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B (4wo D3) (2 — «)/3€
G PF1-E.)/(1 - p) - AT.
(TIT.) - I
and the σ is the Stefan-Boltzman constant, D is the
and RT, is the temperature that a black disk covering the entrance end 14 would attain in the cold radiation field of space. Now R, e, p and T, are independent parameters but E, is dependent on them and S, i.e., E., is a monotonically increasing function of Cm. Unfortunately E.(R,e,p,To,S) is not known apriori. When Cm is large (S small), the temperature achieved deep in the absorber 10, T1, (L ► D) is low. Hence, even though E. is large when Cm is large, the overall efficiency
F(x) = For,(x)
is low because the thermal-to-mechanica¡ power con-
where we have assumed T, is also the Carnot exhaust 65 temperature as if the fluid 42 were also circulated through the Carnot engine as the working fluid. Since in Eq. (10b), T, TM and T' all approach zero as x -8.
0 PS 1
as plausible values for attenuation coefficients of short and long wavelength radiations propagating in the absorber 10. It is also possible to take
In order to find the monotonic function, E. (Cm), and consequently T,(Cm) or T(S) via Eqs. (14) and then E(Cm) or E(S) via Eqs. (15) we first characterize the system under study by a set of values for the parameters of Eq. (11), and also for both p, the wall reflectivity for the incident short wavelength flux, and ƒ (0), its angular distribution, so that 7,(x) can be calculated. Then we select a particular E, of interest, calculate G and guess a test value of Cm wich we shall designate C, .If C, Cm, then as Eq. (11) is solved for T(x) at increasing x, using the initial conditions, the derivative T'(x) will remain too large for x≥ 0 and in fact TL 25 → ∞. Likewise, if C, < Cm, then T → ∞ as x ∞. Consequently, for each physically realistic E, there is a unique value of C, for which T, remains finite as x→ ∞ and the relationship between E, and Cm or S is found from this condition.
But, for a simplified but practical example of this procedure, we assume
as a conservative estimate of the fraction of wall radiation which can be reflected back into the absorber 10 with a good optical design, e.g., a phocon entrance such as will be described hereinafter or external mir
rors. Next for a particular R, i.e. R=2, we assume various values for E, and with Eq. (18) calculate the corresponding value of S and then for this S and E, calculate E from Eq. (156). The results of this R=2 case are shown in FIG. 4 and we see that a maximum overall efficiency of 73% results when E. = 90%. More rapid fluid flow produces higher absorber efficiency but lowers the exit temperature excessively. Likewise less rapid coolant flow can result in better Carnot efficiency, but reradiation losses reduce R. excessively. The efficiency at optimum coolant fluid flow rate for
other values of R is shown in FIG. 5.
A conventional black absorber-radiator in the same solar flux would have much greater reradiation losses, lower E, and reach temperatures far less than T1. For 40 example, a conventional black absorber in an R=2 flux has a peak temperature even with no useful power output of only 2To, thus it's Carnot efficiency would not exceed 50% even if the over all efficiency fell to zero. Thus, the present absorber 10 is three four times more efficient and functions well in poorly concentrated sunlight.
We can define an effective emissivity, e, for the surface of the entrance end 14 in terms of the exhaust temperature achieved and the reradiation losses, i.e. F. (1-E) ATL
and a = 1 as we have already noted
ale = (T¿RT.)* (1−E.)~'
or in terms of the dimentionless variables of our model,
Often the true value of Cm (or S) differs from the
This effective ale at optimum coolant flow rate is also
This analysis has assume that the absorber 10 was deployed in the cold radiation field of space. Because of its high efficiency, relatively little waste heat must be
11 rejected. Thus, in space, with a relatively small waste infrared radiation from the walls of the absorber by the heat radiator located in the shadow of the concentrat- water molecules in the air decreases the wall radiation ing mirror 40, T, << 300° K would be possible. Then escape probability and further improves thermal effi. rather large values of T/T, could be tolerated without ciency. Thus, any fluid 104 so used an be chosen for its damage to a quartz absorber. In addition to higher s infrared radiation absorptive ability as well as for its predicted efficiency, for units producing several KW or heat transfer capability. Alternately, desireable fluid more, this absorber and advanced turbine generators 104 may be a mixture having one or more components developed for sapce applications offer significantly with infrared absorption ability. The use of water valower cost and lift off weights compared to either solar por-laden air as the fluid 104 is simply an example of an cells or isotopic power supplies.
10 inexpensive, non-polluting, non-toxic, readily available On earth T, 2 300° K and material problems limit fluid having adequale heat transfer capability and infrathe T/T, ratio to about 5. Thus for most of the day, red absorbing ability. While not shown in detail, a comeven in northern lattitudes, the fluid flow rate would be bination of fluid flow against the external walls of an automatically controlled to maintain the highers possi- absorber, such as the absorber 10 of FIG. 1, and ble Carnot efficiency permitted by the construction is through the central cavity of a absorber, such as the materials and the absorber 10 would operate at greater absorber 100, is useful, heat being thereby transferred than optimum efficiency. A linear slot absorber (not from such an absorber both internally and externally shown) over a parabolic mirror such as 40 is also at- thereof while infrared absorption by the interior fluid tractive and may also be able to produce a materials- adds its benefit to the structure. The only significant limited exhaust temperature.
20 requirement of the fluid 104 is that it be transparent to In spite of the fact that E, is nearly unity, economic the desired electromagnetic wavelengths of sunlight. considerations would result in a significant part of the Further referring to FIG. 2, a solar power plant is sunlight collected by the concentrating mirror 40 being generally shown at 110 to utilize the energy obtained poorly focused and wasted. However, unlike the uncol- from the absorber 100 through thermal storage of said lected waste heat that goes up the chimney of a conven- 25 energy. Referring back to the absorber 100, it is seen tional power plant and adds to the local environmental that an optical focusing device, such as a lens 112, heat load, this concentrated sunlight can be reflected focuses solar energy through a transparent dome winso as to escape from the earth at negligible incremental dow 114 into the entrance end or mouth of the abcost. Thus there need be no change in the local albedo. sorber 100. The lens 112 may be operated by suitable Since this simple, economic, absorber 10 is not danger- 30 mechanical apparatus to image the sun into the enous, does not require intense sunlight, and need not trance end of the absorber 100. The interior of the have any net local ecological impact, it could be lo- absorber 100 forms a part of a pressurized flow path for cated in urban power demand areas to avoid transmis- the fluid 104 through the plant 110, the walls of the sion losses. It could also be used to make fuel by pro- absorber 100 extending to the dome window 114 at the ducing hot steam for known chemical cracking pro- 35 entrance end thereof and being insulated by insulation
116 at and near the outlet end thereof. The fluid used to extract heat from the absorber 10 A solar energy entering the absorber 100 reflects through the walls thereof may be in the gaseous or deeper thereinto, the temperature of the walls inliquid state. A mixture of gases, such as air, is perfectly creases. The fluid 104 passing through the central cavsuitable as well as would a mixture of liquids, such as 40 ity 102 extracts heat from the walls and emerges as a sodium and potassium. While a sodium-potassium mix- relatively hot fluid at the outlet 108. The hot fluid then ture would be particularly suited to use for direct drive enters a subterranean thermal energy storage tank 118 of a turbine or the like, any substance in a fluid state is which is suitably insulated. The storage tank 118 can be useful in the practice of the invention since any fluid made of iron and filled with a brick lattice work which substance would have heat transfer capability. 45 permits the fluid 104 to circulate through it with effi
As can be seen in FIG. 2, an absorber 100 has a cient energy transfer between the fluid and the conlongitudinal cross-section at its inner end, or cold end tents of the tank. The insulation for the tank 118 might which is generated by revolution of a paraboloidal simply be dry and 10 to 20 feet thick surrounding the segment as will be described hereinafter. The absorber iron tank on all sides, the dry sand being contained in a 100 further has a central cavity 102 defined by the 50 vented masonry chamber (not shown) to prevent exwalls thereof. A heat transfer fluid 104 is drawn cessive intrusion of ground water. The heat and the through the central cavity 102 itself to absorb heat vent assure that the sand remains dry. The inner most from the interior walls of the absorber 100. The heated layers of and adjacent to the tank can provide addifluid 104 is ducted through the absorber 100 from an tional energy storage. Radial fins can be attached to the inlet 106, substantially through the length of the central 55 iron tank, to facilitate radial heat flow. Longitudinal cavity 102, and through an outlet 108, the fluid 104 fins should not be used as axial heat coduction through absorbing heat from the walls of the absorber 100 on the tank 118 is undesirable as will be explained hereinmovement therethrough. Thus, transfer of energy after. through the walls of the absorber 100 is avoided in this Some or all of the hot fluid 104 passes through a tank embodiment. The heated fluid 104 withdrawn from the 60 bypass tube 120 and a tank bypass alve 122 to enter a outlet 108 may be used as desired, one potential man- motor (expansion) unit 124 and produce useful work. ner of its use being described hereinafter. The Now of The fluid 104 is still warm when it enters a counterflow the fluid 104 through the absorber 100 acts to over- heat exchanger 126 which extracts heat from the fluid come heat loss by conduction within said absorber and so that a relatively cold, low pressure flow of fluid also acts to extend the high temperature region further 65 enters a compressor 128 located in the system. The into the absorber, thereby improving the thermal effi- output flow from the compressor 128 is a cool high ciency thereof. If the Nuid 104 be taken to be air having pressure fluid which is directed through a day valve 130 water vapor as a component part thereof, absorption of back into the tubular absorber 100 if sunshine is avail
24-215 0.78 - 59
14 able or through a night valve 132 if inadequate sun- storage mass within the tank 118, there is less danger shine is available.
than in a conventional steam boiler. At night time or during periods of low light levels, Enclosure of the absorber 100 as shown in FIG. 2 to when the night valve 132 is open, the relatively cool protect the device from the elements is desirable. The high pressure Nuid from the compressor 128 passes S concentrating optics may also be economically and through a night line 134, into the left end of the thermal advantageously enclosed for protection. Use of a fluid energy storage tank 118 remote from the absorber 100 104 having strong absorption capability in the infrared and a "store energy" valve 136 is closed. Thus, the prevents escape of wall radiation as described previnight time flow of fluid 104 through the storage tank ously by internally reabsorbing the energy. This absorp118 cools an increasing volume of the left end of the 10 tion effectively prevents wall radiation from escaping storage tank but is heated to almost the temperature of and at high temperatures significantly aids in the radial the right end in a relatively short section of the storage transport of energy in the cooling fluid 104 and reduces tank and does not appreciably reduce the temperature radial temperature radients. Unfortunately, the radiaof the right end. Thus, the storage tank 118 has a cool tion from the hot fluid 104 partially replaces the wall left region, a relatively short temperature transition 15 radiation it prevents. However, at no wavelength can zone, and a high temperature right region. During the this hot fluid radiation exceed the essentially black body night or other times when energy is extracted from the radiation it replaces. Thus, the net effect is beneficial. storage tank, the transition zone moves into the high With uniform solar reflectivity the thermal flux on temperature region which decreases in volume, and the the walls of the absorber decreases with distance from cool, left region grows in volume. Axial conduction in 20 the entrance end. Because of this fact and the fact that the brick lattice work is undesirable as it tends to make the fluid temperature is steadily increasing, the heat the temperature of the storage tank more uniform and flux into the fluid decreases with distance more rapidly thus lower the temperature of the gasses entering the than the thermal flux on the walls. Economic considerexpansion motor unit 124.
ations related to the insulation cost can make an intenDuring those daylight hours when more energy is 25 tional reduction in the solar reflectivity with distance available than required, the store energy valve 136 is from the entrance end desirable even though the rerapartially open and tank bypass valve 122 is partially diation losses would increase. Thus, shorter absorber closed. Then part of the hot flow of fluid 104 from the tube lengths with the same net solar absorption are tubular absorber 100 is drawn through the energy stor- possible.
30 age tank 118 and the temperature transition zone is The conformation shown in FIG. 2 for the absorber moved into the cool left region which decreases in 100 at its entrance end, or cold end, should now be volume as energy is added to the energy storage tank, described in greater detail due to the great increase in This part of the now passing through the store energy absorber efficiency which can be attained with the use valve 136 is cool and mixes with the hot flow from the thereof. This particular conformation can be employed
35 tank bypass valve 122 as shown. Under certain circum- to advantage with any of the embodiments described stances, it is desirable to avoid excessive reduction in herein, even though paraboloidal sections or any virtuthe inlet temperature of the expansion motor unit 124 ally any shape having a longitudinal cross-section and yet also desirable to make the flow through the whereby the absorber increases in section with distance energy storage tank 118 relatively large. This is possi- 40 from the inner (or entrance) end thereof. As seen in ble if part or all of the flow through the energy storage
FIG. 6, an absorber tube 200, is shown to be formed as tank 118 is forced by a pump (not shown in FIG. 2) a right circular cylinder except at its entrance end 202, backwards through the night line 134 and the night the entrance end 202 having a cross-section which valve 132. If no output power from the motor unit 124 increases with distance from the entrance end 202 is desired, then all of the flow through the absorber 100 4s toward the cylindrical body of the absorber tube 200 so can be pumped backwards through the night line 134 that solar radiation collected by the surface of the conand night valve 132 to achieve maximum storage of centrating optics of radius R, associated therewith near energy
the rim of said optics is converted into more nearly During hours of intense sunlight, the flow through the paraxial rays after the first reflection inside the ab absorber 100 is relatively large and maintained to avoid so sorber and thus travels much further thereinto before damage to the absorber. At night and at other times being absorbed. The entrance end 202 is formed of a when the flow downward through the absorber 100 is paraboloidal segment 204 of rotation, the segment 204 inadequate to prevent natural convective heat transfer having one end fixed at the point (-79,0) on the Carteupwards through the absorber, it is closed off by an sian axis, the parabola of which the segment 204 is internal insulating plug (not shown in FIG. 2). The ss taken having its focus at the point (ro) and having its thermodynamic cycle for the plant 110 is closed and axis inclined to the y-axis by the angle a. Thus, the the working gas of the expansion motor unit 124 is the equation for the segment 204 is given by: same as employed in the absorber 100 in the system shown in FIG. 2. Carbon dioxide and/or steam are
l(1-1.) cos a - y sin al' - 45,11+sin a) (x sin aty
cos a + 1.) attractive for use as the fluid 104 as they are chemically 60 stable at high temperatures, have strong infrared ab
Rotation of this curved segment 204 about the y-axis sorption bands, are relatively noncorrosive and have
generates the "paraboloidotoridal phocon" which is adequate molecular weight to permit economical tur
the shape taken by the entrance end 202. In the prebo-compressor designs. Further, the energy storage ferred embodiment, the choice of the angle a is usually tank 118 is far below ground level; thus, even a rapid 65 related to the rim angle of the concentrator optics @by pressure failure in the high temperature storage tank 118 is unlikely to cause damage at ground level. Since
a-2/2 most of energy in the system is stored in the thermal
16 but other relationships between 0, and a are practical. given, it should be recognized that chemical, electrical, The length of this entrance end 202 is arbitrary but may and other mechanical apparatus may be so employed. be usefully limited by its intersection with the line given For example, the hot fluid absorber according to the by:
invention could be used for smelting a metal ore by y tan a--X
5 direct contact with the hot fluid. Further, the fluid in an This shape acts to decrease the angle by which rays are
absorber according to the invention can be chosen so inclined to the axis of the tube 200. It is to be pointed
as to be capable of maintaining a net electric charge, out that r, is taken to be the radius of a circle contain
the absorber being arranged as a thermoelectric genering all rays in the focal plane of the concentrating op 10 for both) of the absorber. The invention, as described
ator to produce a useful effect either inside or outside tics and subtends a half angle 8, equal to the source. The relationships described can be used to generate
hereinabove and defined by the following claims, is entrance end conformations suitable to varying uses therefore seen to be useful in a variety of applications depending on the maximum angle of inclination of where radiant energy is to be collected and utilized. those rays which are desired to be focused into the I claim:
15 absorber tube 200. As an example, if the rim angle of a 1. Apparatus for facilitating energy flow, comprising: concentrating mirror is 60° the length of this initial body means having walls which define a cavity and an phocon entrance end 202 required to convert all rays entrance opening to the cavity; to 30° or less inclination to the absorber axis is only a flowable mass of material; at least a portion of 1.15 maintube (tube 200) diameters. The entrance
which material is disposed within the cavity and area for this example would be only 28% of the ab
comprises a fluid composition capable of undergosorber cross section and consequently much of the ing a chemical change on exposure to energy; shortest wavelength wall radiation or hot gas radiation
means for directing energy into the entrance opening not blocked by the selective mirror action of the walls
of the body means; would fail to escape from this convergent phocon exit.
means surmounting the entrance opening of the body Both the increased distance between reflections for the
means and sealing said cavity from ambient, said solar radiation propagating into the absorber tube 200 and the relatively larger main tube diameter also act to
means being transparent to the energy being di
rected into said entrance opening; and, make the thermal wall flux load very much smaller than the entrance flux. It is to be understood that any in
means for directing a flow of said mass along the creasing cross-sectional portion at the entrance end of 30
walls of the body means away from the entrance an absorber improves performance. The cross-sec
opening thereof to cool certain portions of said tional shape may be conical or otherwise than is shown body means which are near the entrance opening particularly in FIGS. 2 or 6.
relative to other portions of said body means relaReferring to FIG. 3, a sealed absorber 150 is shown tively further away from said entrance opening. to comprise an absorber body 152 silvered for reflec. 35 2. The apparatus of claim 1 wherein the energy ditive purposes by a silver layer 154 and insulated by an rected into the entrance opening of the body means is insulative layer 156. The body 152 has an integral win
non-thermal energy. dow portion 158 which encloses an optical focusing 3. The apparatus of claim 1 wherein the walls of the mirror 160. In this embodiment of the invention, the body means are at least partially transparent and absorinterior of the cavity defined by the body 152 is sealed 40 bent to the energy directed into the entrance opening from ambient and has an internal atmosphere of a de- of the body means, the walls being covered over at least sired nature, such as gases which are capable of under- a portion of their surfaces opposite those surfaces degoing a chemical change on heating thereof by the fining the cavity with a reflective layer, the energy absorbed solar energy. The flow of fluid for cooling the entering the cavity of the body means through the enabsorber 150 ( not shown) could also be external of the 4S trance opening being reflected by said layer into the absorber body 152 in this embodiment. The window
cavity in a direction away from the entrance opening portion 158 may be a focusing optical element itself or
for absorption of said energy by said walls, the flow of may be a bundle of optical fibers for concentrating
mass along the walls cooling those portions of the body energy into the entrance end of the body 152 by inter
means nearest the entrance opening relative to those nal reflection.
portions of the body means located relatively more Energy developed in the present absorber structures
distant from the entrance opening, thereby to prevent may also be stored chemically such as heating water (or
thermal reradiation from the cavity through the enother suitable fluid) either internally or externally (or both) of the absorber structure to produce steam at a
trance opening. desired temperature, such as 1300° to 1400° K, and 55
4. The apparatus of claim 1 and further comprising then directing the heated steam against a substance or
insulation disposed about the body means, the insulamixture of substances to cause a reaction which effec
tion comprising alternate layers of thin metal and dusttively stores energy. As an example, an alkali oxide may
like particles separating the layers of thin metal. be decomposed in this fashion. On cooling of the steam
5. The apparatus of claim 1 wherein the walls are (to 600° to 700° K) some of the steam could be used to 60 formed of a material more transparent to the energy react with the alkali metal previously produced to pro
entering the cavity than to the radiation from the walls duce hydrogen, this substance essentially storing the resulting from energy absorbed by said walls. energy developed in the absorber for later use, such as 6. The apparatus of claim 1 wherein the walls are by burning. The chemistry of such an operation is simi- formed of material relatively near the entrance opening lar to that described in U.S. Pat. No. 3,490,871. 65 which is a good absorber of infrared radiation relative
As is obvious, many techniques may be employed to to the material of which the walls are formed at por. utilize the energy-laden fluid as it exists either one of tions of the body means relatively further away from the absorbers 10 or 100. While one example has been the entrance opening.