A plumbers guide to starships
Part 5- Pumps, turbines and compressors
Image 1) From a water wheel to a gas turbine; what next?
Secondary systems
The Icarus starship will be powered by a glorious fusion drive pumping out tens of thousands of GigaWatts of power. This will serve as a handy power source for secondary electrical systems, such as injectors, implosion lasers or propellant ionisation systems, that will themselves require hundreds of GigaWatts of power for their operation. However, before the drive is turned on, and during the seventy year long coast period during which the drive is off, more modest third tier power systems, providing a few MegaWatts of power to heat the ship, charge capacitors or drive maneuvering thrusters, will also be needed. An independent, mid sized nuclear fission of fusion power source is therefore required for the starship.
It is possible to exploit the energy from nuclear fusion and fission directly, using some form of direct energy conversion; although the method used today, thermionic power, is a very inefficient process and seems likely to remain so in the foreseeable future, various direct energy conversion systems, such as fission fragment(1) or electromagnetic induction, hold the promise of very high efficiency. In fact, as we will show in this text, direct energy conversion is probably the only way to provide the large energy requirements of the drive’s secondary systems.
But for the third tier lower power systems, if small scale direct energy conversion doesn’t materialize in the near future, we can use thermodynamic cycles, such as Brayton or Rankine cycles, to extract energy from the heat of the reactors. These two cycles use the movement of fluids in pipes between hot and cold spaces, exactly like what we have been exploring in these posts for the waste heat from the deuterium deuterium fusion drive, to create power; using pumps, turbines and compressors linked by piping and cooled by radiators. Therefore making this a fitting subject of study for a space plumber.
The two most common thermodynamic cycles are the Brayton cycle and the Rankine cycles. The Brayton cycle uses the compression and circulation of a gas to transfer heat, the Rankine cycle uses the phase change energy of a gas to a liquid to transfer heat. We will look at the Brayton cycle first.
The Brayton cycle for cooling and power production
Image 2) Brayton cycle cooling
In a Brayton cycle, the cooling gas leaves the radiators at the lowest temperature in the cycle. It goes through a compressor, that raises its pressure and pushes it through the rest of the circuit, using power that it takes from the shaft. In the radiation shield, or the nuclear reactor, the gas gains energy and increases its temperature to the maximum temperature in the circuit. The gas also expands, following the perfect gas laws. The gas then goes through the turbine, where it is slowed down and cooled, and the pressure that was added is lost. This movement turns the turbine, that powers the shaft and therefore the compressor. The gas then enters the radiator, where it is cooled back down to its initial temperature and it begins the cycle again, ready for another spin.
This is the thermal cycle of gas turbines, both in aircraft and electrical production (open cycles) and for some nuclear reactors using helium (closed cycle).
The Brayton cycle equation can be written in the following way:
1) e= 1-[(T4-T1)/(T3-T2)]=1-(P1/P2)(y-1/y) = 1-(Qm-Qc)/Qt
Where:
e = Brayton Cycle efficiency
y = Heat capacity ratio of the working fluid = 1.67 for noble gases = 1.41 for other gases, including air
T1 = Temperature at the inlet of the compressor
T2 = Temperature at the outlet of the compressor
T3 = Temperature at the inlet of the turbine
T4 = Temperature at the outlet of the turbine
P1 = Pressure at the inlet of the compressor
P2 = Pressure at the outlet of the compressor
Qm = Mechanical Power, also called turbine power
Qc = Compression power
Qe = Electrical power = Qm-Qc
Qt = Thermal power
Qr = Radiator power =Qt -Qe
For the Icarus cooling shown in image 2)
e=1-[(2590 -1790)/(2600-1800)] = 1-600/600=0
Large turbines and compressors are very efficient, with system losses under 10%. But The efficiency of the cycle usually quoted in literature ( 30 to 40%) is not the measure of its losses, it is the measure of the amount of mechanical energy that can be extracted from the heat.
In the cooling example above, the thermal power is equal to the radiator power, so the cycle efficiency is 0; there is no power output. This does not mean it is not doing any work, just that all the work done is returned to the system in the compression, decompression cycle. The only output of this system is heat, which is exactly what we want from a cooling system.
To use the Brayton cycle to produce power, we need lower the temperature in the radiator, while keeping the source temperature high.
Image 3) Brayton cycle producing power and cooling
In this case, e=1-[(2000 -1600)/(2600-1800)] = 1-400/800=0,5 =50%
So we are now producing a lot of power! But at a cost: the shaft power has gone from 500 MW to 75 GW, 150 times more. So everything will be much bigger in proportion.
It’s also important to note that the compression ratio has changed as well:
e=1-(P1/P2)(y-1/y)
P1/P2=(1-e)-0.66 = 1.58
In this case, the pressure will be about 40% lower in the radiator than in the radiation shield. Which means that to move the same amount of gas in the radiator, the velocity will be considerably increased. However, there is also less energy that needs to be radiated away, so the area of the radiators will be decreased. But the average radiator temperature has also decreased, so the radiator area will go up! Do all these changes lead to a heavier system? In the previous chapters we have seen how to evaluate the changing weight of the radiators. Here we will be exploring how to determine the weight of the turbomachinery, and how it impacts the ship’s performance.
The weight of turbomachinery
A first order method to determine equipment weight is to use analogies. The space shuttle’s main turbopumps are known to have achieved the highest specific power to weight ratio yet: 153 kW per kg. For the 500 to 1,000 MW of pumping that might be required for the Icarus cooling systems, this represents a weight of 4 to 8 tonnes. For a system producing 50 GW, or 150 times more power, we could guess an overall weight of 600 to 1200 tons.
Image 4) Space Shuttle Main Engine Fuel turbo pump, combustion chamber, oxygen turbo pump (Pratt &Witney)
Image 5) Schematic of the Space shuttle main engines (Wikipedia)
However, as a reference, the Space shuttle turbopumps are problematic. The goal for operating time between overhauls for the shuttle turbopumps was 7 hours. The Icarus would require at least 15 years. The space shuttle turbopumps were cooled using cryogenic fuels in an open cycle; the Icarus will probably be running constantly at very high temperatures. Finally, the space shuttle turbopumps were quite small, and could have a relatively robust construction.
Another possible analog for the pumps that will be required for the Icarus are theis helium turbines and compressors designed for nuclear reactors.(1)(2)
6) The Japanese HTTR nuclear reactor core and Brayton Power circuit(x)
An interesting element of this design is that it is built to use magnetic bearings. The compressor and turbine assembly turns at 23 000 rpm, not much less than the 30 000 rpm the shuttle turbopumps were designed for, but the planned operating time between overhauls rises dramatically, up to at least the 15 years planned for Icarus and more. Although no weight data is available, it should be possible to meet (and perhaps surpass) the power to weight ratio values of 10 kW/kg reached in modern aircraft engines, so the overall weight of these turbo compressor assemblies for Icarus would be from about 60 to 120 tons if used as pumps, and from 9,000 to 18,000 tons if used for power production.
Obviously, as a main power producing system for the drive secondaries, turbomachinery is just too heavy. As a third tiersecondary power system though, producing a more modest 500 MW for support systemsexample, a weight of 50 tonnes might be both achievable and acceptable .
One significant difference between the Icarus turbo compressors use exclusively for coolant circulation and those of either the Space Shuttle main engines, aircraft engines or nuclear reactors is the much lower pressure ratio required for the Icarus compressors, stemming from the very high operating temperatures. This leads to lighter construction, with less stages and smaller shafts. But it is still unlikely to reduce the weight to acceptable numbers for main power.
Sizing Considerations
Sizing turbomachinery is something of a black art, that even today includes the construction of a physical scale model to ensure everything works as expected. But there are some preliminary design notions than can give us a good feel for the dimensions of the equipment.
Inlets and outlets
The size of the inlets and outlets is determined by the fluid velocity in the circuit. For pumps, the outlet will be directly proportional to the inlet divided by the ratio of velocities. For gas turbines and compressors, the dimensions will also vary according to the compression ratio; compressor outlets are smaller than inlets, and turbine outlets are larger than inlets.
Basically, the inlets and outlets will be the same size as the pipes leading to and from the turbomachine and are therefore a function of the selected pipe velocity. To get the size, you simply divide the volume flow by the velocity, which gives you the area.
A(m2)= Q(m3/s) / V (m/s)
Impeller
The diameter of the impeller, or turbine, will be a factor of the radius and the rotation speed, as well as the pressure we want to reach. The limitation is again materials, since the strain in the blades goes up with the rotation speed. The higher the revolution rate the smaller the diameter and the lighter the equipment. However, wear increases on the bearings.
The detailed velocity calculation are rather complex, involving the exact arrangement and angles of the impeller vanes, and not realty required for conceptual design. However a very rough guess can be obtained by:
D=V*10/rps
Where:
V= velocity of fluid leaving the pump (m/s)
D= Impeller radius (m)
rps=number of revolutions per second
Shaft
The size of the shaft and of the rotor is a factor of the power being transmitted.
The length of the shaft depends on the number of stages in the compressor, and is a factor of the pressure ratio. Each stage in a compressor feeds the next one, to achieve the overall compression ratio required. This is really hard to design; for conceptual work, you can simply include the shaft weight in your general mass allocations for accessories.
Casing
The thickness of the casing is a factor of the pressure in the system and of the energy in the turbomachinery. It is a good idea to plan for stagnant spaces in the turbomachinery, to use the gas as an insulator and reduce the heat load on the bearings. This increase the size of the casing. But in simpler terms, we can expect the casing to be about 10% larger than the impeller.
Secondaries
Finally secondaries and accessories , including starter motors, bearings, cooling systems, instruments, various bypasses and control elements add weight to the machine.
Again, this is very variable and may range from 5 to 50% or more of the weight of the other components, the lower value being for simple turbo pumps and the upper values for turbo power generators.
The Rankine cycle and liquid metal pumping
The Rankine cycle is the thermodynamic cycle of both steam turbines and air conditioning units. It uses the energy in the phase change between gases and liquids to transport heat. The heat source produces a gas, that condenses in the heat sink. So compressors are used on the gas side, and pumps on the liquid side.
Can we do the energy extraction and pumping using liquid metals? And could we actually simplify the system and eliminate the turbomachinery altogether, by using magnetic fields, for example?
Yes, we can produce electrical energy directly from a gas stream by using a direct energy converter called a magnetohydrodynamic (MHD) generator. And we can use this electric current to drive an induction pump. However, this is not as great an advantage as it used to be, since the advent of magnetic bearings has allowed us to design centrifugal equipment where the shaft is entirely enclosed in the pump casing, with no shaft sticking out. Still, the thermal limitations of the materials that compose the rotor and impeller remain acute.
Gases are intrinsically bad electrical conductors. Even if a lithium stream is still a conductor as a liquid, it becomes an insulator as a gas. The reason is the separation of the molecules in the gas, that creates an obstacle to the transfer of electrons from one molecule to the next, and therefore stops the propagation of the electrical current. This can be overcome by ionizing the gas; effectively turning it into a plasma, where the electrons are no longer bonded to the nucleus. This is the mechanism used in all electromagnetic thrusters, such as the Vasimir or MPD thrusters. So we need a mechanism to ionize the gas. Radio frequency emitters and lasers are some of the options. Once the gas is ionized, it can carry a current and becomes susceptible to magnetic fields. We then run it through a nozzle, and extract the energy using Magnetohydrodynamic principles.
The exhaust from the MHD generator goes into the radiator, where it condenses back into liquid form, freeing energy by radiation through both direct cooling and phase change. The cooled liquid metal, which has become a conductor again, can be circulated by magnetic pumps into the radiation shield, that then acts as a boiler, turning the liquid metal back into steam. The gas goes back through the ionizer and the cycle continues. The cycle, purely theoretical, might look something like this:
7) Rankine cycle, using MHD cooling and pumping
Some might object that having what amounts to a multi megawatt electromagnetic thruster built into the cooling circuit is not really a simplification. The answer to this is to remark that the alternative is to use a large jet engine in the cooling circuit instead, and that these are not known for their simplicity either. From the design point of view, using MHD turns the cooling system into a single gigantic heat pipe, overcoming the carrying distance limitations of heat pipes but keeping the attractive feature of no moving parts, except for the coolant itself. These advantages have been known for some time, and over the years there have been a certain number of experiments carried out, mainly for nuclear reactor cooling and power production.
Another extremely important aspect of the Rankine cycle it that there is a lot of energy in the liquid to gas phase change, which can lead to significant weight reduction. Without going into the details, that will be explored in our next post, the following information is of interest, showing the mass flow required to transport 100 GW of thermal power:
|
Substance |
Boiling point |
Latent Heat of vaporisation |
Specific heat |
Temperature difference required to equal vaporisation |
for 500 C temp. diff. in fluid |
By phase change |
|
K |
kJ/kg |
kJ/kg°C |
°C |
Tons/s |
Tons/s |
|
|
Lithium |
1615 |
21159 |
3.58 |
5910 |
56 |
5 |
We see that the Rankine Cycle uses 10 times less mass to transport as much energy as a purely liquid heat transfer system. And that the ratio would be even larger if we hadn’t chosen the very high temperature difference of 500 C for the lithium.
8) Liquid metal pump, Russian CLIP-3/3500
A real world example of liquid metal pumping, the Russian CLIP 3/3500 liquid sodium pump provided a flow of 3500 m3/hr at 320 kPa, 30% efficiency, 3000 Amperes at 650 Volts and required 2MW (2600 hp) to power it(4). It was 5m high, 1,8m in diameter and weighed 18 tons, with 10 tons of windings. It was designed to pump sodium at 573 K. The pump was built and tested for over 20 000 hours of operation, starting in 1984. So how does this translate for use with the Icarus probe?
For purely liquid heat transfer, about 60 of these would be required to pump the 56 tons per second of liquid metal coolant for Icarus. But with a pressure difference of about 8000 kPa, they would have to be much more powerful, or installed with a series of impeller sections, for a weight of way over 10,000 tons of pump, and a pumping power of about 1,2 GW.
For the phase change of the Rankine cycle, the number of pumps is reduced by a factor of ten, to 1000 tons and 120 MW of power. That is still too heavy though.
Optimisation is definitely required, and it appears that the high head required for Icarus is a serious problem, since it forces the use of a series of pumps that may add an unacceptable weight penalty to the ship. It would be a good idea to reduce the coolant velocity to reduce head, and therefore work with more reasonably sized pumps. Going back to table 1 the ‘Liquids in pipes’ article, we find that at 9m/s instead of 20m/s we’ve divided the pressure by almost 4 and the power required by 10. This should reduce the weight of the pumps to a more manageable 1000 tons, but would double the weight of the coolant required for purely liquid heat transfer systems. However, for a phase change system, the weight of the electromagnetic pumps would go down to 100 tons or less. This makes the solution of electromagnetic pumps practical for the starship, provided it is combined with the weight and pressure loss reductions associated with the Rankine cycle.
Research in future aircraft propulsion may provide further weight savings by developing powerful superconducting magnetic equipment(). But careful design will be required to avoid excessive cooling needs for the magnets, in very close proximity with the liquid metal. Since the magnet cooling will be done using very low temperature fluids, even modest increases in cooling requirements will again add to the radiator surfaces required for the ship.
It’s important to note the low efficiency of the MHD pumps, 30% in the case of the CLIP(). These are actual system losses, that must be compensated by the production of extra power. To compare, large compressors can have an efficiency of 90 to 95%. At least one of the system losses, electrical resistance in the liquid metal, is an inherent system loss that cannot be reduced. Unfortunately, it increases with system temperature, as conductors become more resistive as they get hotter. So this means that the MHD pump heats the coolant significantly, therefore reducing the efficiency of the cooling overall and increasing the required coolant flow, as well as increasing the size of the required MHD generator.
The basic pump equation is the Lorentz force equation, describing the influence of an electromagnetic field on a point charge :
2) F=q(E+v x B)
Where:
F= Force (Newton)
q = electric charge (Coulomb)
E = Electric field (Newton/Coulomb or Volt/meter)
v = Velocity (m/s)
B = Magnetic field (Tesla)
x = Not a simple multiplication!!! It is a vectorial operation,where the resulting force will be perpendicular to both the magnetic field and the current, following the right hand law. In this case, the current corresponds to the direction of motion of the charge q.
9) Right hand law, source: (Wikicommons)
For our magnetic pump to exert a pumping force on the fluid, the different vectors must be arranger this way:
10) Simplified electromagnetic DC pump showing basic configuration
In this case the equation is :
3) P=IB/s
Where:
P = Pressure (Pa)
B = Magnetic field (Tesla)
S = area (m2)
I = Current (Amperes)
So for a 1m square channel, a 10 Tesla magnet and 10 000 A current
P = 1000*1/1 = 100 000 Pa = 100 kPa of pressure
The current is perpendicular to the moving liquid metal, as is the magnetic field.
Note that the CLIP pump shown in image (x) above uses a different configuration; instead of direct current through the liquid metal, the current is induced in the metal coolant by varying magnetic fields and this induced current exerts a force on the coolant. In a way, the coolant pushes itself by creating a magnetic field that in turn pushes against the pumps induction fields. In practice, things quickly get complicated as the magnet is a solenoid with multiple spires, there are resistive losses in the liquid metal and in the magnet, etc. For detailed equations, Interested readers are referred to the following papers ()()().
Turbopower against MHD
System wise, if we compare turbomachinery and MHD with induction pumps, we are replacing the turbine by a MHD generator, the shaft by an electrical conducting circuit and the compressor by an electromagnetic pump. We want to do all the circuit with a single voltage, if possible, to avoid the weight of electrical transformation systems, and use DC systems, although the pumps will required additional power systems to create the varying magnetic fields that induce the current. The liquid metal MHD generator also needs an additional ionizer. Both systems require cooling and control accessories. The major problems with a MHD solution are the weight of the magnetic coils and of the support structures required, as well as the large cooling loads. The corrosion from a liquid metal in ionized state is also likely to be a severe challenge in the generator. And although there are no moving parts, the operation of the MHD pump requires cyclical electromagnetic loading of the various pump coils, that will induce fatigue problems similar to these of turbomachinery. The MHD pump is also much less efficient than a compressor; that means larger conductors and a larger generator as well.
The major problems with turbomachinery are maintenance requirements and the thermal and structural limits of available materials.
Compromises are possible between the various types of systems. For example, the Ghost team ship uses a Brayton cycle with a MHD generator to run a compressor. This does away with the ultra hot turbine, while keeping the more efficient compressor.
10) Brayton cycle cooling with MHD power production
It is also possible to use creative piping to increase the efficiency of the cycle, and to lower the system temperatures.
Existing MHD generator experiments have peeked out at system efficiencies of 21%. So there is a lot of work required before these systems can be accepted as replacements for the more conventional turbines and compressors of turbomachinery that routinely reach efficiencies of 40% and could theoretically provide 60% and more with sufficiently heat resistant materials.
We can conclude from this analysis that turbomachinery is a competitive solution for pumping coolant or generating power is a starship system. This required some form of direct energy conversion. Although turbomachinery isn’t viable as a solution for the power production of the main drive accessories, it can serve in third tier power systems, and as a main coolant circuit element. Electromagnetic analogs exist, but are not necessarily as advantageous as might be thought at first glance.
Is that all?
Well, we can fit in a bit more stuff:
Exoskeletal rotor
An interesting recent development in the world of aircraft engines, and by extension for mechanical turbopumps is the concept of exoskeletal rotors. These replace the current standard assembly of blades on a shaft by using a turning drum with blades on the inside, and a fixed core. The main interest here is that the blades are no longer in tension, they are now in compression. Most ceramic materials are much stronger in compression than in tension, so this might allow for higher rotation speeds, and perhaps for higher operation temperatures.The large surface of the drum may also allow for a simple arrangement of magnetic bearings, and the reduction of friction.
Compression power equation
When the compression is small, we can get away with the following simple equation:
4) W=(Q*dp)/n
Where:
W= compressor power (kW)
dp=pressure change (kPa)
Q=flow=32,000 (m3/s)
n=compressor efficiency (usually between 0.6 and 0.8)
But when the compression becomes significant, we need to take into account the work done in compressing the gas. The equation for adiabatic compression (no heat loss at the compressor) is still not exact, but it is OK for our requirements.
5) W=(y/y-1)*[(Q*R*T)/(w*n)]*[(P2/P1)(y-1/y)-1]
Where:
W= power (Watts),
y= Heat capacity ratio of the working fluid = 1.67 for noble gases = 1.41 for other gases, including air
Q= mass flow (kg/s)
R= Ideal gas constant = 8.314 J/kg mole
T= Absolute gas temperature before the compressor (K)
w= Molecular weight of the gas (g/mole)
n= Efficiency
P2= Absolute gas pressure after the compressor (kPa)
P1= Absolute gas pressure before the compressor(kPa)
|
Gas |
molecular weight |
|
Hydrogen (H2) |
2 |
|
Deuterium (D2) |
4 |
|
Helium |
4 |
|
Nitrogen (N2) |
28 |
|
Air |
28.9 |
|
Oxygen (O2) |
32 |
|
CO2 |
44 |
|
Fluorine (F2) |
38 |
|
Argon |
40 |
|
Neon |
20 |
Table 1, gas molecular weight, many gases are diatomic in their natural state
Tools of the trade
Here is a spreadsheet with the tables and equations from this article: please copy and use to your heart’s content.
Other articles in the series
References
(1) Fission fragment reactor
http://en.wikipedia.org/wiki/Fission_fragment_reactor
Unfortunately the link to the paper is broken, so here is the Wikipedia as a substitute.
(1) HEE CHEON NO*, JI HWAN KIM and HYEUN MIN KIM, A REVIEW OF HELIUM GAS TURBINE TECHNOLOGY FOR HIGH-TEMPERATURE GAS-COOLED REACTORS
Department of Nuclear and Quantum Engineering,
Korea Advanced Institute of Science and Technology, Korea, 2007
http://www.kns.org/jknsfile/v39/JK0390021.pdf
(2) Takakazu TAKIZUKA, Reactor development under the HTTR project, Japan Atomic Energy Research Institute, The 1st COE-INES International Symposium, INES-1, 2004
(3) B.G. Karasev, I.R. Kirillov, A.P. Ogorodnikov, 3500 m3/h MHD pump for fast breeder reactor,
A similar pump, with almost three times the flow rate, was build by Toshiba and tested in the United States, but the facility used, Boeing Santa Suzanna test facility in California, has since been dismantled, and information is sadly lacking. However, a good paper is available:
(4) Giant Electromagnetic Pump for Sodium Cooled Reactor Applications
Alan Fanning. Gerald Kliin, Life Fellow, IEEE, Walter Kwant, Les Dahl, Tatsutoshi hag&, Masahiro Veta,
Nobuak Nibe, Huoyuki Ota, Kenji Katsuki, Yoshihiro Doi, Isamu Maekawa
The characteristics of this pump where the following: 9600 m3/h, 250 kPa, 1800 A at 1800 V for 1,8 MW of power (4 400 hp). The pump was 10m high and weighed 100 tons fully assembled. So about twice as heavy as the russian pumps.
(5) Next Generation More-Electric Aircraft: A Potential Application for HTS Superconductors
Cesar A. Luongo, Senior Member, IEEE, Philippe J. Masson, Senior Member, IEEE, Taewoo Nam,
Dimitri Mavris, Hyun D. Kim, Gerald V. Brown, Mark Waters, David Hall
(6) W. Determan, D. Wait and P. Frye, Electromagnetic Pump Technology for Space Flight Applications
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070018816.pdf
Great basic text.
(7) Hee Reyoung Kim, Design and Experimental Characterization of an EM Pump, Seoul National University
(8) Carlos O. Maidana, James E. Werner Design of an Annular Linear Induction Pump for Nuclear Space Applications, Idaho National Laboratory
This is the most accessible of the three papers
(9) Nassima BERGOUG, NUMERICAL MODELLING OF THE COUPLING ELECTROMAGNETIC- HYDRODYNAMIC EQUATIONS OF AN ANNULAR INDUCTION MHD PUMP
This could be used to create a numerical model of a pump
The cat
The cat image source has been lost. Sorry.