Why does it look like that? (Part 3)

Previously, we examined why lasers and exhaust look they way they do, in addition to spacecrafts’ shapes. Now we’ll look more closely at one specific part of spacecrafts: the heat radiators.

Fleet Carrier cutaway, also showing all radiators glowing at peak temperature.

Heat radiators are necessary for spacecrafts in order to cool their internal systems. Nuclear reactors produce tremendous amounts of waste heat, and other subsystems produce smaller yet substantial amounts as well. Nuclear-enabled naval ships on Earth can cool their reactors via convection since they are sitting in an enormous bath of coolant already: the ocean. Aircraft and ground craft also have the air to use as coolant to constantly soak away heat.

No such solution exists in space. The lack of any sort of fluid medium in space prevents convective cooling, and there exists no solid material in space to support conductive cooling either. This leaves the one remaining method of cooling: radiation. All materials always radiate photons via Blackbody Radiation, and the amount and kind they do depends on the temperature: hotter materials emit much more energy.

This is where heat radiators come in. These are already in use on the ISS.

Heat radiators on the ISS on the right and bottom. Solar panels on the left.

They are flat panels with tiny pipes running through their entirety, pumping in scalding hot coolant through one side, and cooled off coolant out the other side. In this way, the radiators form a closed coolant loop with the system that needs cooling. Each set of radiators cools a different system, which is also why some radiators glow orange hot, some glow yellow hot, and some don’t even glow at all (well, they’re actually glowing in infrared, too cold for the visible spectrum).

Unfortunately, you can’t simply dump all of your systems’ coolant loops into a single loop and pipe them through a single enormous radiator because of the second law of thermodynamics. Closed thermodynamic systems will maximize entropy over time. Put another way, heat always flows from hot to cold.

This means that if you have a nuclear reactor running at 1000 K (degrees Kelvin) with its radiators dumping out heat at 1000 K, and you hook it up to a crew module running at 293 K, you have a problem. The crew module and nuclear reactor coolant loop will combine to yield a temperature partway between the two. This will still cool off the nuclear reactor, but then it heats up the crew module until the people inside are cooked.

Module design of a radiator. Silicon Carbide ceramic core with Stainless Steel finish.

Why are radiators shaped like that? Heat emitted is directly proportional to surface area, so flat plates are the most mass-efficient way to radiate heat: maximum surface area, minimum volume. The jagged shape is to allow them to be retracted inwards to temporarily reduce heat signature (if enemy missiles are homing on you) or to protect them from damage.

Certain other designs of radiators exist, but many of them have issues. Liquid droplet radiators use a liquid pumped between a sprayer and a collector. The liquid allows a much higher temperature since the boiling point of the material is the limiting temperature instead of the melting point for solid radiators. Problem with this is that temperature is by far not the limiting factor of radiators. Silicon Carbide and other similar refractory ceramics can be heated to excess of 3000 K without melting. Even more exotic materials, like Hafnium Carbide, can exceed 4000 K (For comparison, the Sun’s surface is 5778 K) without melting! Their material properties are weaker at that temperature, but they remain still usable as radiators, and as long as they are never dropped below a certain temperature, they will never crack from thermal expansion stress. For reasons I’ll outline below, the internal systems will never emit coolant hot enough to take advantage of these refractory materials’ high melting points.

Another kind of liquid radiator, the Belt Radiator.

The radiators can never be hotter than the system they cool due to the laws of thermodynamics. However, the nuclear reactors in game can reach up to 3000 K, yet the radiators rarely ever exceed half that. In fact, for one of the reactors used for power production only in game, the reactor core never exceeds 1688 K and the radiators radiate at 1200 K. This reactor’s design is shown below.

13 MW electric solid core nuclear reactor.

Why are the temperatures so low when the materials used can withstand temperatures twice as high? Two things: the machinery between the reactor core and the radiators all needs to be able to withstand this heat, and the system works best when the temperature drops.

The reactor uses a thermocouple to convert the heat gradient from the reactor into power (note that a turbine-powered system would have somewhat similar limitations). The thermocouple first must withstand the high temperatures. Thermocouples require materials with high Seebeck Coefficients, and these materials tend to have low melting points. On top of that, the high temperature difference involves very significant thermal expansion stress, which is also not something these materials are good at withstanding.

Secondly, thermocouples are most efficient when the temperature drops significantly across them. This yields an interesting optimization problem. If the temperature drop from reactor to thermocouple is high, then the temperature drop from the radiators to space must be low, and the reverse is true. Remember that radiators perform best when their temperature is high.

This means the more efficient the reactor is at producing power, the harder it is to cool the system. On the other hand, a low efficiency reactor is very good at cooling itself. This problem yields two different valuable qualities that are inversely proportional to each other, and no local maxima can be found for both simultaneously.

In the end, for the above system, the somewhat reasonable point for both properties was at 1688 K for the reactor and 1200 K for the radiators.

Color temperature of Blackbody radiators.

That 1200 K temperature is why the largest radiators on spacecrafts glow orange. In fact, you estimate the temperature of radiators by their color, and from that you could estimate their purpose.

What about inter-reflection? Inter-reflection of radiators is a problem, since the heat from one radiator can be re-absorbed into another. This is exacerbated by Kirchhoff’s Law of Thermal Radiation, which states that the emissivity and absorptivity of a material is identical for any given wavelength of light.

Tail end of a spacecraft, showing how radiators will re-absorb each other’s heat radiated to some degree.

Blackbody radiation emits not simply perpendicular to the emitting surface, but in a full hemisphere of directions. Note that the intensity does fall off with the cosine of the angle from the perpendicular, however, so emission is most intense perpendicular to the radiator, and it falls to zero directly parallel to the surface. This does mean that these radiators will suffer inter-reflection, which will reduce their total efficiency, but they still will do the job, and can still be placed next to each other at narrow angles to each other.

Finally, can these radiators be armored? The answer is yes, contrary to what other sources may claim. Radiators are simply panels with material with tubes hollowed out in them to pass coolant through. One can simply increase the panel thickness beyond the tubes to add monolithic armor, and the refractory nature of the radiator materials means they will remain very strong even at orange-hot temperatures.

But, thicker monolithic plating reduces the efficiency of the radiators, because it will negatively impact the Heat Transfer Coefficient of the convection-radiation system. Thus, this yields yet another optimization problem, with radiator protection being inversely proportional to radiator efficiency. One will generally find that the added mass and poorer efficiency is often a fair trade for radiators that can actually withstand a serious beating.

That’s all for radiators! Next time, we’ll look into moment-to-moment space combat itself.