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Adapting Heat Exchangers for Solar Dynamic Power

Posted by: Jonathan Burns - Thu Jun 14, 2007 4:19 am
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Adapting Heat Exchangers for Solar Dynamic Power 
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Post Adapting Heat Exchangers for Solar Dynamic Power   Posted on: Thu Jun 14, 2007 4:19 am
Greetings all.

I have been thinking hard about beam launch for some months, working mostly from Kare [1], and Parkin et al [2,3].

I've been working toward a concept and some estimates for the kind of space architecture that we could build on the basis of 20,000 * 100 kg payloads per year.

To state the obvious, we need an extremely reliable and highly automated system for navigation, docking and cargo handling. There is also the question, what to do with the spent vehicles? It's these issues which have driven my thinking.

Since Jordin Kare published his paper above, I have felt that a combination of beam launch, tethers and robotics should promise an economical alternative to conventional launchers, as a means to establish in-space industry. With beam launch and tethers, we'd be tackling the Rocket Equation from both ends, Isp and delta-v; with robotics, we could manage navigation and cargo handling; and also with robotics, we could manage the manifold degrees of freedom in long tethers, and turn them to advantage. The combination is more than the sum of its parts.

I have my own mental sketch of a development path, in four stages, the first stage being the trickiest. I was trying to see what we could construct in orbit with nothing but vehicles and payloads. (This is a bit quixotic; it might well be most economical to start in orbit with a basic system launched with a conventional heavy launch vehicle; but the more that can be done with beam launch, the better.)

For this, I was entirely willing to make use of the vehicles themselves (I've come to refer to them as "pods", since Kare's vehicle concept is so simple) as components. Pods can be very useful: they can be inertial mass, anchor points, tether ballast, micrometeorite shielding, gas containers and more. It may seem a bit heretical, since these vehicles will cost $30,000 each in Kare's estimate, and recycling them through multiple launches is critical in reducing payload $/kg; but in the early stages of a bootstrap process, they are extremely useful up there, and impose an extra cost to de-orbit.

The first stage involved building three indispensable components:

(1) Docking system; able to intercept and secure vehicles up to 1000 kg incoming at several m/s.
(2) Power system; able to provide and distribute up to 1 MW electrical among some hundreds of components.
(3) Robotics system. able to move and fasten some hundreds of robotic manipulators, for unloading and deploying payloads.

I was quite ignorant of robotics in thinking this - I wanted to identify the most basic problems first, those rooted in raw physics, and I was aware that there is a huge potential space of mechanical options; I didn't want to be optimizing small parts of the concept prematurely. In fact, once I began to look around, I found there are a fascinating variety of robotic systems currently in prototyping or proving phases. I'm beginning to think there's a rule of thumb: the basic problems get harder when you look at them closely, and see the inefficiencies, the vulnerabilties, the need for adaptation and maintenance; but the robotic problems get easier, because the number of options increases combinatorially.

I was drawn to one problem in particular, the power system. This is because I had been thinking all along in terms of solar power satellite architecture, which is my ultimate goal in all this.

I have read a few times that solar heat engines are made impractical by their radiator requirements. Actually, I don't think it's that bad. A black body radiates the solar flux at Te = 394 K (Te for "solar equilibrium temperature"); NASA model power satellites have solar intakes at 1000-2000 K, i.e. up to 5 * Te. Radiated flux varies as temperature^4, so radiator surface can be only some tens of times the intake, and a small fraction of the concentrator aperture. Still, radiators are necessarily a significant fraction of the mass of any solar heat engine.

But in both the Kare and Parkin models, for every 100 kg of payload, one also places in orbit about 100 kg of heat exchanger panel! - a robust, refractory item, able to sustain a rapidly changing flux up to 10 MW/m^2. The consequent questions are:

1. Would it be practical to adapt these panels in orbit as components of solar generators?

2. Would the provision of lower waste heat temperatures allow for a higher system efficiency?

3. Would it allow an engine with power and efficiency comparable standard designs, but with a lower input temperature? (And therefore longer life or relaxed concentrator pointing requirement?)

I am not an engineer (B.Sc. theoretical physics, M.Sc. astronomy, non-specialist math,); my knowledge of engine thermodynamics is very sketchy. My main scale of reference has been NASA's Glenn Research Center's published extrapolations of possible power satellites [4]. After reading several introductions to Brayton cycle turbines and some commercial websites, I downloaded M. Dhar, "1999, Stirling Space Engine Program" [7] about tests done on a 25 kW Stirling cycle engine built for NASA as part of the canceled SP-100 nuclear generator program. This gave me realistic figures, and better comprehension of the engineering conventions.

I do not yet have satisfactory answers for my three questions, and I'm still researching.

For question number 2, a rough realistic answer is that, although one certainly doesn't want a low Carnot efficiency crowding the engine efficiency (i.e. net work output / thermal energy input), reducing the ratio of output to input temperatures is not as effective as one might think. The ideal Carnot cycle is a sum of reversible processes, but one needs to accept some irreversibility in the heat-to-work conversion in order to attain useful power. The overall (or "system") efficiency of an engine is better predicted by the Callen efficiency, (1 - sqrt(Tout/Tin)). (Wikipedia, [5])

In my application, Tout varies as radiator area^(-1/4), so the effect on efficiency would vary as area^(-1/8).

In the Stirling case above, one has:

Carnot efficiency: 0.50
Thermodynamic (i.e. engine) efficiency: 0.658 * Carnot = 0.329
Mechanical efficiency: 0.92
Electrical efficiency: 0.88
System efficiency: (0.329 * 0.92 * 0.88) = 0.266

The Glenn Research Center figures estimate that near-future space power systems can do somewhat better, with engine efficiencies of 0.35-0.52 and system efficiencies of 0.25-0.30. The figures don't include the radiator sizes, so I still can't exclude the possibility that they are economizing on radiator mass, and accepting a higher Tout/Tin than they would choose if radiator mass were equal to all other payload.

For question number 3, one can make a scaling argument from the ideal gas law, P V = n R T, where n is molar quantity. Work varies as P d V, and so as n R dT on a constant mass of gas. If we hold Tout/Tin constant, scaling both temperatures down in proportion, we need to scale up mass and volume reciprocally, to get the same work. That means a larger engine; but engine mass is a significant fraction of the system (the NASA Stirling engine was designed for 6 kg/kWe, so its mass should be about 150 kg).

All that shows what the practical scale of space power is at present. However, heat engine research is far from completion, and with an energy crisis in prospect a lot of innovative effort is being funded (for instance, in thermionics and thermoacoustics). One effort I paid attention to is by the StarRotor Corporation - mostly, I admit, because they published their estimates in a form I could easily use.

StarRotor make their money producing rotary compressors and expanders, in an unusual "gerotor" design. They have yet to produce a working engine, but plan to begin at a 20 kW size. Their claim (based on simulations) is that the gerotor, being able to process large volumes of gas at 6:1 pressure ratios, could enable Brayton cycle turbines at powers from 50 to 50 million watts. (Holzapple, [6]) Comment I have read includes some heavy skepticism. Nonetheless I am taking their estimates as an indication of near-term possibility - much as I do with 25 kW CW lasers, after all.

StarRotor's enticing estimate is that the compressors and expanders for a 50 kWe turbine, with engine efficiency 0.44, could weigh 22 kg; this would not include the combustor or any of the heat exchangers making up a complete turbine. I assume this as a working scale in the following.

Now, I have two solar heat engine concepts in mind ("designs" would be badly exaggerating).

The Standard Model occupies five Kare-model pods at launch, comprising:

1. 100 kg - 50 kW turbine, including solar intake panel, recuperator, connections for separate radiator loop, and internal plumbing.
2. 100 kg - alternator and electric power storage and distribution.
3. 100 kg - 100 m^2 point-focus concentrator (1000:1) and deployment system.
4. 100 kg - plumbing kit for connecting pod radiators via propellant inlet and nozzle.
5. 100 kg - structural kit for assembling the five pods and payloads into te complete structure.

The working fluids for the engine have to be squeezed in with this somewhere; and I make the assumption that the pods will contain attitude-control reaction wheels which can also be used.

I would like to claim an electrical output of 40-50 kW. The power equation is roughly:

Solar power to intake: 137 kW
Reradiated flux at intake: 5 kW
Turbine work output: 50 kW
Radiated heat: 80 kW

The Kare model pods have 28 m^2 of HX panel (25 m^2 in later estimate). If we use more than two for the radiator, we will be radiating at less than the solar flux:

Panels: 1 2 3 4 5
Radiated flux (kW/m^2) 2.857 1.428 0.952 0.714 0.571
Tout =Temp : Te 1.300 1.093 0.987 0.919 0.869

From the Glenn models, assume an intake temperature of 1100 K = 2.79 * Te.

Tout/Tin 0.466 0.396 0.355 0.330 0.312
Carnot efficiency 0.534 0.608 0.646 0.670 0.688
Callen efficiency 0.317 0.374 0.404 0.425 0.442

You can see that we don't get much extra value after using three panels. Taking the figures from that column, we can compare them with the NASA Stirling engine tests:

Engine efficiency: 0.329 0.44 (StarRotor)
Carnot efficiency: 0.50 0.646
System efficiency: 0.266 ???

The system efficiency cannot be deduced from our in-principle thermodynamic figures; even the Callen efficiency is an argument in principle which happens to predict actual system efficiencies fairly well. On that basis, I would like to claim a system efficiency of 0.385 = 50/130; but I'll settle for 0.308 = 40/130.

As well as this Standard Model, I am thinking of a Mini Model, which would be more ambitious. It would use a single HX panel for all the heat exchanger functions of a Brayton cycle engine: solar intake, recuperator and radiator, by routing the working gas back and forth through alternate channels. It would take its input from a line-focus concentrator at a factor of 60-200, have a lower intake temperature, and be subject to heat losses by conduction through the panel; but might be transportable in one or two pods. It could be worth the difficulty if it resulted in 15-20 kW per pod.

This model would be much more challenging to deploy, because it requires removing the panel from its rocket manifold and bonding it to a pair of new manifold terminators. This would be a tricky task to automate, and I'm not sure that the adaptation process is even possible. The adaption process would have to match the material of the panel; match each of a couple of hundred millimeter-wide channels; sustain tens of atmospheres pressure; and be robust against repeated shape changes due to differing thermal expansion between the hot and cool extremities.

Nevertheless I have not convinced myself that it is impossible, and I am thinking of writing a paper on the topic. For this reason I am keen to follow progress in the fabrication of HX panels suitable for beam launch. So far, I only have the Kare and Parkin papers to work with; I hope to gather more relevant information from the "fifth-generation" nuclear power-plant effort.

10 kW per pod would not likely change the world energy market, but that is not my initial intent. The standard model, if it could be achieved, would be an effective way to provide megawatts of power to a growing satelite robotics platform. The power could be delivered by normal sockets or by non-contact induction (and there has been a recent demonstration of efficient near-field electromagnetic resonance coupling), or microwaved over kilometer distances. This would enable architectures which are impeded at present because each actuator needs either connection to a power bus or else a separate generator and battery store.

My hope is to make plausible the concept of an automated and teleoperated "space mall", at which multiple suppliers could deal with multiple customers, so that satellites of any reasonable description could be constructed in orbit, mainly from off-the-shelf parts, and then re-boosted into required orbits. Such platforms could markedly extend the satellite market and add value to conventionally launched systems.
In conclusion: thank you, all who have taken the trouble to set up this forum. When one is working on a secondary aspect of a newly developing field, it is hard to find an audience for mutual benefit. I am especially grateful to Dr Parkin for making his work available and for lending his time to the forum.


Jordin T. Kare, Kare Technical Consulting
Modular Laser Launch Architecture: Analysis and Beam Module Design.
NIAC Phase I Fellows Meeting.
2004. meetings/fellows/mar04/897Kare.pdf

Kevin L.G. Parkin, Leo D. DiDomenico, Fred E.C. Culick.
The Microwave Thermal Thruster Concept
Division of Engineering and Applied Science
2004 ... pcp04b.pdf

Parkin, Kevin L. G.; Culick, Fred E. C.
Feasibility and Performance of the Microwave Thermal Rocket Launcher
Second International Symposium on Beamed Energy Propulsion.

Advanced Solar Dynamic Technology
Glenn Research Center, Thermo-Mechanical Systems Branch
2002 ... _tech.html

Heat engine [ for Callen efficiency ]

Holzapple, Mark
StarRotor Engine: A Novel Power Source for the Military
StarRotor Corporation

Dhar, Manmohan,
Stirling Space Engine Program, Volume 1-Final Report, NASA/CR-1999-209164
1999 ... 210593.pdf

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Post    Posted on: Sat Jun 23, 2007 7:03 pm
A little OT, but what about SPS satellites orbiting the sun itself--using rotating sections as a heat sheild with coills inside--perhaps also fluid filled?

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Post    Posted on: Sun Jun 24, 2007 4:08 pm
A little OT, but what about SPS satellites orbiting the sun itself--using rotating sections as a heat sheild with coills inside--perhaps also fluid filled?

Thanks for this.

Moving closer to the Sun makes the Sun bigger in angular terms, meaning we can economize on concentrator aperture (area). Our angular pointing problems get easier, and we can do with a smaller concentrator. Beyond some point, we can use a simple line-focus "trough" concentrator rather than a point-focus "dish", and the pointing becomes easier again. (This is the current state of affairs for photovoltaics, which don't depend on high temperatures for their efficiency - a concentration factor of 10 or less provides all the photons the cells can handle.)

Some useful figures. The Sun subtends 1/215 radians out here at 1 astronomical unit. The solar flux is about 1370 W/m^2. With a perfect parabolic mirror we could produce an image flux of (1370 * 215^2 W/m^2= 63.3 MW/m^2), the flux at the Sun's surface. NASA's proposed SPS models assume (1370 * 10,000 /m^2=13.7 MW/m^2), because practical concentrators won't be astronomically perfect. So we see that concentrators really have the purpose of recreating the surface solar flux in defiance of the inverse square law, and that practically we can get quite close.

Now these heat-engine models of NASA's (and I'm just extrapolating from them) have just one solar-image "hot spot", which is cooled by gas flow to say 2000 K. If not cooled, the solar intake would be up around 3940 K.

We could get our 10,000:1 concentration ratio with no concentrator at all, by moving the SPS to 1/100 AU. But then we'd have the whole system approaching 3940 K, including crucial stuff like ducts and seals, and the whole electrical system. We simply couldn't manage that with present materials science. We might manage to hide the cool parts behind reflectors and the solar intake; but we would still need to radiate our waste heat at 3000 K or less, so we would still need a radiator area tens of times the intake. (I calculated radiator:intake at 40:1 or so for the NASA models, and my cheap-radiator suggestion went to 70-100:1.)

Now you have an interesting idea, if I understand it right: have a ring of solar intake sections, and rotate them through a hot spot, so that they spend most of their time cooling off, and only a little as engine intakes. I can't knock this out on principle, but it seems as if it would be a quite complex design, with components shifting between high and low temperatures each revolution - and the repeated stresses of thermal expansion would be terrible. I'd rather say, keep the solid components at stable temperatures, and let the working fluid circulate past the hot spot instead!

But I'm not arguing for near-future SPS designs in close solar orbit. If the time comes when we can exploit upper temperatures around 4000 K, it won't be with gas turbines, but a completely different engine concept - possibly thermionic or magnetohydrodynamic. And I think it would need a very different radiator concept as well. There used to be talk of "dust radiators" - streams of charged dust manipulated by electric fields - and I know there's been work by Robert Sheldon et al on dusty plasma lightsails, so perhaps there's hope in that direction; but it's definitely frontier science.

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