tbuelna, I have worked on this off and on since 1975. I have an *intimate* appreciation of the economics of the problem. I came here not to discuss economics or business financing problems, but to see if this engineering forum had any thoughts on thermodynamic cycles to skim off more of the energy from solar energy in GEO (which can get to really high temperature). Total power, efficiency and temperature determines the radiator area. The radiator mass is proportional to area. It's a little disappointing that you don't have suggestions. Most of the design work since the original studies in the late 70s have used PV.
This is part of design study document for a thermal power satellite.
General considerations
There are only two frequencies being considered for power satellites, 2.45 GHz and 5.8 GHz
For microwave optics reasons and the minimum forward voltage of the receiver diodes, power satellites have to be large. The higher the frequency, the smaller the optics, but atmospheric loses and rectification loses go up as well. This analysis uses 2.45 GHz, the same as the original designs investigated in the 1970s, and a power level of 5 GWe, that is power to the grid on the ground.
The electricity to electricity microwave path loss is 50% (3 db) which makes the power fed to the microwave transmitter at GEO 10 GW.
Turbines
Ten GW is a _lot_ of power. The largest generators constructed to date are 1.5 GW, and far too heavy to consider moving into space in one piece.
A GE90 engine on a Boeing 777 aircraft puts out 75,000 kW with a mass of ~7500 kg or 0.1 tons per MW. Given a 20 ton shipping limit, a turbine could put out 200 MW at this specific power. It would take 50 turbines of this scale to generate 10 GW. 10,000 MW of turbines at 0.1 tons/MW would mass 1000 tons.
Generators
The generators may mass more than the turbines. One example is an aircraft 400 Hz, generator, 40-50 KVA that massed 15 kg, or .33 kg/kW, or 330 tons per GW.
Superconducting generators may be a lot lighter, and given that we may have to use super conductors anyway, may be acceptable. Tentatively we will assume the generator and power transmission mass to be 3300 tons with the understanding that this may be off either way by a substantial amount.
Thermal cycles
Thermal power satellite design is concerned with radiator area. For 50% efficient thermal engines (difficult but possible with two stages) the amount of heat radiated would be 10 GW and the sunlight input 20 GW. (This assumes no re radiation loss at the boiler.)
50% efficient thermal is beyond what is practical with steam (Rankine) cycles. It is possible for combined cycle plants (on earth) to exceed 60%. Efficiency isn't a direct economic concern (sunlight is free), but a substantial fraction of the mass is in the waste heat radiators. High efficiency reduces the size of the radiators. This analysis will assume 60% thermal efficiency with a non-steam topping cycle. Potassium may be a good choice. This document makes a case for 54.6% and notes that a better vacuum on the steam condenser (which we have) would add a percentage point or two.
Other candidates for topping cycles include helium Brayton cycle, MHD and thermo-ionic (proposed in the original Boeing studies). There is also the possibility of using supercritical CO2 instead of water. The reason to consider this is the much smaller machine size and good efficiency of supercritical CO2 turbines. The cold end of the cycle (32 deg C) would be a good fit to a 10 deg C delta heat exchanger to a circulation of water/steam through the radiator tubes at 22 deg C (10 deg C delta T).
Efficiency and power set the collector area and radiator area.
Collectors and Radiators
For 60% efficient and 10 GW out, the input thermal energy will be 16.67 GW, and the radiator will need to dispose of 6.67 GW of low grade heat. The solar collecting area will be 16.67 GW/1.365 GW/km2 or 12.21 km2. The mass of the structure holding the reflectors and the reflectors will be taken as 0.5 kg/m2 or 500 tons per km2. The reflector surface will most likely be stretched aluminized plastic at no more than 0.1 kg/m2
Collectors would be ~6100 tons.
The ratio of collector to radiator optimizes with a radiator area of about twice the collector. (A. Bejan, Advanced Engineering Thermodynamics, 2nd ed., Wiley, New York, 1997, pg 495) Counting both sides of the radiator, the projected area is about the same.
For 6.76 GW / 12.21*2 km2 the heat level is ~273 W/m2. This number, substituted back into the Stefan–Boltzmann law is cooler than is actually useful for steam cycles (below freezing).
From previous work, (Drexler/Henson 1979) radiators tubes must be in a loop heated on both ends to eliminate massive return headers. Also, a minimum mass radiator has a square shape. A recent conceptual advance made while working on space based laser propulsion is to condense the low pressure working fluid (steam) only partway to prevent "water logging" in the radiator tubes and high fluid mass. There may be a better fraction, but the assumption in this analysis is that 80% of the steam condenses, an increment in density by a factor of 5. This increases the steam/water mass over the length of tube by an average of 3, (1+5)/2.
[And so on.]
I doubt you care, but the artwork on Google drive shows a Skylon cargo container being added to a LEO to GEO stage. The second slide shows the cargo under way using VASIMR engines making the purple glow. The engines are powered by microwave from the ground.
