Space Power Resources, Manufacturing and Development Volume 9 Number 4 1990
SPACE POWER Published under the auspices of the SUNSAT Energy Council EDITOR Andrew Hall Cutler, Space Studies Institute, and the Space Engineering Research Center, University of Arizona ASSOCIATE EDITORS V. I. Avduyevsky, Soviet Academy of Sciences R. A. Binot, European Space Technology Centre Eleanor A. Blakely, Lawrence Berkeley Laboratory Richard Boudreault, Oerlikon Aerospace Lars Broman, Solar Energy Research Centre, Borlange, Sweden William C. Brown, Consultant Gay Canough, Extraterrestrial Materials, Inc. Lucien Deschamps, Electricite de France Ben Finney, University of Hawaii Josef Gitelson, BIOS Project, Krasnoyarsk, USSR Peter E. Glaser, Arthur D. Little, Inc Praveen K. Jain, Northern Telecomm Ltd Mikhail Marov, Soviet Academy of Sciences Gregg Maryniak, Space Studies Institute Michael Mautner, University of Canterbury, New Zealand Rashmi Mayur, Global Futures Network, Bombay Makoto Nagatomo, Institute of Space and Astronautical Science, Tokyo Mark Nelson, Institute of Ecotechnics John R. Page, University of New South Wales Geoffrey Pardoe, Brunel Science Park Tanya Sienko, Association for Research on Japanese Space Development Gerry Webb, Commercial Space Technologies, UK Ray A. Williamson, Office of Technology Assessment/US Congress Andrew R. Wolff, Cleveland, OH Space Power is an international journal for the presentation, discussion and analysis of advanced concepts, initial treatments and ground-breaking basic research on the technical, economic and societal aspects of large-scale, space-based solar power, space resource utilization, space manufacturing, and other areas related to the development and use of space for the long-term benefit of humanity. Papers should be of general and lasting interest and should be written so as to make them accessible to technically educated professionals who may not have worked in the specific area discussed in the paper. Editorial and opinion pieces of approximately one journal page in length will occasionally be considered if they are well argued and pertinent to the content of the journal. Submissions should represent the original work of the authors and should not have appeared elsewhere in substantially the same form. Proposals for review papers are encouraged and will be considered by the Editor on an individual basis. Editorial Correspondence: Dr Andrew Hall Cutler can be reached by telephone at (602) 322-2997, by Facsimile at (602) 326-0938 and by mail at 4717 East Fort Lowell, Tucson, AZ 85712, USA. Dr Cutler should be consulted to discuss the appropriateness of a given paper or topic for publication in the journal, or to submit papers to it. Questions and suggestions about editorial policy, scope and criteria should initially be directed to him, although they may be passed on to an Associate Editor. Details concerning the preparation and submission of manuscripts can be found on the inside back cover of each issue. Business correspondence, including orders and remittances for subscriptions, advertisements, back numbers and offprints, should be addressed to the publisher: Carfax Publishing Company, PO Box 25, Abingdon, Oxfordshire 0X14 3UE, UK. The journal is published in four issues which constitute one volume. An annual index and titlepage is bound in the December issue. ISSN 0883-6272
SPACE POWER Volume 9 Number 4 1990 Stephen M. Lord & Walter Venable. Lunar Waste Heat Radiator Design 283 V. F. Prisnyakov, Y. K. Gontarev, Y. V. Navroozov & V. N. Serebryanksy. Factors Affecting the Selection of Parameters for Low Temperature Heat Pipes for Spacecraft Thermal Control 307 V. Badescu. On the Thermodynamics of the Conversion of Diluted and Undiluted Black-body Radiation 317 Jesko A. von Windheim. On Innovation, Error and Space Exploration 323 John A. Dearien & Judson F. Whitbeck. Multi-megawatt Space rower Reactors 325 Kitt C. Carlton-Wippem. Statistical Analysis of Elliptical Keplerian Orbits, with Applications to Search and Surveillance Algorithms 349 Geoffrey A. Landis. An Evolutionary Path to Satellite Solar Power Systems 365 Title-page and Contents, Volume 9 372
Lunar Waste Heat Radiator Design STEPHEN M. LORD & WALTER VENABLE Summary Heat rejection requirements for an advanced lunar base are estimated. Various potential designs for waste heat radiators fabricated from local materials are discussed, compared and contrasted. The various designs are found to be more or less suitable depending on base latitude. Local fabrication is found to provide a substantial advantage over importation. Introduction Demand There will be significant demand for electrical power at a prospective lunar base. Any large-scale industrial processing such as lunar oxygen production [1] requires 2-4 MW of power. The largest single portion (40%) of the mass required for power generation is for the waste heat radiator even with efficient designs such as the liquid droplet radiator [2]. Other designs such as the SP100 [3] minimize the weight penalty by operating the radiator at high temperatures, which reduces the efficiency. In fact it is recognized by French [3] that use of an SP100 for a lunar base would be improved by adding a “bottoming cycle” with its associated low temperature radiator. Distribution of the power plant mass and heat load for the liquid droplet and lunar ceramic waste heat radiators are shown in Fig. 1. The areas which require inherently low temperature heat rejection are cooling of industrial processes, agriculture, and life support. The electrical power generated to support these areas will ultimately be rejected as low grade heat. We can therefore calculate the heat rejection from these areas from knowledge of their electrical consumption and the total rejection will equal the total electrical production. Lunar oxygen plant at 1000 tons per year: 2.4 MW Agriculture for 100 people at 13 kW each [4]: 1.3 MW Life support and other services for 100 people: 0.2 MW All this heat will ultimately come from the power plant, but will be rejected at low temperatures, e.g. 90°F or 308 K (the usual temperature of cooling water on Earth) [6]. There is a demand for a low temperature, large area radiator. If such a design were cost-effective, more efficient power generation could be used either directly or via a bottoming cycle. S. M. Lord, SML Associates, 157 Rancho Santa Fe Road, Encinitas, CA 92024, USA; W. Venable, San Diego L5, P.O. Box 4636, San Diego, CA 92104, USA.
Supply To meet this demand we can supply radiators from Earth or from lunar-derived materials. Radiators derived from Earth can use exotic materials such as liquid metal heat pipes or liquid droplet radiators, but pay high shipping costs based on their weight. Lunar-derived radiators can be of any weight but are constrained by the capacity of the imported processing plant and the time available for fabrication. Since manufacturability is the key, a simple design is required which can be made in a low weight processing plant. Therefore the elements of a lunar waste heat radiator made from lunar soil can be large but must be simple to minimize the processing plant mass. A radiator design is proposed which would use lunar ceramic pipes or plates made by the simplest possible processing techniques of mechanical/electrostatic beneficiation of the soil plus solar melting. (See Fig. 2). The working fluid is water which can be obtained by hydrogen reduction of ilmenite. The mass of water required is minimized by using a two-phase system for heat transfer. The ceramics formed are slowly cooled by direct radiation so no waste heat rejection system is required; although radiation shielding may be necessary to control
cool down rate. The water production is done in a plant which normally produces water for electrolysis to oxygen [7]. Use of other lunar derived materials such as lunar iron for radiator fabrication is also possible and may be preferable if the mass of the fabrication plant and mining
equipment is lower than that for the ceramics. Potential corrosion problems can be easily overcome by standard techniques of boiler feedwater treatment and the addition of small amounts of corrosion inhibiting chemicals. One such chemical, hydrazine, will be available in quantity due to its use in rocketry. Radiator Design A list of desired features is shown in Table I and is discussed below. Low Imported Weight The cost of payload launch from Earth is the overwhelming cost factor in establishing and maintaining a lunar base. Thus it is the weight imported to the moon that is crucial. Minimizing this weight can be done by use of exotic materials and inherently low weight designs or it can be done by using lunar materials. The plant for processing the lunar materials must be imported as must some other lightweight but sophisticated materials. The design should also be optimized to minimize the weight of the imported materials, not the overall weight. This can be done by simplification and avoidance of complicated equipment which needs to be imported. Use of lightweight imported materials such as radiation shields can reduce the weight of the radiator and working fluid and result in a reduction of imported mass. Unaffected by the Day-Night Cycle The significant swing in temperature on the lunar surface between day and night means that it is much easier to radiate heat at night than during the day. A system designed to handle the peak noon temperatures may be very oversized at night. This overcapacity may require reduction of the radiating area by shutdown of sections. Such shutdown and start-up is to be avoided if at all possible because it will be a constant source of problems in thermal stresses, sticking of moving parts etc. Start-up and shutdown of cooling equipment on Earth such as cooling towers and air cooled condensers is avoided by a variety of means for this very reason. Fortunately, on the moon it is possible to obtain the benefits of nighttime operation during the day if the radiator can be shielded from solar radiation as well as radiation from the lunar surface. This will give stable day and night operation as the environment of the radiator is not significantly changing, and give improved efficiencies. Optimized Heat Rejection It is desirable to avoid oversizing the radiator to handle peak loads which cause large swings in radiator temperature. It is also desirable to avoid unnecessary degradation of heat sources, so several temperatures of heat rejection may be desirable to minimize radiator area. Therefore it is desirable to match heat load to radiator performance as much as possible and be able to transfer heat to lower levels when heat rejection drops. The power plant is the major source of heat and electricity for the base and so must
balance these loads. On Earth, this is done by integrated cogeneration units where some heat can be distributed, converted to electricity, or dumped. On the moon it would be desirable to have high temperature radiators which could dump such heat as needed either directly to space or indirectly to maintain temperature in a lower temperature radiator. Ease of Maintenance and Operation The expense of manpower on the moon is very high and the dangers from failure are very real, therefore lunar systems must be reliable and easily maintained. There are several unique problems such as the high vacuum, dust, micrometeorites and high intensity radiation. Other problems are the more standard leaks, leak detection and repair. Repairing of any system usually involves isolating, draining and shutting down the section to be repaired. Sufficient spare capacity must also be available to maintain normal services. Dust and vacuum are not a problem for completely enclosed systems except for pumps which should be canned. Micrometeorites are a real problem because the large area of the radiators means that impacts will be relatively frequent. Several techniques have been suggested including double wall pipes but there is also the simple solution of using thicker and tougher pipes. The preferred approach is to use the lunar soil to reradiate heat from the backside of the pipes thus reducing the area which can be damaged. Whatever protection is chosen, it is possible that a sufficiently large meteorite will land, or some other failure will occur to produce a leak. Therefore a leak detection and repair capability is necessary. Detection of water vapor over large distances is possible using lightweight solid state detectors. Use of heat sensors would also be useful in leak detection and in finding hot or cold spots, perhaps due to blockages. Repair capability is desirable and should be capable of all repairs from pinhole leaks to replacement of whole panels. Use of small amounts of imported materials for leak sealing is sensible with larger repairs requiring isolation and replacement of leaking sections. Normal practice will be isolation and drainage with repair of all broken sections during a scheduled turnaround. Radiator System Efficiency The overall radiator system efficiency is the key parameter which may be significantly different from the efficiency of the radiator itself. This parameter is based on the temperature of the process stream before it goes into the heat exchanger that rejects the heat to the radiator system. This temperature, To is the lowest temperature that the process system can usefully use for work of some kind. In a turbine it controls the backpressure of the system and is very important in determining system efficiency. An ideal radiator with perfect emissivity would radiate that heat at To to an environment with no back radiation. Thus the theoretical maximum radiation is oTf with o being the Stefan-Boltzman constant. Other losses are shown on Table II and the typical effect of those losses on the overall performance of a radiator system are shown in Table III. It can be seen that the two-phase system is generally better than the single phase system with the exception of the losses through the wall where a liquid droplet system has no losses. A two phase
system can also have essentially zero losses if it has a thin highly conductive wall or the wall is transparent in the infrared (e.g. pure quartz). Unfortunately lunar soil has high concentrations of iron which make the glass opaque, thus transparent material cannot be produced without extensive beneficiation or downstream processing. It is possible that lunar oxygen production may produce an iron-free material which would be suitable but this is unlikely. The orientation of the radiator in the vertical or horizontal plane has the single largest impact on losses (the liquid droplet radiator must be operated in the vertical position as it is the best single phase radiator for wall losses is also the worst from the standpoint of reradiation losses). A two-phase radiator can operate at any angle but it is harder to remove the condensate from a horizontal radiator so a slight angle of 5-10° is required. This has a minor effect on efficiency if properly designed.
Radiator Configurations Four configurations are shown in Fig. 3. Vertical Radiator The vertical radiator is superficially attractive because it can radiate from both sides, however it is not possible to screen the radiator from reradiation from the lunar surface or to completely block the sun. It is possible to block the peak sun periods and to reduce reradiation by covering the soil near the radiator with a lightweight reflector [2]. If it is attempted to block more sunlight by use of a larger sunscreen then the bottom of the sunscreen interferes with radiation from the radiator and re-emits radiation picked up from the Lunar soil. Such a radiator requires a complete radiation analysis over the solar day and it must also take into account the tilt of the lunar pole and the variations in the angle of inclination of the moon’s orbit relative to the ecliptic. The tilt of the poles is only 1.53° but the maximal orbital inclination is 5.32° for a total of 6.85°. Performance of this style radiator will vary during the day-night cycle and with the seasons. Radiating power varied from 300 W/m2 with a sunscreen equal to the radiator area to 414 W/m2 for a minimal sunscreen of 12% of the area. The major problem with this system is its nighttime performance—the equilibrium temperature varied between 232 K and 252 K. Inclined Radiator The inclined radiator can be completely blocked from the sun if the angle of slope is great enough for the latitude. To guarantee complete blockage of the sun at all times we must take into account the effect of the above 6.85° variations due to inclination of the poles and the orbit. Thus at a latitude of 52° the required angle is 90-52°+ 6.85° = 45. The sun will shine on the opposing bank but this surface can be modified with a coating to reduce the reradiation effect. Calculations have been done with a solar reflector, MgO, and a metallic reflector, vacuum deposited aluminum on mylar. Radiating power varied from 383 W/m2 for the solar reflector to 418 W/m2 for the aluminum reflector. The equilibrium nighttime temperatures are 294 K and 301 K, respectively, which is an acceptable swing and well above freezing. Since these surfaces are both reflectors it is important that the solar radiation be reflected away from the radiator therefore the angle between the two slopes should be greater than 90°. Horizontal Radiator A simple design uses a horizontal radiator coated with a solar reflector. Reradiation from the soil is avoided by the horizontal location and the radiating power is a reasonable 257 W/m2 but the nighttime temperature is 266 K which is below freezing. Horizontal Radiator with Vertical Sunshield Modifying the above design with a sunshield gives several benefits. The sunshield blocks the sun and although it also absorbs reradiation from the lunar soil it can be made to preferentially radiate it away from the radiator.
This is done by using a solar radiator coating on the sun side and a metallic reflector on the radiator side. Thus although the sunshield gets hotter, 353 K, than the radiator, 308 K, its emissivity is so low on the side next to the radiator that it does not affect the radiator. This is reflected in the radiating power of 444 W/m2 and the night time temperature of 305 K. The disadvantages of this system are that the vertical sunshield becomes taller as the equator is approached with a practical limit of 15° north or south of the equator and that radiators must be widely spaced to prevent reflected radiation from one sunshield impacting the next radiator. A practical distance is ten times the height of the sunshield.
Horizontal Radiator with Active Horizontal Sunshield In equatorial regions the sunscreen must be modified to be horizontal and some 50 m above the radiator (five times the radiator width). The sunshield has a solar reflector coating on top and a black underside to prevent reflection from the lunar soil. Active pointing is needed to maintain the radiator in shadow at all times without an excessively large sunscreen, because the larger the sunscreen the worse the radiator performance. The radiating power is 395 W/m2 and the nighttime temperature is 296 K for a 10 m wide radiator and a 10 m wide sunscreen at 50 m elevation. Active pointing could be accomplished by slinging the sunscreen between four poles and controlling the location and angle with pulleys. It should be noted that perfect shadowing is not required in the early morning or late evening when the soil temperature is lower. Radiation Analysis The approach taken in analysis is the network technique of Edwards [7]. Figure 4 shows the radiation diagrams and networks derived from them for two of the radiator
designs. Once the networks have been developed then energy balances can be taken round each node and the set of simultaneous equations solved by any network solving technique. The techniques used for these relatively simple networks were iterative calculation for the large network and direct substitution for the small network. It is very important to use the correct view factors in these network equations and these were taken from the Chemical Engineers’ Handbook [8] for plates at right angles or were calculated using the crossed strings method. The use of radiation reflectors is often beneficial in obtaining high radiation efficiency but care must be taken to treat it properly, (see Fig. 5). For example, in the vertical radiator case it is very beneficial to coat the underside of the sunshield with aluminum as a radiating power of over 429 W/nr can be achieved compared to 300 W/m2 for the Kapton surface. But since lunar surface radiation is reflected to the radiator surface, as can be shown by simple geometry, this actually turns the radiator into a solar collector.
If extensive use of reflectors is planned, a thorough reflection analysis must be undertaken which must also take into account the changing angles of incidence as the sun rises and sets. A thorough radiation analysis has been made of the present configurations which has led to the present selection of the horizontal radiator with sunshield as the optimum case because of its high radiating power, good day-night stability and relatively wide range of latitudes for which it is suitable. The horizontal radiator with active horizontal shielding is suitable for equatorial regions and the inclined plate system may be suitable for higher latitudes i.e., >45°. It should be noted that shielding is very light at 1 g/m2 so extensive use is justified. In equatorial locations it is necessary to use mobile shielding in a dynamic manner to compensate for day-night shifts and annual shifts in sun angle. Manufacturing Techniques Plate Two methods were developed for manufacturing plates in situ and are shown in Fig. 6. Each has the same first step of grading a lunar surface at an angle of 5° in both the width and the length directions. Next the surface is grooved at an angle of 30° with 5 cm separation with the grooves running across the width. Next the soil is melted using solar concentrators one section at a time. Then the process is repeated for a mirror image plate on the other side. The zone between the two plates is used as the central condensate collection gutter.
The difference arises in the formation of the top plate. In method 1, pre-sifted soil is piled on the plate and grooved and fused in a similar manner to the bottom plate. The soil is then flushed out with water or gas and separated in a filter. In method 2, a mold or caul is used which is grooved top and bottom to fit the desired groove pattern. The soil is then piled on top and grooved and fused as in method 1. The caul is then pulled out of the side and placed back on the base plate for the process to be completed. A steam supply header must also be formed and a similar caul method can be used with the caul being pulled progressively along the plate. Connections between the header and the radiator proper can be made with pipes of diameter 1-3 in. In the event of a leak the pipe leading to the radiator would be fused shut until such time that repair could be undertaken. Alternatively a glass patch could be melted over the leak spot. Such techniques may be feasible with unbeneficiated regolith and previous work on glass fusion using penetrators have shown there is no significant difference in glass forming abilities between different areas of the soil. It would be beneficial to use pre-
sifted soil as an even thickness is desirable and incorporation of large stones would not be desirable. Use of the caul should be feasible if a layer of unfused soil is left between the caul and the glass so that the caul does not stick. Alternatively some high melting point fibers might be used which would have the benefit of providing some reinforcement but would need to be imported. The basic process of focusing sunlight to melt lunar regolith in place is desirable but may not be practical without advanced mirrors and/or effective radiation shields. The heat provided must be greater than the heat lost by radiation as the soil heats up, in order to provide energy to continue heating and ultimately melt the regolith. Thus the melting rate is dependent on the difference between the heat input from the mirror and the heat lost by radiation. The heat input depends on the focusing power of the mirror and the radiation loss depends on the melting point of the lunar soil and the effectiveness of the radiation shield in reducing losses. Calculations have been done to show the effect of these parameters in producing a melting rate of 1 m2/h using an 8 m diameter mirror. Figure 7 illustrates the effect and
interrelationship of the melting point, the mirror focusing power and the effectiveness of the radiation shield. For greater thicknesses the areal rates would be less in proportion, e.g. a 1 cm thickness would be half as fast. Detail of the flat plate radiator is shown in Fig. 8. Pipe Manufacturing The pipe manufacturing process is shown in Fig. 9. It is more complicated than the in situ approach and can be better controlled. Most importantly, research by SSI and Goldsworthy Engineering has already shown the feasibility of the process. The beneficiation process is not currently defined but work on ilmenite beneficiation has shown this is not particularly mass intensive. There is also the significant possibility of using the ilmenite facility beneficiation plant for this process. This is particularly relevant because an ilmenite facility will
require a large power plant and radiator and similarly a large radiator will not be built without some industrial purpose. The timing of the use of the beneficiation system is good because the radiator must be completed before the ilmenite facility can come on stream. The fabrication of the pipes into manifolds is complicated and many joints will be required. Each panel has between 7000-8000 pipes, each of which has two joints and there are four panels. The conventional technique on Earth is to use mechanical joints with a rubber gasket. The clamps could be made from lunar iron but the rubber would have to be imported. There is also the likelihood of leaks. A technique to weld or fuse the pipes to the manifold is desired which would preferably not require use of a hydrogen torch as is done in conventional glassblowing. Use of solar heating may be feasible or the older technique of frictional welding by rotation could be used. The need for isolation of leaking sections suggests that the pipes should be grouped in headers which could have a shutoff valve or other isolation technique. A remotely controlled diaphragm valve would be leakproof and reliable. The steam valves would be 10-12 in. in size and would need to be a lightweight design if imported. The condensate isolation valves would be only 1.5 in. Detail of the pipe radiator and tubular radiator designs are shown in Figs. 10 and 11.
Layout A proposed layout is shown on Fig. 12. This layout is shown because it is very efficient in water inventory. A wider radiator may be desirable in order to use longer tubes and such trade-off calculations are very valuable. It is in fact common terrestrial practice to make heat exchangers 20 ft long because the tubes come in 20 ft lengths. The convenience of fabrication out weighs any theoretical benefits of different lengths. Since the lunar tube factory would be constructed to make radiator tubes, any length can be considered. The key fabrication question may well be how long a pipe can be made and handled. If water is made from lunar oxygen then the water inventory question becomes moot. This may not occur because the water is required to operate the radiator before the large oxygen plant comes on line. However very little oxygen is required and it would be good engineering practice to build a small pilot facility first which would probably have enough capacity to fill the radiator.
Mass Requirements Water Inventory The water inventory is calculated for three major radiator elements: the steam line, the radiators, and the collection gutters and condensate return line. The layout is shown in Fig. 12 along with a weight breakdown. The calculational technique is similar for the pipes and plates. The difference is in the separation of the collection gutters or pipes. It is desirable to maintain the liquid film as thin as possible. This is done by sloping the plates at 30° slope and bringing them to a drip point where the film drips directly into a collection gutter. The film thickness varies across the plate between the top and bottom of each indentation, but the average thickness is consistent across the plate. Similarly the depth in the collection gutter increases down the gutter as more condensate drips in. The gutter was divided into ten sections to do this calculation accurately. In the pipe the film flows round the walls to the bottom where it then flows down to the collection gutter. The collection gutter is divided into 30 sections in this case to accurately model this flow. An increase in slope was evaluated but it was not as beneficial as reducing the width to 5 m from 10 m. Should it prove desirable to increase the tube length for fabrication reasons while maintaining the same water inventory, the slope could be increased. A disadvantage of this technique is that the effective radiating area varies as the cosine of the angle of slope. Thus a radiator on a 5° slope is 99.7% efficient whereas at 10° slope it is only 98.4% efficient. Thus at a 5° slope we need an extra 85 m2 whereas at 10° slope we need 342. Mass of the Radiator The area of the radiator equals the load of 10 MW divided by the radiating power of the selected radiator. For the horizontal radiator with a vertical sun screen, this is 444 W/m2. The area is thus 22 522 m2. For a pipe radiator it is desirable to separate the pipes by three times their diameter which de-rates the radiating power by a view factor of 0.72 to 320 W/m2 thus the radiating area is 31250 m2. The pipe area per unit radiator area is equal to the circumference divided by the pipe separation (i.e. Tt/d or 3.142/3=1.05). Thus the pipe weight equals the radiator areaX 1.05XthicknessX density. For pipe with a 3 mm wall thickness and a density of 2.2 g/cc the total mass is 220 000 kg, for 4 mm pipe it is 290 000 kg, for 5 mm it is 360 000 kg. Thus the radiator mass can vary between 220 000 and 360 000 kg depending on the degree of protection desired against micrometeorite damage and the amount of temperature gradient that the glass wall can tolerate. The imported mass is not particularly dependent on the radiator mass since there is a certain minimum mass required. In this case a 2000 kg facility can produce between 100000 and 150000 kg per year of pipe. The pipe can be produced in a two year time span—a reasonable construction time—and construction of the radiators can begin as soon as some pipe is available. The mining and beneficiation facility is not well defined. Preliminary mass estimates have been made for ilmenite beneficiation, where a plant handling 100000 tons of regolith was estimated to have a mass of 10.8 tons [1]. The majority of the regolith should be usable for matrix or fiber. Conservatively assuming only 10% usable product means processing at most 1500 tons per year. Using a scale factor of 0.62 (which is conservative for solids handling equipment) gives 704 kg. Two cases have been shown, a conservative one where the mining and beneficiation is assumed to be
2000 kg and an optimistic one where it is assumed to be 0 kg because it uses the ilmenite beneficiation facility’s equipment. An equatorial radiator would be 10% larger and thus require 10% more water. It would also require additional hardware for the sunscreen support towers and active pointing system. This is estimated to be 500 kg of imported structure [2]. Plate manufacturing is more difficult to evaluate but appears cheaper. A single 8 m mirror can melt sufficient soil for both the top and bottom plates in under one year whatever the soil conditions or radiator thickness required. Such a mirror is estimated to have a mass of 250 kg. Mining equipment is needed to level the soil and some beneficiation equipment is required for rock removal. A reasonable estimate would be 750 kg. If a mold or caul is required then this could have significant mass, depending on its size. For a graphite composite mold 25 m2 and 5 mm thick the weight would be 50 kg. Ten of them are required to obtain 250 m2/hr rate without moving a caul more than once an hour. This means a total mass of 500 kg for cauls. The total system mass is therefore 1500 kg compared to 4000 kg for the pipe factory. Such estimates are very crude and are sensitive to operational concerns. A much more detailed study would be required to make good estimates and select the optimal approach. Results are summarized in Fig. 13 and Table IV. Discussion The lunar radiator design problem has been discussed in the context of the lunar radiation environment and two optimal radiator designs have been developed which are
essentially unaffected (3-7 K) by day-night temperature changes and which give very high efficiencies. The radiating efficiencies are 96% and 91% or 444 and 418 W/m2 at 308 K for the two best cases. These are the horizontal radiator with a vertical shield and the radiator at a 45° slope with an aluminum shield, respectively. This compares to a theoretical efficiency of 459 W/m2. A third case using an active sunshield was developed for equatorial regions and has an efficiency of 86% with a radiating power of 395 W/m2 and a nighttime temperature of 296 K. The use of vertical radiators, even when shielded, was not attractive because it was not possible to shield the radiators from direct sun and soil radiation at the same time. The calculated value of 150 W/m2, for a full sunshield was mitigated by the use of both sides to a tolerable 300 W/m2, but the extra area was very detrimental to day-night stability with a nighttime equilibrium temperature of 232 K. A minimal sunshield of 12% of the radiator area improved the radiative power to 415 W/m2 using both sides and the nighttime temperature improved to 252 K at the cost of more daytime and seasonal variability. It should be noted that previous work [2] on liquid droplet radiators did not take into account re-emitted and reflected radiation from the underside of the sunshield and used a radiating power of 694 W/m2. Use of the optimistic number above would mean increasing the area by 67% which is feasible by increasing the height of the radiator to 100 m. The resulting 10% increase in mass is due to the collector which would have to be 1.67 times wider and the structure which would have to be higher and stronger. Two types of surface finishes could be used on the sun shields, a white solar reflector, MgO, and a metallic reflector, vacuum deposited aluminum on mylar. Use of these surface finishes in appropriate combination was critical to the improved performance of the radiators. The mass of the sunshields is considered equivalent to a conservative solar sail design of 1 g/m2 for a total mass of 25 kg. Supports can be fabricated from pipes and guy wires can be made from glass fiber, but another 25 kg is estimated for imported hardware to be on the safe side. The equatorial radiator requires a more extensive structure for the active sunshields and an additional 500 kg is estimated if all the structure is imported. The towers could be made from locally produced pipe which would cut the import mass to 100 kg. Two types of ceramic radiator were studied: one fused in place, and one fabricated of glass pipe. The melt-in-place radiator had the advantage of simplicity and low imported mass. It was remarkably insensitive to the required regolith melting temperatures (1700-2000 K). Not being reinforced it had to be thicker than the glass pipes. The fabricated pipe required beneficiation to produce matrix and fiber fractions, and a processing plant. The pipe was stronger, much tougher and thinner than the melt-in-place glass plate. Good mass estimates were available for the pipe processing
equipment, of 2000 kg for a 100-150000 kg/annum facility. No estimates were available for beneficiation, but some kind of mechanical separation using shaking tables and/or magnetic or electrostatic separation was felt to be feasible. An estimate of 2000 kg for the beneficiation plant was made. This is believed to be conservative, as a scaled estimate from ilmenite processing [1] was only 704 kg. Furthermore a large scale power plant and radiator will be associated with a lunar oxygen plant which has a very large beneficiation facility. The incremental cost to produce the required fractions for a lunar radiator could be small or zero. The pipe radiator can take advantage of the good emissivity of the lunar soil by radiating to it from the underside of the pipe. A separation of 2-3 times the pipe diameter was believed to be optimal. The optimal diameter was 1-1.5 in. (2.5-4 cm). Selecting 1.5 in. (4 cm) allowed standardization with the condensate return lines. The wider separation for larger pipe gives easier access for pipe assembly, but increases the condensate return line water inventory. The problem of micrometeorites was considered and a double tube design was evaluated and compared to a single tube or flat plate. The manufacturing problems of a double tube are considerable and clear silica glass needed for the outer tube is not readily available because of iron contamination. Furthermore, the major advantages of a double tube are a reduction in weight—which is not particularly relevant for lunar derived construction materials. A thicker reinforced single tube design with automatic leak detection and section isolation capability may be preferable. Water inventory was calculated for various layouts and the final choice for the flat plate panels was four separate radiators of 6000 m2 each. Each radiator consisted of four panels of 300 m X 5 m with the collection gutter centrally located. Loss of one of the four sections would mean raising the radiating temperature to 330 K. Loss of one panel would mean an increase to 313 K. The panels are somewhat larger for the pipes because of the pipe separation and consequent reduction in W/m2 of panel. For a separation of 2 pipe diameters (3 in.) there would be 8740 pipes in 666 m. For 3 pipe diameters it would be 7288 pipes and 833 m. If the dimensions were broader rather than longer the water inventory in the radiator would increase while that in the condensate line would be reduced. The slope of the radiators to the central gutter could be increased from its current 5° thus reducing inventory but this would mean increasing the tube length to compensate for the loss in radiating area. The steam header lines are 12 in. (30 cm) diameter to minimize pressure drop as are the isolation valves. The condensate return lines are only 1| in. diameter and operate at 20 GPM. This yields a 12 psi pressure drop for the 400 m transfer. This corresponds to 152 ft or 50 m of head in th gravity. Gravity flow is easily possible for 2 in. diameter pipe where the head requirement is only 21 ft or 7 m. It is suggested that the reactor be located where gravity feed is possible. Gravity flow is desirable for ease of operation and reliability. The ability to completely drain a radiator by gravity would also protect against freezing in a shut down condition. Radiation protection afforded by a lava tube roof would also enable the radiators to be located closer to the reactor thus cutting water inventory should the reactor be located in a lava tube or other roofed structure. Freezing is always a concern when using water as a heat transfer medium, but many remedies are available. The simplest is insulation and the condensate return pipes would be well insulated by their covering of lunar soil. A second solution is to keep the water moving as moving water freezes at a lower temperature. This requires avoiding dead legs in the detailed design. A third solution is to completely drain the
system during shutdown. A fourth is to avoid use of shutdowns to respond to changes in environmental conditions or fluctuations in heat load. Finally one can design to prevent damage in the event of freezing by leaving sufficient vapor space above the liquid to allow for expansion on freezing. All of these remedies are incorporated in the above design with the exception of heat load management, although 25% swings could be easily handled. Since the primary source of the heat load is the reactor, efforts should be taken to run the reactor steadily. Suggestions have been made to use surplus electricity for batteries and fuel cells. An alternative would be to spin up large flywheels which should operate very efficiently in the lunar vacuum and lower gravity. Sophisticated load shedding of, e.g., electrolysis units required for oxygen production would also be an alternative. Research Needs The beneficiation process is very poorly defined and needs detailed study as part of an overall beneficiation study for a lunar oxygen plant to determine what synergisms exist. Direct use of lunar regolith is very attractive because of the reduction in handling. Methods of in situ beneficiation should be studied, perhaps in conjunction with Kraft Ehricke’s suggestion [11] for a nuclear-powered sweeper for runway preparation. Fabrication of the pipes is being pursued by Goldsworthy Engineering [10] and the Space Studies Institute, but methods for making multiple connections to piping manifolds require further study and experimentation. A study of the waste heat load requirements for a realistic base and its evolution over time would be very useful in producing more realistic designs and evaluating operational concerns. The design of the radiators is sensitive to the degree of radiation shielding that is feasible. More work should be done to look at different geometries and different surface coatings. Measurement of the emissivity and thermal conductivity of lunar based ceramics would be useful as would tests with simulated micro-meterorites. Research needs are summarized in Table V.
Conclusions The terrestrially derived mass of the radiator for a 10 MWth power plant can be kept to between 2100-4100 kg thus giving a total power plant mass of between 32 500-34 500 kg. This compares favorably to all terrestrial sourced radiators which weigh in at about 20 000 kg. The use of a two phase system allows better heat transfer and thus a turbine outlet temperature some 7% lower which in turn increases the electrical output from 3.36 MWe to 3.5 MWe. The combined effect of the mass reduction and energy efficiency have raised the specific power of the plant to approximately 100 W/kg (101.5-107.5). This significant improvement gives important benefits to any large-scale user of electricity e.g. use of such a power plant would reduce the mass of a 1000 ton/yr oxygen facility to 68.6 tons from 104.6 tons. The development of a waste heat radiator of this design has a significant effect on all base designs. It significantly alters tradeoffs involving power systems and users and
allows the use of standard terrestrial energy conservation techniques without undue worry about the cost of removal of low-grade waste heat. The designs presented here show the disadvantages of the vertical radiators and significant advantages of shielding and use of surface coatings for horizontal and inclined radiators. These results will be applicable to any design at or near daytime lunar surface temperatures. Even higher temperature designs can benefit in terms of avoiding day-night changes. The optimal designs are latitude dependent and would lose the benefit of passive sun shielding for locations within 15° of the lunar equator. An actively shielded radiator for equatorial regions has been described that has an approximately 10% wt penalty. Figure 14 summarises the conclusions. REFERENCES [1] Cutler, A.H. & Krag (1985) A carbothermal scheme for oxygen production, in: Wendell W. Mendell (Ed.) Lunar Bases and Space Activities in the 21st Century, p. 559 (Lunar and Planetary Institute). [2] Panchyshyn, Multimegawatt Nuclear Power System for Lunar Base Applications, AMS 86-308, Advances in the Astronautical Sciences, 64, Part II. [3] French, J.R. (1985) Nuclear Power plants for Lunar Bases, in: Wendell W. Mendell, op. cit., p. 99. [4] Salisbury & Bugbee (1985) Wheat farming in a lunar base, ibid. [5] Sedej, Melaine Meyer (1985) Implementing supercritical water oxidation technology in a lunar base environment, ibid, p. 653. [6] Cutler, A.H. (1986) Power demands for space resource utilization, Space Nuclear Power Systems (Malabar, FL, Orbit Books). [7] Edwards, D.K. (1981) Radiation Heat Transfer Notes (UCLA, Hemisphere Publishing). [8] Perry, Chemical Engineering Handbook. [9] Rowley & Neudecker (1985) In-situ Rock melting Applied to Lunar Base Construction, in: Wendell W. Mendell, op. cit., p. 465. [10] Brandt Goldsworthy, personal communication. [11] Ehricke, Krafft A. (1985) Lunar Industrialization and Settlement, in: Wendell W. Mendell, op. cit.
Factors Affecting the Selection of Parameters for Low Temperature Heat Pipes for Spacecraft Thermal Control V. F. PRISNYAKOV, Y. K. GONTAREV, Y. V. NAVROOZOV & V. N. SEREBRYANKSY Summary Various aspects of heat pipe behavior were studied both theoretically and experimentally. Useful results are presented for a variety of wick structures and working fluids. Both static and dynamic behaviors are covered. This treatment leads to a discussion of how to determine appropriate heat pipe design parameters for space applications. Introduction The evaporation and condensation of a working fluid inside a closed system—a heat pipe—is an efficient means of removing heat from the interior of a spacecraft. It appears to be reasonable to use heat pipes as heat transport devices in active temperature control systems where the latent heat of vaporization provides significant benefits. The use of heat pipes in heat rejection radiators is of practical importance. Lower radiator thermal resistance leads to a better spacecraft mass to power ratio, and more precise control of the internal temperature. Using heat pipes to distribute waste heat to the radiator reduces its mass, simplifies its construction and increases its reliability. Radiator efficiency (temperature drop) depends on the heat fluxes in the vaporization and condensation zones of the heat pipes. Radiator efficiency is optimized by maximizing the heat flux obtainable for a given temperature drop through appropriate design. The influence of heat pipe parameters such as size and pore structure on achievable heat flux must be understood in order to properly design heat rejection radiators. We are only aware of one paper [1] which reports such relations. Experimental Research We report here a wide range of experiments on heat exchange processes in heat pipes. Our experimental apparatus [2] consists of a recirculating temperature regulated liquid bath for cooling the heat pipe’s condensing zone and an electric heater for heating the V. F. Prisnyakov, Y. K. Gontarev, Y.V. Navroozov and V. N. Serebryanksy, Dniepropetrovsk State University.
heat pipe evaporation zone. We were able to carry out experiments under a wide range of temperatures and heat flows in various heat pipe orientations using this apparatus. We used cylindrical heat pipes with diameters from 10 to 24 mm, and lengths from 100 to 600 mm. The heat pipes were either water-filled copper, or ammonia-filled stainless steel. The wick structure was made of sintered metal fibers and porosities from 60 to 85% and a thickness of 0.5 to 1.0 mm. Heat pipe wall temperatures in the evaporating, adiabatic and condensing sections were measured by thermocouples placed along the midline. The thermocouples were read by an electronic voltmeter through a commutator. The thermal power transferred by the heat pipe was determined from the heat generated by the electric heater and that absorbed by the cooling bath. The 95% confidence interval for the true heat transfer coefficients is ± 20% of the measured heat transfer coefficients. We determined the thermal resistance and heat flux of our heat pipes under appropriate operating conditions by varying the cooling bath temperature. The working fluid most well matched to spacecraft thermal control system needs was ammonia. Experimental data on the thermal resistance of the evaporator and condenser were then used to explore heat transfer models for the capillary pore structure in order to come up with appropriate relations. We included other worker’s data on water, acetone, ethanol, ammonia and freons 11 and 113; taken with evaporators made of sintered fiber, sintered powder and wire in order to extend the scope of our formulae. Theoretical Investigations Under low heat flux, heat is conducted through the evaporator to the internal meniscus, where evaporation from the liquid surface takes place without bubble formation. In this regime the convective heat transfer coefficient is independent of the heat flux. Prior theoretical work [3] predicts heat fluxes 25 to 30% lower than those obtained in the present work. This discrepancy appears to be due to a failure to take account of the specific heat flow transformation under heat flowing from the wall to the evaporating surface through the capillary structure [2], The following relation for heat transfer can be obtained using the assumption below. Nomenclature is given before the references. Figure 1 shows that the experimental data is consistent with equation (1) for conditions corresponding to a range of Reynolds numbers from 0.4 to 60. Continuing with the assumption of specific heat flow transformation, the effective thickness of the pore coat is Increased heat flow causes nucleate boiling to begin in the coat pores. This is a complex process, and its mathematical treatment is extremely difficult. Thus we must use semiempirical relationships based on models similar to our heat pipe evaporators [4], This relationship gives good results for water, ethanol and freon, but is off by up to 100% for ammonia and nitrogen, a distinct group of thermodynamically similar liquids.
The differing physical properties of some heat transfer agents result in different conditions for steam generation [5], causing the convective heat transfer relations for boiling in porous media to differ from those for smooth heat transfer surfaces. Considering convective heat transfer during the growth of a vapor bubble in combination with the results reported in [5] according to the procedures described in [6] permit us to derive the convective heat transfer law we seek in general form: Figures 2 and 3 show the agreement of various experimental results with this relation, and also permit us to evaluate the arbitrary constant in equation (3). Thus, for water, acetone, ethanol, and freons 11 and 113, providing the convective heat transfer law has the form a~qj. For ammonia, this constant equals and the convective heat transfer law has the form a~q\
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