Reply To: Mind, Spirit, Science connection?

[redsnapper]

Let’s take a possible scenario – granted, this is again making some ballpark assumptions:
1) The 4MW of waste heat originates at 1000K (probably not this high – because probably the X-ray converter and the ion decelerator are made of material more delicate than solid Be or any other solid material – but for the sake of argument, let’s suppose they can handle 1000K)
2) Ambient is 300K
3) We “split the difference” between some sort of local conduction/convection/impingement whatever cooling at the heat source itself, so that 4MW emerges in the form of something like steam or another coolant capable of carrying that heat somewhere we can dispose of it safely. That means (for instance), we’ve got 4MW of power at 650K (375degC).
4) Based on the above, that means we need an “environmental” heat exchanger capable of unloading 4MW with a delta-T of 350degC. (Again, in thermal resistance terms, that’s on the order of 0.0009degC/W.)

Lowest tech, cheapest solution:

Free convection from large fins. A bit of circular/iterative computation is in order, but textbook values for free convection film coefficients at this scale (TBD) turn out to be anywhere between 3 (laminar) and 10 (turbulent) W/m^2/degC. Again, at this scale and temperature difference, we’re well into the turbulent regime. Indeed, textbook correlations yield a film coefficient (vertical, heated flat plate) of 9.2 W/m^2/degC, so at the 350degC delta-T, this implies a heat exchanger surface area of 1200m^2! Now, coming from the semiconductor business, I hardly qualify as a power-plant cooling expert, but at first, I thought cramming 1200m^2 of fin area into a two-car-garage model seemed a bit of a stretch. But maybe not: for instance, if you had 20 fins, 3m tall and 10m long, spaced at 1m, you’d have 1200m^2 of total fin area (counting both sides of each fin) – in a space 3x10x20 m^3. Sounds like a two-car garage to me. So I guess we’re not outside the realm of feasibility. Obviously there are other logistics involved, like the volume of fluid you have to pump from the compact heat source (DPF reactor core, Rogoski coils, X-ray converter), and so forth – but it’s probably doable. Remember, too, a heat exchanger using air as the external working fluid it going to suck a lot of air, and that air is going to come out hot. The same calculations above show that the minimum volume flow rate of air is going to be 15m^3/s (STP), and that’s if it comes out at the maximum fin temperature (i.e. 375degC, in this case). If you don’t want to dump air that hot into the environment, you’ll have to move a lot more air. (Actually, for free convection, the amount of air that moves isn’t an independent variable. That 15m^3/s figure isn’t based on free convection principles, it’s simply based on the heat capacity of air. So the actual value is likely to be a much higher figure, but it won’t be a back-of-the-envelope calculation with stuff I carry around in my head.) You can also lower the fin temperature, but at the expense of needing more fin area. But I think my original impression that the physical size of the final-stage heat exchanger was ridiculously large was unnecessarily pessimistic for low tech cooling methods. (I don’t think it will “fit on a truck.”)

I do remember studying the design of large cooling towers (passive, free convection cooling) in one of my grad-school classes. It can certainly be done, and should be considered in more detail. If you do have a source of water and can otherwise justify it environmentally, you can also vastly reduce the size of the cooling system. I mentioned in my first post that it only takes 2kg/s of water to absorb 5MW, if you take it through the liquid-vapor phase change. That’s 40,000 gal/day. For many reasons, that wouldn’t be my first choice for the final-stage cooling, but it’s also something to consider. (In the context of my first post, that was a possibility for cooling the core – and that water would be in a closed loop, not a continuous external supply.)

Also trying to put the waste-heat figures into perspective – sanity check on the above rough figures: a 5MW power plant is large enough to supply the needs of approximately 2000 homes. Each of those homes ultimately dumps all that energy as waste heat into the environment. So we’re taking 80% of that figure (i.e. 4MW ), which would be the equivalent of 1600 homes, and injecting it into the environment “locally” to the reactor. That’s a pretty dense compression of power into a small space. It should be no surprise that this takes some fairly large fins. (A relatively small “neighborhood” power plant – mainly oil-fired – near my home is a 110MW output plant. The whole facility covers hundreds of acres and has some very large cooling towers. It most certainly does not make optimal use of its real estate, but there’s a reason they gave it so much room!)

Actually, AaronB made a comment about using the waste heat from a 5MW reactor for something as mundane as heating at a hotel. That’s actually a great idea, and in my mind, the sort of thinking that should be pursued. Any operation for which a few MW is the expected low-entropy power requirement, if you can think of other high-entropy needs that could simultaneously be met, a 5MW-sized fusion reactor would be amazing. Come to think of it, any open-ocean applications – like cruise ships (AaronB) – would be excellent candidates, because you’ve got all that water to use for cooling. Cruise ships dump their waste heat into the environment anyway, and the fusion source of energy is so much cleaner in every other respect!

Don’t get me wrong – I still think there are issues at the core end, and knowing sizes and materials of the Rogowski coils and X-ray converter would help better establish the parameters there.