason why only a small portion of the nuclear fuel gets burned in any fission reactor is because the fission products after awhile build-up and inhibit the fission process. And the higher the power the reactors are run at for their size, the faster is the build-up of these fission products.
 Then a proposal that might lengthen the lifetime of the space reactors is not to burn the fuel all at once but burn it in layers, outside in. If the layers are thin enough, we should get little blockage from the fission products. Once an outer layer fuel got consumed, we would remove that layer and allow the next layer in to react.
 If we could get most of the fuel to be consumed, then we would need much less radioactive material to be sent to space so nuclear space propulsion would be much less controversial.
 This method might also work for the ground based reactors. If the ground based reactors could use most of the fuel, much less uranium would be needed to operate a reactor and you would have lower operation costs and radioactive waste being produced.

  Bob Clark


  1. Im not sure you got this right.

    You are heating some mass of hydrogen to maximum temperature allowed by the wall of the reactor. Then trough the turbine to near vacuum. Electrical power produced is thermal energy at the start minus losses. Then use that energy to give a small amount of hydrogen alot of kinetic energy, trough vasimir system.

    Mass of hydrogen going trough the turbine is many times greater than that being expelled trough vasimir. And 30 to 40% of the reactor energy still has to be expelled with radiators. As if you are expelling hydrogen at the end of turbine cycle, ISP goes down down down...

    1. As you indicated in your follow-up comment, the idea was for this to be closed-loop reactor system. So you would have a working-fluid for the nuclear reactor system that went through a heating and cooling cycle. But separate from that you would have a propellant that got accelerated by the electric propulsion system for thrust.

      However, I'm looking at the possibility that we could use a single fluid for both. We would have to optimize the heating through the nuclear thermal component and the electric acceleration component.

      Bob Clark

  2. To expand on ma previous comment.

    I know the system you were thinking of would be closed loop. But afaik for efficiency reasons Brayton systems are designed for lower pressure and temperature ratios.

    Like for example project Prometheus, where the system is designed to operate at full power for 10 years. Power to weight ratio is low, 30w/kg. Which includes 500m2 of radiators for 1mw of thermal output from the reactor. Generator efficiency is about 20%.

    SSME turbopump is bad comparison for these systems as it was only supposed to operate for 7 hours before overhaul. And it ran cooled by cyrogenic propellants. Btw, turbine in the case of Prometheus was suposed to be also 85+% efficient.

  3. Thanks for the response. Ten years for the Prometheus would be a long time for a nuclear reactor. In the reference I cite in the post, "A One-year, Short-Stay Crewed Mars Mission Using Bimodal Nuclear Thermal Electric Propulsion (BNTEP) - A Preliminary Assessment", to get long lifetime in the range of years they have to run the reactor at greatly reduced power level. This reduces the power-to-weight ratio.

    In my proposal since it only has to run for days, you run the reactor at an intermediate power level. This means the power to weight ratio is much higher, in fact higher than the 1kW/kg level required for VASIMR and other plasma propulsion methods such as Hall effect thrusters.

    Actually in an upcoming blog post I'll discuss that since the time it needs to run is shorter than 39 days, you can run it at even higher power level so the power-to-weight ratio is even higher than I indicated here.

    I cited the case of the SSME hydrogen turbopumps because they had high power-to-weight and high efficiency of 80%. However, in looking up other turbine generators I found that even 90% efficiency is not uncommon. So this high efficiency is actually a common occurrence for long running power turbines.

    In regards to getting lightweight turbines, recent research shows supercritical CO2 for the working fluid gives turbines a fraction of the size for steam turbines.

    I'll discuss these factors in an upcoming blog post.

    Bob Clark

  4. Reactor with Cermet fuel tubes has maximum tolerable temperature of 3000k. Below that, its almost indefinite. Reason for lower power level is that radiator is too small or not efficient enough. Operating as NTR there is no problem rejecting this much heat with hydrogen exhaust.

    Your fuel canister idea wouldnt fly, as canister is basically the whole reactor, and 200kg of uranium is enclosed in cermet matrix, which is about as heavy. Not to mention it could be used for more than one mission.

    You might have noticed that 1MWe module had a mass of about 25t, which is about 40w/kg.

    In the prometheus concept, they limited the temperature to the turbine to 1150K. Limited by material. Maybe in the last 10 years the state of the art moved to 1300K, maybe. That still leaves the reactor waay hotter than needed. Lowering the temperature in the reactor would not reduce its power output. It could in fact increase it as the temperature difference between uranium fuel core and coolant is greater.

    Heat rejection in prometheus was at 500K. That gives the temperature range. Lower heat rejection temperature means bigger radiator. Higher turbine temperature is limited to material durability. There seem to be commercial gas turbines that operate at higher temperatures, but they have their blades cooled by channels inside them.

    As for supercritical fluids:

    This assumes heat rejection at 800+K. Minimising radiator mass while keeping efficiency at somewhere around 20%.

    To make the powerplant specific power greater than 1kw/kg means all the parts that pass power has to have greater specific power. And even higher to compensate for structure, coolant, and shielding.

    For a bonus:

    A rankine cycle power concept, 1mwe, up to 95% efficient turbine while cycle efficiency is 11%. No weight citations sadly.

    Basically most of what you mentioned on these 2 blog posts is just a miss in terms of physics limits.

    For last:
    A detailed case, 17kg/kw or 59w/kg power system and comparison with hall and vasimir. In which vasimr loses...

  5. Thanks for that link:

    Conceptual Design of a CERMET NTR Fission Core Using Multiphysics Modeling Techniques.

    For a 512 megawatt thermal reactor it gives the reactor mass as 2761 kg. You are quite correct the total reactor mass, with the containment vessel, CERMET (ceramic-metallic) high temperature materials, and control rods is much more than just the uranium fuel. For this reactor it is at about 185,000 watts thermal per kg specific power.

    It turns out this would still work to provide the needed 1,000 watts electric per kg specific electric power needed for the plasma propulsion IF you dispensed with the used up fuel elements. This is for the scenario I mentioned where you run continually at full power, while getting a longer run time by replacing the used fuel elements with new stored ones. I mentioned in the blog post you could improve the average specific power by jettisoning the used fuel elements. The average specific power then, even with the ten times higher reactor mass, calculates out still to give the high specific power needed.

    And the situation becomes even better when you take into account you actually only have to run the reactor a few days, not the full 39 days, to get the speeds needed for the fast trip, due to the low habitat mass when you have a fast trip.

    If it is the case you can have almost indefinite lifetime when run at low power then that would be actually better since I would not need to keep unboard the extra fuel elements so the overall specific power would be even higher. However, there should still be the problem of "burn-up" that should limit lifetime.

    BTW, there was recently published a new proposal for a space nuclear reactor that has even better specific power:

    Innovative concept for an ultra-small nuclear thermal rocket utilizing a new moderated reactor.
    Nuclear Engineering and Technology.
    Volume 47, Issue 6, October 2015, Pages 678–699

    It would give 100 MWt at a reactor mass of only 180 kg, for a specific thermal power of 550,000 watts thermal per kg.

    About the poor specific power of the proposed Prometheus nuclear reactor I suspect the reason it had such long lifetime was specifically because it ran at greatly reduced power. For instance, in that "ultra-small" reactor discussed in the above paper, it has a low power electricity generator mode at only 100 kWt, 1/1000th the power of full power. So when you take this into account the Prometheus reactor would have a much better specific power if it had been run at full power, though then at much shorter lifetime.

    In regards to the higher radiator mass for high efficiency conversion, due to the low output temperature, in a follow up blog post I'll show you can have actually zero radiator mass due to the low output temperature. This is possibility that does not obtain for the low efficiency, high output temperature scenario.

    1. The last link I provided is a study of 1mwe cargo transport.

      On the page 13 there is a list of masses of individual components of power supply. Reactor core itself makes only 6% of that, a turboalternator (im assuming its turbine compressor and an alternator) only 1.3%.

      Turbine temperature at 1150k and heat exchanger at 450K. Im assuming the designers are competent and designed the least heavy system they could.

      As for low output temperature, in case second law still holds, and you use a liquid droplet radiator. The boom that dispenses this liquid and collector and the liquid in question still have some weight. Physics of it is similar to a normal radiator, just that the surface are is made of individual droplets.

    2. A key distinction not being considered is the possibility of running the reactor at an intermediate power level. They are either run at full power for propulsion of at 1/1,000th power for electricity generation.

      It is the greatly reduced power that allows them to run for years, in the range of 5 years in this report, in the electricity generation mode. But for the plasma propulsion we only need it to run for a few days. In this case the power level may only need to be reduced by ca. 1/10th. This results in a much higher specific thermal power.

      About the conversion to electrical power the recent advances discussed in Part 1 plus cryogenics can give specific electrical power also above the 1,000 W per kg mark.