Evacuated-tube directional-radiating cooling system

Solar Energy Vol. 35, No, 5, pp. 429-434, 1985

0038-092X/85 $3.00 + .00 ~ 1985 Pergamon Press Ltd.

Printed in the U.S.A.

EVACUATED-TUBE DIRECTIONAL-RADIATING COOLING SYSTEM J O H N R . H U L L a n d W I L L I A M W . SCHERTZ

Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, U.S.A. (Received 10 August 1984; revision accepted 6 May 1985) A b s t r a e t ~ A new type of radiative cooling system is described. The radiator makes use of nonimaging

optics and evacuated-tube technology to radiate significant amounts of heat to the 3 K environment of outer space. The nonimaging optics are used to direct the radiation overhead, through the most transparent part of the 8-13 ~xm atmospheric window. The required optical concentration is small, and relatively simple mirror geometries are possible. The evacuated-tube technology is used to attain storage temperatures at or below the freezing point, even when dewpoint temperatures are well above the freezing point.

1. INTRODUCTION

Radiative cooling of terrestrial objects has been used for centuries to obtain temperatures below ambient. This type of cooling rejects heat to the 3 K environment of outer space mainly in the spectral region between approximately 8 and 13 I~m, referred to as the main infrared "atmospheric wind o w . " The actual transparency of this window depends on atmospheric properties such as ambient temperature, ozone content, and aerosol content, but mainly on the precipitable water content. F o r a given sky condition, the window transmittance is highest directly overhead and decreases with increasing zenith angle as the thickness of the atmosphere along the radiative path increases. Many investigations have examined the use of selective surfaces and infrared filters to aid radiatively cooled surfaces in attaining temperatures below ambient (e.g. [1-4]). One method, employing the inverse greenhouse effect, uses a blackbody radiator that is shielded from the sky by one or more films that transmit in the atmospheric window region, but absorb at all other wavelengths[5]. More commonly, a radiator that emits only in the window region, but reflects in all other regions, is used[6]. Most simple designs of this type fail to reject the expected amount of heat due to the deleterious heat-transfer effects in the presence of wind[7], and a film that is transparent over the entire infrared region is often used as a windscreen over the radiating surface. Alternatively, a blackbody radiator can be screened by an infrared filter that is transparent in the window region and reflecting for all other wavelengths. The use of passive directional-radiating cooling systems is commonly employed for spacecraft applications[8]; however, the investigation of its use in terrestrial applications has been l i m i t e d - - m o s t l y to the provision of sunscreens for horizontal radiators[9]. Landro and McCormick[10] concluded that

conductive heat gains eliminated most of the benefit from the use of directional-radiating surfaces. The use of selective surfaces in radiative cooling has an inherent problem that has been seldom addressed in the literature. Once the radiating surface or windscreen cools to a temperature below the dewpoint, water condenses on the cold surface and effectively blocks the transmission through the atmospheric window. This effect provides an effective minimum temperature, below which the use of selective surfaces for radiative cooling has so far proved useless. Except for winter conditions where the cold ambient temperature is readily utilized for cooling, the dewpoint is usually above the freezing point of water, and efforts to couple selective-surface radiative cooling with ice storage have so far been frustrating. The evacuated, directional-radiating cooling device discussed in this article can be used with several different storage methods in a number of applications. In the discussion the radiator is coupled with seasonal ice storage (e.g. [11, 12]) for space cooling, a combination that appears to have many advantages.

2. SYSTEM DESCRIPTION

In order to maximize ice production at ambient temperatures above the freezing point, we consider a vacuum-enclosed radiating surface that is optically coupled to the most transparent part of the sky. The optics necessary to limit radiative exchange of a receiver to certain parts of the sky have been explored in great detail during the technological development of concentrating solar collectors. Study of the directional radiation properties of the sky[13] indicates that maximum transparency in the atmospheric window does not sharply decrease until zenith angles over 45 ° are reached. Because rather wide areas of the sky are acceptable for ra429

430

J. R. HULLand W. W. SCHERTZ

diative exchange with the cooling device discussed here, nonimaging concentrators, as adapted for solar collectors, are appropriate[14]. 2.1 2-D Geometry The essential features of a directional radiator with two-dimensional (2-D) geometry are illustrated in Fig. 1, using a Compound Parabolic Concentrator (CPC) design. The radiating surface is in the shape of a tube and is surrounded on the outside by a tubular cover. Heat-transfer fluid circulates through the inside of the radiator tube. A vacuum is maintained between the radiating surface and the cover. Trough-shaped mirrors surround the evacuated tube, except for an open-surface exit aperture which is pointed at the sky. There are two major design options for the evacuated tube: (1) the radiating tube can have a selective surface that emits only in the atmospheric window region and reflects for all other wavelengths, while the cover is transparent in the window region; or (2) the radiating surface can be a blackbody, while the cover is transparent in the window region and reflecting for all other wavelengths. F o r wavelengths within the atmospheric window, energy is emitted at the radiating surface, passes through the cover, and escapes to the sky through the exit aperture, either directly or after one or more reflections from the mirror. Radiation with wavelengths outside the atmospheric window is either not emitted or is emitted by the radiating surface and reflected by the cover back to the surface, where it is reabsorbed. Assuming the device normal is pointed toward the zenith, the exit aperture receives radiation from all parts of the sky, each ray impinging on the exit aperture at angle 0 when projected onto the transverse plane of the device. The shape of the mirror surface defines an acceptance angle 0~. When 0 > 0a, the sky radiation is reflected by the mirror back

EXIT APERTURE .

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Fig. 1. Cross-section of 2-D CPC evacuated-tube radiator.

to the sky without impinging on the radiating surface. When 0 < 0~, the sky radiation either impinges directly on the evacuated tube or reaches the tube after one or more reflections from the mirror. Incident sky radiation that is within the acceptance angle but has a wavelength outside the window region is reflected back to the sky from either the cover or the radiating surface. In 2-D geometry the limitation on sky-radiation acceptance only applies to the azimuthal angle (circumferentially around the tube). Radiation with longitudinal angles (with respect to the tube axis) up to 90 ° can impinge on the tube, and some parts of the poorly transparent sky near the horizon will be in radiative exchange with the device. A basic theorem of nonimaging optics[14] relates the acceptance angle to the ratio of the exit aperture area Ae with the area of the radiating surface Ar. In a 2-D geometry, this theorem can be formalized for the radiating system as (ICR)max =

(Ar/Ae)max =

sin 0a,

(1)

where ICR denotes inverse concentration ratio, to distinguish it from the CR used in concentrating solar collectors, and Ar is proportional to the circumference of the radiating tube. For a given Ae, we want to maximize Ar to increase the energy radiated. At the same time, we want to minimize 0a to utilize the most transparent part of the sky. The dependence of total radiated energy on these parameters is explored further in Sec. 3. The infrared reflectivity of mirror material such as aluminum approaches unity, and radiation emitted from the mirrors is small and will have a negligible effect on the evacuated tube to a first approximation. In CPC collector design, the mirrors are often truncated in order to lower material costs. This truncation slightly reduces the obtainable concentration ratio[15]. For the case of the directionalradiating system, truncation will also decrease the ICR obtainable for a given 0a. However, because the mirrors can also be used as nonradiative heat rejectors, truncation may not be necessary, in which case the mirrors can always be designed to produce a maximum ICR. The cover is in good thermal contact with the ambient and will have a similar temperature. With ideal selective surfaces, the cover is not in radiative exchange with the radiating surface, and because a vacuum separates the radiating surface from the cover, the temperatures of the radiating surface and the cover are independent of each other. Because there is no water vapor in the vacuum, the radiating surface can attain temperatures well below the dew point without condensing water on the radiating surface. Because the cover is always at or near ambient, no moisture will condense on the cover unless the ambient temperature is less than the dew point. Thus, unless the air is foggy, the radiator can reject heat at temperatures below the dew point.

431

Evacuated-tube directional-radiating cooling system The vacuum also eliminates the conductive heat problems emphasized by Landro and McCormick[10].

where a is the angle with the zenith along the longitudinal axis of the trough, 13 is the angle with the zenith along the transverse axis of the trough, and

2.2 3-D Geometry For the case of a directional radiator with threedimensional (3-D) geometry the mirror optics, cover, and radiating surface are symmetric about the device normal. The cover and radiating surface are circular plates perpendicular to the normal, and the mirrors are cone shaped or, preferably, 3-D CPCs. The use of selective surfaces and vacuum is identical to that for the 2-D geometry. The major difference is the relation for ICR. For 3-D geometries, the relation is

cos 0 = cos a cos 13.

(ICR)m~x

=

(Ar/Ae)max = sin 2 0a.

(2)

For a given Ae and 0a, Ar is smaller than in the 2D case. This is more than compensated by the 3-D limitation imposed on the acceptance of sky radiation. In the 3-D case, if the device is aimed upward, no part of the horizon is in radiative exchange with the device. Only the most transparent part of the sky is coupled to the radiator. A practical consideration may introduce another difference between the two geometries. A trough collector may always be oriented (e.g. longitudinal axis oriented north-south and normal pointed slightly north of the zenith) so that rain, snow, and debris do not accumulate in the trough and deteriorate the optics. This accumulation problem is much more severe in the 3-D case, and it may be necessary to install an additional infrared transparent cover at the exit aperture. Alternatively, a single cover could be placed at the aperture, but this would result in a much larger evacuated volume and larger stress on the cover due to its larger size. 3. EXPECTED PERFORMANCE

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(3)

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(6)

where A B C and D

= 1.792, = -1.113, = 1.807, = 1.034,

3.2 Radiated power The emissivities discussed in the previous section relate the actual radiance to that of a blackbody: B(h, T)

=

2'rrcZh -5

[ e x p ( c h k ~ l h - l T -1) - 1] -1,

(7) where B(h,T) is Planck's blackbody spectral distribution of emissive power, h is wavelength, T is temperature, c is the speed of light, h is Planck's constant, and kB is Boltzmann's constant. The net outgoing radiative flux in terms of the surface area of the radiator is given by

fO ~

dha(h)[B(X, Tr) - ~(0~, X)B(h, T~)],

(8)

where a(h) is the emissivity of the radiating device, Tr is the temperature of the radiating surface, Ta is the ambient temperature, and e(0a, X) is the effective sky emissivity for a given acceptance angle. For an ideal selective-surface radiator, ~(h) = 1 when X is in the window region, and a(h) = 0 for h elsewhere. For a 3-D geometry 13 tzm

where ~(0) is the emissivity of the sky at angle 0 from the zenith. In general, this emissivity is also a function of wavelength and sky condition. For a 2-D geometry, the effective sky emissivity e2.o is given by E2.D = 4 ¢ r - - 1 s i n -

Martin and Berdahl[13] give a phenomenological relation for ~(0) as a function of the total sky emissivity, ~s, which appears to be valid for a wide variety of geographic locations on a monthly average basis. For the 8-14 I~m region

R =

3.1 Effective sky emissivity In order to calculate the radiative power of a geometry with a given acceptance angle, we need to know the effective emissivity of that part of the sky in radiative exchange with the device. For a 3D geometry with acceptance angle 0~, the effective sky emissivity, e3-D, is given by

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d[3 cos0e(0), (4)

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f./8 p,m

dh B(h, Tr) --

6.3_D(0a)

fJ 8

13 ~rn v.m

dh B(k, T,).

(9)

For a 2-D geometry, •2-D replaces tE3.D in eqn (9). If the radiator behaves like an ideal blackbody, additional terms, representing the spectral region outside the atmospheric window, must be added to (9). For these terms, e3-D is set to unity.

432

J.R. HULLand

The effect of acceptance angle on radiative power is shown in Figs. 2-4. For each of the ambient air temperature curves, the radiator temperature is held at the ice-making point, T~ -- 0°C, and dewpoint considerations are ignored. The sky condition chosen for Figs. 2 and 3 is ~ = 0.8, a clear but moderately humid sky (~3-D = 0.388 and eZ-D = 0.425 for 0~ = 0% E-3.D 0.516 for 0~ = 90°). A relatively dry sky with ks = 0.7 (es-D = 0.317 at 0a = 90°; e3-D = 0.238 for 0a = 0°) is used in Fig. 4. A drier sky always produces more cooling for both global and directional radiators. It is interesting to note that even at the relatively hot ambient temperature of 40°C, ice production is maintained, even for the moderately humid sky. One desires a large 0a to maximize the radiating surface for a given exit aperture area. Inspection of Figs. 2-4 indicates that for humid skies (~ = 0.8) performance is relatively flat for 0~ less than about 45°, while for drier skies (~ = 0.7) performance does not appreciably deteriorate until 0a is larger =

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Fig. 4. Radiative flux of 3-D ideal selective-surface CPC radiator as a function of acceptance angle 0a for several values of ambient temperature Ta. The radiator temperature is Tr = 0°C, and the total sky emissivity is ¢s = 0.7. than 60°. As expected, the 2-D geometry radiates less at lower 0a, especially for large Ta. Although the selective surface is the dominating factor in producing large radiative power, the directional properties always help, especially at large temperature differences. In practice, the selective surface character of the radiator will not be ideal. The radiator will emit less than a blackbody in the window region and will not be able to totally reflect all radiation outside the window region. We let cg denote the effective emissivity of the device within the window region and a2 denote the effective emissivity outside the region. For an ideal selective surface, ~x~ = 1.0 and az = 0.0. We investigate two departures from the ideal case. Catalanotti et al.[2] investigated an inexpensive system (nonevacuated) with approximately al = 0.85 and et2 = 0.15. It appears reasonable to assume that modern thin-film coating technology could do better, e.g. eq = 0.92 and ct2 = 0.05. The radiative power of these two systems compared to the ideal case is shown in Fig. 5. Radiative power is still appreciable with these nonideal, but technologically attainable, systems.

~s = 0

S C H E R T Z

3.3 Annual performance In order to determine the potential of the radiator for seasonal cooling applications, it is necessary to predict performance for a 1 yr period. Martin and Berdahl[13] have correlated the daily average total sky emissivity to the dewpoint temperature Tdp for clear skies. This correlation is

Tit ,*C e~

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=

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+

0.56 (TdrJ100)

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100

Fig, 3. Radiative flux of 3-D ideal selective-surface CPC radiator as a function of acceptance angle 0a for several

values of ambient temperature Ta. The radiator temperature is T~ = 0°C, and the total sky emissivity is ~ = 0.8.

+ 0.73(TdJ100) 2,

(10

valid for - 13 < Tap < 24°C. We use this correlation, the results of the previous sections, and SOLMET weather data[16] to estimate the annual performance of several radiating cooling systems. We com-

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T a - T r . °C Fig. 5. Radiative flux as a function of the difference between ambient temperature Ta and radiation temperature Tr = 0°C for several types of selective surfaces, al is the effective emissivity of the radiator in the atmospheric window from approximately 8-14 txm, % is the effective emissivity of the radiator outside the window region, and ~ is the total sky emissivity.

pare a perfect blackbody radiator with 0, = 90°, a nonevacuated 3-D selective surface with 0 a = 45 °, and a 3-D selective surface inside an evacuated enclosure with 0a = 45 °. The properties of the selective surface are al = 0.92 and a2 = 0.05. Because the presence of water effectively blocks transmission through the atmospheric window, the total sky emissivity is taken as unity when the sky has a cloud over of 1.0. Whenever Tdp exceeds the storage temperature, the nonevacuated selective surface is expected to condense out water and is assumed to radiate as a perfect blackbody. Also, whenever Tap exceeds Ta, water is expected to condense out on the cover, and each system is assumed to radiate as a blackbody. Whenever the net radiated power is negative, it is assumed that Tr goes above the freezing point and the flow of heat transfer fluid from storage to the radiator shuts off, resuiting in no net loss. The effects of solar radiation are ignored. The predicted monthly average radiative fluxes for the three systems are shown in Fig. 6 for an hour-by-hour simulation of an ice-storage system (T~ = 0°C) in Dodge City, Kansas. On an annual basis the evacuated-tube radiator rejects approximately 50% more heat than either of the other two systems. The blackbody radiator performs better in the winter, because the ambient temperatures are often below the freezing point. During these times the blackbody radiates to the colder sky over the nonwindow wavelengths, as well as over the window region, whereas the selective surfaces are limited to radiating within the window region. It is interesting to note that for this simulation, the nonevacuated selective-surface radiator performs no better than the blackbody radiator on an annual basis. The dewpoint temperature in this particular climate is such that operating a nonevacuated ra-

5

10

MONTH Fig. 6. Simulated monthly and annual average radiative flux for three radiators producing ice at Tr = 0°C in Dodge City, Kansas. Both the evacuated and nonevacuated radiators have selective surfaces to radiate mostly in the atmospheric window region. diator at ice-making temperatures effectively "shorts out" any selective surface properties most of the time. Greater use of ambient air temperatures in seasonal cold-storage applications can be gained by using a clathrate storage that has a higher freezing point than pure water. It is then important to estimate the annual radiative power of the three systems as a function of storage temperature. The resuits of a number of simulations for Dodge City are shown in Fig. 7, where average annual radiated power is plotted as a function of storage temperature. As the storage temperature is raised, the performance of all systems improve; however, the radiating temperature is above the dewpoint temperature more often. The performance of the nonevacuated selective surface approaches that of the evacuated one, and the relative advantage of the evacuated-tube radiator decreases. At higher storage temperatures, the radiating temperature is also above the ambient temperature more often,

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EVACUATED

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Fig. 7. Simulated annual average radiative flux as a function of storage temperature Tstr for three radiators in Dodge City, Kansas. Radiators are same as in Fig. 6.

434

J. R. HULLand W. W. SCHERTZ

and the radiation of the blackbody outside of the window region eventually leads to better annual performance than that of the evacuated-tube radiator.

3.

4. 4. CONCLUSIONS A new type of radiative cooling system has been presented. The proposed system uses evacuatedtube technology, nonimaging optics, and selectivesurface materials to make efficient use of the angular dependence of sky emissivity. The selective surface and nonimaging optics optimize the radiative flux, while the vacuum allows the radiator to achieve freezing temperatures when the radiating surface is below the dewpoint temperature and still maintain the selective surface characteristics of the radiation. The radiator couples well to annual icestorage systems, and the annual radiative cooling is significantly higher than that of a nonevacuated radiator in this application.

Acknowledgment--This work was sponsored by the U.S. Department of Energy under Contract W-31-109-Eng-38. The authors thank J. Mehta for help in obtainingthe SOLMET weather data. The authors also greatly appreciate discussions with A. J. Gorskiand A. I. Michaels on seasonal cold storage and J. Allen on CPC technology.

5. 6. 7. 8. 9. 10.

11. 12.

13.

REFERENCES

14.

1. F. Trombe, Nouvelles experiences sur le refroidissement de corps noirs rayonnant sur l'espace. Comptes rendus 256, 2013-2015 (1963). 2. S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Sil-

15. 16.

vestrini and G. Troise, The radiative cooling of selective surfaces. Solar Energy 17, 83-89 (1975). C. G. Granqvist and A. Hjortsberg, Radiative cooling to low temperatures: General considerations and application to selectively emitting SiO films. J. Appl. Phys. 52, 4205-4220 (1981). P. Berdahl, M, Martin and F. Sakkal, Thermal performance of radiative cooling panels. Int. J. Heat Mass Transfer 26, 871-880 (1983). Ph. Grenier, R~frig~ration radiative: Effet de serre inverse. Revue de Physique Appliqu~ 14, 87-90 (1979). E. M. Lushiku and C. G. Granqvist, Radiative cooling with selectively infrared-emitting gases. Appl. Opt. 23, 1835-1843 (1984). T. E. Johnson, Radiative cooling of structures with infrared transparent wind screens. Solar Energy 17, 173-178 (1975). R. V. Annable, Radiant cooling. Appl. Opt. 9, 185193 (1970). F. Trombe, Sur des grands abalssements de temp6rature obtenus par rayonnement du corps noir sur l'espace. Comptes rendus 256, 735-738 (1963). B. Landro and P. G. McCormick, Radiative cooling characteristics of surfaces exhibiting spectral and directional selectivity. Proc. Int. Solar Energy Soc., Atlanta, pp. 1656-1659 (1979). W. W. Schertz, Long-term ice storage for cooling applications. U.S. Patent No. 4,271,681 (June 9, 1981). A. J. Gorski, W. W. Schertz, A. S. Wantroba, A. E. McGarity and E. H. Buyco, Ice production and storage for seasonal applications utilizing heat pipe technology. Argonne National Laboratory, Argonne, Illinois, ANL-82-87 (1982). M. Martin and P. Berdahl, Summary of results for the spectral and angular sky radiation measurement program (submitted for publication). W. T. Welford and R. Winston, The Optics of Nonimaging Concentrators. Academic Press (1978). R. Winston and H. Hinterberger, Principles of cylindrical concentrators. Solar Energy 17, 255-258 (1975). SOLMET Volume l b U s e r ' s Manual. TD-9724, U.S. Dept. of Commerce (1978).