Liquid Rhenium Solar Thermal Rocket

The maximum temperature concentrated sunlight can heat a material to is 5800K. How do we approach this limit?

We will describe existing and potential designs for solar thermal rockets. 

Solar thermal rockets

The Solar Moth

The principle of a solar thermal rocket is simple. You collect sunlight and focus it to heat a propellant headed for a nozzle. 

A rocket engine's performance is determined by its thrust, exhaust velocity and efficiency. A solar thermal rocket's thrust can be increased by sending more propellant through the nozzle. Its exhaust velocity can be increased by raising the propellant temperature. Doing either required more power, so more sunlight needs to be collected. Efficiency will depend on the design.

The main advantages of a solar thermal rocket are its potential for high power density, high efficiency and high exhaust velocity. 

Collecting and heating with sunlight does not need massive equipment - unlike solar electric spacecraft that need solar panels, extremely lightweight reflective metal films can be used. A heat exchanger above a nozzle is compact and masses much less than the electrical equipment and electromagnetic or electrostatic accelerators a solar electric craft uses. Radiators are not needed either, as the propellant carries away the heat it absorbs with it. Put together, a solar thermal rocket can achieve power densities of 1MW/kg while solar electric craft struggle to rise above 1kW/kg. 

Sunlight would follow the same path as the laser beam here.

As the sunlight is being absorbed by a propellant and expanded through a nozzle, there are only two energy conversion steps: sunlight to heat, then heat to kinetic energy. The first step can be assumed to be 99% efficient. The second step depends on nozzle design, but is generally better than 80%. 

Thermal exhaust velocity will be determined by the motion of the gas particles composing the propellant. The equation is:

• Thermal Exhaust velocity: (3 * R * Temp. * 1000 / Molar mass ) ^ 0.5

Temperature is in Kelvins. Molar mass is the average g/mol value of the propellant at the temperature it is heated to. R is the molar gas constant, equal to 8.314 J/mol/K. 

For the very hot gasses we will be considering, we can assume complete dissociation of all molecules. H2 (2g/mol) will become atomic hydrogen (1g/mol), water (18g/mol) becomes a hydrogen-oxygen vapor (6g/mol) and so on. Low molar masses are preferred, with the best propellant being mono-atomic hydrogen unless other factors are considered. 

A nozzle can expand the hot propellant into a fast-moving stream of gas. Monoatomic gas can receive a x2.42 increase to exhaust velocity from a perfect nozzle, but this is situational and specific to each rocket engine design, so we will ignore this increase for now. 

These advantages are all the critical elements that allow for travel throughout the inner solar system without requiring vast quantities of propellant. The result is smaller spacecraft and lower travel times. 

Heat exchangers and exhaust velocity

The limiting factor for solar thermal rockets is how hot they can heat the propellant.

Directly heating the propellant is a difficult task. The lowest molar mass propellant, hydrogen, has terrible absorption. For all practical purposes, it is transparent to sunlight. Seeding the propellant with dust particles that absorb sunlight and heat the hydrogen indirectly through conduction has a major catch: the dust particles get dragged along by the hydrogen propellant flow and increase the average molar mass. 

Indirect heating involved using a heat exchanger as an intermediary between the sunlight collected and the propellant being heated. 

So far, designs have required the use of a solid mass of metal that is heated up by concentrated sunlight. The propellant is run over the metal, or through channels in the metal, to absorb the heat. Tungsten is often selected for this task, as it has a high resistance to heat, is strong even near its melting point and has a good thermal conductivity. 

Testing a Hafnium/Silicon Carbide coating.

More modern designs make the most of the latest advances in materials technology to allow for higher operating temperatures. Carbon, notably, stays solid at temperatures as high as 4000K. Tantalum hafnium carbide and a new Hafnium-Nitrogen-Carbon compound melt at temperatures of 4200 and 4400K respectively. 

However, looking at our exhaust velocity equation, the limits of modern materials technology will only provide a 21% increase over common tungsten. This is the reason why so many propulsion technologies that rely on exchanging heat between a heat source, such as a nuclear fuel or a laser beam, and a propellant using a solid interface are said to be 'materials limited' to an exhaust velocity of 9.6km/s with tungsten, or 10km/s with carbon. THC or HNC would allow for an exhaust velocity of 10.5km/s.

This is the deltaV equation, also known as the Tsiolkovsky rocket equation:  

• DeltaV = ln (Wet mass / Dry mass) * Exhaust Velocity

Wet mass is how much spaceship masses with a full load of propellant. Dry mass is the mass without any propellant. The wet to dry mass is also referred to as the 'mass ratio' of a rocket. 

We can rewrite the rocket equation to work out the required mass ratio to achieve a certain deltaV using a rocket engine's exhaust velocity:

• Mass ratio = e ^ (DeltaV required/Exhaust Velocity)

'e' is the exponent 2.7182... in simpler terms, the mass ratio increases exponentially as the deltaV required increases. Or, put another way, the mass ratio required decreases exponentially as the exhaust velocity rises. It is critical to have a higher exhaust velocity for rapid space travel without requiring massive rockets and towers of propellant. 

You might also have noticed that 'solid' is a keyword up to this point. Why must the heat exchanger remain solid?

Liquid Rhenium

There is a method to achieve the true maximal performance of a solar thermal rocket, which is heating up the propellant as far as it can go. This is incidentally the temperature of the surface of the sun (5800K). At this temperature, hydrogen propellant reaches an exhaust velocity of 12km/s.

A rare, silver-black metal.

Rhenium is a rare metal with a surprising number of qualities, one of which is a very high boiling point. Rhenium melts at 3459K but remains liquid up to 5903K.  

The trick to achieving higher exhaust velocities is to use a molten heat exchanger, specifically liquid rhenium at a temperature of 5800K. Rhenium is also very stable and does not react with hydrogen even at high temperatures, which is something carbon-based materials struggle to survive. It has already been considered as a heat exchanger, in solid form, by NASA.

Here is a design that can use liquid rhenium as a heat exchanger:

The diagram is for illustrative purposes only - a functional schematic would be more detailed. Here is an explanation for each component:

Solar collector: A very large, very lightweight reflective film based on solar sails that can collect sunlight and focus it through a series of lens onto the heat exchanger fluid's inner surface.

Rotating drum: The drum's inner surface contains a liquid heat exchanger. The outer surface is actively cooled. The drum is dotted with tiny channels that allow the propellant to enter the liquid from the bottom and bubble through to the top. It is made of Tantalum-Hafnium Carbide.

Fluid surface: The fluid here is liquid rhenium. Its surface is heated to 5800K by concentrated sunlight. The lower layers nearer the drum holding the fluid is cooler. The centripetal forces hold the fluid in place

Pressure chamber: The rotating gas mix gets separated here. Dense rhenium vapours fall back down, hot hydrogen escapes.

Bubble-through heating: The rotation induces artificial gravity, allowing the hydrogen to heat up and rise through the denser rhenium. As it rises, it reaches hotter layers of the fluid heat exchanger. At the surface, it has reached 5800K. Small bubbles in direct contact with the rhenium allows for optimal thermal conductivity. More detail below.

Active cooling loop: liquid hydrogen from the propellant tanks makes a first pass through the drum walls, lowering the temperature below the melting point of THC. It emerges as hot, high pressure gaseous hydrogen.

High pressure loop: The heated hydrogen is forced through the channels in the drum. It emerges into the fluid heat exchanger as a series of tiny bubbles. 

Here is a close up of the drum wall, which contains both active cooling and high pressure channels:

The configuration displayed above allows the hydrogen to enter the basin bottom at 4000K, then be heated further to 5800K before being ejected into the pressure chamber. If higher quantities of liquid hydrogen for active cooling are used, the drum and high pressure channel temperatures can be lowered to 3800, 3500, 3000K or lower. 

This pebble-bed nuclear thermal reactor has most of the components of our solar thermal rocket, except that instead using pebbles of nuclear, fuel, we use a liquid rhenium bed heated by sunlight.

If the liquid hydrogen active cooling cannot handle the full heat load, radiators will be needed to cool down the drum below its melting point of 4215K. Thankfully, these radiators will receive coolant at 4000K. Their operating temperature will be incredibly high, allowing for tiny surface areas to reject tens of megawatts of waste heat. Electricity can also be generated by exploiting the temperature difference across the radiators' entrance and exit flows, and at very high efficiency. 

Operation

The design is a Rotating Drum Fluid Heat Exchanger Solar Thermal Rocket (RD-FHE STR). It allows for hydrogen propellant to reach 5800K and achieve the maximum performance of a Solar Thermal Rocket. 

Liquid rhenium does not boil at 5800K, so it remain liquid and can be held inside the basin by simple centripetal forces.

Vapor pressure of rhenium at 5800K (0.87atm) was determined to be low enough for our purposes. A surface of rhenium exposed to vacuum at that temperature would lose 0.076g/cm^2/s, or 762g/m^2/s. It is unknown how much centripetal force affects the loss rate of rhenium. The pressure chamber would operate at several dozens of atmospheres of pressure, which is known to increase the boiling point and reduce the evaporation rate of fluids. 

The same techniques used in Open-Cycle Gas Core nuclear reactors to prevent the loss of uranium gas can be applied to reducing the loss of rhenium vapours.

At worst, the rhenium heat exchanger loses 0.76 kg of rhenium for square meter per second of operation. Looking at the designs below, the mass flow rate is measured in tons of hydrogen per second. This is a ratio of 1000:1, to be improved by various rhenium-retaining techniques.  

It should also be noted that rhenium is a very expensive material. A tungsten-rhenium mix has very similar thermal properties and is much cheaper.

Sunlight at 1AU provides 1367W/m^2. A broad-spectrum reflecting surface such as polished aluminium would capture and concentrate over 95% of this energy, so more than 1298W would be available per square meter. Solar sails materials such as 5um Mylar sheets are preferred, massing only 7g/m^2. More advanced materials technology, such as aluminium film resting on graphene foam, might mass as little as 0.1g/m^2.

The 'Solar Moth' used inflatable support structure for its mirrors. 

Based on data for the Solar Moth concept, we have estimated that a solar thermal propulsion system can attain power densities of 1MW/kg. So, each square meter of collector area will require another 1.29 grams of equipment to convert sunlight into propulsive power. 

Performance

Robot Asteroid Prospector

We will calculate the performance of two versions of the RD-FHE STR. The first version uses modern materials and technologies, such as a 7g/m^2 Mylar sheet to collect sunlight and a 167kW/kg engine power density. The second version is more advanced, using 0.1g/m^2 sunlight collectors and a 1MW/kg power density.

Modern RD-FHE
5 ton collection area => 714285m^2
927MW of sunlight focused onto the drum. 
5.56 ton propulsion system
Exhaust velocity: 12km/s
Thrust: 123.4kN (80% efficiency)
Thrust-to-weight ratio: 1.19
Overall power density: 87kW/kg

Advanced RD-FHE
5 ton collection area =>50000000m^2
64.9GW of sunlight received
64.9 ton propulsion system
Exhaust velocity: 12km/s
Thrust: 10.8MN
Thrust-to-weight ratio: 15.75
Overall power density: 928kW/kg

The principal argument against solar thermal rockets, that their TWR is too low and their acceleration would take too long to justify the increase in Isp, can be beaten by using very high temperatures and very low mass sunlight collectors. 

For example, a 50 ton propulsion system based on the modern RD-FHE STR design, would be able to push 100 ton payloads to Mars (6km/s mission deltaV) using only 97 tons of propellant. It would leave Earth orbit at a decent 0.24g of acceleration, averaging 0.32g. The departure burn would take only 20 minutes. Using the advanced version of the RD-FHE solar thermal rocket would allow for a positively impressive acceleration of 3.1g.

With 12km/s exhaust velocity, multiple missions that chemical rockets struggled to do with low-energy Hohmann transfers can be avoided. A chemical rocket such as SpaceX's BFR might achieve an Isp of 375s, which corresponds to an exhaust velocity of 3.67km/s. It would need a mass ratio of 5.13 to barely produce enough deltaV for a Mars mission. 

Earth to Destination.

If our solar thermal rocket is granted the same mass ratio, it would have a deltaV of 19.6km/s. This allows for a Mars mission to be completed in under two months (10km/s departure, 9km/s insertion). It is also enough deltaV to reach Jupiter with a single stage. 

Other benefits include a vast reduction in the propellant-producing infrastructure needed to supply orbital refuelling depots and the ability to land on Mercury. 

Alternative versions:

Blown hydrogen:

Instead of bubbling hydrogen from the bottom of the liquid rhenium basin, hydrogen is blown into the pressure chamber from the top. It is heated by simply passing over the fluid heat exchanger.

The advantage is that the rotating drum does not have to be riddled by microchannels, allowing it to be stronger and rotate faster, which would reduce rhenium losses, and also accept a higher rate of active cooling by leaving more room for liquid hydrogen channels. Another advantage is that there is less chance of hydrogen bubbles merging and exploding in showers at the surface, dragging along rhenium as they escape. 

The disadvantages is vastly reduced heat conduction rate between the rhenium and the hydrogen. This would require a long and thin pressure chamber to increase the time the hydrogen stays in contact with the rhenium, potentially making the propulsion system heavier than it needs to be and forcing sunlight to enter the chamber at very acute angles. 

ISRU propellants:

Instead of hydrogen, other gaseous propellants might be used. Nitrogen is a good choice, as it is inert and only reduces the exhaust velocity by a factor 3.7 compared to hydrogen. 

Powering a hydrogen extraction process on Mars requires huge areas of solar panels.

Nitrogen is easily sourced from Earth's atmosphere by gas scoops. Other options, such as water or carbon dioxide, are also viable and available on other planets. 

The advantage is that non-hydrogen propellants are easy to contain and are much denser than hydrogen, so their propellant tanks can be lightweight and small. They are easily sourced and only need to be scooped up and filtered, unlike hydrogen that has to undergo electrolysis.

The disadvantage is that there propellants cannot serve as expandable coolant for the rotating drum. A radiator using a closed gas loop is necessary - helium is a likely candidate. This adds mass. A lower exhaust velocity also removes the principal advantage the RD-FHE STR has over other propulsion systems.