Post by matterbeam on Jul 20, 2017 2:17:04 GMT
We will look at how this critical component works and then at existing, future and possible designs.
On Earth, heat leaves a vehicle through conduction, convection and radiation. In the vacuum of space, only radiation works to remove excess heat.
The International Space Station's radiators.
Spaceships are exposed to sunlight in space, which they absorb as heat through the hull. The various equipment on-board produces waste heat through their various inefficiencies, at different rates and temperatures. Even the crew contributes to producing waste heat. If this waste heat is not removed, it will accumulate and increase the spaceship's temperature until it melts. Radiators are critical for this reason.
Radiators work by emitting electromagnetic energy. It consists of photons of a wavelength determined by the radiator's temperature.
Guess what temperature this exhaust manifold is at.
Examples include the infrared wavelengths our body emits (300K), the red-orange visible wavelengths molten iron emits (1430K) and the bright white of the sun's surface (5800K).
For our purposes, we will focus on the energy removal capacity of a radiator. The rate is measured in watts: the waste heat watts absorbed and produced by the spaceship's systems, to be compared to the waste heat watts radiated away by a radiator. The relationship between the energy removal capacity and the radiator's temperature is given by the Stefan Boltzmann equation:
Waste heat removed: E * A * Sb * Temperature^4
E is the emissivity of the radiating surface. It is a property between 1 and 0. Extremely black surfaces approach 1 emissivity. Shiny surfaces have lower emissivity.
A is the surface area of a radiator, in square meters. Make sure to count it twice for a double-sided radiator.
Sb is the Stefan Boltzmann constant, equal to 5.67*10^-8.
Temperature is in Kelvin.
Using the Stefan Boltzmann equation, we can quickly see that a radiator with better emissivity, higher surface area and higher temperature removes more waste heat.
On the left, 1100K radiators. On the right, 2700K radiators. The latter is actually handling three times as much waste heat.
On spaceships, it is important to use the lightest possible components for each task. A spaceship with lighter radiators will accelerate faster and have more deltaV, meaning it can go further and do more for less propellant.
If we want a lightweight radiator, we want it to have the highest emissivity. We can accomplish this by using naturally dark materials, such as graphite, or painting over shiny metals with black paint.
A larger radiator weighs more. We therefore want the smallest radiators possible. To compensate for lower surface area, we can increase the operating temperature. A small increase in temperature leads to a massive increase in waste heat removed. This means that hot radiators are massively lighter and smaller than cold radiators.
The ISS's EAC system
A typical radiator accepts coolant from a hot component. The coolant's component exit temperature is the initial temperature at the radiator. The radiator serves as an interface that radiates away the coolant's heat, leading to a lower radiator exit temperature. The coolant is fed back to the component to complete the waste heat removal cycle.
Note how the maximum temperature the heat exchanger's maximum temperature, delivered to the steam, is the lowest temperature of the liquid sodium in the reactor core.
Heat only flows from a hot object to a cooler object. A radiator can therefore only operate when the component's temperature is higher than the radiator's coolant exit temperature. For example, if a nuclear reactor operates at 2000K, the radiator must work at 2000K or less.
A reactor from COADE. The reactor operates at 2907K but the radiator receives coolant at 2400K.
The difference between the entry and exit temperatures in a radiator depends on many factors, but generally we want the largest difference possible. This difference in temperature is especially important for power generation. A large difference means more energy can be extracted from a heat source. It also means that less coolant is needed to cool a component.
This creates problems with realistic designs.
A general solution is to use two sets of radiators operating at different temperatures: one low-temperature circuit and one high temperature one. It works fine when your low temperature waste heat is a few kilowatts from life support and avionics. Other solutions have to be found for components that must be kept at low temperatures yet generate megawatts of waste heat, such as lasers.
This design has three sets of radiators of decreasing area for different temperature components.
For low temperature high heat components, heat pumps must be used. They can move waste heat against a temperature gradient, allowing, for example, a a 1000K radiator to cool down a 500K component. However, this costs energy. Moving heat from 500K to 1000K costs 1 watt to the pump for every watt moved. A realistic pump will not be 100% efficient and will require more than 1 watt to move a watt of waste heat.
Pump power: (Waste heat * Tc / (Th - Tc)) / Pump Efficiency
Pump power is how many watts the heat pumps consume. Waste heat is how many watts must be removed from the component. Tc is the component's temperature. Th is the radiator's temperature, both in Kelvins. Pump efficiency is a coefficient.
The refrigeration cycle is an example of a heat pump.
A coolant must generally be kept liquid. This imposes a lower and upper limit to the coolant temperature; any colder and it will freeze and block the pipes, any hotter it boils and stops flowing. Water coolant, for example, can only be used between 273 and 373K. More importantly, it limits the temperature difference that can be obtained from a radiator.
Large temperature differences require that the coolant spend a long time inside the radiator. This requires larger radiators or long, circuitous paths for the pipes. As the coolant becomes colder, it radiates at lower rates, meaning that the last 10 kelvin drop in temperature can take exponentially more time than the first 10 kelvin reduction. There are strong diminishing returns.
There are also structural concerns. Large temperature differences impose thermal stresses. These might be too great to handle. Lightweight, stressed radiators are prone to reacting badly to any sort of battle damage, making radiators a weak-spot for any sort of warship.
The ISS radiators' support spars. A spaceship under acceleration will need much more support.
All in all, we must keep in mind that there is a restricted range of temperatures between the hot and cold ends of a radiator, and that its performance cannot simply be obtained by using the Stefan Boltzmann equation on the maximum temperature. We cannot use a simple average either, because the coolant loses heat at a quadratically declining rate as it moves from higher to lower temperatures.
Here is an example of 1 kg of sodium at 1000K being cooled by a 0.8 emissivity one-sided 1m^2 radiator panel:
We can see that it takes 17 seconds for the sodium to cool down from 1000K to close to its melting point of 370K. Any cooler and it'll solidify in the pipes. If we average the radiated watts, we get a value close to 11.46kW. This corresponds to an average radiating temperature of 545K.
Finally, a radiator suffers stresses when a spaceship accelerates. Some types of radiator break or disperse under strong accelerations, so the spaceship's performance needs to be considered before selecting a design.
A straightforward design used today.
It consists of a slab of metal run through with hollow tubes for a coolant to flow. The waste heat conducts out of the coolant and into the radiator material, which radiates it away from its exposed surfaces.
This design has a rather high mass per area and low temperature limits, making it one of the worst performing designs. The maximum temperature is whatever keeps the radiator materials both solid and strong, which is important as many metals rapidly lose strength as they approach their melting point.
The coolant must remain liquid throughout the cooling cycle, so this limits the temperature difference that can be achieved. Using metals such as tin or salts such as sodium allows for better temperature differences, but pumping them requires specialized, sometime non-reactive, sometimes power consuming equipment.
Multiple radiators will shine their heat into each other and lose efficiency.
The arrangement of radiators around a spaceship must take into account inter-reflection, which is when one radiator's heat it intercepted and absorbed by another radiator. This reduces their efficiency. Anything more than two radiators per axis absorbs some of the heat of another radiator... at four radiators, only 70% of the heat escapes to space, at eight radiators, the efficiency falls to 38%.
NASA has studied solid radiators for use in its Nuclear Electric Propulsion concepts. It has specified 2kg/m^2 area density as a requirement for any thermal management system. The ISS's radiators mass 8 kg per square meter, or 2.75kg/m^2 if we only consider the exposed panels.
So far, only bare carbon fibre radiators operating at 800-1000K have reached this area density.
An alternative design achieves better area density by removing the coolant loops and pumps. The heat pipe has a hot end and a cold end, separated by a vacuum.
Heat Pipe moving waste heat into a heatsink.
Solid coolant is boiled away and then condensed on the cold end, then re-circulated through capillary action or centrifugal acceleration. This method allows for high operating temperatures and does not require any pumps of moving parts, but high mass per area negates many of its advantages.
On a warship, radiators are a weakpoint. Bright, exposed and hard to defend, they are easy to hit and once the are damaged, they can render a spaceship unable to function. They can mission-kill a warship without ever having to penetrate any armor. Redundant radiators impose a mass penalty. Covering the radiators in plates of armor massively decreases their thermal conductivity between coolant and exposed surfaces, which in turn reduces their efficiency.
Solutions for reducing the vulnerability of radiators include pointing them edge-on to the enemy, moving them to the back of the ship, or using retractable designs.
On the right, the radiators are exposed the enemy fire. On the left, the hull bulge protects the radiators from damage.
If all radiators are retracted, the spaceship must rely on heat sinks for its cooling needs. A megawatt heat source can boil off a ton of water in less than seven minutes, so this will only work over very short time periods.
A compact collapsible and retractable radiator design.
Read the rest in proper format, with in-text links, on the blog.