however, T and consequently E are also unknown functions of Cm (or S) assuming the parameters R,e,p and T, are fixed.

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 T → ∞. Likewise, if C, < Cm, then TL ∞. 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.

15

20

25

30

b= 0.5

(196)

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. (15b). 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.

45

50

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 Thus

ale (TJRT.)* (1−E ̧)~'

(20)

(216)

or in terms of the dimentionless variables of our model,

11 rejected. Thus, in space, with a relatively small waste heat radiator located in the shadow of the concentrating mirror 40, T. << 300° K would be possible. Then rather large values of T/T, could be tolerated without damage to a quartz absorber. In addition to higher 5 predicted efficiency, for units producing several KW or more, this absorber and advanced turbine generators developed for sapce applications offer significantly lower cost and lift off weights compared to either solar cells or isotopic power supplies.

12

On earth T, 300° K and material problems limit the TT, ratio to about 5. Thus for most of the day, even in northern lattitudes, the fluid flow rate would be automatically controlled to maintain the highers possible Carnot efficiency permitted by the construction 15 materials and the absorber 10 would operate at greater than optimum efficiency. A linear slot absorber (not shown) over a parabolic mirror such as 40 is also attractive and may also be able to produce a materialslimited exhaust temperature.

In spite of the fact that E, is nearly unity, economic considerations would result in a significant part of the sunlight collected by the concentrating mirror 40 being poorly focused and wasted. However, unlike the uncollected waste heat that goes up the chimney of a conventional power plant and adds to the local environmental heat load, this concentrated sunlight can be reflected so as to escape from the earth at negligible incremental cost. Thus there need be no change in the local albedo. Since this simple, economic, absorber 10 is not dangerous, does not require intense sunlight, and need not have any net local ecological impact, it could be located in urban power demand areas to avoid transmission losses. It could also be used to make fuel by producing hot steam for known chemical cracking pro

cesses.

20

25

30

35

The fluid used to extract heat from the absorber 10 through the walls thereof may be in the gaseous or liquid state. A mixture of gases, such as air, is perfectly suitable as well as would a mixture of liquids, such as 40 sodium and potassium. While a sodium-potassium mixture would be particularly suited to use for direct drive of a turbine or the like, any substance in a fluid state is useful in the practice of the invention since any fluid substance would have heat transfer capability.

45

50

55

As can be seen in FIG. 2, an absorber 100 has a longitudinal cross-section at its inner end, or cold end which is generated by revolution of a paraboloidal segment as will be described hereinafter. The absorber 100 further has a central cavity 102 defined by the walls thereof. A heat transfer fluid 104 is drawn through the central cavity 102 itself to absorb heat from the interior walls of the absorber 100. The heated fluid 104 is ducted through the absorber 100 from an inlet 106, substantially through the length of the central cavity 102, and through an outlet 108, the fluid 104 absorbing heat from the walls of the absorber 100 on movement therethrough. Thus, transfer of energy through the walls of the absorber 100 is avoided in this embodiment. The heated fluid 104 withdrawn from the outlet 108 may be used as desired, one potential manner of its use being described hereinafter. The flow of the fluid 104 through the absorber 100 acts to overcome heat loss by conduction within said absorber and also acts to extend the high temperature region further 65 into the absorber, thereby improving the thermal efficiency thereof. If the fluid 104 be taken to be air having water vapor as a component part thereof, absorption of

60

Further referring to FIG. 2, a solar power plant is generally shown at 110 to utilize the energy obtained from the absorber 100 through thermal storage of said energy. Referring back to the absorber 100, it is seen that an optical focusing device, such as a lens 112, focuses solar energy through a transparent dome window 114 into the entrance end or mouth of the absorber 100. The lens 112 may be operated by suitable mechanical apparatus to image the sun into the entrance end of the absorber 100. The interior of the absorber 100 forms a part of a pressurized flow path for the fluid 104 through the plant 110, the walls of the absorber 100 extending to the dome window 114 at the entrance end thereof and being insulated by insulation 116 at and near the outlet end thereof.

A solar energy entering the absorber 100 reflects deeper thereinto, the temperature of the walls increases. The fluid 104 passing through the central cavity 102 extracts heat from the walls and emerges as a relatively hot fluid at the outlet 108. The hot fluid then enters a subterranean thermal energy storage tank 118 which is suitably insulated. The storage tank 118 can be made of iron and filled with a brick lattice work which permits the fluid 104 to circulate through it with efficient energy transfer between the fluid and the contents of the tank. The insulation for the tank 118 might simply be dry and 10 to 20 feet thick surrounding the iron tank on all sides, the dry sand being contained in a vented masonry chamber (not shown) to prevent excessive intrusion of ground water. The heat and the vent assure that the sand remains dry. The inner most layers of and adjacent to the tank can provide additional energy storage. Radial fins can be attached to the iron tank, to facilitate radial heat flow. Longitudinal fins should not be used as axial heat coduction through the tank 118 is undesirable as will be explained hereinafter.

Some or all of the hot fluid 104 passes through a tank bypass tube 120 and a tank bypass alve 122 to enter a motor (expansion) unit 124 and produce useful work. The fluid 104 is still warm when it enters a counterflow heat exchanger 126 which extracts heat from the fluid so that a relatively cold, low pressure flow of fluid enters a compressor 128 located in the system. The output flow from the compressor 128 is a cool high pressure fluid which is directed through a day valve 130 back into the tubular absorber 100 if sunshine is avail

24-215 O-78-59

able or through a night valve 132 if inadequate sunshine is available.

5

14

At night time or during periods of low light levels, when the night valve 132 is open, the relatively cool high pressure fluid from the compressor 128 passes through a night line 134, into the left end of the thermal energy storage tank 118 remote from the absorber 100 and a "store energy" valve 136 is closed. Thus, the night time flow of fluid 104 through the storage tank 118 cools an increasing volume of the left end of the storage tank but is heated to almost the temperature of the right end in a relatively short section of the storage tank and does not appreciably reduce the temperature of the right end. Thus, the storage tank 118 has a cool left region, a relatively short temperature transition zone, and a high temperature right region. During the night or other times when energy is extracted from the storage tank, the transition zone moves into the high temperature region which decreases in volume, and the cool, left region grows in volume. Axial conduction in 20 the brick lattice work is undesirable as it tends to make the temperature of the storage tank more uniform and thus lower the temperature of the gasses entering the expansion motor unit 124.

15

25

30

35

During those daylight hours when more energy is available than required, the store energy valve 136 is partially open and tank bypass valve 122 is partially closed. Then part of the hot flow of fluid 104 from the tubular absorber 100 is drawn through the energy storage tank 118 and the temperature transition zone is moved into the cool left region which decreases in volume as energy is added to the energy storage tank, This part of the flow passing through the store energy valve 136 is cool and mixes with the hot flow from the tank bypass valve 122 as shown. Under certain circumstances, it is desirable to avoid excessive reduction in the inlet temperature of the expansion motor unit 124 and yet also desirable to make the flow through the energy storage tank 118 relatively large. This is possi- 40 ble if part or all of the flow through the energy storage tank 118 is forced by a pump (not shown in FIG. 2) backwards through the night line 134 and the night valve 132. If no output power from the motor unit 124 is desired, then all of the flow through the absorber 100 can be pumped backwards through the night line 134 and night valve 132 to achieve maximum storage of energy.

45

During hours of intense sunlight, the flow through the absorber 100 is relatively large and maintained to avoid 50 damage to the absorber. At night and at other times when the flow downward through the absorber 100 is inadequate to prevent natural convective heat transfer upwards through the absorber, it is closed off by an internal insulating plug (not shown in FIG. 2). The 55 thermodynamic cycle for the plant 110 is closed and the working gas of the expansion motor unit 124 is the same as employed in the absorber 100 in the system shown in FIG. 2. Carbon dioxide and/or steam are attractive for use as the fluid 104 as they are chemically 60 stable at high temperatures, have strong infrared absorption bands, are relatively noncorrosive and have adequate molecular weight to permit economical turbo-compressor designs. Further, the energy storage tank 118 is far below ground level; thus, even a rapid 65 pressure failure in the high temperature storage tank 118 is unlikely to cause damage at ground level. Since most of energy in the system is stored in the thermal

With uniform solar reflectivity the thermal flux on the walls of the absorber decreases with distance from the entrance end. Because of this fact and the fact that the fluid temperature is steadily increasing, the heat flux into the fluid decreases with distance more rapidly than the thermal flux on the walls. Economic considerations related to the insulation cost can make an intentional reduction in the solar reflectivity with distance from the entrance end desirable even though the reradiation losses would increase. Thus, shorter absorber tube lengths with the same net solar absorption are possible.

The conformation shown in FIG. 2 for the absorber 100 at its entrance end, or cold end, should now be described in greater detail due to the great increase in absorber efficiency which can be attained with the use thereof. This particular conformation can be employed to advantage with any of the embodiments described herein, even though paraboloidal sections or any virtually any shape having a longitudinal cross-section whereby the absorber increases in section with distance from the inner (or entrance) end thereof. As seen in FIG. 6, an absorber tube 200, is shown to be formed as a right circular cylinder except at its entrance end 202, the entrance end 202 having a cross-section which increases with distance from the entrance end 202 toward the cylindrical body of the absorber tube 200 so that solar radiation collected by the surface of the concentrating optics of radius R, associated therewith near the rim of said optics is converted into more nearly paraxial rays after the first reflection inside the absorber and thus travels much further thereinto before being absorbed. The entrance end 202 is formed of a paraboloidal segment 204 of rotation, the segment 204 having one end fixed at the point (−r,,o) on the Cartesian axis, the parabola of which the segment 204 is taken having its focus at the point (r., o) and having its axis inclined to the y-axis by the angle a. Thus, the equation for the segment 204 is given by:

((x−r,) cos a − y sin a)'= 4r,(1+sin a) (x sin a + y cos a + r.)

Rotation of this curved segment 204 about the y-axis generates the "paraboloidotoridal phocon" which is the shape taken by the entrance end 202. In the preferred embodiment, the choice of the angle a is usually related to the rim angle of the concentrator optics, by

a =/2 - 4。

but other relationships between 0, and a are practical. The length of this entrance end 202 is arbitrary but may be usefully limited by its intersection with the line given by:

y tan am-x.

This shape acts to decrease the angle by which rays are inclined to the axis of the tube 200. It is to be pointed out that r, is taken to be the radius of a circle contain

ing all rays in the focal plane of the concentrating op tics and subtends a half angle e, equal to the source. The relationships described can be used to generate entrance end conformations suitable to varying uses depending on the maximum angle of inclination of those rays which are desired to be focused into the absorber tube 200. As an example, if the rim angle of a concentrating mirror is 60° the length of this initial phocon entrance end 202 required to convert all rays to 30° or less inclination to the absorber axis is only 1.15 maintube (tube 200) diameters. The entrance area for this example would be only 28% of the absorber cross section and consequently much of the shortest wavelength wall radiation or hot gas radiation not blocked by the selective mirror action of the walls would fail to escape from this convergent phocon exit. Both the increased distance between reflections for the solar radiation propagating into the absorber tube 200 and the relatively larger main tube diameter also act to make the thermal wall flux load very much smaller than the entrance flux. It is to be understood that any increasing cross-sectional portion at the entrance end of an absorber improves performance. The cross-sectional shape may be conical or otherwise than is shown particularly in FIGS. 2 or 6.

40

Referring to FIG. 3, a sealed absorber 150 is shown to comprise an absorber body 152 silvered for reflec- 35 tive purposes by a silver layer 154 and insulated by an insulative layer 156. The body 152 has an integral window portion 158 which encloses an optical focusing mirror 160. In this embodiment of the invention, the interior of the cavity defined by the body 152 is sealed from ambient and has an internal atmosphere of a desired nature, such as gases which are capable of undergoing a chemical change on heating thereof by the absorbed solar energy. The flow of fluid for cooling the absorber 150 (not shown) could also be external of the absorber body 152 in this embodiment. The window portion 158 may be a focusing optical element itself or may be a bundle of optical fibers for concentrating energy into the entrance end of the body 152 by internal reflection.

45

50

Energy developed in the present absorber structures may also be stored chemically such as heating water (or other suitable fluid) either internally or externally (or both) of the absorber structure to produce steam at a desired temperature, such as 1300° to 1400° K, and 55 then directing the heated steam against a substance or mixture of substances to cause a reaction which effectively stores energy. As an example, an alkali oxide may be decomposed in this fashion. On cooling of the steam (to 600° to 700° K) some of the steam could be used to 60 react with the alkali metal previously produced to produce hydrogen, this substance essentially storing the energy developed in the absorber for later use, such as by burning. The chemistry of such an operation is similar to that described in U.S. Pat. No. 3,490,871.

As is obvious, many techniques may be employed to utilize the energy-laden fluid as it exists either one of the absorbers 10 or 100. While one example has been

65

16

given, it should be recognized that chemical, electrical, and other mechanical apparatus may be so employed. For example, the hot fluid absorber according to the invention could be used for smelting a metal ore by direct contact with the hot fluid. Further, the fluid in an absorber according to the invention can be chosen so as to be capable of maintaining a net electric charge, the absorber being arranged as a thermoelectric gener(or both) of the absorber. The invention, as described ator to produce a useful effect either inside or outside hereinabove and defined by the following claims, is therefore seen to be useful in a variety of applications where radiant energy is to be collected and utilized. I claim:

1. Apparatus for facilitating energy flow, comprising: body means having walls which define a cavity and an entrance opening to the cavity;

a flowable mass of material; at least a portion of which material is disposed within the cavity and comprises a fluid composition capable of undergoing a chemical change on exposure to energy; means for directing energy into the entrance opening of the body means;

means surmounting the entrance opening of the body means and sealing said cavity from ambient, said means being transparent to the energy being directed into said entrance opening; and,

means for directing a flow of said mass along the walls of the body means away from the entrance opening thereof to cool certain portions of said body means which are near the entrance opening relative to other portions of said body means relatively further away from said entrance opening. 2. The apparatus of claim 1 wherein the energy directed into the entrance opening of the body means is non-thermal energy.

3. The apparatus of claim 1 wherein the walls of the body means are at least partially transparent and absorbent to the energy directed into the entrance opening of the body means, the walls being covered over at least a portion of their surfaces opposite those surfaces defining the cavity with a reflective layer, the energy entering the cavity of the body means through the entrance opening being reflected by said layer into the cavity in a direction away from the entrance opening for absorption of said energy by said walls, the flow of mass along the walls cooling those portions of the body means nearest the entrance opening relative to those portions of the body means located relatively more distant from the entrance opening, thereby to prevent thermal reradiation from the cavity through the entrance opening.

4. The apparatus of claim 1 and further comprising insulation disposed about the body means, the insulation comprising alternate layers of thin metal and dustlike particles separating the layers of thin metal.

5. The apparatus of claim 1 wherein the walls are formed of a material more transparent to the energy entering the cavity than to the radiation from the walls resulting from energy absorbed by said walls.

6. The apparatus of claim 1 wherein the walls are formed of material relatively near the entrance opening which is a good absorber of infrared radiation relative to the material of which the walls are formed at portions of the body means relatively further away from the entrance opening.