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Submitted on 1 Jan 1981
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SELECTIVE SURFACES FOR NATURAL COOLING
DEVICES
A. Andretta, B. Bartoli, B. Coluzzi, V. Cuomo
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque C l , suppldment au nO1, Tome 42, janvier 1981 page Cl-423
SELECTIVE SURFACES FOR NATURAL COOLING DEVICES A. Andretta, B. Bartoli, B. C o l u z z i and V . Cuomo
I s t i tuto d i F i s i c a d e l l a F a c o l t d d ' I n g e g n e r i a , U n i v e r s i t y of N a p l e s , N a p l e s , I t a l y
Resume.- L'espace extra-atmospherique fonctionne en pratique comme un absorbeur de radiation et il peut Otre utilise ainsi qu'une sour- ce non conventionnelle d'energie.
Les surfaces ayant une 6missivit6 qui s'accorde avec la fenstre at- mosph6rique de transparence (8-13) p m interagissent avec l'espace froid tant qu'elles sont exposees au ciel serein pendant la nuit et refroidissent considerablement.
Pendant le jour, la temperature radiative du ciel se maintient bas- se, mais la radiation solaire est tellement plus grande qu'on ne peut pas obtenir un effet de refroidissement. Cependant il est pos- sible de proteger la surface radiante en se servant de couvertures selectives, qui arrstent la radiation solaire sans empOcher l'in- teraction infrarouge avec l'esgace froid.
Dans cet ouvrage nous decrivons les propriet6s optiques de quelques films bon march6 en plastique, que nous avons d6veloppes pour le refroidissement radiatif et nous montrons les resultats dans des applications telles qu'une serre inverse et un entrepat frigorifs- re qui emploient ces films s6lectifs.
Abstract.- Extra-atmospheric space is gracticallv a pure sink of radiation, and can be'used as a nonconventional energy source. Sur- faces with an emissivity matched with the atmospheric (8 t 13) pm transparency window interact with cold space when exposed to clear sky at night, and undergo a sizeable cooling effect.
During the day the sky radiative temperature remains low, but so- lar radiation i s so much larger that no cooling effect can be ob- tained : it is however possible to shade the radiating surface using selective covers which stop the solar radiation without pre- venting infrared emission.
In this paper we describe the optical properties of some cheap plastic films for radiative cooling, and present a simnle analysis of the net radiated power as a function of the optical properties of the selective radiator and cover.
1. Introduction.- If a body is exposed to clear sky at night, it usually reaches an equilibrium temperature a few degrees below the tem- perature of the ambient air. This natural radiative cooling is a well known phenomenon which can be'of interest for practical a~plications. The use of selective surfaces matched to the atmospheric transparency window (8 + 13 pm) has been shown /l, 2 / to give total emitted power
around 5 0 + 1 0 0 w/m2 and a minimum temperature 15 t 3 0 K under the am- bient temperature.
61-424 JOURNAL DE PHYSIQUE
The thermal i n f r a r e d e m i s s i v i t y of t h e sky does n o t change awpre- c i a b l y from n i g h t t o daytime, s o t h a t r a d i a t i v e c o o l i n g should i n p r i n - c i p l e be p o s s i b l e even d u r i n g sunshine hours. P r a c t i c a l s e l e c t i v e s u r - f a c e s however h e a t up when exposed t o d i r e c t s o l a r r a d i a t i o n , t h e sun power b e i n g much l a r g e r t h a n t h e n e t i n f r a r e d power r a d i a t e d t o t h e sky. Geometrical shading with s c r e e n s , which i s e f f e c t i v e f o r e x p e r i m e n t a l purposes w i t h s m a l l s e t u p s , becomes u n p r a c t i c a l w i t h t h e l a r g e a r e a de- v i c e s r e q u i r e d by most a p p l i c a t i o n s .
N a t u r a l r a d i a t i v e c o o l i n g during t h e day can be o b t a i n e d c o u p l i n g t h e s e l e c t i v e r a d i a t o r with s e l e c t i v e covers t r a n s p a r e n t t o i n f r a r e d r a d i a t i o n i n t h e wavelength r e g i o n of t h e atmospheric t r a n s p a r e n c y win- dow and opaque t o s o l a r r a d i a t i o n / 3 / . This s e l e c t i v e cover must be r e - f l e c t i v e t o s o l a r r a d i a t i o n on i t s unDer f a c e and a b s o r p t i v e i n i t s lower f a c e : a cover with t h e s e o p t i c a l p r o p e r t i e s i n t h e v i s i b l e does n o t absorb s o l a r energy and conseuuently does n o t h e a t up i n t h e sun, moreover, t h e f r a c t i o n of s o l a r r a d i a t i o n which goes through t h e cover w i l l n o t be t r a p p e d i n t h e gag between cover and r a d i a t o r being f i n a l l y
absorbed by t h e r a d i a t o r .
We have made s e l e c t i v e covers coupling t o g e t h e r two p o l y e t h y l e n e f i l m s charged w i t h s t a n d a r d pigments, Ti02 and carbon black. The pig- ments c o n c e n t r a t i o n s must be chosen c o n s i d e r i n g t h e c o n f l i c t i n g r e a u i -
rements of i n f r a r e d t r a n s p a r e n c y and s o l a r opaqueness. We h e r e p r e s e n t t h e o p t i c a l p r o p e r t i e s of t h e r e a l i s e d f i l m s , and an a n a l y s i s o f t h e n e t r a d i a t e d power u s i n g a simple p a r a m e t r i z a t i o n i n terms of v i s i b l e and i n f r a r e d sky r a d i a t i o n d a t a : t h i s a n a l y s i s p e r m i t s t o o p t i m i s e t h e pigment c o n c e n t r a t i o n s t o be used f o r a p p l i c a t i o n s and t o e s t i m a t e t h e performances of n a t u r a l r a d i a t i v e c o o l i n g d e v i c e s .
With t h e s e inexpensive cover f i l m s a very chean n a t u r a l p a s s i v e a i r c o n d i t i o n i n g o v e r l a r g e s u r f a c e s can be o b t a i n e d . An experimental shed of about 10 X 10 mZ was b u i l t , and g a v e i n t e r e s t i n g r e s u l t s , i . e . temperatures i n s i d e t h e shed % 5 K lower t h a n t h e e x t e r n a l temperature. Experimenting i s now going on w i t h l a r g e r sheds and greenhouses.
2 . S e l e c t i v e covers.- I n o r d e r t o have r a d i a t i v e c o o l i n g d u r i n g t h e day, t h e cover must be t r a n s p a r e n t t o i n f r a r e d r a d i a t i o n and opaque t o t h e s o l a r spectrum. These i d e a l o p t i c a l p r o p e r t i e s cannot be o b t a i n e d i n p r a c t i c e : i f t h e o p t i c a l p r o p e r t i e s of t h e s e l e c t i v e cover a r e i d e n t i - c a l on both s i d e s , it i s e a s i l v seen t h a t t h e d i u r n a l performances of t h e e m i t t e r d e t e r i o r a t e cruickly a s t h e s p e c t r a l t r a n s p a r e n c y moves away from t h e i d e a l shape. P r e l i m i n a r y c a l c u l a t i o n s /3/ have shown t h a t b e t - t e r r e s u l t s can be o b t a i n e d w i t h double f a c e f i l m covers, s p e c u l a r ( o r w h i t e ) on t h e f a c e exposed t o t h e sun and black on t h e o t h e r f a c e .
c o o l i n g should be extremely cheap. A cover w i t h t h e r e q u i r e d p r o n e r t i e s can b e made coupling t o g e t h e r two f i l m s of a g l a s t i c polymer t r a n s g a r e n t t o thermal i n f r a r e d , e.g. p o l y e t h y l e n e , changing t h e i r o p t i c a l groper- t i e s i n t h e v i s i b l e w i t h some dyes o r pigments.
A s e a r c h h a s consequently been done on w h i t e and black dyes and pigments, and we have found t h a t some o f t h e pigments most commonly u- s e d w i t h polythene a r e t r a n s p a r e n t t o thermal i n f r a r e d . For t h e w h i t e f i l m we used Titanium Dioxide (TiO2) i n t h e r u t i l e form, t y p i c a l sFec-
t r a l p r o p e r t i e s of polythene f i l m charged w i t h TiO2 a r e shown i n f i g u -
res 1 and 2.
Fig. 1.- I n f r a r e d t r a n s p a r e n c y of a 1 0 0 pm t h i c k Polythene f i l m charged w i t h 2 . 4 % of Ti02
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TRANSPARENCY REFLECTANCE J * # l l t . o 1 0 .5 1 . 0 1.5 2 . 0 2 . 5 WAVELENGTH, p m3. Optimal pigment c o n c e n t r a t i o n s f o r t h e d o u b l e f i l m . - I t was shown i n r e f e r e n c e /2/ t h a t t h e n e t power e m i t t e d by t h e r a d i a t o r can be exwres- s e d i n t h e form :
where T = TA
-
TR i s t h e t e m p e r a t u r e d i f f e r e n c e between t h e e x t e r n a l a i r and t h e r a d i a t i n g s u r f a c e , a n d Q i s t h e e n e r g y f l u x i n t h e v i s i b l e f r o m t h e sun.t h e b e s t v a l u e s f o r t h e c o n c e n t r a t i o n o f b l a c k and w h i t e ~ i g m e n t s f o r t h e p o l y t h e n e c o v e r w i l l be t h o s e which maximize t h e n e t r a d i a t e d power : i t i s t h e r e f o r e n e c e s s a r y t o know i n which wav W O , B and y de- pend on t h e o p t i c a l p r o p e r t i e s o f r a d i a t o r and c o v e r . T h i s dependance can be e x p l i c i t l y c a l c u l a t e d u s i n g t h e e n e r g y e q u i l i b r i u m e q u a t i o n s f o r t h e r a d i a t o r and some model f o r t h e i n f r a r e d and v i s i b l e r a d i a t i o n from t h e sky.
The f i r s t e q u a t i o n s we can w r i t e a r e t h o s e f o r t h e e l e c t r o m a g n e t i c r a d i a t i o n . Using t h e two-f l u x e s a p v r o x i m a t i ~ n we have :
E4 ( X ) = E4 (1) r l ( X )
+
14 (1) t ( X )+
el(X) w ( X , T C )I + ( X ) = E4 ( X ) t ( X ) + I4 ( h ) r 2 ( X )
+
e 2 ( X ) w(X,TC) (2 I4 ( A ) = I + ( X ) ( 1-
a ( X ) ) + a ( X ) w ( X , T R )where we have e x p l i c i t l y shown t h e dependance o f e v e r y t h i n g from t h e wavelength X o f t h e r a d i a t i o n , and t h e symbols have t h e f o l l o w i n g mea- n i n g ( s e e F i g 5 ) :
I * ( > ) , I*(%) F i g . 5.- Schematic drawing of a r a d i a -
/ / / / / / / / / / / I / / / / / / / / / / / / / I / / ///,L// t i v e c o o l i n g d e v i c e
-
E4 ( X ) ( E + ( X ) ) : power f l u x o f r a d i a t i o n w i t h wavelength X g o i n g uwward (downward) i n t h e r e g i o n j u s t above t h e c o v e r-
I 4 ( X ) ( I + ( X ) ) : power f l u x o f r a d i a t i o n between c o v e r andr a d i a t o r
-
t ( X ) : t r a n s p a r e n c y o f t h e c o v e r-
r, ( X ) , e l ( X ) ( r 2 ( X ) , e 2 ( X ) ) : r e f l e c t a n c e and e m i s s i v i t y o f t h e upper ( l o w e r ) s u r f a c e o f t h e c o v e r-
a ( X ) : e m i s s i v i t y o f t h e r a d i a t o r s u r f a c e-
TC, TR : t e m p e r a t u r e s o f t h e c o v e r and r a d i a t o r-
W ( X , T ) : black-body power spectrum f o r a t e m p e r a t u r e T.JOURNAL DE PHYSIQUE
IE+
( X ) el ( X ) d ~+
$14 ( X ) e 2 ( X ) d ~+
ha ( T ~-
T ~ )( 3
+ h~~ ( T ~
-
T ~ )+
l
( e l(X)
+
e2 ( X ) ) w ( X,
TC) dX = 0i n which TA i s t h e a m b i e n t t e m p e r a t u r e and ha, hCR a r e t h e t h e r m a l con- d u c t a n c e s between c o v e r and ambient o r r a d i a t o r due t o c o n d u c t i o n and c o n v e c t i o n o n l y .
E q u a t i o n s ( 2 ) and ( 3 ) c o m p l e t e l y d e t e r m i n e t h e n e t power r a d i a t e d t o t h e s k y when T R , T A and t h e incoming r a d i a t i o n spectrum E + ( X ) a r e f i x e d . A s o l u t i o n i n t h e form of e q u a t i o n (1) can b e o b t a i n e d i n t h e f o l l o w i n g way. The r a d i a t i o n from t h e s k y , E + ( X ) , i s w r i t t e n a s
E + ( X ) =
o
H ( X ) + W ( X,
TA) ( 1-
$a(X) ( 4 )T h i s s i g n i f i e s t h a t t h e v i s i b l e p a r t o f t h e s g e c t r u m i s g i v e n a s t a n - d a r d form H ( X ) n o r m a l i s e d w i t h a c o n s t a n t D , w h i l e t h e t h e r m a l i n f r a - r e d i s a b l a c k body spectrum f o r t h e ambient t e m p e r a t u r e TA m u l t i ~ l i e d by a n e m i s s i v i t y 1
-
@ a ( X ) which r e p r o d u c e s t h e a t m o s p h e r i c t r a n s p a - rency windows, w i t h a n o r m a l i s a t i o n c o n s t a n t $ which v a r i e s a c c o r d i n g t o c l i m a t i c c o n d i t i o n s . F o r t h e f u n c t i o n H ( X ) we have used a t y p i c a l s o l a r spectrum a t t h e e a r t h s u r f a c e a s can be found f o r example i n r e f e - r e n c e / 4 / ; f o r t h e i n f r a r e d a t m o s p h e r i c e m i s s i v i t y we have u s e d the d a t a o f r e f e r e n c e /S/.The l a s t s t e p i s t o expand t h e Planck b l a c k body f u n c t i o n s w ( X , T ) i n a power s e r i e s i n T
-
TA r e t a i n i n g o n l y t h e l i n e a r term, which i s p o s s i b l e b e i n g a l l t h e t e m ~ e r a t u r e s q u i t e n e a r t h e ambient t e m p e r a t u r eWith t h e s e a p p r o x i m a t i o n s i t i s e a s y t o o b t a i n t h e n e t r a d i a t e d power P (I4 ( X )
-
I+ ( X ) ) dX from e q u a t i o n s ( 2 ) and ( 3 ) i n t h e form o f e q u a t i o n (1) :w i t h
a t l - a
6 = /dh w(TA) a ( + ~ (1 e+ e2 t ) 1
+
/dh2
1
e2
h~~ aT T~ 1-
r 2 ( l-
a )P = l - c r
( e l + e~
-
1-
r 2 ( l-
a) e: 1where f o r r e a d a b i l i t y we have omitted a l l t h e e x p l i c i t dependance on t h e wavelength X.
4 . Experimental r e s u l t s . - From t h e r a d i a t i n g power e s t i m a t e s of t h e pre- ceding s e c t i o n it i s p o s s i b l e t o determine which a r e t h e b e s t concen- t r a t i o n s f o r t h e b l a c k and w h i t e pigments. The procedure i s somewhat involved because even i f t h e c o e f f 5 c i e n t s B, y and 6 o f e q u a t i o n ( 5 ) depend o n l y on the r a d i a t o r and cover f i l m s , t h e n e t r a d i a t e d Dower i s a f u n c t i o n of t h e c l i m a t i c c o n d i t i o n s (through
4 ,
@ a n d T A ) and a l s o o f t h e temperature o f t h e r a d i a t o r i t s e l f . The optimal c o n c e n t r a t i o n s f o r t h e pigments t h e r e f o r e depend on t h e f i n a l use of r a d i a t i v e c o o l i n g , f o r example c o o l i n g a s t o r e h o u s e r e q u i r e s r a d i a t o r s and covers d i f f e - r e n t from an i n v e r s e greenhouse.A s an example we g i v e i n f i g u r e 6 t h e i n f r a r e d t r a n s p a r e n c y o f a 100 urn t h i c k black-white cover f i l m of t h e k i n d d e s c r i b e d b e f o r e . We have produced l a r g e q u a n t i t i e s of t h i s f i l m and a r e now experimenting it a s a cover f o r i n v e r s e greenhouses. I n f i g u r e 7 a r e shown some ty- p i c a l r e s u l t s f o r t h e temperature i n s i d e a s m a l l i n v e r s e greenhouse
2
( 1 0 X 10m ) , compared w i t h t h e e x t e r n a l ambient temperature.
-
TRANSPARENCYJOURNAL DE PHYSIQUE
